diff --git a/.gitignore b/.gitignore
index 87df5a1..b57c62c 100644
--- a/.gitignore
+++ b/.gitignore
@@ -22,3 +22,5 @@ share/python-wheels/
 .installed.cfg
 *.egg
 MANIFEST
+ag_ckpt_vocab/
+meliad_lib/
\ No newline at end of file
diff --git a/CACHEDIR.TAG b/CACHEDIR.TAG
new file mode 100644
index 0000000..837feef
--- /dev/null
+++ b/CACHEDIR.TAG
@@ -0,0 +1,4 @@
+Signature: 8a477f597d28d172789f06886806bc55
+# This file is a cache directory tag created by Python virtualenv.
+# For information about cache directory tags, see:
+#   https://bford.info/cachedir/
\ No newline at end of file
diff --git a/alphageometry.py b/alphageometry.py
index f6a3aa8..8262114 100644
--- a/alphageometry.py
+++ b/alphageometry.py
@@ -29,7 +29,6 @@
 import pretty as pt
 import problem as pr
 
-
 _GIN_SEARCH_PATHS = flags.DEFINE_list(
     'gin_search_paths',
     ['third_party/py/meliad/transformer/configs'],
@@ -174,6 +173,20 @@ def write_solution(g: gh.Graph, p: pr.Problem, out_file: str) -> None:
       'r38': '(Similar Triangles)',
       'r39': '(Similar Triangles)',
       'r40': '(Congruent Triangles)',
+      'r43': '(Menelaus)',
+      'r44': '(Menelaus)',
+      'r45': '(Ceva)',
+      'r46': '(Ceva)',
+      'r47': '(Circle Power)',
+      'r48': '(Circle Power)',
+      'r49': '(Circle Power)',
+      'r50': '(Circle Power)',
+      'r51': '(Radical Axis)',
+      'r52': '(Pascal)',
+      'r53': '(Pascal)',
+      'r54': '(Pascal)',
+      'r55': '(Pascal)',
+      'r56': '(Pascal)',
       'a00': '(Distance chase)',
       'a01': '(Ratio chase)',
       'a02': '(Angle chase)',
@@ -189,6 +202,7 @@ def write_solution(g: gh.Graph, p: pr.Problem, out_file: str) -> None:
 
   solution += '==========================\n'
   logging.info(solution)
+  print(solution)
   if out_file:
     with open(out_file, 'w') as f:
       f.write(solution)
@@ -380,7 +394,8 @@ def try_translate_constrained_to_construct(string: str, g: gh.Graph) -> str:
   """
   if string[-1] != ';':
     return 'ERROR: must end with ;'
-
+  if ':' not in string:
+    return 'ERROR: must contain :'
   head, prem_str = string.split(' : ')
   point = head.strip()
 
@@ -571,7 +586,7 @@ def run_alphageometry(
 
         # Update the constructive statement of the problem with the aux point:
         candidate_pstring = insert_aux_to_premise(pstring, translation)
-
+        print(candidate_pstring)
         logging.info('Solving: "%s"', candidate_pstring)
         p_new = pr.Problem.from_txt(candidate_pstring)
 
@@ -604,7 +619,6 @@ def run_alphageometry(
 def main(_):
   global DEFINITIONS
   global RULES
-
   # definitions of terms used in our domain-specific language.
   DEFINITIONS = pr.Definition.from_txt_file(_DEFS_FILE.value, to_dict=True)
   # load inference rules used in DD.
@@ -649,3 +663,4 @@ def main(_):
 
 if __name__ == '__main__':
   app.run(main)
+
diff --git a/ar.py b/ar.py
index 01dd8cc..33fd53e 100644
--- a/ar.py
+++ b/ar.py
@@ -17,7 +17,7 @@
 
 from collections import defaultdict  # pylint: disable=g-importing-member
 from fractions import Fraction as frac  # pylint: disable=g-importing-member
-from typing import Any, Generator
+from typing import Any, Generator, Union
 
 import geometry as gm
 import numpy as np
@@ -219,9 +219,16 @@ def update_groups(
   Returns:
     groups1, links, history: result of the update.
   """
+  print("len1",len(groups1))
+  print("len2",len(groups2))
+  cnt = 0
+  lenall = len(groups2)
   history = []
   links = []
   for g2 in groups2:
+    cnt += 1
+    if cnt % 1000 == 0:
+      print(f'{cnt}/{lenall}')
     joins = [None] * len(groups1)  # mark which one in groups1 is merged
     merged_g1 = set()  # merge them into this.
     old = None  # any elem in g2 that belong to any set in groups1 (old)
@@ -265,8 +272,7 @@ def update_groups(
       new_groups1 += [set(new)]
 
     groups1 = new_groups1
-    history.append(groups1)
-
+    #history.append(groups1)
   return groups1, links, history
 
 
@@ -363,7 +369,7 @@ def register(self, vc: list[tuple[str, float]], dep: pr.Dependency) -> None:
   def register2(
       self, a: str, b: str, m: float, n: float, dep: pr.Dependency
   ) -> None:
-    self.register([(a, m), (b, -n)], dep)
+    self.register([(a, n), (b, -m)], dep)
 
   def register3(self, a: str, b: str, f: float, dep: pr.Dependency) -> None:
     self.register([(a, 1), (b, -1), (self.const, -f)], dep)
@@ -373,6 +379,11 @@ def register4(
   ) -> None:
     self.register([(a, 1), (b, -1), (c, -1), (d, 1)], dep)
 
+  def register5(
+      self, a: str, b: str, c: str, dep: pr.Dependency
+  ) -> None:
+    self.register([(a, 1), (b, -1), (c, -1)], dep)
+
   def why(self, e: dict[str, float]) -> list[Any]:
     """AR traceback == MILP."""
     if not self.do_why:
@@ -401,7 +412,7 @@ def why(self, e: dict[str, float]) -> list[Any]:
     deps = []
     for i, dep in enumerate(self.deps):
       if x[2 * i] > 1e-12 or x[2 * i + 1] > 1e-12:
-        if dep not in deps:
+        if dep is not None and dep not in deps:
           deps.append(dep)
     return deps
 
@@ -426,7 +437,7 @@ def add_eq2(
       self, a: str, b: str, m: float, n: float, dep: pr.Dependency
   ) -> None:
     # a/b = m/n
-    if not self.add_expr([(a, m), (b, -n)]):
+    if not self.add_expr([(a, n), (b, -m)]):
       return []
     self.register2(a, b, m, n, dep)
 
@@ -455,10 +466,32 @@ def add_eq4(self, a: str, b: str, c: str, d: str, dep: pr.Dependency) -> None:
         self.groups, [{(a, b), (c, d)}, {(b, a), (d, c)}]
     )
 
+
+  def add_eq5(self, a: str, b: str, c: str, dep: pr.Dependency) -> None:
+    # a = b + c
+    self.eqs.add((a, b, c))
+    self.eqs.add((a, c, b))
+
+    expr = list(minus({a: 1, b: -1}, {c: 1}).items())
+
+    if not self.add_expr(expr):
+      return []
+
+    self.register5(a, b, c, dep)
+
   def pairs(self) -> Generator[list[tuple[str, str]], None, None]:
     for v1, v2 in perm2(list(self.v2e.keys())):  # pylint: disable=g-builtin-op
       if v1 == self.const or v2 == self.const:
         continue
+      # v1s = [v1]
+      # v2s = [v2]
+      # if '*' in v1:
+      #   v1s = v1.split('*')
+      # if '*' in v2:
+      #   v2s = v2.split('*')
+      # vs = [v for v in v1s if v in v2s]
+      # if vs != []:
+      #   continue
       yield v1, v2
 
   def modulo(self, e: dict[str, float]) -> dict[str, float]:
@@ -503,16 +536,36 @@ def get_all_eqs_and_why(
           value = simplify(frac.numerator, frac.denominator)
           yield v1, v2, value, self.why(why_dict)
         continue
-
+      
       groups.append(vv)
 
     if not return_quads:
       return
 
     self.groups, links, _ = update_groups(self.groups, groups)
+    lenall = len(links)
+    cnt = 0
     for (v1, v2), (v3, v4) in links:
+      cnt += 1
+      if cnt % 1000 == 0:
+        print(f'{cnt}/{lenall}')
       if self.check_record_eq(v1, v2, v3, v4):
         continue
+      # v1s = [v1]
+      # v2s = [v2]
+      # v3s = [v3]
+      # v4s = [v4]
+      # if '*' in v1:
+      #   v1s = v1.split('*')
+      # if '*' in v2:
+      #   v2s = v2.split('*')
+      # if '*' in v3:
+      #   v3s = v3.split('*')
+      # if '*' in v3:
+      #   v4s = v4.split('*')
+      # v14 = v1s + v4s
+      # v23 = v2s + v3s
+      # vs = [v for v in v14 if v in v23]
       e12 = minus(self.v2e[v1], self.v2e[v2])
       e34 = minus(self.v2e[v3], self.v2e[v4])
 
@@ -520,6 +573,7 @@ def get_all_eqs_and_why(
           minus({v1: 1, v2: -1}, {v3: 1, v4: -1}), minus(e12, e34)
       )
       self.record_eq(v1, v2, v3, v4)
+      #if vs == []:
       yield v1, v2, v3, v4, self.why(why_dict)
 
 
@@ -543,6 +597,7 @@ def get_all_eqs_and_why(
     for out in super().get_all_eqs_and_why(return_quads):
       if len(out) == 3:
         x, y, why = out
+        #print('out2', x, y)
         x, y = self.map2obj([x, y])
         yield x, y, why
       if len(out) == 4:
@@ -551,6 +606,7 @@ def get_all_eqs_and_why(
         yield x, y, f, why
       if len(out) == 5:
         a, b, x, y, why = out
+        #print('out4', a, b, x, y)
         a, b, x, y = self.map2obj([a, b, x, y])
         yield a, b, x, y, why
 
@@ -575,19 +631,32 @@ def add_const_ratio(
 
   def add_eqratio(
       self,
-      l1: gm.Length,
-      l2: gm.Length,
-      l3: gm.Length,
-      l4: gm.Length,
+      l1: Union[gm.Length, gm.Length_Pro],
+      l2: Union[gm.Length, gm.Length_Pro],
+      l3: Union[gm.Length, gm.Length_Pro],
+      l4: Union[gm.Length, gm.Length_Pro],
       dep: pr.Dependency,
   ) -> None:
     l1, l2, l3, l4 = self.get_name([l1, l2, l3, l4])
-    return self.add_eq4(l1, l2, l3, l4, dep)
+    return super().add_eq4(l1, l2, l3, l4, dep)
+
+  def add_length_pro(
+      self,
+      lp: gm.Length_Pro,
+      l1: gm.Length,
+      l2: gm.Length,
+      dep=None,
+  ) -> None:
+    if lp.name in self.v2obj:
+      return
+    lp, l1, l2 = self.get_name([lp, l1, l2])
+    return super().add_eq5(lp, l1, l2, dep)
 
   def get_all_eqs_and_why(self) -> Generator[Any, None, None]:
     return super().get_all_eqs_and_why(True)
 
 
+
 class AngleTable(GeometricTable):
   """Coefficient matrix A for slope(direction)."""
 
diff --git a/bin/activate b/bin/activate
new file mode 100644
index 0000000..33ab5d2
--- /dev/null
+++ b/bin/activate
@@ -0,0 +1,87 @@
+# This file must be used with "source bin/activate" *from bash*
+# you cannot run it directly
+
+
+if [ "${BASH_SOURCE-}" = "$0" ]; then
+    echo "You must source this script: \$ source $0" >&2
+    exit 33
+fi
+
+deactivate () {
+    unset -f pydoc >/dev/null 2>&1 || true
+
+    # reset old environment variables
+    # ! [ -z ${VAR+_} ] returns true if VAR is declared at all
+    if ! [ -z "${_OLD_VIRTUAL_PATH:+_}" ] ; then
+        PATH="$_OLD_VIRTUAL_PATH"
+        export PATH
+        unset _OLD_VIRTUAL_PATH
+    fi
+    if ! [ -z "${_OLD_VIRTUAL_PYTHONHOME+_}" ] ; then
+        PYTHONHOME="$_OLD_VIRTUAL_PYTHONHOME"
+        export PYTHONHOME
+        unset _OLD_VIRTUAL_PYTHONHOME
+    fi
+
+    # The hash command must be called to get it to forget past
+    # commands. Without forgetting past commands the $PATH changes
+    # we made may not be respected
+    hash -r 2>/dev/null
+
+    if ! [ -z "${_OLD_VIRTUAL_PS1+_}" ] ; then
+        PS1="$_OLD_VIRTUAL_PS1"
+        export PS1
+        unset _OLD_VIRTUAL_PS1
+    fi
+
+    unset VIRTUAL_ENV
+    unset VIRTUAL_ENV_PROMPT
+    if [ ! "${1-}" = "nondestructive" ] ; then
+    # Self destruct!
+        unset -f deactivate
+    fi
+}
+
+# unset irrelevant variables
+deactivate nondestructive
+
+VIRTUAL_ENV=/home/featurize/work/alphageometry
+if ([ "$OSTYPE" = "cygwin" ] || [ "$OSTYPE" = "msys" ]) && $(command -v cygpath &> /dev/null) ; then
+    VIRTUAL_ENV=$(cygpath -u "$VIRTUAL_ENV")
+fi
+export VIRTUAL_ENV
+
+_OLD_VIRTUAL_PATH="$PATH"
+PATH="$VIRTUAL_ENV/"bin":$PATH"
+export PATH
+
+if [ "x"'' != x ] ; then
+    VIRTUAL_ENV_PROMPT=''
+else
+    VIRTUAL_ENV_PROMPT=$(basename "$VIRTUAL_ENV")
+fi
+export VIRTUAL_ENV_PROMPT
+
+# unset PYTHONHOME if set
+if ! [ -z "${PYTHONHOME+_}" ] ; then
+    _OLD_VIRTUAL_PYTHONHOME="$PYTHONHOME"
+    unset PYTHONHOME
+fi
+
+if [ -z "${VIRTUAL_ENV_DISABLE_PROMPT-}" ] ; then
+    _OLD_VIRTUAL_PS1="${PS1-}"
+    PS1="(${VIRTUAL_ENV_PROMPT}) ${PS1-}"
+    export PS1
+fi
+
+# Make sure to unalias pydoc if it's already there
+alias pydoc 2>/dev/null >/dev/null && unalias pydoc || true
+
+pydoc () {
+    python -m pydoc "$@"
+}
+
+# The hash command must be called to get it to forget past
+# commands. Without forgetting past commands the $PATH changes
+# we made may not be respected
+hash -r 2>/dev/null || true
diff --git a/bin/activate.csh b/bin/activate.csh
new file mode 100644
index 0000000..f0dbb15
--- /dev/null
+++ b/bin/activate.csh
@@ -0,0 +1,55 @@
+# This file must be used with "source bin/activate.csh" *from csh*.
+# You cannot run it directly.
+# Created by Davide Di Blasi <davidedb@gmail.com>.
+
+set newline='\
+'
+
+alias deactivate 'test $?_OLD_VIRTUAL_PATH != 0 && setenv PATH "$_OLD_VIRTUAL_PATH:q" && unset _OLD_VIRTUAL_PATH; rehash; test $?_OLD_VIRTUAL_PROMPT != 0 && set prompt="$_OLD_VIRTUAL_PROMPT:q" && unset _OLD_VIRTUAL_PROMPT; unsetenv VIRTUAL_ENV; unsetenv VIRTUAL_ENV_PROMPT; test "\!:*" != "nondestructive" && unalias deactivate && unalias pydoc'
+
+# Unset irrelevant variables.
+deactivate nondestructive
+
+setenv VIRTUAL_ENV /home/featurize/work/alphageometry
+
+set _OLD_VIRTUAL_PATH="$PATH:q"
+setenv PATH "$VIRTUAL_ENV:q/"bin":$PATH:q"
+
+
+
+if ('' != "") then
+    setenv VIRTUAL_ENV_PROMPT ''
+else
+    setenv VIRTUAL_ENV_PROMPT "$VIRTUAL_ENV:t:q"
+endif
+
+if ( $?VIRTUAL_ENV_DISABLE_PROMPT ) then
+    if ( $VIRTUAL_ENV_DISABLE_PROMPT == "" ) then
+        set do_prompt = "1"
+    else
+        set do_prompt = "0"
+    endif
+else
+    set do_prompt = "1"
+endif
+
+if ( $do_prompt == "1" ) then
+    # Could be in a non-interactive environment,
+    # in which case, $prompt is undefined and we wouldn't
+    # care about the prompt anyway.
+    if ( $?prompt ) then
+        set _OLD_VIRTUAL_PROMPT="$prompt:q"
+        if ( "$prompt:q" =~ *"$newline:q"* ) then
+            :
+        else
+            set prompt = '('"$VIRTUAL_ENV_PROMPT:q"') '"$prompt:q"
+        endif
+    endif
+endif
+
+unset env_name
+unset do_prompt
+
+alias pydoc python -m pydoc
+
+rehash
diff --git a/bin/activate.fish b/bin/activate.fish
new file mode 100644
index 0000000..903de66
--- /dev/null
+++ b/bin/activate.fish
@@ -0,0 +1,103 @@
+# This file must be used using `source bin/activate.fish` *within a running fish ( http://fishshell.com ) session*.
+# Do not run it directly.
+
+function _bashify_path -d "Converts a fish path to something bash can recognize"
+    set fishy_path $argv
+    set bashy_path $fishy_path[1]
+    for path_part in $fishy_path[2..-1]
+        set bashy_path "$bashy_path:$path_part"
+    end
+    echo $bashy_path
+end
+
+function _fishify_path -d "Converts a bash path to something fish can recognize"
+    echo $argv | tr ':' '\n'
+end
+
+function deactivate -d 'Exit virtualenv mode and return to the normal environment.'
+    # reset old environment variables
+    if test -n "$_OLD_VIRTUAL_PATH"
+        # https://github.com/fish-shell/fish-shell/issues/436 altered PATH handling
+        if test (echo $FISH_VERSION | head -c 1) -lt 3
+            set -gx PATH (_fishify_path "$_OLD_VIRTUAL_PATH")
+        else
+            set -gx PATH $_OLD_VIRTUAL_PATH
+        end
+        set -e _OLD_VIRTUAL_PATH
+    end
+
+    if test -n "$_OLD_VIRTUAL_PYTHONHOME"
+        set -gx PYTHONHOME "$_OLD_VIRTUAL_PYTHONHOME"
+        set -e _OLD_VIRTUAL_PYTHONHOME
+    end
+
+    if test -n "$_OLD_FISH_PROMPT_OVERRIDE"
+       and functions -q _old_fish_prompt
+        # Set an empty local `$fish_function_path` to allow the removal of `fish_prompt` using `functions -e`.
+        set -l fish_function_path
+
+        # Erase virtualenv's `fish_prompt` and restore the original.
+        functions -e fish_prompt
+        functions -c _old_fish_prompt fish_prompt
+        functions -e _old_fish_prompt
+        set -e _OLD_FISH_PROMPT_OVERRIDE
+    end
+
+    set -e VIRTUAL_ENV
+    set -e VIRTUAL_ENV_PROMPT
+
+    if test "$argv[1]" != 'nondestructive'
+        # Self-destruct!
+        functions -e pydoc
+        functions -e deactivate
+        functions -e _bashify_path
+        functions -e _fishify_path
+    end
+end
+
+# Unset irrelevant variables.
+deactivate nondestructive
+
+set -gx VIRTUAL_ENV /home/featurize/work/alphageometry
+
+# https://github.com/fish-shell/fish-shell/issues/436 altered PATH handling
+if test (echo $FISH_VERSION | head -c 1) -lt 3
+    set -gx _OLD_VIRTUAL_PATH (_bashify_path $PATH)
+else
+    set -gx _OLD_VIRTUAL_PATH $PATH
+end
+set -gx PATH "$VIRTUAL_ENV"'/'bin $PATH
+
+# Prompt override provided?
+# If not, just use the environment name.
+if test -n ''
+    set -gx VIRTUAL_ENV_PROMPT ''
+else
+    set -gx VIRTUAL_ENV_PROMPT (basename "$VIRTUAL_ENV")
+end
+
+# Unset `$PYTHONHOME` if set.
+if set -q PYTHONHOME
+    set -gx _OLD_VIRTUAL_PYTHONHOME $PYTHONHOME
+    set -e PYTHONHOME
+end
+
+function pydoc
+    python -m pydoc $argv
+end
+
+if test -z "$VIRTUAL_ENV_DISABLE_PROMPT"
+    # Copy the current `fish_prompt` function as `_old_fish_prompt`.
+    functions -c fish_prompt _old_fish_prompt
+
+    function fish_prompt
+        # Run the user's prompt first; it might depend on (pipe)status.
+        set -l prompt (_old_fish_prompt)
+
+        printf '(%s) ' $VIRTUAL_ENV_PROMPT
+
+        string join -- \n $prompt # handle multi-line prompts
+    end
+
+    set -gx _OLD_FISH_PROMPT_OVERRIDE "$VIRTUAL_ENV"
+end
diff --git a/bin/activate.nu b/bin/activate.nu
new file mode 100644
index 0000000..df25455
--- /dev/null
+++ b/bin/activate.nu
@@ -0,0 +1,96 @@
+# virtualenv activation module
+# Activate with `overlay use activate.nu`
+# Deactivate with `deactivate`, as usual
+#
+# To customize the overlay name, you can call `overlay use activate.nu as foo`,
+# but then simply `deactivate` won't work because it is just an alias to hide
+# the "activate" overlay. You'd need to call `overlay hide foo` manually.
+
+export-env {
+    def is-string [x] {
+        ($x | describe) == 'string'
+    }
+
+    def has-env [...names] {
+        $names | each {|n|
+            $n in $env
+        } | all {|i| $i == true}
+    }
+
+    # Emulates a `test -z`, but better as it handles e.g 'false'
+    def is-env-true [name: string] {
+      if (has-env $name) {
+        # Try to parse 'true', '0', '1', and fail if not convertible
+        let parsed = (do -i { $env | get $name | into bool })
+        if ($parsed | describe) == 'bool' {
+          $parsed
+        } else {
+          not ($env | get -i $name | is-empty)
+        }
+      } else {
+        false
+      }
+    }
+
+    let virtual_env = r#'/home/featurize/work/alphageometry'#
+    let bin = r#'bin'#
+
+    let is_windows = ($nu.os-info.family) == 'windows'
+    let path_name = (if (has-env 'Path') {
+            'Path'
+        } else {
+            'PATH'
+        }
+    )
+
+    let venv_path = ([$virtual_env $bin] | path join)
+    let new_path = ($env | get $path_name | prepend $venv_path)
+
+    # If there is no default prompt, then use the env name instead
+    let virtual_env_prompt = (if (r#''# | is-empty) {
+        ($virtual_env | path basename)
+    } else {
+        r#''#
+    })
+
+    let new_env = {
+        $path_name         : $new_path
+        VIRTUAL_ENV        : $virtual_env
+        VIRTUAL_ENV_PROMPT : $virtual_env_prompt
+    }
+
+    let new_env = (if (is-env-true 'VIRTUAL_ENV_DISABLE_PROMPT') {
+      $new_env
+    } else {
+      # Creating the new prompt for the session
+      let virtual_prefix = $'(char lparen)($virtual_env_prompt)(char rparen) '
+
+      # Back up the old prompt builder
+      let old_prompt_command = (if (has-env 'PROMPT_COMMAND') {
+              $env.PROMPT_COMMAND
+          } else {
+              ''
+        })
+
+      let new_prompt = (if (has-env 'PROMPT_COMMAND') {
+          if 'closure' in ($old_prompt_command | describe) {
+              {|| $'($virtual_prefix)(do $old_prompt_command)' }
+          } else {
+              {|| $'($virtual_prefix)($old_prompt_command)' }
+          }
+      } else {
+          {|| $'($virtual_prefix)' }
+      })
+
+      $new_env | merge {
+        PROMPT_COMMAND      : $new_prompt
+        VIRTUAL_PREFIX      : $virtual_prefix
+      }
+    })
+
+    # Environment variables that will be loaded as the virtual env
+    load-env $new_env
+}
+
+export alias pydoc = python -m pydoc
+export alias deactivate = overlay hide activate
diff --git a/bin/activate.ps1 b/bin/activate.ps1
new file mode 100644
index 0000000..3333e2b
--- /dev/null
+++ b/bin/activate.ps1
@@ -0,0 +1,61 @@
+$script:THIS_PATH = $myinvocation.mycommand.path
+$script:BASE_DIR = Split-Path (Resolve-Path "$THIS_PATH/..") -Parent
+
+function global:deactivate([switch] $NonDestructive) {
+    if (Test-Path variable:_OLD_VIRTUAL_PATH) {
+        $env:PATH = $variable:_OLD_VIRTUAL_PATH
+        Remove-Variable "_OLD_VIRTUAL_PATH" -Scope global
+    }
+
+    if (Test-Path function:_old_virtual_prompt) {
+        $function:prompt = $function:_old_virtual_prompt
+        Remove-Item function:\_old_virtual_prompt
+    }
+
+    if ($env:VIRTUAL_ENV) {
+        Remove-Item env:VIRTUAL_ENV -ErrorAction SilentlyContinue
+    }
+
+    if ($env:VIRTUAL_ENV_PROMPT) {
+        Remove-Item env:VIRTUAL_ENV_PROMPT -ErrorAction SilentlyContinue
+    }
+
+    if (!$NonDestructive) {
+        # Self destruct!
+        Remove-Item function:deactivate
+        Remove-Item function:pydoc
+    }
+}
+
+function global:pydoc {
+    python -m pydoc $args
+}
+
+# unset irrelevant variables
+deactivate -nondestructive
+
+$VIRTUAL_ENV = $BASE_DIR
+$env:VIRTUAL_ENV = $VIRTUAL_ENV
+
+if ('' -ne "") {
+    $env:VIRTUAL_ENV_PROMPT = ''
+}
+else {
+    $env:VIRTUAL_ENV_PROMPT = $( Split-Path $env:VIRTUAL_ENV -Leaf )
+}
+
+New-Variable -Scope global -Name _OLD_VIRTUAL_PATH -Value $env:PATH
+
+$env:PATH = "$env:VIRTUAL_ENV/" + 'bin' + ':' + $env:PATH
+if (!$env:VIRTUAL_ENV_DISABLE_PROMPT) {
+    function global:_old_virtual_prompt {
+        ""
+    }
+    $function:_old_virtual_prompt = $function:prompt
+
+    function global:prompt {
+        # Add the custom prefix to the existing prompt
+        $previous_prompt_value = & $function:_old_virtual_prompt
+        ("(" + $env:VIRTUAL_ENV_PROMPT + ") " + $previous_prompt_value)
+    }
+}
diff --git a/bin/activate_this.py b/bin/activate_this.py
new file mode 100644
index 0000000..cdd1106
--- /dev/null
+++ b/bin/activate_this.py
@@ -0,0 +1,38 @@
+"""
+Activate virtualenv for current interpreter:
+
+import runpy
+runpy.run_path(this_file)
+
+This can be used when you must use an existing Python interpreter, not the virtualenv bin/python.
+"""  # noqa: D415
+
+from __future__ import annotations
+
+import os
+import site
+import sys
+
+try:
+    abs_file = os.path.abspath(__file__)
+except NameError as exc:
+    msg = "You must use import runpy; runpy.run_path(this_file)"
+    raise AssertionError(msg) from exc
+
+bin_dir = os.path.dirname(abs_file)
+base = bin_dir[: -len('bin') - 1]  # strip away the bin part from the __file__, plus the path separator
+
+# prepend bin to PATH (this file is inside the bin directory)
+os.environ["PATH"] = os.pathsep.join([bin_dir, *os.environ.get("PATH", "").split(os.pathsep)])
+os.environ["VIRTUAL_ENV"] = base  # virtual env is right above bin directory
+os.environ["VIRTUAL_ENV_PROMPT"] = '' or os.path.basename(base)
+
+# add the virtual environments libraries to the host python import mechanism
+prev_length = len(sys.path)
+for lib in '../lib/python3.10/site-packages'.split(os.pathsep):
+    path = os.path.realpath(os.path.join(bin_dir, lib))
+    site.addsitedir(path.decode("utf-8") if '' else path)
+sys.path[:] = sys.path[prev_length:] + sys.path[0:prev_length]
+
+sys.real_prefix = sys.prefix
+sys.prefix = base
diff --git a/bin/cmark b/bin/cmark
new file mode 100755
index 0000000..3d7dd2f
--- /dev/null
+++ b/bin/cmark
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from commonmark.cmark import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/estimator_ckpt_converter b/bin/estimator_ckpt_converter
new file mode 100755
index 0000000..0f5aa0d
--- /dev/null
+++ b/bin/estimator_ckpt_converter
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow_estimator.python.estimator.tools.checkpoint_converter import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/f2py b/bin/f2py
new file mode 100755
index 0000000..e1d3c77
--- /dev/null
+++ b/bin/f2py
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from numpy.f2py.f2py2e import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/f2py3 b/bin/f2py3
new file mode 100755
index 0000000..e1d3c77
--- /dev/null
+++ b/bin/f2py3
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from numpy.f2py.f2py2e import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/f2py3.10 b/bin/f2py3.10
new file mode 100755
index 0000000..e1d3c77
--- /dev/null
+++ b/bin/f2py3.10
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from numpy.f2py.f2py2e import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/fonttools b/bin/fonttools
new file mode 100755
index 0000000..a6b63d5
--- /dev/null
+++ b/bin/fonttools
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.__main__ import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/futurize b/bin/futurize
new file mode 100755
index 0000000..d4df95b
--- /dev/null
+++ b/bin/futurize
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from libfuturize.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/gdown b/bin/gdown
new file mode 100755
index 0000000..80af0ed
--- /dev/null
+++ b/bin/gdown
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from gdown.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/gin b/bin/gin
new file mode 100755
index 0000000..4c77d4d
--- /dev/null
+++ b/bin/gin
@@ -0,0 +1,225 @@
+#!/home/featurize/work/alphageometry/bin/python
+"gin - a Git index file parser"
+version = "0.1.006"
+
+# https://github.com/git/git/blob/master/Documentation/technical/index-format.txt
+
+import binascii
+import collections
+import json
+import mmap
+import struct
+
+def check(boolean, message):
+    if not boolean:
+        import sys
+        print("error: " + message, file=sys.stderr)
+        sys.exit(1)
+
+def parse(filename, pretty=True):
+    with open(filename, "rb") as o:
+        f = mmap.mmap(o.fileno(), 0, prot=mmap.PROT_READ)
+
+        def read(format):
+            # "All binary numbers are in network byte order."
+            # Hence "!" = network order, big endian
+            format = "! " + format
+            bytes = f.read(struct.calcsize(format))
+            return struct.unpack(format, bytes)[0]
+
+        index = collections.OrderedDict()
+
+        # 4-byte signature, b"DIRC"
+        index["signature"] = f.read(4).decode("ascii")
+        check(index["signature"] == "DIRC", "Not a Git index file")
+
+        # 4-byte version number
+        index["version"] = read("I")
+        check(index["version"] in {2, 3},
+            "Unsupported version: %s" % index["version"])
+
+        # 32-bit number of index entries, i.e. 4-byte
+        index["entries"] = read("I")
+
+        yield index
+
+        for n in range(index["entries"]):
+            entry = collections.OrderedDict()
+
+            entry["entry"] = n + 1
+
+            entry["ctime_seconds"] = read("I")
+            entry["ctime_nanoseconds"] = read("I")
+            if pretty:
+                entry["ctime"] = entry["ctime_seconds"]
+                entry["ctime"] += entry["ctime_nanoseconds"] / 1000000000
+                del entry["ctime_seconds"]
+                del entry["ctime_nanoseconds"]
+
+            entry["mtime_seconds"] = read("I")
+            entry["mtime_nanoseconds"] = read("I")
+            if pretty:
+                entry["mtime"] = entry["mtime_seconds"]
+                entry["mtime"] += entry["mtime_nanoseconds"] / 1000000000
+                del entry["mtime_seconds"]
+                del entry["mtime_nanoseconds"]
+
+            entry["dev"] = read("I")
+            entry["ino"] = read("I")
+
+            # 4-bit object type, 3-bit unused, 9-bit unix permission
+            entry["mode"] = read("I")
+            if pretty:
+                entry["mode"] = "%06o" % entry["mode"]
+
+            entry["uid"] = read("I")
+            entry["gid"] = read("I")
+            entry["size"] = read("I")
+
+            entry["sha1"] = binascii.hexlify(f.read(20)).decode("ascii")
+            entry["flags"] = read("H")
+
+            # 1-bit assume-valid
+            entry["assume-valid"] = bool(entry["flags"] & (0b10000000 << 8))
+            # 1-bit extended, must be 0 in version 2
+            entry["extended"] = bool(entry["flags"] & (0b01000000 << 8))
+            # 2-bit stage (?)
+            stage_one = bool(entry["flags"] & (0b00100000 << 8))
+            stage_two = bool(entry["flags"] & (0b00010000 << 8))
+            entry["stage"] = stage_one, stage_two
+            # 12-bit name length, if the length is less than 0xFFF (else, 0xFFF)
+            namelen = entry["flags"] & 0xFFF
+
+            # 62 bytes so far
+            entrylen = 62
+
+            if entry["extended"] and (index["version"] == 3):
+                entry["extra-flags"] = read("H")
+                # 1-bit reserved
+                entry["reserved"] = bool(entry["extra-flags"] & (0b10000000 << 8))
+                # 1-bit skip-worktree
+                entry["skip-worktree"] = bool(entry["extra-flags"] & (0b01000000 << 8))
+                # 1-bit intent-to-add
+                entry["intent-to-add"] = bool(entry["extra-flags"] & (0b00100000 << 8))
+                # 13-bits unused
+                # used = entry["extra-flags"] & (0b11100000 << 8)
+                # check(not used, "Expected unused bits in extra-flags")
+                entrylen += 2
+
+            if namelen < 0xFFF:
+                entry["name"] = f.read(namelen).decode("utf-8", "replace")
+                entrylen += namelen
+            else:
+                # Do it the hard way
+                name = []
+                while True:
+                    byte = f.read(1)
+                    if byte == "\x00":
+                        break
+                    name.append(byte)
+                entry["name"] = b"".join(name).decode("utf-8", "replace")
+                entrylen += 1
+
+            padlen = (8 - (entrylen % 8)) or 8
+            nuls = f.read(padlen)
+            check(set(nuls) == {0}, "padding contained non-NUL")
+
+            yield entry
+
+        indexlen = len(f)
+        extnumber = 1
+
+        while f.tell() < (indexlen - 20):
+            extension = collections.OrderedDict()
+            extension["extension"] = extnumber
+            extension["signature"] = f.read(4).decode("ascii")
+            extension["size"] = read("I")
+
+            # Seems to exclude the above:
+            # "src_offset += 8; src_offset += extsize;"
+            extension["data"] = f.read(extension["size"])
+            extension["data"] = extension["data"].decode("iso-8859-1")
+            if pretty:
+                extension["data"] = json.dumps(extension["data"])
+
+            yield extension
+            extnumber += 1
+
+        checksum = collections.OrderedDict()
+        checksum["checksum"] = True
+        checksum["sha1"] = binascii.hexlify(f.read(20)).decode("ascii")
+        yield checksum
+
+        f.close()
+
+def parse_file(arg, pretty=True):
+    if pretty:
+       properties = {
+           "version": "[header]",
+           "entry": "[entry]",
+           "extension": "[extension]",
+           "checksum": "[checksum]"
+       }
+    else:
+        print("[")
+
+    for item in parse(arg, pretty=pretty):
+        if pretty:
+            for key, value in properties.items():
+                if key in item:
+                    print(value)
+                    break
+            else:
+                print("[?]")
+
+        if pretty:
+            for key, value in item.items():
+                print(" ", key, "=", value)
+        else:
+            print(json.dumps(item))
+
+        last = "checksum" in item
+        if not last:
+            if pretty:
+                print()
+            else:
+                print(",")
+
+    if not pretty:
+        print("]")
+
+def main():
+    import argparse
+    import os.path
+    import sys
+
+    parser = argparse.ArgumentParser(description="parse a Git index file")
+    parser.add_argument("-j", "--json", action="store_true",
+        help="output JSON")
+    parser.add_argument("-v", "--version", action="store_true",
+        help="show script version number")
+    parser.add_argument("path", nargs="?", default=".",
+        help="path to a Git repository or index file")
+    args = parser.parse_args()
+
+    if args.version:
+        print("gin " + version)
+        sys.exit()
+
+    if os.path.isdir(args.path):
+        path = os.path.join(args.path, ".git", "index")
+        if os.path.isfile(path):
+            args.path = path
+        else:
+            print("error: couldn't find a .git/index file to use", file=sys.stderr)
+            print("use -h or --help for some documentation", file=sys.stderr)
+            sys.exit(1)
+
+    if not args.path:
+        parser.print_usage()
+        sys.exit(2)
+
+    parse_file(args.path, pretty=not args.json)
+
+if __name__ == "__main__":
+    main()
diff --git a/bin/google-oauthlib-tool b/bin/google-oauthlib-tool
new file mode 100755
index 0000000..013a7cf
--- /dev/null
+++ b/bin/google-oauthlib-tool
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from google_auth_oauthlib.tool.__main__ import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/huggingface-cli b/bin/huggingface-cli
new file mode 100755
index 0000000..e65189e
--- /dev/null
+++ b/bin/huggingface-cli
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from huggingface_hub.commands.huggingface_cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/import_pb_to_tensorboard b/bin/import_pb_to_tensorboard
new file mode 100755
index 0000000..30ce73d
--- /dev/null
+++ b/bin/import_pb_to_tensorboard
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.python.tools.import_pb_to_tensorboard import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/markdown_py b/bin/markdown_py
new file mode 100755
index 0000000..b280004
--- /dev/null
+++ b/bin/markdown_py
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from markdown.__main__ import run
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(run())
diff --git a/bin/nltk b/bin/nltk
new file mode 100755
index 0000000..d7d29ba
--- /dev/null
+++ b/bin/nltk
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from nltk.cli import cli
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(cli())
diff --git a/bin/normalizer b/bin/normalizer
new file mode 100755
index 0000000..08c2aa4
--- /dev/null
+++ b/bin/normalizer
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from charset_normalizer.cli import cli_detect
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(cli_detect())
diff --git a/bin/pasteurize b/bin/pasteurize
new file mode 100755
index 0000000..c51dc5e
--- /dev/null
+++ b/bin/pasteurize
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from libpasteurize.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pip b/bin/pip
new file mode 100755
index 0000000..23311c6
--- /dev/null
+++ b/bin/pip
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pip-3.10 b/bin/pip-3.10
new file mode 100755
index 0000000..23311c6
--- /dev/null
+++ b/bin/pip-3.10
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pip3 b/bin/pip3
new file mode 100755
index 0000000..23311c6
--- /dev/null
+++ b/bin/pip3
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pip3.10 b/bin/pip3.10
new file mode 100755
index 0000000..23311c6
--- /dev/null
+++ b/bin/pip3.10
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pybabel b/bin/pybabel
new file mode 100755
index 0000000..a58a105
--- /dev/null
+++ b/bin/pybabel
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from babel.messages.frontend import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pyftmerge b/bin/pyftmerge
new file mode 100755
index 0000000..9a2ace5
--- /dev/null
+++ b/bin/pyftmerge
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.merge import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pyftsubset b/bin/pyftsubset
new file mode 100755
index 0000000..3872489
--- /dev/null
+++ b/bin/pyftsubset
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.subset import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pygmentize b/bin/pygmentize
new file mode 100755
index 0000000..ab50b42
--- /dev/null
+++ b/bin/pygmentize
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pygments.cmdline import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/pyrsa-decrypt b/bin/pyrsa-decrypt
new file mode 100755
index 0000000..99cc427
--- /dev/null
+++ b/bin/pyrsa-decrypt
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.cli import decrypt
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(decrypt())
diff --git a/bin/pyrsa-encrypt b/bin/pyrsa-encrypt
new file mode 100755
index 0000000..d5e9f18
--- /dev/null
+++ b/bin/pyrsa-encrypt
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.cli import encrypt
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(encrypt())
diff --git a/bin/pyrsa-keygen b/bin/pyrsa-keygen
new file mode 100755
index 0000000..fbe3c52
--- /dev/null
+++ b/bin/pyrsa-keygen
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.cli import keygen
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(keygen())
diff --git a/bin/pyrsa-priv2pub b/bin/pyrsa-priv2pub
new file mode 100755
index 0000000..da6f72f
--- /dev/null
+++ b/bin/pyrsa-priv2pub
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.util import private_to_public
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(private_to_public())
diff --git a/bin/pyrsa-sign b/bin/pyrsa-sign
new file mode 100755
index 0000000..8274800
--- /dev/null
+++ b/bin/pyrsa-sign
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.cli import sign
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(sign())
diff --git a/bin/pyrsa-verify b/bin/pyrsa-verify
new file mode 100755
index 0000000..3d8f0d1
--- /dev/null
+++ b/bin/pyrsa-verify
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from rsa.cli import verify
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(verify())
diff --git a/bin/python b/bin/python
new file mode 120000
index 0000000..ec7dcb9
--- /dev/null
+++ b/bin/python
@@ -0,0 +1 @@
+/environment/miniconda3/bin/python
\ No newline at end of file
diff --git a/bin/python3 b/bin/python3
new file mode 120000
index 0000000..d8654aa
--- /dev/null
+++ b/bin/python3
@@ -0,0 +1 @@
+python
\ No newline at end of file
diff --git a/bin/python3.10 b/bin/python3.10
new file mode 120000
index 0000000..d8654aa
--- /dev/null
+++ b/bin/python3.10
@@ -0,0 +1 @@
+python
\ No newline at end of file
diff --git a/bin/sacrebleu b/bin/sacrebleu
new file mode 100755
index 0000000..a35e5a1
--- /dev/null
+++ b/bin/sacrebleu
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from sacrebleu.sacrebleu import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/saved_model_cli b/bin/saved_model_cli
new file mode 100755
index 0000000..b045532
--- /dev/null
+++ b/bin/saved_model_cli
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.python.tools.saved_model_cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/seqio_cache_tasks b/bin/seqio_cache_tasks
new file mode 100755
index 0000000..9aed395
--- /dev/null
+++ b/bin/seqio_cache_tasks
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from seqio.scripts.cache_tasks_main import console_entry_point
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(console_entry_point())
diff --git a/bin/t5_cache_tasks b/bin/t5_cache_tasks
new file mode 100755
index 0000000..9aed395
--- /dev/null
+++ b/bin/t5_cache_tasks
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from seqio.scripts.cache_tasks_main import console_entry_point
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(console_entry_point())
diff --git a/bin/t5_inspect_tasks b/bin/t5_inspect_tasks
new file mode 100755
index 0000000..3cf5e75
--- /dev/null
+++ b/bin/t5_inspect_tasks
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from seqio.scripts.inspect_tasks_main import console_entry_point
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(console_entry_point())
diff --git a/bin/t5_mesh_transformer b/bin/t5_mesh_transformer
new file mode 100755
index 0000000..d72e2c6
--- /dev/null
+++ b/bin/t5_mesh_transformer
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from t5.models.mesh_transformer_main import console_entry_point
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(console_entry_point())
diff --git a/bin/tabulate b/bin/tabulate
new file mode 100755
index 0000000..dba254d
--- /dev/null
+++ b/bin/tabulate
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tabulate import _main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(_main())
diff --git a/bin/tensorboard b/bin/tensorboard
new file mode 100755
index 0000000..ff9e467
--- /dev/null
+++ b/bin/tensorboard
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorboard.main import run_main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(run_main())
diff --git a/bin/tf_upgrade_v2 b/bin/tf_upgrade_v2
new file mode 100755
index 0000000..97fa08a
--- /dev/null
+++ b/bin/tf_upgrade_v2
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.tools.compatibility.tf_upgrade_v2_main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/tfds b/bin/tfds
new file mode 100755
index 0000000..cc6bb04
--- /dev/null
+++ b/bin/tfds
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow_datasets.scripts.cli.main import launch_cli
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(launch_cli())
diff --git a/bin/tflite_convert b/bin/tflite_convert
new file mode 100755
index 0000000..2926286
--- /dev/null
+++ b/bin/tflite_convert
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.lite.python.tflite_convert import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/toco b/bin/toco
new file mode 100755
index 0000000..2926286
--- /dev/null
+++ b/bin/toco
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.lite.python.tflite_convert import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/toco_from_protos b/bin/toco_from_protos
new file mode 100755
index 0000000..45922d0
--- /dev/null
+++ b/bin/toco_from_protos
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tensorflow.lite.toco.python.toco_from_protos import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/tqdm b/bin/tqdm
new file mode 100755
index 0000000..c780036
--- /dev/null
+++ b/bin/tqdm
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from tqdm.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/transformers-cli b/bin/transformers-cli
new file mode 100755
index 0000000..1a047de
--- /dev/null
+++ b/bin/transformers-cli
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from transformers.commands.transformers_cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/ttx b/bin/ttx
new file mode 100755
index 0000000..d807cab
--- /dev/null
+++ b/bin/ttx
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.ttx import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/wheel b/bin/wheel
new file mode 100755
index 0000000..81aab92
--- /dev/null
+++ b/bin/wheel
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from wheel.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/wheel-3.10 b/bin/wheel-3.10
new file mode 100755
index 0000000..81aab92
--- /dev/null
+++ b/bin/wheel-3.10
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from wheel.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/wheel3 b/bin/wheel3
new file mode 100755
index 0000000..81aab92
--- /dev/null
+++ b/bin/wheel3
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from wheel.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/bin/wheel3.10 b/bin/wheel3.10
new file mode 100755
index 0000000..81aab92
--- /dev/null
+++ b/bin/wheel3.10
@@ -0,0 +1,8 @@
+#!/home/featurize/work/alphageometry/bin/python
+# -*- coding: utf-8 -*-
+import re
+import sys
+from wheel.cli import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())
diff --git a/chiaya.sh b/chiaya.sh
new file mode 100644
index 0000000..d542495
--- /dev/null
+++ b/chiaya.sh
@@ -0,0 +1,67 @@
+source ./bin/activate
+
+DATA=ag_ckpt_vocab
+MELIAD_PATH=meliad_lib/meliad
+export PYTHONPATH=$PYTHONPATH:$MELIAD_PATH
+
+DDAR_ARGS=(
+  --defs_file=$(pwd)/defs.txt \
+  --rules_file=$(pwd)/rules1.txt \
+);
+
+SIZE=4
+
+BATCH_SIZE=8
+BEAM_SIZE=16
+DEPTH=4
+
+SEARCH_ARGS=(
+  --beam_size=$BEAM_SIZE
+  --search_depth=$DEPTH
+)
+
+LM_ARGS=(
+  --ckpt_path=$DATA \
+  --vocab_path=$DATA/geometry.757.model \
+  --gin_search_paths=$MELIAD_PATH/transformer/configs \
+  --gin_file=base_htrans.gin \
+  --gin_file=size/medium_150M.gin \
+  --gin_file=options/positions_t5.gin \
+  --gin_file=options/lr_cosine_decay.gin \
+  --gin_file=options/seq_1024_nocache.gin \
+  --gin_file=geometry_150M_generate.gin \
+  --gin_param=DecoderOnlyLanguageModelGenerate.output_token_losses=True \
+  --gin_param=TransformerTaskConfig.batch_size=$BATCH_SIZE \
+  --gin_param=TransformerTaskConfig.sequence_length=128 \
+  --gin_param=Trainer.restore_state_variables=False
+);
+
+INPUT_FILE=speed.txt
+SERIES=Menelaus_a
+
+python -m alphageometry \
+--alsologtostderr \
+--problems_file=$(pwd)/$INPUT_FILE \
+--problem_name=test_pascal6_rev \
+--mode=alphageometry \
+"${DDAR_ARGS[@]}" \
+"${SEARCH_ARGS[@]}" \
+"${LM_ARGS[@]}" \
+--out_file="kirine.txt"\
+
+
+# for pro in $(cat $INPUT_FILE | grep $SERIES); 
+# do
+#   echo "solve problem $pro$"
+#   python -m alphageometry \
+#   --alsologtostderr \
+#   --problems_file=$(pwd)/$INPUT_FILE \
+#   --problem_name=${pro} \
+#   --mode=alphageometry \
+#   "${DDAR_ARGS[@]}" \
+#   "${SEARCH_ARGS[@]}" \
+#   "${LM_ARGS[@]}" \
+#   --out_file="./output_old/${pro}.txt"\
+
+#   echo "finish problem $pro$"
+# done
\ No newline at end of file
diff --git a/circle.txt b/circle.txt
new file mode 100644
index 0000000..19e9a7d
--- /dev/null
+++ b/circle.txt
@@ -0,0 +1,58 @@
+example_cyclic2power
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; p = on_line p a b, on_line p c d ? eqratio p a p c p d p b
+example_radical_axis3
+a b c = triangle a b c; d = on_line a b; o1 = circle o1 a b c; e = on_line e c d, on_circle e o1 a; o2 = on_bline o2 c e; f = on_circle f o2 c; g = on_circle g o2 c, on_line g d f ? cyclic a b f g
+example7_1
+b c = segment b c; a = on_bline a b c; d = on_line d a b; h = on_pline h d b c, on_line h a c; e = mirror e h c; f = on_line f d e, on_line f b c; o1 = circle o1 b d f; o2 = circle o2 c e f; g = on_circle g o1 f, on_circle g o2 f ? perp g f d e
+example7_2
+b c = segment b c; a = on_bline a b c; i = incenter i a b c; o = on_bline o b i; p = on_circle p a b, on_circle p o b; q = on_circle q i b, on_circle q o b; r = on_line r i p, on_line r b q ? perp b r c r
+example7_4
+a b c = triangle a b c; o = circle o a b c; a1 = midpoint a1 b c; a2 = on_line a2 a a1, on_circle a2 o a; qa = foot qa a1 a o; pa = on_line pa a1 qa, on_tline pa a2 o a2; b1 = midpoint b1 c a; b2 = on_line b2 b b1, on_circle b2 o b; qb = foot qb b1 b o; pb = on_line pb b1 qb, on_tline pb b2 o b2; c1 = midpoint c1 a b; c2 = on_line c2 c c1, on_circle c2 o c; qc = foot qc c1 c o; pc = on_line pc c1 qc, on_tline pc c2 o c2 ? coll pa pb pc
+example7_5
+a b c = triangle a b c; d e f x = excenter2 d e f x a b c; o1 = circle o1 a e f; p = on_line p b c, on_circle p o1 a; q = on_line q b c, on_circle q o1 a; m = midpoint m a d; o2 = circle o2 m p q; t = on_circle t o2 m, on_circle t x d ? coll o2 x t
+example7_6
+a b c = triangle a b c; o = circle o a b c; h = orthocenter h a b c; s = on_circle s o a; p = on_line p b c, on_tline p s a s; o2 = circle o2 a s p; x = on_line x s h, on_circle x o2 a; r = on_line r a b, on_line r o p; q = on_line q a c, on_line q o p; y = foot y q a r; z = foot z r a q ? coll x y z
+example7_7_1
+a b = segment a b; o1 = on_tline o1 a a b; o2 = on_tline o2 b b a; p = on_circle p o1 a, on_circle p o2 b; q = on_circle q o1 a, on_circle q o2 b; c = on_tline c p p o1, on_circle c o2 b; t = on_line t a p, on_line t b c; o3 = circle o3 p q t ? perp b p p o3
+example7_7_2
+a b = segment a b; o1 = on_tline o1 a a b; o2 = on_tline o2 b b a; p = on_circle p o1 a, on_circle p o2 b; q = on_circle q o1 a, on_circle q o2 b; c = on_tline c p p o1, on_circle c o2 b; t = on_line t a p, on_line t b c; o3 = circle o3 p q t ? perp b t t o3
+example7_8
+a b c = triangle a b c; o = circle o a b c; d = on_line d a o, on_line d b c; u = foot u d a c; v = foot v d a b; e = on_tline e a a o, on_line e d u; f = on_tline f a a o, on_line f d v; p = on_line p e c, on_line p f b ? perp p d b c
+example7_9
+a b c = triangle a b c; o = circle o a b c; h = orthocenter h a b c; d = on_line d a h, on_line d b c; e = on_line e a h, on_circle e o a; x = midpoint x d e; p = on_circle p o a, on_circle p x e; q = on_circle q p h, on_tline q p p h; m = midpoint m b c ? cyclic p d m q
+example7_10
+a b c = triangle a b c; h = orthocenter h a b c; o = circle o a b c; d = on_circle d o a, on_circle d a c; k = on_line k a d, on_circle k a b; l = on_line l b c, on_pline l k c d; m = midpoint m b c; n = foot n h a l; t = midpoint t a h ? coll m n t
+exercise7_1
+a b = segment a b; x = on_bline x a b; y = on_bline y a b; c = on_circle c x a; d = on_circle d y a, on_line d b c; e = on_circle e x a, on_line e d a; f = on_circle f y a, on_line f c a; o = circle o a e f ? perp o b c d
+exercise7_2
+a b c = segment a b c; d = foot d a b c; e = foot e b c a; f = foot f c a b; h = on_line h a d, on_line h b e; p = on_line p b e, on_line p d f; q = on_line q a b, on_tline q p b c; n = on_line n e q, on_line n a d ? cong a n a h
+exercise7_4
+a b c = triangle a b c; o = circle o a b c; i = circle i o b c; g = on_circle g i o; x = circle x a b g; y = circle y a c g; e = on_line e a c, on_circle e x a; f = on_line f a b, on_circle f y a; k = on_line k b e, on_line k c f; t = on_line t a k, on_line t b c ? coll t o g
+exercise7_5
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a d, on_line e b c; m = midpoint m a d; n = midpoint n b c; w = circle w e m n; x = on_circle x o a, on_circle x w e; y = on_circle y o a, on_circle y w e; z = on_line z a b, on_line z c d ? coll x y z
+exercise7_7
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; p = on_line p a d, on_circle p i d; q = on_line q e f, on_tline q p a d; x = on_line x d e, on_line x a q; y = on_line y d f, on_line y a q ? cong a x a y
+exercise7_8
+a b c = triangle a b c; x y z i = incenter2 x y z i a b c; g = on_line g b y, on_line g c z; r = on_pline r y b c, on_pline r b c y; s = on_pline s z b c, on_pline s b c z ? cong g r g s
+exercise7_9
+b c = segment b c; a = on_bline a b c; i = incenter i a b c; o = circle o a b c; m = on_circle m b i, on_circle m o b; n = on_circle n c i, on_circle n o c; d = on_circle d o a; e = on_line e a d, on_line e b i; f = on_line f a d, on_line f c i; p = on_line p d m, on_line p c i; q = on_line q d n, on_line q b i; x = on_line x c e, on_line x b f ? cyclic d p i x
+exercise7_10
+a b c = triangle a b c; i = incenter i a b c; d = foot d i b c; o1 = incenter o1 a b d; o2 = incenter o2 a c d; e = foot e o1 a b; f = foot f o1 a d; g = foot g o2 a c; p = on_line p e g, on_circle p o1 e; q = on_line q e g, on_circle q o2 g; x = on_tline x p o1 p, on_tline x q o2 q ? coll x a d
+exercise7_11
+b c = segment b c; a = on_bline a b c; d = on_line d a c; o = circle o b c d; k = on_circle k o b; t = on_line t c k, on_pline t a b c; m = midpoint m d t ? eqangle k t k a a c a m
+exercise7_12
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; z = midpoint z b c; m = midpoint m a b; n = midpoint n a c; x = on_circle x i d, on_circle x z b; y = on_circle y i d, on_circle y z b; p = on_line p e f, on_line p x y ? coll p m n
+exercise7_13
+a b c = triangle a b c; d = foot d a b c; e = foot e b c a; m = midpoint a b; o = circle o a b c; f = on_line f d e, on_circle f o a; k = on_line k d e, on_circle k o a; w = circle w m d e; p = on_line p m k, on_circle p w m; q = on_line q m f, on_circle q w m ? cyclic a p q b
+exercise7_14_1
+a b = segment a b; o = on_bline o a b; p = on_bline p a b; c = on_tline c a a p, on_circle c o a; d = on_tline d a a o, on_circle d o a; e = midpoint e a c; f = midpoint f a d ? cyclic a e b f
+exercise7_14_2
+a b = segment a b; o = on_bline o a b; p = on_bline p a b; c = on_tline c a a p, on_circle c o a; d = on_tline d a a o, on_circle d o a; e = midpoint e a c; w = circle w a b e; f = on_circle f w a, on_line f a d; g = on_circle g o a; h = on_line h a g, on_circle h p a; k = on_line k a g, on_circle k w a ? cong k g k h
+exercise7_15
+a b = segment a b; o = on_bline o a b; p = on_tline p a o a, on_tline p b o b; c = on_circle c o a; d = on_line d p c, on_circle d o a; e = on_pline e c p b, on_circle e o a; f = on_line f a e, on_line f p b; g = on_line g d e, on_line g p b ? cong g f g b
+example6_1
+a b c = triangle a b c; o = circle o a b c; p = free; a1 = on_line a1 a p, on_circle a1 o a; b1 = on_line b1 b p, on_circle b1 o b; c1 = on_line c1 c p, on_circle c1 o c; q = on_circle q o a; x = on_line x q a1, on_line x b c; y = on_line y q b1, on_line y a c; z = on_line z q c1, on_line z a b ? coll x y z
+example6_2
+a b = segment a b; o = midpoint o a b; p = on_tline p b o b; c = on_circle c o a; d = on_line d p c, on_circle d o a; e = on_line e a c, on_line e p o; f = on_line f a d, on_line f p o ? cong o e o f
+example6_3
+a b c = triangle a b c; d = foot d a b c; e = foot e b c a; f = foot f c a b; h = on_line h a d, on_line h b e; p = reflect p e a d; q = reflect q f a d; x = on_line x b q, on_line x c p; y = on_line y b p, on_line y c q; z = on_line z a x, on_line z h y ? coll z b c
\ No newline at end of file
diff --git a/dd.py b/dd.py
index 19325ff..d5dc879 100644
--- a/dd.py
+++ b/dd.py
@@ -27,6 +27,7 @@
 import problem as pr
 from problem import Dependency, EmptyDependency
 
+import time
 
 def intersect1(set1: set[Any], set2: set[Any]) -> Any:
   for x in set1:
@@ -34,6 +35,17 @@ def intersect1(set1: set[Any], set2: set[Any]) -> Any:
       return x
   return None
 
+def intersect2(set1: set[Any], set2: set[Any]) -> Any:
+  a = None
+  b = None
+  for x in set1:
+    if x in set2:
+      if a == None:
+        a = x
+      else:
+        b = x
+        break
+  return a,b
 
 def diff_point(l: gm.Line, a: gm.Point) -> gm.Point:
   for x in l.neighbors(gm.Point):
@@ -41,6 +53,7 @@ def diff_point(l: gm.Line, a: gm.Point) -> gm.Point:
       return x
   return None
 
+import time
 
 # pylint: disable=protected-access
 # pylint: disable=unused-argument
@@ -87,9 +100,10 @@ def match_eqratio_eqratio_eqratio(
         c, d = g.two_points_of_length(l12)
         m, n = g.two_points_of_length(l3)
         p, q = g.two_points_of_length(l34)
-        # eqangle a b c d m n p q
+        # eqangle a b c d m n p q (eqratio)
         e, f = g.two_points_of_length(l2)
         r, u = g.two_points_of_length(l4)
+        #debugname([a, b, c, d, e, f, m, n, p, q, r, u])
         yield dict(zip('abcdefmnpqru', [a, b, c, d, e, f, m, n, p, q, r, u]))
 
 
@@ -442,13 +456,695 @@ def match_cyclic_eqangle(
     record.add((b, a, d, c))
     yield dict(zip('ABPQ', [a, b, c, d]))
 
+def match_cyclic2power(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match cyclic A B C D, coll P A B, coll P C D => eqratio P A P C P D P B"""
+  ta = time.time()
+  record = set()
+  for a,b,c,d in g_matcher('cyclic'):
+    if (a,b,c,d) in record:
+      continue
+    points = [a,b,c,d]
+    perms = utils.perm4(points)
+    for p in perms:
+      record.add(p)
+    ab = g._get_line(a, b)
+    cd = g._get_line(c, d)
+    if ab and cd:
+      p1s = ab.neighbors(gm.Point, return_set=True)
+      p2s = cd.neighbors(gm.Point, return_set=True)
+      p = intersect1(p1s, p2s)
+      if p:
+        yield dict(zip('PABCD',[p,a,b,c,d]))
+    ac = g._get_line(a, c)
+    bd = g._get_line(b, d)
+    if ac and bd:
+      p1s = ac.neighbors(gm.Point, return_set=True)
+      p2s = bd.neighbors(gm.Point, return_set=True)
+      p = intersect1(p1s, p2s)
+      if p:
+        yield dict(zip('PABCD',[p,a,c,b,d]))
+    ad = g._get_line(a, d)
+    bc = g._get_line(b, c)
+    if ad and bc:
+      p1s = ad.neighbors(gm.Point, return_set=True)
+      p2s = bc.neighbors(gm.Point, return_set=True)
+      p = intersect1(p1s, p2s)
+      if p:
+        yield dict(zip('PABCD',[p,a,d,b,c]))
+  tb = time.time()
+  print('c2p:',tb-ta)
+
+def match_cyclic2power_tan(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match circle O A B C, perp O A A P, coll P B C => eqratio P A P B P C P A """
+  ta = time.time()
+  for o,a,b,c in g.all_circles():
+    bc = g._get_line(b,c)
+    if not bc:
+      continue
+    oa = g._get_line(o, a)
+    if not (oa and oa.val): 
+      continue
+    for l in a.neighbors(gm.Line):
+      if g.check_perpl(oa, l):
+        p1s = l.neighbors(gm.Point, return_set=True)
+        p2s = bc.neighbors(gm.Point, return_set=True)
+        p = intersect1(p1s, p2s)
+        if p:
+          yield dict(zip('OPABC', [o, p, a, b, c]))
+        break
+  tb = time.time()
+  print('c2pt:',tb-ta)
+
+
+def match_power2cyclic(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match coll P A B, coll P C D, ncoll A B C D, eqratio P A P C P D P B => cyclic A B C D"""
+  ta = time.time()
+  all_lines = g.type2nodes[gm.Line]
+  for l1,l2 in utils.comb2(all_lines):
+      l1s = l1.neighbors(gm.Point, return_set=True)
+      l2s = l2.neighbors(gm.Point, return_set=True)
+      p = intersect1(l1s,l2s)
+      if not p:
+        continue
+      l1s = list(l1s)
+      l2s = list(l2s)
+      for a,b in utils.comb2(l1s):
+        for c,d in utils.comb2(l2s):
+          if g.check_eqratio([p, a, p, c, p, d, p, b]) and not g.check_coll([p,a,c]):
+            yield dict(zip('PABCD', [p, a, b, c, d]))
+  tb = time.time()
+  print('p2c:',tb-ta)
+          
+def match_pascal6(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match cyclic A B C D E F, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A => coll G H I"""
+  ta = time.time()
+  recordc = set()
+  record = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op))
+    for a, b, c, d, e, f in utils.perm6(circle.neighbors(gm.Point)):
+      if (a,b,c,d,e,f) in record:
+        continue
+      # 6! = 60 * 12
+      record.add((a,b,c,d,e,f))
+      record.add((b,c,d,e,f,a))
+      record.add((c,d,e,f,a,b))
+      record.add((d,e,f,a,b,c))
+      record.add((e,f,a,b,c,d))
+      record.add((f,a,b,c,d,e))
+      record.add((f,e,d,c,b,a))
+      record.add((e,d,c,b,a,f))
+      record.add((d,c,b,a,f,e))
+      record.add((c,b,a,f,e,d))
+      record.add((b,a,f,e,d,c))
+      record.add((a,f,e,d,c,b))
+
+      ab = g._get_line(a, b)
+      bc = g._get_line(b, c)
+      cd = g._get_line(c, d)
+      de = g._get_line(d, e)
+      ef = g._get_line(e, f)
+      fa = g._get_line(f, a)
+
+      if ab and bc and cd and de and ef and fa:
+        g1s = ab.neighbors(gm.Point, return_set=True)
+        g2s = de.neighbors(gm.Point, return_set=True)
+        h1s = bc.neighbors(gm.Point, return_set=True)
+        h2s = ef.neighbors(gm.Point, return_set=True)
+        i1s = cd.neighbors(gm.Point, return_set=True)
+        i2s = fa.neighbors(gm.Point, return_set=True)
+        gg = intersect1(g1s, g2s)
+        h = intersect1(h1s, h2s)
+        i = intersect1(i1s, i2s)
+        if gg and h and i:
+          yield dict(zip('ABCDEFGHI',[a,b,c,d,e,f,gg,h,i]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_pascal6_rev(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match cyclic A B C D E, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A, coll G H I => cyclic A B C D E F"""
+  ta = time.time()
+  recordc = set()
+  record = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op))
+    for a, b, c, d, e in utils.perm5(circle.neighbors(gm.Point)):
+      if (a,b,c,d,e) in record or (e,d,c,b,a) in record:
+        continue
+      record.add((a,b,c,d,e))
+
+      ab = g._get_line(a, b)
+      bc = g._get_line(b, c)
+      cd = g._get_line(c, d)
+      de = g._get_line(d, e)
+
+      if not (ab and bc and cd and de):
+        continue
+      
+      g1s = ab.neighbors(gm.Point, return_set=True)
+      g2s = de.neighbors(gm.Point, return_set=True)
+      gg = intersect1(g1s, g2s)
+      if not gg:
+        continue
+
+      for f in g.all_points():
+        if f in {o,a,b,c,d,e}:
+          continue
+        ef = g._get_line(e, f)
+        fa = g._get_line(f, a)
+        if ef and fa:
+          h1s = bc.neighbors(gm.Point, return_set=True)
+          h2s = ef.neighbors(gm.Point, return_set=True)
+          i1s = cd.neighbors(gm.Point, return_set=True)
+          i2s = fa.neighbors(gm.Point, return_set=True)
+          h = intersect1(h1s, h2s)
+          i = intersect1(i1s, i2s)
+          if h and i and g.check_coll([gg,h,i]):
+            yield dict(zip('OABCDEFGHI',[o,a,b,c,d,e,f,gg,h,i]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_pascal5(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match cyclic A B C D E, perp O A A G, coll G C D, coll H A B, coll H D E, coll I B C, coll I E A => coll G H I"""
+  ta = time.time()
+  recordc = set()
+  record = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op))    
+    for a,b,c,d,e in utils.perm5(circle.neighbors(gm.Point)):
+      if (a,b,c,d,e) in record or (a,e,d,c,b) in record:
+        continue
+      record.add((a,b,c,d,e))
+
+      ab = g._get_line(a, b)
+      bc = g._get_line(b, c)
+      cd = g._get_line(c, d)
+      de = g._get_line(d, e)
+      ea = g._get_line(e, a)
+
+      if not (ab and bc and cd and de and ea):
+        continue
+      oa = g._get_line(o, a)
+      if not (oa and oa.val):
+        continue
+      la = None
+      for l in a.neighbors(gm.Line):
+        if g.check_perpl(oa, l):
+          la = l
+          break
+      if not la:
+        continue
+      g1s = la.neighbors(gm.Point, return_set=True)
+      g2s = cd.neighbors(gm.Point, return_set=True)
+      h1s = ab.neighbors(gm.Point, return_set=True)
+      h2s = de.neighbors(gm.Point, return_set=True)
+      i1s = bc.neighbors(gm.Point, return_set=True)
+      i2s = ea.neighbors(gm.Point, return_set=True)
+      gg = intersect1(g1s, g2s)
+      h = intersect1(h1s, h2s)
+      i = intersect1(i1s, i2s)
+      if gg and h and i:
+        yield dict(zip('OABCDEGHI',[o,a,b,c,d,e,gg,h,i]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_pascal41(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """circle O A B C, cong O A O D, perp O A A G, coll G B C, coll H A B, coll H C D, perp O B B I, coll I D A => coll G H I (AABBCD)"""
+  ta = time.time()
+  recordc = set()
+  record = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op))    
+    for a,b,c,d in utils.perm4(circle.neighbors(gm.Point)):
+      if (a,b,c,d) in record or (b,a,d,c) in record:
+        continue
+      record.add((a,b,c,d))
+      ab = g._get_line(a, b)
+      bc = g._get_line(b, c)
+      cd = g._get_line(c, d)
+      da = g._get_line(d, a)
+      if not (ab and bc and cd and da):
+        continue
+      oa = g._get_line(o, a)
+      if not (oa and oa.val): 
+        continue
+      la = None
+      for l in a.neighbors(gm.Line):
+        if g.check_perpl(oa, l):
+          la = l
+          break
+      if not la:
+        continue
+      ob = g._get_line(o, b)
+      if not (ob and ob.val): 
+        continue
+      lb = None
+      for l in b.neighbors(gm.Line):
+        if g.check_perpl(ob, l):
+          lb = l
+          break
+      if not lb:
+        continue
+      
+      g1s = la.neighbors(gm.Point, return_set=True)
+      g2s = bc.neighbors(gm.Point, return_set=True)
+      h1s = ab.neighbors(gm.Point, return_set=True)
+      h2s = cd.neighbors(gm.Point, return_set=True)
+      i1s = lb.neighbors(gm.Point, return_set=True)
+      i2s = da.neighbors(gm.Point, return_set=True)
+      gg = intersect1(g1s, g2s)
+      h = intersect1(h1s, h2s)
+      i = intersect1(i1s, i2s)
+      if gg and h and i:
+        yield dict(zip('OABCDGHI',[o,a,b,c,d,gg,h,i]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_pascal42(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """circle O A B C, cong O A O D, perp O A A G, perp O B B G, coll H A C, coll H B D, coll I C B, coll I D A => coll G H I (AACBBD)"""
+  ta = time.time()
+  recordc = set()
+  record = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op)) 
+    for a,b,c,d in utils.perm4(circle.neighbors(gm.Point)):
+      if (a,b,c,d) in record or (b,a,c,d) in record or (a,b,d,c) in record or (b,a,d,c) in record:
+        continue
+      record.add((a,b,c,d))
+      ac = g._get_line(a, c)
+      bd = g._get_line(b, d)
+      bc = g._get_line(c, b)
+      ad = g._get_line(d, a)
+      if not (ac and bc and ad and bd):
+        continue
+      oa = g._get_line(o, a)
+      if not (oa and oa.val): 
+        continue
+      la = None
+      for l in a.neighbors(gm.Line):
+        if g.check_perpl(oa, l):
+          la = l
+          break
+      if not la:
+        continue
+      ob = g._get_line(o, b)
+      if not (ob and ob.val): 
+        continue
+      lb = None
+      for l in b.neighbors(gm.Line):
+        if g.check_perpl(ob, l):
+          lb = l
+          break
+      if not lb:
+        continue
+      
+      g1s = la.neighbors(gm.Point, return_set=True)
+      g2s = lb.neighbors(gm.Point, return_set=True)
+      h1s = ac.neighbors(gm.Point, return_set=True)
+      h2s = bd.neighbors(gm.Point, return_set=True)
+      i1s = ad.neighbors(gm.Point, return_set=True)
+      i2s = bc.neighbors(gm.Point, return_set=True)
+      gg = intersect1(g1s, g2s)
+      h = intersect1(h1s, h2s)
+      i = intersect1(i1s, i2s)
+      if gg and h and i:
+        yield dict(zip('OABCDGHI',[o,a,b,c,d,gg,h,i]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_radical_axis(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """cyclic A B C D, cyclic A B E F, cyclic C D E F, coll P A B, coll P C D => coll P E F"""
+  ta = time.time()
+  circles = set()
+  recordc = set()
+  for o,x,y,z in g.all_circles():
+    if (o,x) in recordc:
+      continue
+    circle = g.get_circle_thru_triplet(x,y,z)
+    for op in circle.neighbors(gm.Point):
+      recordc.add((o,op)) 
+    circles.add(circle)
+  
+  intersectps = {}
+  circles = list(circles)
+  for c1,c2 in utils.comb2(circles):
+    c1s = c1.neighbors(gm.Point, return_set=True)
+    c2s = c2.neighbors(gm.Point, return_set=True)
+    intersectps[(c1,c2)] = intersectps[(c2,c1)] = {x for x in c1s if x in c2s}
+
+  for c1,c2,c3 in utils.comb3(circles):
+    c12 = intersectps[(c1,c2)]
+    c13 = intersectps[(c1,c3)]
+    c23 = intersectps[(c2,c3)]
+    if len(c12) == 2 and len(c13) == 2 and len(c23) == 2:
+      a,b = c12
+      c,d = c13
+      e,f = c23
+      assert a and b and c and d and e and f
+      ab = g._get_line(a,b)
+      cd = g._get_line(c,d)
+      ef = g._get_line(e,f)
+      if ab and cd and ef:
+        pab = ab.neighbors(gm.Point, return_set=True)
+        pcd = cd.neighbors(gm.Point, return_set=True)
+        pef = ef.neighbors(gm.Point, return_set=True)
+        p1 = intersect1(pab,pcd)
+        p2 = intersect1(pab,pef)
+        p3 = intersect1(pcd,pef)
+        # if p1 and p2 and p3:
+        #   continue
+        if p1:
+          yield dict(zip('ABCDEFP',[a,b,c,d,e,f,p1]))
+        if p2:
+          yield dict(zip('ABCDEFP',[a,b,e,f,c,d,p2]))
+        if p3:
+          yield dict(zip('ABCDEFP',[c,d,e,f,a,b,p3]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_menelaus(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match coll A F B, coll B D C, coll C E A, coll D E F => eqratio30 A F F B B D D C C E E A"""
+  #print("menelaus")
+  recordl = set()
+  ta = time.time()
+  all_lines = g.type2nodes[gm.Line]
+  for l1,l2,l3 in utils.comb3(all_lines):
+      l1s = l1.neighbors(gm.Point, return_set=True)
+      l2s = l2.neighbors(gm.Point, return_set=True)
+      l3s = l3.neighbors(gm.Point, return_set=True)
+      # l1: bc, l2: ca, l3: ab
+      a = intersect1(l2s,l3s)
+      b = intersect1(l1s,l3s)
+      c = intersect1(l1s,l2s)
+      if not (a and b and c):
+        continue
+      if a == b or b == c or c == a:
+        continue
+      if (a, b, c) in recordl:
+        continue
+      recordl.add((a, b, c))
+      recordl.add((a, c, b))
+      recordl.add((b, a, c))
+      recordl.add((b, c, a))
+      recordl.add((c, a, b))
+      recordl.add((c, b, a))
+      recordp = set()
+      for d, e, f in utils.cross3(l1s, l2s, l3s):
+        if d in {a, b, c} or e in {a, b, c} or f in {a, b, c}:
+          continue
+        if (d, e, f) in recordp:
+          continue
+        recordp.add((d, e, f))
+        recordp.add((d, f, e))
+        recordp.add((e, d, f))
+        recordp.add((e, f, d))
+        recordp.add((f, d, e))
+        recordp.add((f, e, d))
+        if g.check_coll([d, e, f]):
+          #debugname([a, b, c, d, e, f])
+          yield dict(zip('ABCDEF', [a, b, c, d, e, f]))
+  tb = time.time()
+  print(tb-ta)
+
+
+def match_ceva(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match coll A F B, coll B D C, coll C E A, coll B P E, coll C P F, coll A P D => eqratio30 A F F B B D D C C E E A"""
+  print("ceva")
+  recordl = set()
+  ta = time.time()
+  all_lines = g.type2nodes[gm.Line]
+  for l1,l2,l3 in utils.comb3(all_lines):
+      l1s = l1.neighbors(gm.Point, return_set=True)
+      l2s = l2.neighbors(gm.Point, return_set=True)
+      l3s = l3.neighbors(gm.Point, return_set=True)
+      # l1: bc, l2: ca, l3: ab
+      a = intersect1(l2s,l3s)
+      b = intersect1(l1s,l3s)
+      c = intersect1(l1s,l2s)
+      if not (a and b and c):
+        continue
+      if a == b or b == c or c == a:
+        continue
+      if (a, b, c) in recordl:
+        continue
+      recordl.add((a, b, c))
+      recordl.add((a, c, b))
+      recordl.add((b, a, c))
+      recordl.add((b, c, a))
+      recordl.add((c, a, b))
+      recordl.add((c, b, a))
+      recordp = set()
+      for d, e, f in utils.cross3(l1s, l2s, l3s):
+        if d in {a, b, c} or e in {a, b, c} or f in {a, b, c}:
+          continue
+        if (d, e, f) in recordp:
+          continue
+        recordp.add((d, e, f))
+        recordp.add((d, f, e))
+        recordp.add((e, d, f))
+        recordp.add((e, f, d))
+        recordp.add((f, d, e))
+        recordp.add((f, e, d))
+
+        ad = g._get_line(a, d)
+        be = g._get_line(b, e)
+        if not (ad and be):
+          continue
+        ads = ad.neighbors(gm.Point, return_set=True)
+        bes = be.neighbors(gm.Point, return_set=True)
+        p = intersect1(ads, bes)
+        if p is not None and g.check_coll([p, c, f]):
+          #debugname([p, a, b, c, d, e, f])
+          yield dict(zip('PABCDEF', [p, a, b, c, d, e, f]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_menelaus_rev(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match coll A F B, coll B D C, coll C E A, eqratio30 A F F B B D D C C E E A => coll D E F"""
+  #print("menelaus_rev")
+  recordl = set()
+  ta = time.time()
+  all_lines = g.type2nodes[gm.Line]
+  for l1,l2,l3 in utils.comb3(all_lines):
+      l1s = l1.neighbors(gm.Point, return_set=True)
+      l2s = l2.neighbors(gm.Point, return_set=True)
+      l3s = l3.neighbors(gm.Point, return_set=True)
+      # l1: bc, l2: ca, l3: ab
+      a = intersect1(l2s,l3s)
+      b = intersect1(l1s,l3s)
+      c = intersect1(l1s,l2s)
+      if not (a and b and c):
+        continue
+      if a == b or b == c or c == a:
+        continue
+      if (a, b, c) in recordl:
+        continue
+      recordl.add((a, b, c))
+      recordl.add((a, c, b))
+      recordl.add((b, a, c))
+      recordl.add((b, c, a))
+      recordl.add((c, a, b))
+      recordl.add((c, b, a))
+      recordp = set()
+      for d, e, f in utils.cross3(l1s, l2s, l3s):
+        if d in {a, b, c} or e in {a, b, c} or f in {a, b, c}:
+          continue
+        if (d, e, f) in recordp:
+          continue
+        recordp.add((d, e, f))
+        recordp.add((d, f, e))
+        recordp.add((e, d, f))
+        recordp.add((e, f, d))
+        recordp.add((f, d, e))
+        recordp.add((f, e, d))
+
+        x1 = int(g.check_onseg([d, b, c]))
+        x2 = int(g.check_onseg([e, c, a]))
+        x3 = int(g.check_onseg([f, a, b]))
+        if x1 + x2 + x3 not in {0, 2}:
+          continue
+        if g.check_eqratio30([a, f, f, b, b, d, d, c, c, e, e, a]):
+          yield dict(zip('ABCDEF', [a, b, c, d, e, f]))
+  tb = time.time()
+  print(tb-ta)
+  
+def match_ceva_rev(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match coll A F B, coll B D C, coll C E A, coll B P E, coll C P F, eqratio30 A F F B B D D C C E E A => coll A P D"""
+  #print("ceva_rev")
+  recordl = set()
+  ta = time.time()
+  all_lines = g.type2nodes[gm.Line]
+  for l1,l2,l3 in utils.comb3(all_lines):
+      l1s = l1.neighbors(gm.Point, return_set=True)
+      l2s = l2.neighbors(gm.Point, return_set=True)
+      l3s = l3.neighbors(gm.Point, return_set=True)
+      # l1: bc, l2: ca, l3: ab
+      a = intersect1(l2s,l3s)
+      b = intersect1(l1s,l3s)
+      c = intersect1(l1s,l2s)
+      if not (a and b and c):
+        continue
+      if a == b or b == c or c == a:
+        continue
+      if (a, b, c) in recordl:
+        continue
+      recordl.add((a, b, c))
+      recordl.add((a, c, b))
+      recordl.add((b, a, c))
+      recordl.add((b, c, a))
+      recordl.add((c, a, b))
+      recordl.add((c, b, a))
+      recordp = set()
+      for d, e, f in utils.cross3(l1s, l2s, l3s):
+        if d in {a, b, c} or e in {a, b, c} or f in {a, b, c}:
+          continue
+        if (d, e, f) in recordp:
+          continue
+        recordp.add((d, e, f))
+        recordp.add((d, f, e))
+        recordp.add((e, d, f))
+        recordp.add((e, f, d))
+        recordp.add((f, d, e))
+        recordp.add((f, e, d))
+
+        x1 = int(g.check_onseg([d, b, c]))
+        x2 = int(g.check_onseg([e, c, a]))
+        x3 = int(g.check_onseg([f, a, b]))
+        if x1 + x2 + x3 not in {1, 3}:
+          continue
+        #print(x1+x2+x3)
+        if g.check_eqratio30([a, f, f, b, b, d, d, c, c, e, e, a]):
+          ad = g._get_line(a, d)
+          be = g._get_line(b, e)
+          cf = g._get_line(c, f)
+          if ad and be:
+            ads = ad.neighbors(gm.Point, return_set=True)
+            bes = be.neighbors(gm.Point, return_set=True)
+            pab = intersect1(ads, bes)
+            if pab:
+              #debugname([pab, c, a, b, f, d, e],(x3,x1,x2))
+              yield dict(zip('PABCDEF', [pab, c, a, b, f, d, e]))
+          if be and cf:
+            bes = be.neighbors(gm.Point, return_set=True)
+            cfs = cf.neighbors(gm.Point, return_set=True)
+            pbc = intersect1(bes, cfs)
+            if pbc:
+              #debugname([pbc, a, b, c, d, e, f],(x1,x2,x3))
+              yield dict(zip('PABCDEF', [pbc, a, b, c, d, e, f]))
+          if cf and ad:
+            cfs = cf.neighbors(gm.Point, return_set=True)
+            ads = ad.neighbors(gm.Point, return_set=True)
+            pca = intersect1(cfs, ads)
+            if pca:
+              #debugname([pca, b, c, a, e, f, d],(x2,x3,x1))
+              yield dict(zip('PABCDEF', [pca, b, c, a, e, f, d]))
+  tb = time.time()
+  print(tb-ta)
+
+def match_eqratio6_coll_coll_eqratio(
+    g: gh.Graph,
+    g_matcher: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem,
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match eqratio6 B A B C Q P Q R, coll A B C, coll P Q R => eqratio B A A C Q P P R"""
+  """Avoid harmonic"""
+  enums = g_matcher('eqratio6')
+
+  record = set()
+  for b, a, b, c, q, p, q, r in enums:  # pylint: disable=redeclared-assigned-name,unused-variable
+    if (a, b, c) == (p, q, r):
+      continue
+    if any([x in record for x in rotate_simtri(a, b, c, p, q, r)]):
+      continue
+    if not (g.check_coll([a, b, c]) and g.check_coll([p, q, r])):
+      continue
+    if not (g.check_onseg([b, a, c]) == g.check_onseg([q, p, r])): # Avoid harmonic
+      continue
+
+    record.add((a, b, c, p, q, r))
+    #debugname([a, b, c, p, q, r])
+    yield dict(zip('ABCPQR', [a, b, c, p, q, r]))
+    yield dict(zip('ABCPQR', [c, b, a, r, q, p]))
 
 def rotate_simtri(
     a: gm.Point, b: gm.Point, c: gm.Point, x: gm.Point, y: gm.Point, z: gm.Point
 ) -> Generator[tuple[gm.Point, ...], None, None]:
   """Rotate points around for similar triangle predicates."""
-  yield (z, y, x, c, b, a)
+  #yield (z, y, x, c, b, a)
   for p in [
+      (a, b, c, x, y, z),
       (b, c, a, y, z, x),
       (c, a, b, z, x, y),
       (x, y, z, a, b, c),
@@ -731,14 +1427,14 @@ def match_eqratio6_coll_ncoll_eqangle6(
     theorem: pr.Theorem,
 ) -> Generator[dict[str, gm.Point], None, None]:
   """Match eqratio6 d b d c a b a c, coll d b c, ncoll a b c => eqangle6 a b a d a d a c."""
-  records = set()
+  record = set()
   for b, d, c in g_matcher('coll'):
     for a in g.all_points():
       if g.check_coll([a, b, c]):
         continue
-      if (a, b, d, c) in records or (a, c, d, b) in records:
+      if (a, b, d, c) in record or (a, c, d, b) in record:
         continue
-      records.add((a, b, d, c))
+      record.add((a, b, d, c))
 
       if g.check_eqratio([d, b, d, c, a, b, a, c]):
         yield dict(zip('abcd', [a, b, c, d]))
@@ -750,14 +1446,14 @@ def match_eqangle6_coll_ncoll_eqratio6(
     theorem: pr.Theorem,
 ) -> Generator[dict[str, gm.Point], None, None]:
   """Match eqangle6 a b a d a d a c, coll d b c, ncoll a b c => eqratio6 d b d c a b a c."""
-  records = set()
+  record = set()
   for b, d, c in g_matcher('coll'):
     for a in g.all_points():
       if g.check_coll([a, b, c]):
         continue
-      if (a, b, d, c) in records or (a, c, d, b) in records:
+      if (a, b, d, c) in record or (a, c, d, b) in record:
         continue
-      records.add((a, b, d, c))
+      record.add((a, b, d, c))
 
       if g.check_eqangle([a, b, a, d, a, d, a, c]):
         yield dict(zip('abcd', [a, b, c, d]))
@@ -775,7 +1471,6 @@ def match_eqangle6_ncoll_cyclic(
     if nm.check_ncoll([x.num for x in [a, b, c, x]]):
       yield dict(zip('ABPQ', [b, c, a, x]))
 
-
 def match_all(
     name: str, g: gh.Graph
 ) -> Generator[tuple[gm.Point, ...], None, None]:
@@ -804,6 +1499,10 @@ def match_all(
     return g.all_midps()
   if name == 'circle':
     return g.all_circles()
+  if name == 'cyclic6':
+    return g.all_cyclics6()
+  if name == 'cyclic5':
+    return g.all_cyclics5()
   raise ValueError(f'Unrecognize {name}')
 
 
@@ -858,6 +1557,8 @@ def match_generic(
     theorem: pr.Theorem
 ) -> Generator[dict[str, gm.Point], None, None]:
   """Match any generic rule that is not one of the above match_*() rules."""
+  debugname(theorem)
+  ta = time.time()
   clause2enum = {}
 
   clauses = []
@@ -899,6 +1600,76 @@ def match_generic(
 
     yield mapping
 
+  tb = time.time()
+  print(tb-ta)
+
+
+def match_generic_debug(
+    g: gh.Graph,
+    cache: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem
+) -> Generator[dict[str, gm.Point], None, None]:
+  """Match any generic rule that is not one of the above match_*() rules."""
+  
+  tchiaya = time.time()
+  clause2enum = {}
+  clauses = []
+  numerical_checks = []
+  for clause in theorem.premise:
+    if clause.name in ['ncoll', 'npara', 'nperp', 'sameside']:
+      numerical_checks.append(clause)
+      continue
+
+    enum = cache(clause.name)
+    if len(enum) == 0:  # pylint: disable=g-explicit-length-test
+      return 0
+
+    clause2enum[clause] = enum
+    clauses.append((len(set(clause.args)), clause))
+
+  clauses = sorted(clauses, key=lambda x: x[0], reverse=True)
+  _, clauses = zip(*clauses)
+
+  for mapping in try_to_map([(c, clause2enum[c]) for c in clauses], {}):
+    if not mapping:
+      continue
+
+    checks_ok = True
+    for check in numerical_checks:
+      args = [mapping[a] for a in check.args]
+      if check.name == 'ncoll':
+        checks_ok = g.check_ncoll(args)
+      elif check.name == 'npara':
+        checks_ok = g.check_npara(args)
+      elif check.name == 'nperp':
+        checks_ok = g.check_nperp(args)
+      elif check.name == 'sameside':
+        checks_ok = g.check_sameside(args)
+      if not checks_ok:
+        break
+    if not checks_ok:
+      continue
+
+    yield mapping
+  tkirine = time.time()
+  #print(theorem.name,tkirine-tchiaya)
+
+def match_test(
+    g: gh.Graph,
+    cache: Callable[str, list[tuple[gm.Point, ...]]],
+    theorem: pr.Theorem
+) -> Generator[dict[str, gm.Point], None, None]:
+  """test"""
+  debugname(theorem)
+  tchiaya = time.time()
+  
+  for o,x,y,z in g.all_circles():
+    circle = g.get_circle_thru_triplet(x,y,z)
+    sox = g._get_segment(o,x).val
+    #print(vars(sox))
+  
+  tkirine = time.time()
+  #print(tkirine-tchiaya,theorem.name)
 
 BUILT_IN_FNS = {
     'cong_cong_cong_cyclic': match_cong_cong_cong_cyclic,
@@ -933,6 +1704,22 @@ def match_generic(
     'eqratio6_coll_ncoll_eqangle6': match_eqratio6_coll_ncoll_eqangle6,
     'eqangle6_coll_ncoll_eqratio6': match_eqangle6_coll_ncoll_eqratio6,
     'eqangle6_ncoll_cyclic': match_eqangle6_ncoll_cyclic,
+    'cyclic_coll_coll_eqratio': match_cyclic2power,
+    'circle_perp_coll_eqratio': match_cyclic2power_tan,
+    'coll_coll_ncoll_eqratio_cyclic': match_power2cyclic,
+    'cyclic_cyclic_cyclic_coll_coll_coll': match_radical_axis,
+    'cyclic_coll_coll_coll_coll_coll_coll_coll': match_pascal6,
+    'circle_cong_cong_perp_coll_coll_coll_coll_coll_coll' : match_pascal5,
+    'circle_cong_perp_coll_coll_coll_perp_coll_coll' : match_pascal41,
+    'circle_cong_perp_perp_coll_coll_coll_coll_coll' : match_pascal42,
+    #'circle_cong_cong_coll_coll_coll_coll_coll_coll_coll_cong' : match_pascal6_rev,
+    'coll_coll_coll_coll_eqratio30': match_menelaus,
+    'coll_coll_coll_coll_coll_coll_eqratio30': match_ceva,
+    'coll_coll_coll_eqratio30_coll': match_menelaus_rev,
+    'coll_coll_coll_coll_coll_eqratio30_coll': match_ceva_rev,
+    'eqratio6_coll_coll_eqratio': match_eqratio6_coll_coll_eqratio,
+    #'circle_perp_coll_eqratio': match_generic_debug,
+    #'cyclic_cyclic_cong': match_test,
 }
 
 
@@ -1090,7 +1877,6 @@ def bfs_one_level(
       hash_conclusion = pr.hashed(name, args)
       if hash_conclusion in g.cache:
         continue
-
       add = g.add_piece(name, args, deps=deps)
       added += add
 
@@ -1154,3 +1940,9 @@ def apply_derivations(
     for arg in args:
       applied += g.do_algebra(name, arg)
   return applied
+
+def debugname(ps,n=0):
+  if type(ps) is list:
+    print(n,[p.name for p in ps])
+  else:
+    print(n,ps.name)
diff --git a/dd_test.py b/dd_test.py
index 6cb2c40..22a98b1 100644
--- a/dd_test.py
+++ b/dd_test.py
@@ -44,6 +44,9 @@ def test_imo_2022_p4_should_succeed(self):
     g, _ = gh.Graph.build_problem(p, DDTest.defs)
     goal_args = g.names2nodes(p.goal.args)
 
+    for _,rule in DDTest.rules.items():
+      print(rule.name)
+
     success = False
     for level in range(MAX_LEVEL):
       added, _, _, _ = dd.bfs_one_level(g, DDTest.rules, level, p)
diff --git a/ddar.py b/ddar.py
index 8f910cb..7a6813e 100644
--- a/ddar.py
+++ b/ddar.py
@@ -42,10 +42,9 @@ def saturate_or_goal(
   eq4s = []
   branching = []
   all_added = []
-
   while len(level_times) < max_level:
     level = len(level_times) + 1
-
+    print(f"hello from {level}")
     t = time.time()
     added, derv, eq4, n_branching = dd.bfs_one_level(
         g, theorems, level, p, verbose=False, nm_check=True, timeout=timeout
@@ -55,6 +54,7 @@ def saturate_or_goal(
 
     derives.append(derv)
     eq4s.append(eq4)
+
     level_time = time.time() - t
 
     logging.info(f'Depth {level}/{max_level} time = {level_time}')  # pylint: disable=logging-fstring-interpolation
@@ -62,15 +62,21 @@ def saturate_or_goal(
 
     if p.goal is not None:
       goal_args = list(map(lambda x: g.get(x, lambda: int(x)), p.goal.args))
-      if g.check(p.goal.name, goal_args):  # found goal
+      #print(p.goal.name, [ag.name for ag in goal_args])
+      qicong = g.check(p.goal.name, goal_args)
+      if qicong:  # found goal
+        print("yattaze")
         break
+      else:
+        print("yamero")
+        pass
 
     if not added:  # saturated
+      print("satori")
       break
 
     if level_time > timeout:
       break
-
   return derives, eq4s, branching, all_added
 
 
@@ -93,10 +99,10 @@ def solve(
 
   while len(level_times) < max_level:
     dervs, eq4, next_branches, added = saturate_or_goal(
-        g, theorems, level_times, controller, max_level, timeout=timeout
+        g, theorems, level_times, controller, max_level/10, timeout=timeout
     )
     all_added += added
-
+    print(len(level_times),level_times)
     derives += dervs
     eq4s += eq4
     branches += next_branches
@@ -104,9 +110,15 @@ def solve(
     # Now, it is either goal or saturated
     if controller.goal is not None:
       goal_args = g.names2points(controller.goal.args)
-      if g.check(controller.goal.name, goal_args):  # found goal
+      #print(controller.goal.name, [ag.name for ag in goal_args])
+      ifcong = g.check(controller.goal.name, goal_args)
+      if ifcong:  # found goal
         status = 'solved'
+        print("solved")
         break
+      else:
+        pass
+        #print("failed")
 
     if not derives:  # officially saturated.
       break
@@ -154,4 +166,4 @@ def get_proof_steps(
   setup = [(prems, [tuple(p)]) for p, prems in setup]
   aux = [(prems, [tuple(p)]) for p, prems in aux]
 
-  return setup, aux, log, refs
+  return setup, aux, log, refs
\ No newline at end of file
diff --git a/draw.py b/draw.py
new file mode 100644
index 0000000..0fa8087
--- /dev/null
+++ b/draw.py
@@ -0,0 +1,16 @@
+import unittest
+from absl.testing import absltest
+import dd
+import graph as gh
+import problem as pr
+
+txt = 'f g h i j = pentagon f g h i j; a = intersection_ll a f j g h; b = intersection_ll b f g h i; c = intersection_ll c g h i j; d = intersection_ll d h i f j; e = intersection_ll e f g i j; o1 = circle o1 a f g; o2 = circle o2 b g h; o3 = circle o3 c h i; o4 = circle o4 d j i; o5 = circle o5 e j f; k = intersection_cc k o5 o1 f; l = intersection_cc l o1 o2 g; m = intersection_cc m o2 o3 h; n = intersection_cc n o3 o4 i; o = intersection_cc o o4 o5 j; ox = circle k l m ? cyclic k l m n'
+defs = pr.Definition.from_txt_file('defs.txt', to_dict=True)
+p = pr.Problem.from_txt(txt,translate=False)
+g, _ = gh.Graph.build_problem(p, defs)
+goal_args = g.names2nodes(p.goal.args)
+gh.nm.draw(
+      g.type2nodes[gh.Point],
+      g.type2nodes[gh.Line],
+      g.type2nodes[gh.Circle],
+      g.type2nodes[gh.Segment])
\ No newline at end of file
diff --git a/geometry.py b/geometry.py
index ba9463f..62bdc74 100644
--- a/geometry.py
+++ b/geometry.py
@@ -17,6 +17,7 @@
 from __future__ import annotations
 from collections import defaultdict  # pylint: disable=g-importing-member
 from typing import Any, Type
+from multiset import Multiset
 
 # pylint: disable=protected-access
 
@@ -122,7 +123,6 @@ def merge(self, nodes: list[Node], deps: list[Any]) -> None:
 
   def merge_one(self, node: Node, deps: list[Any]) -> None:
     node.rep().set_rep(self.rep())
-
     if node in self.merge_graph:
       return
 
@@ -131,14 +131,18 @@ def merge_one(self, node: Node, deps: list[Any]) -> None:
 
   def is_val(self, node: Node) -> bool:
     return (
-        isinstance(self, Line)
-        and isinstance(node, Direction)
-        or isinstance(self, Segment)
-        and isinstance(node, Length)
-        or isinstance(self, Angle)
-        and isinstance(node, Measure)
-        or isinstance(self, Ratio)
-        and isinstance(node, Value)
+        (isinstance(self, Line)
+        and isinstance(node, Direction))
+        or (isinstance(self, Segment)
+        and isinstance(node, Length))
+        or (isinstance(self, Angle)
+        and isinstance(node, Measure))
+        or (isinstance(self, Ratio)
+        and isinstance(node, Value))
+        or (isinstance(self, Ratio_Pro)
+        and isinstance(node, Value))
+        or (isinstance(self, Length_Pro)
+        and isinstance(node, Value))
     )
 
   def set_val(self, node: Node) -> None:
@@ -169,7 +173,7 @@ def connect_to(self, node: Node, deps: list[Any] = None) -> None:
       rep.edge_graph[node].update({self: deps})
     else:
       rep.edge_graph[node] = {self: deps}
-
+  
     if self.is_val(node):
       self.set_val(node)
       node.set_obj(self)
@@ -521,6 +525,45 @@ def lengths(self) -> tuple[Length, Length]:
     if l1 is None or l2 is None:
       return l1, l2
     return l1.rep(), l2.rep()
+  
+
+class Length_Pro(Node):
+  """Node of type Length Product."""
+  def new_val(self) -> Value:
+    return Value()
+
+  def set_lengths(self, l1: Length, l2: Length) -> None:
+    if l1.name > l2.name:
+      l1, l2 = l2, l1
+    self._l = Multiset([l1, l2])
+
+  @property
+  def lengths(self) -> tuple[Length, Length]:
+    l1, l2 = self._l
+    if l1 is None or l2 is None:
+      return l1, l2
+    l1r = l1.rep()
+    l2r = l2.rep()
+    if l1r.name > l2r.name:
+      l1r, l2r = l2r, l1r
+    return Multiset([l1r, l2r])
+
+class Ratio_Pro(Node):
+  """Node of type Ratio Product. l1/l2 * l3/l4 = (l1*l3) / (l2*l4)"""
+
+  def new_val(self) -> Value:
+    return Value()
+
+  def set_lengths(self, lp13: Length_Pro, lp24: Length_Pro) -> None:
+    self._lp = lp13, lp24
+   
+
+  @property
+  def muls(self) -> tuple[Length_Pro, Length_Pro]:
+    lp13, lp24 = self._lp
+    if lp13 is None or lp24 is None:
+      return lp13, lp24
+    return lp13.rep(), lp24.rep()
 
 
 class Value(Node):
@@ -541,16 +584,40 @@ def all_angles(
 
 
 def all_ratios(
-    d1, d2, level=None
-) -> tuple[Angle, list[Direction], list[Direction]]:
+    l1, l2, level=None
+) -> tuple[Ratio, list[Length], list[Length]]:
   level = level or float('inf')
-  d1s = d1.equivs_upto(level)
-  d2s = d2.equivs_upto(level)
+  l1s = l1.equivs_upto(level)
+  l2s = l2.equivs_upto(level)
+
+  for rat in l1.rep().neighbors(Ratio):
+    l1_, l2_ = rat._l
+    if l1_ in l1s and l2_ in l2s:
+      yield rat, l1s, l2s
+      
+def all_ratios2(
+    lp1: Length_Pro, lp2: Length_Pro, level=None
+) -> tuple[Ratio_Pro, list[Length_Pro], list[Length_Pro]]:
+  level = level or float('inf')
+  lp1s = lp1.equivs_upto(level)
+  lp2s = lp2.equivs_upto(level)
+  # lp1sname = [lp.name for lp in lp1s]
+  # lp2sname = [lp.name for lp in lp2s]
+  
+  # print("\nlp1s:",lp1sname,lp1s)
+  # print("lp2s:",lp2sname,lp2s)
+  for ratp in lp1.neighbors(Ratio_Pro,do_rep = False):
+    # print("rprp:", ratp.name)
+    lp1_, lp2_ = ratp._lp
+    # lp1_name = lp1_.name
+    # lp2_name = lp2_.name
+    # print("\nrpv:",ratp.name)
+    # print("lp1name:", lp1_name,lp1_)
+    # print("lp2name:", lp2_name,lp2_)
+    
+    if lp1_ in lp1s and lp2_ in lp2s:
+      yield ratp, lp1s, lp2s
 
-  for ang in d1.rep().neighbors(Ratio):
-    d1_, d2_ = ang._l
-    if d1_ in d1s and d2_ in d2s:
-      yield ang, d1s, d2s
 
 
 RANKING = {
@@ -576,3 +643,7 @@ def val_type(x: Node) -> Type[Node]:
     return Measure
   if isinstance(x, Ratio):
     return Value
+  if isinstance(x, Length_Pro):
+    return Value
+  if isinstance(x, Ratio_Pro):
+    return Value
diff --git a/graph.py b/graph.py
index ddadb4a..e068c6c 100644
--- a/graph.py
+++ b/graph.py
@@ -24,14 +24,14 @@
 from absl import logging
 import ar
 import geometry as gm
-from geometry import Angle, Direction, Length, Ratio
+from geometry import Angle, Direction, Length, Ratio, Length_Pro, Ratio_Pro
 from geometry import Circle, Line, Point, Segment
 from geometry import Measure, Value
 import graph_utils as utils
 import numericals as nm
 import problem
 from problem import Dependency, EmptyDependency
-
+from multiset import Multiset
 
 np = nm.np
 
@@ -105,6 +105,8 @@ def __init__(self):
         Ratio: [],
         Measure: [],
         Value: [],
+        Length_Pro: [],
+        Ratio_Pro: [],
     }
     self._name2point = {}
     self._name2node = {}
@@ -186,6 +188,7 @@ def add_algebra(self, dep: Dependency, level: int) -> None:
         'aconst',
         'rconst',
         'cong',
+        'eqratio30'
     ]:
       return
 
@@ -212,7 +215,40 @@ def add_algebra(self, dep: Dependency, level: int) -> None:
         self.rtable.add_eq(ab, cd, dep)
       else:
         self.rtable.add_eqratio(ab, cd, mn, pq, dep)
-
+        _abpq_, _ = self._get_or_create_length_pro_l(ab, pq)
+        _cdmn_, _ = self._get_or_create_length_pro_l(cd, mn)
+        self.rtable.add_length_pro(_abpq_, ab, pq)
+        self.rtable.add_length_pro(_cdmn_, cd, mn)
+        self.rtable.add_eq(_abpq_, _cdmn_, dep)
+        
+    
+    if name == 'eqratio30': #TODO
+      ab, cd, mn, pq, xy, zw = dep.algebra
+      _abmn_, _ = self._get_or_create_length_pro_l(ab, mn)
+      _abxy_, _ = self._get_or_create_length_pro_l(ab, xy)
+      _mnxy_, _ = self._get_or_create_length_pro_l(mn, xy)
+      _cdpq_, _ = self._get_or_create_length_pro_l(cd, pq)
+      _cdzw_, _ = self._get_or_create_length_pro_l(cd, zw)
+      _pqzw_, _ = self._get_or_create_length_pro_l(pq, zw)
+      
+      
+      self.rtable.add_length_pro(_abmn_, ab, mn)
+      self.rtable.add_length_pro(_abxy_, ab, xy)
+      self.rtable.add_length_pro(_mnxy_, mn, xy)
+      self.rtable.add_length_pro(_cdpq_, cd, pq)
+      self.rtable.add_length_pro(_cdzw_, cd, zw)
+      self.rtable.add_length_pro(_pqzw_, pq, zw)
+
+      self.rtable.add_eqratio(ab, cd, _pqzw_, _mnxy_ , dep)
+      self.rtable.add_eqratio(ab, pq, _cdzw_, _mnxy_ , dep)
+      self.rtable.add_eqratio(ab, zw, _cdpq_, _mnxy_ , dep)
+      self.rtable.add_eqratio(mn, cd, _pqzw_, _abxy_ , dep)
+      self.rtable.add_eqratio(mn, pq, _cdzw_, _abxy_ , dep)
+      self.rtable.add_eqratio(mn, zw, _cdpq_, _abxy_ , dep)
+      self.rtable.add_eqratio(xy, cd, _pqzw_, _abmn_ , dep)
+      self.rtable.add_eqratio(xy, pq, _cdzw_, _abmn_ , dep)
+      self.rtable.add_eqratio(xy, zw, _cdpq_, _abmn_ , dep)
+      
     if name == 'aconst':
       bx, ab, y = dep.algebra
       self.atable.add_const_angle(bx, ab, y, dep)
@@ -364,6 +400,16 @@ def do_algebra(self, name: str, args: list[Point]) -> list[Dependency]:
       if not (a != b and c != d and (a != c or b != d)):
         return []
       return self.add_cong([a, b, c, d], dep)
+    
+    if name == 'eqratio30': # TODO
+      a, b, c, d, e, f, dep = args
+      a1, a2 = a._obj.points
+      b1, b2 = b._obj.points
+      c1, c2 = c._obj.points
+      d1, d2 = d._obj.points
+      e1, e2 = e._obj.points
+      f1, f2 = f._obj.points
+      return self.add_eqratio30([a1, a2, b1, b2, c1, c2, d1, d2, e1, e2, f1, f2], dep)
 
     return []
 
@@ -385,31 +431,127 @@ def derive_algebra(
     # Separate eqangle and eqratio derivations
     # As they are too numerous => slow down DD+AR.
     # & reserve them only for last effort.
-    eqs = {'eqangle': derives.pop('eqangle'), 'eqratio': derives.pop('eqratio')}
+    eqs = {'eqangle': derives.pop('eqangle'), 'eqratio': derives.pop('eqratio'), 'eqratio30': derives.pop('eqratio30')}
     return derives, eqs
 
   def derive_ratio_algebra(
       self, level: int, verbose: bool = False
   ) -> dict[str, list[tuple[Point, ...]]]:
     """Derive new eqratio predicates."""
-    added = {'cong2': [], 'eqratio': []}
-
+    added = {'cong2': [], 'eqratio': [], 'eqratio30': []}
+    new_products = set()
     for x in self.rtable.get_all_eqs_and_why():
       x, why = x[:-1], x[-1]
       dep = EmptyDependency(level=level, rule_name='a01')
       dep.why = why
+      A = []
+      B = []
 
       if len(x) == 2:
         a, b = x
-        if gm.is_equiv(a, b):
-          continue
-
-        (m, n), (p, q) = a._obj.points, b._obj.points
-        added['cong2'].append((m, n, p, q, dep))
+        if type(a) is gm.Length and type(b) is gm.Length:
+          A = [a]
+          B = [b]
+        else:
+          assert type(a) is gm.Length_Pro and type(b) is gm.Length_Pro
+          a1, a2 = a._l
+          b1, b2 = b._l
+          A = [a1, a2]
+          B = [b1, b2]
 
       if len(x) == 4:
         a, b, c, d = x
+        if type(a) is gm.Length and type(d) is gm.Length:
+          assert type(b) is gm.Length, f"b.type:{type(b)}"
+          assert type(c) is gm.Length, f"c.type:{type(c)}"
+          A = [a,d]
+          B = [b,c]
+        if {type(a),type(d)} == {gm.Length, gm.Length_Pro}:
+          assert {type(b), type(c)} == {gm.Length, gm.Length_Pro}, f"b.type:{type(b)}, c.type:{type(c)}"
+          if type(a) is gm.Length: # type(d) is gm.Length_Pro
+            a, d = d, a
+          if type(b) is gm.Length: # type(c) is gm.Length_Pro
+            b, c = c, b
+          a1, a2 = a._l
+          b1, b2 = b._l
+          A = [a1, a2, d]
+          B = [b1, b2, c]
+
+        if type(a) is gm.Length_Pro and type(d) is gm.Length_Pro:
+          assert type(b) is gm.Length_Pro, f"b.type:{type(b)}"
+          assert type(c) is gm.Length_Pro, f"c.type:{type(c)}"
+          a1, a2 = a._l
+          b1, b2 = b._l
+          c1, c2 = c._l
+          d1, d2 = d._l
+          A = [a1, a2, d1, d2]
+          B = [b1, b2, c1, c2]
+
+      #print('before',[ag.name for ag in A],[ag.name for ag in B])
+      A_ = []
+      for x in A:
+        for y in B:
+          if gm.is_equiv(x, y):
+            B.remove(y)
+            A_.append(x)
+            break
+      for x in A_:
+        A.remove(x)
+
+      #print('after',[ag.name for ag in A],[ag.name for ag in B])
+      if len(A) == 0:
+        continue
+      elif len(A) == 1:
+        a = A[0]
+        b = B[0]
+        m, n = a._obj.points
+        p, q = b._obj.points
+        added['cong2'].append((m, n, p, q, dep))
+      elif len(A) == 2:
+        a, d = A
+        b, c = B
         added['eqratio'].append((a, b, c, d, dep))
+      elif len(A) == 3:
+        a1, a2, d = A
+        b1, b2, c = B
+        _a1a2_, _ = self._get_or_create_length_pro_l(a1, a2)
+        _a1d_, _ = self._get_or_create_length_pro_l(a1, d)
+        _a2d_, _ = self._get_or_create_length_pro_l(a2, d)
+        _b1b2_, _ = self._get_or_create_length_pro_l(b1, b2)
+        _b1c_, _ = self._get_or_create_length_pro_l(b1, c)
+        _b2c_, _ = self._get_or_create_length_pro_l(b2, c)
+        new_products.update([_a1a2_,_a1d_,_a2d_,_b1b2_,_b1c_,_b2c_])
+        added['eqratio30'].append((a1, b1, a2, b2, d, c, dep))
+      else : #len(A) == 4
+        a1, a2, d1, d2 = A
+        b1, b2, c1, c2 = B
+        _a1a2_, _ = self._get_or_create_length_pro_l(a1, a2)
+        _a1d1_, _ = self._get_or_create_length_pro_l(a1, d1)
+        _a1d2_, _ = self._get_or_create_length_pro_l(a1, d2)
+        _a2d1_, _ = self._get_or_create_length_pro_l(a2, d1)
+        _a2d2_, _ = self._get_or_create_length_pro_l(a2, d2)
+        _d1d2_, _ = self._get_or_create_length_pro_l(d1, d2)
+        _b1b2_, _ = self._get_or_create_length_pro_l(b1, b2)
+        _b1c1_, _ = self._get_or_create_length_pro_l(b1, c1)
+        _b1c2_, _ = self._get_or_create_length_pro_l(b1, c2)
+        _b2c1_, _ = self._get_or_create_length_pro_l(b2, c1)
+        _b2c2_, _ = self._get_or_create_length_pro_l(b2, c2)
+        _c1c2_, _ = self._get_or_create_length_pro_l(c1, c2)
+        new_products.update([_a1a2_,_a1d1_,_a1d2_,_a2d1_,_a2d2_,_d1d2_,_b1b2_,_b1c1_,_b1c2_,_b2c1_,_b2c2_,_d1d2_])
+      
+        self._set_ratio_pro_equal(_a1a2_, _b1b2_, _c1c2_, _d1d2_, dep)
+        self._set_ratio_pro_equal(_a1a2_, _b1c1_, _b2c2_, _d1d2_, dep)
+        self._set_ratio_pro_equal(_a1a2_, _b1c2_, _b2c1_, _d1d2_, dep)
+        self._set_ratio_pro_equal(_a1d1_, _b1b2_, _c1c2_, _a2d2_, dep)
+        self._set_ratio_pro_equal(_a1d1_, _b1c1_, _b2c2_, _a2d2_, dep)
+        self._set_ratio_pro_equal(_a1d1_, _b1c2_, _b2c1_, _a2d2_, dep)
+        self._set_ratio_pro_equal(_a1d2_, _b1b2_, _c1c2_, _a2d1_, dep)
+        self._set_ratio_pro_equal(_a1d2_, _b1c1_, _b2c2_, _a2d1_, dep)
+        self._set_ratio_pro_equal(_a1d2_, _b1c2_, _b2c1_, _a2d1_, dep)
+
+    for lp in new_products:
+      l1, l2 = lp._l
+      self.rtable.add_length_pro(lp, l1, l2)
 
     return added
 
@@ -510,10 +652,13 @@ def build_problem(
         g.plevel = plevel
 
       except (nm.InvalidLineIntersectError, nm.InvalidQuadSolveError):
+        print("InvalidError")
         continue
       except DepCheckFailError:
+        print("CheckFailError")
         continue
       except (PointTooCloseError, PointTooFarError):
+        print("PointError")
         continue
 
       if not pr.goal:
@@ -521,6 +666,10 @@ def build_problem(
 
       args = list(map(lambda x: g.get(x, lambda: int(x)), pr.goal.args))
       check = nm.check(pr.goal.name, args)
+      print(check)
+      #check = True
+      #if not check:
+        #return
 
     g.url = pr.url
     g.build_def = (pr, definitions)
@@ -670,6 +819,10 @@ def connect_val(self, node: gm.Node, deps: Dependency) -> gm.Node:
       name = 'l(' + node.name + ')'
     if isinstance(node, Ratio):
       name = 'r(' + node.name + ')'
+    if isinstance(node, Ratio_Pro):
+      name = 'rp(' + node.name + ')'
+    if isinstance(node, Length_Pro):
+      name = 'lp(' + node.name + ')'
     v = self.new_node(gm.val_type(node), name)
     self.connect(node, v, deps=deps)
     return v
@@ -699,6 +852,8 @@ def add_piece(
       return self.add_eqangle(args, deps)
     elif name in ['eqratio', 'eqratio6']:
       return self.add_eqratio(args, deps)
+    elif name == 'eqratio30':
+      return self.add_eqratio30(args, deps)
     # numerical!
     elif name == 's_angle':
       return self.add_s_angle(args, deps)
@@ -807,6 +962,8 @@ def check(self, name: str, args: list[Point]) -> bool:
       if len(args) == 5:
         return self.check_rconst(args)
       return self.check_eqratio(args)
+    if name in ['eqratio30']:
+      return self.check_eqratio30(args)
     if name in ['simtri', 'simtri2', 'simtri*']:
       return self.check_simtri(args)
     if name in ['contri', 'contri2', 'contri*']:
@@ -1002,15 +1159,25 @@ def check_ncoll(self, points: list[Point]) -> bool:
   def check_sameside(self, points: list[Point]) -> bool:
     return nm.check_sameside([p.num for p in points])
 
+  def check_onseg(self, points: list[Point]) -> bool:
+    return nm.check_onseg([p.num for p in points])
+
+  def check_offseg(self, points: list[Point]) -> bool:
+    return nm.check_offseg([p.num for p in points])
+
   def make_equal(self, x: gm.Node, y: gm.Node, deps: Dependency) -> None:
     """Make that two nodes x and y are equal, i.e. merge their value node."""
+    if {type(x),type(y)} == {Ratio,Ratio_Pro}:
+      pass
+      #print(x.name, y.name)
+
     if x.val is None:
       x, y = y, x
-
     self.connect_val(x, deps=None)
     self.connect_val(y, deps=None)
     vx = x._val
     vy = y._val
+    
 
     if vx == vy:
       return
@@ -1028,6 +1195,55 @@ def make_equal(self, x: gm.Node, y: gm.Node, deps: Dependency) -> None:
 
     self.merge(merges, deps)
 
+    if type(x) is Ratio and type(y) is Ratio:
+      return
+      assert x != y.opposite, f'{x.name},{y.name}'
+      x1, x2 = x._l
+      y1, y2 = y._l
+      for z in x.neighbors(Ratio_Pro, do_rep=False):
+        lp13, lp24 = z._lp
+        l1, l3 = lp13.lengths
+        l2, l4 = lp24.lengths
+        if self.is_equal(l3, x1):
+          l1, l3 = l3, l1
+        if self.is_equal(l4, x2):
+          l2, l4 = l4, l2
+        assert self.is_equal(l1, x1) and self.is_equal(l2, x2), f'{l1.name},{l2.name},{l3.name},{l4.name},{x1.name},{x2.name}'
+        # (x1 * l3) / (x2 * l4) -> (y1 * l3) / (y2 * l4)
+        if self.is_equal(l3, y2) and self.is_equal(l4, y1):
+          continue
+        #print(f'{l1.name},{l2.name},{l3.name},{l4.name},{z.name},{x.name},{y.name}')
+        if self.is_equal(l3, y2): #simplify
+          r, _, _ = self._get_or_create_ratio_l(y1, l4)
+          self.make_equal(z, r, deps)
+        elif self.is_equal(l4, y1): #simplify
+          r, _, _ = self._get_or_create_ratio_l(l3, y2)
+          self.make_equal(z, r, deps)
+        else:
+          rp, _, _ = self._get_or_create_ratio_pro_l(y1, y2, l3, l4)
+          self.make_equal(z, rp, deps)
+      for z in y.neighbors(Ratio_Pro, do_rep= False):
+        lp13, lp24 = z._lp
+        l1, l3 = lp13.lengths
+        l2, l4 = lp24.lengths
+        if self.is_equal(l3, y1):
+          l1, l3 = l3, l1
+        if self.is_equal(l4, y2):
+          l2, l4 = l4, l2
+        assert self.is_equal(l1, y1) and self.is_equal(l2, y2),f'{l1.name},{l2.name},{l3.name},{l4.name},{y1.name},{y2.name}'
+        if self.is_equal(l3, x2) and self.is_equal(l4, x1):
+          continue
+        #print(f'{l1.name},{l2.name},{l3.name},{l4.name},{z.name},{y.name},{x.name}')
+        if self.is_equal(l3, x2): #simplify
+          r, _, _ = self._get_or_create_ratio_l(x1, l4)
+          self.make_equal(z, r, deps)
+        elif self.is_equal(l4, x1): #simplify
+          r, _, _  = self._get_or_create_ratio_l(l3, x2)
+          self.make_equal(z, r, deps)
+        else:
+          rp, _, _  = self._get_or_create_ratio_pro_l(x1, x2, l3, l4)
+          self.make_equal(z, rp, deps)
+
   def merge_vals(self, vx: gm.Node, vy: gm.Node, deps: Dependency) -> None:
     if vx == vy:
       return
@@ -1265,6 +1481,7 @@ def add_perp(
     self.connect_val(cd, deps=None)
 
     if ab.val == cd.val:
+      return []
       raise ValueError(f'{ab.name} and {cd.name} Cannot be perp.')
 
     args = [a, b, c, d]
@@ -1504,6 +1721,7 @@ def add_cyclic(
     """Add a new cyclic predicate that 4 points are concyclic."""
     points = list(set(points))
     og_points = list(points)
+    print([p.name for p in points])
 
     all_circles = []
     for p1, p2, p3 in utils.comb3(points):
@@ -2058,7 +2276,7 @@ def _get_or_create_ratio(
     return self._get_or_create_ratio_l(s1._val, s2._val, deps)
 
   def _get_or_create_ratio_l(
-      self, l1: Length, l2: Length, deps: Dependency
+      self, l1: Length, l2: Length, deps=None
   ) -> tuple[Ratio, Ratio, list[Dependency]]:
     """Get or create a new Ratio from two Lenghts l1 and l2."""
     for r in self.type2nodes[Ratio]:
@@ -2081,6 +2299,150 @@ def _get_or_create_ratio_l(
     r21.opposite = r12
     return r12, r21, why1 + why2
 
+  def _get_or_create_length_pro(
+      self, s1: Segment, s2: Segment, deps=None
+  ) -> tuple[Length_Pro, list[Dependency]]:
+    return self._get_or_create_length_pro_l(s1._val, s2._val, deps)
+
+  def _get_or_create_length_pro_l(
+      self, l1: Length, l2: Length, deps=None
+  ) -> tuple[Length_Pro, list[Dependency]]:
+    """Get or create a new Length_Pro from two Lenghts l1 and l2."""
+    if l1.name > l2.name:
+      l1, l2 = l2, l1
+    for lp in self.type2nodes[Length_Pro]:
+      if lp.lengths == Multiset([l1.rep(), l2.rep()]):
+        l1_, l2_ = lp.lengths
+        if l1.rep() == l1_:# l1.rep() == l1_ and l2.rep() == l2_
+          why1 = l1.why_equal([l1_], None) + l1_.why_rep()
+          why2 = l2.why_equal([l2_], None) + l2_.why_rep()
+          return lp, why1 + why2
+        else: #l2.rep() == l1_ and l1.rep == l2_
+          why1 = l2.why_equal([l1_], None) + l1_.why_rep()
+          why2 = l1.why_equal([l2_], None) + l2_.why_rep()
+        return lp, why1 + why2
+
+    newname = f'{l1.name}*{l2.name}'
+    for lp in self.type2nodes[Length_Pro]:
+      assert lp.name != newname, f'{newname},{len(self.type2nodes[Length_Pro])}'
+    l1, why1 = l1.rep_and_why()
+    l2, why2 = l2.rep_and_why()
+    lp12 = self.new_node(Length_Pro, f'{l1.name}*{l2.name}')
+    self.connect(l1, lp12, deps)
+    self.connect(l2, lp12, deps)
+    lp12.set_lengths(l1, l2)
+    return lp12, why1 + why2
+
+  def _get_or_create_ratio_pro(
+      self, s1: Segment, s2: Segment, s3: Segment, s4: Segment, deps=None
+  ) -> tuple[Ratio_Pro, Ratio_Pro, list[Dependency]]:
+    return self._get_or_create_ratio_pro_l(s1._val, s2._val, s3._val, s4._val, deps)
+
+  def _get_or_create_ratio_pro_l(
+      self, l1: Length, l2: Length, l3:Length, l4: Length, deps=None
+  ) -> tuple[Ratio_Pro, Ratio_Pro, list[Dependency]]:
+    """Get or create a new Ratio_Pro from four Lengths l1*l3 and l2*l4."""
+    if l1.name > l3.name:
+      l1, l3 = l3, l1
+    if l2.name > l4.name:
+      l2, l4 = l4, l2
+    for rp in self.type2nodes[Ratio_Pro]:
+      lp13_, lp24_ = rp._lp
+      if lp13_.lengths == Multiset([l1.rep(), l3.rep()]) and lp24_.lengths == Multiset([l2.rep(), l4.rep()]):
+        l1_, l3_ = lp13_.lengths
+        l2_, l4_ = lp24_.lengths
+        if l1.rep() == l1_:
+          why1 = l1.why_equal([l1_], None) + l1_.why_rep()
+          why3 = l3.why_equal([l3_], None) + l3_.why_rep()
+        else:
+          why1 = l3.why_equal([l1_], None) + l1_.why_rep()
+          why3 = l1.why_equal([l3_], None) + l3_.why_rep()
+        if l2.rep() == l2_:
+          why2 = l2.why_equal([l2_], None) + l2_.why_rep()
+          why4 = l4.why_equal([l4_], None) + l4_.why_rep()
+        else:
+          why2 = l4.why_equal([l2_], None) + l2_.why_rep()
+          why4 = l2.why_equal([l4_], None) + l4_.why_rep()
+        return rp, rp.opposite, why1 + why2 + why3 + why4
+
+    l1, why1 = l1.rep_and_why()
+    l2, why2 = l2.rep_and_why()
+    l3, why3 = l3.rep_and_why()
+    l4, why4 = l4.rep_and_why()
+    lp13, _ = self._get_or_create_length_pro_l(l1, l3)
+    lp24, _ = self._get_or_create_length_pro_l(l2, l4)
+    rp1324 = self.new_node(Ratio_Pro, f'{lp13.name}/{lp24.name}')
+    rp2413 = self.new_node(Ratio_Pro, f'{lp24.name}/{lp13.name}')
+    self.connect(lp13, rp1324, deps)
+    self.connect(lp24, rp2413, deps)
+    self.connect(rp1324, rp2413, deps)
+    rp1324.set_lengths(lp13, lp24)
+    rp2413.set_lengths(lp24, lp13)
+    rp1324.opposite = rp2413
+    rp2413.opposite = rp1324
+    r12, r21, _ = self._get_or_create_ratio_l(l1, l2)
+    r14, r41, _ = self._get_or_create_ratio_l(l1, l4)
+    r32, r23, _ = self._get_or_create_ratio_l(l3, l2)
+    r34, r43, _ = self._get_or_create_ratio_l(l3, l4)
+    self.connect(r12, rp1324, deps)
+    self.connect(r14, rp1324, deps)
+    self.connect(r32, rp1324, deps)
+    self.connect(r34, rp1324, deps)
+    self.connect(r21, rp2413, deps)
+    self.connect(r41, rp2413, deps)
+    self.connect(r23, rp2413, deps)
+    self.connect(r43, rp2413, deps)
+
+    return rp1324, rp2413, why1 + why2 + why3 + why4
+  
+  def _get_or_create_ratio_pro_lp(
+      self, lp1: Length_Pro, lp2: Length_Pro, deps=None
+  ) -> tuple[Ratio_Pro, Ratio_Pro, list[Dependency]]:
+      """Get or create a new Ratio_Pro from two Length_Pro l1*l2."""
+      l1, l3 = lp1._l
+      l2, l4 = lp2._l
+      rp, rpo, _ = self._get_or_create_ratio_pro_l(l1, l2, l3, l4, deps)
+      self.connect(lp1, rp, deps)
+      self.connect(lp2, rp, deps)
+      return rp, rpo, _
+
+  def _get_or_create_ratio_pro_r(
+      self, r1: Ratio, r2: Ratio, deps=None
+  ) -> tuple[Ratio_Pro, Ratio_Pro, list[Dependency]]:
+      """Get or create a new Ratio_Pro from two Length_Pro l1*l2."""
+      l1, l2 = r1._l
+      l3, l4 = r2._l
+      rp, rpo, _ = self._get_or_create_ratio_pro_l(l1, l2, l3, l4, deps)
+      self.connect(r1, rp, deps)
+      self.connect(r2, rp, deps)
+      return rp, rpo, _
+  
+  def _set_ratio_pro_equal(
+      self, lp1: Length_Pro, lp2: Length_Pro, lp3: Length_Pro, lp4: Length_Pro, dep:EmptyDependency
+  ) -> None:
+      l11, l12 = lp1._l
+      l21, l22 = lp2._l
+      l31, l32 = lp3._l
+      l41, l42 = lp4._l
+      a1, b1 = l11._obj.points
+      c1, d1 = l12._obj.points
+      a2, b2 = l21._obj.points
+      c2, d2 = l22._obj.points
+      a3, b3 = l31._obj.points
+      c3, d3 = l32._obj.points
+      a4, b4 = l41._obj.points
+      c4, d4 = l42._obj.points
+      deps = dep.populate('eqratio40', [a1, b1, a2, b2, c1, d1, c2, d2, a4, b4, a3, b3, c4, d4, c3, d3])
+      #deps = dep
+      rp12, rp21, _ = self._get_or_create_ratio_pro_lp(lp1, lp2)
+      rp34, rp43, _ = self._get_or_create_ratio_pro_lp(lp3, lp4)
+      self.make_equal(rp12, rp34, deps=deps)
+      self.make_equal(rp21, rp43, deps=deps)
+      rp13, rp31, _ = self._get_or_create_ratio_pro_lp(lp1, lp3)
+      rp24, rp42, _ = self._get_or_create_ratio_pro_lp(lp2, lp4)
+      self.make_equal(rp13, rp24, deps=deps)
+      self.make_equal(rp31, rp42, deps=deps)
+
   def add_cong2(
       self, points: list[Point], deps: EmptyDependency
   ) -> list[Dependency]:
@@ -2152,6 +2514,9 @@ def _add_eqratio(
     ab_cd, cd_ab, why1 = self._get_or_create_ratio(ab, cd, deps=None)
     mn_pq, pq_mn, why2 = self._get_or_create_ratio(mn, pq, deps=None)
 
+    _abpq_, _ = self._get_or_create_length_pro(ab, pq, deps=None)
+    _cdmn_, _ = self._get_or_create_length_pro(cd, mn, deps=None)
+
     why = why1 + why2
     if why:
       dep0 = deps.populate('eqratio', args)
@@ -2175,6 +2540,7 @@ def _add_eqratio(
       add += [deps1]
     self.cache_dep('eqratio', [a, b, c, d, m, n, p, q], deps1)
     self.make_equal(ab_cd, mn_pq, deps=deps1)
+    self.make_equal(_abpq_, _cdmn_, deps=deps1)
 
     is_eq2 = self.is_equal(cd_ab, pq_mn)
     deps2 = None
@@ -2239,6 +2605,212 @@ def add_eqratio(
           pq,
           deps,
       )
+    return add  
+  
+  def make_equal_pairs30(
+      self,
+      a: Point, b: Point, c: Point, d: Point, m: Point, n: Point, p: Point, q: Point, x:Point, y:Point, z:Point, w:Point,
+      ab: Segment, cd: Segment, mn: Segment, pq: Segment, xy: Segment, zw: Segment,
+      deps: EmptyDependency,
+  ) -> list[Dependency]:
+    """Add ab/cd * mn/pq * xy/zw = 1 in case ab and cd are equal."""
+
+    mn_pq, pq_mn, why1 = self._get_or_create_ratio(mn, pq, deps=None)
+    xy_zw, zw_xy, why2 = self._get_or_create_ratio(xy, zw, deps=None)
+
+    _mnzw_, _ = self._get_or_create_length_pro(mn, zw, deps=None)
+    _pqxy_, _ = self._get_or_create_length_pro(pq, xy, deps=None)
+
+    is_equal = self.is_equal(mn_pq, zw_xy)
+
+    if ab != cd:
+      dep0 = deps.populate('eqratio30', [a, b, c, d, m, n, p, q, x, y, z, w])
+      deps = EmptyDependency(level=deps.level, rule_name=None)
+
+      dep = Dependency('cong', [a, b, c, d], None, deps.level)
+      deps.why = [dep0, dep.why_me_or_cache(self, None)]
+
+    deps = deps.populate('eqratio', [m, n, p, q, z, w, x, y])
+    self.make_equal(mn_pq, zw_xy, deps=deps)
+    self.make_equal(xy_zw, pq_mn, deps=deps)
+    self.make_equal(_mnzw_, _pqxy_, deps=deps)
+
+    deps.algebra = mn._val, pq._val, zw._val, xy._val
+    self.cache_dep('eqratio', [m, n, p, q, z, w, x, y], deps)
+
+    if is_equal:
+      return []
+    return [deps]
+
+  def maybe_make_equal_pairs30(
+      self,
+      a: Point, b: Point, c: Point, d: Point, m: Point, n: Point, p: Point, q: Point, x:Point, y:Point, z:Point, w:Point,
+      ab: Segment, cd: Segment, mn: Segment, pq: Segment, xy: Segment, zw: Segment,
+      deps: EmptyDependency,
+  ) -> Optional[list[Dependency]]:
+    """Add ab/cd * mn/pq * xy/zw = 1 in case either two of (ab,cd,mn,pq,xy,zw) are equal."""
+    level = deps.level
+    if self.is_equal(ab, cd, level):
+      return self.make_equal_pairs30(a, b, c, d, m, n, p, q, x, y, z, w, ab, cd, mn, pq, xy, zw, deps)
+    elif self.is_equal(ab, pq, level):
+      return self.make_equal_pairs30(a, b, p, q, m, n, c, d, x, y, z, w, ab, pq, mn, cd, xy, zw, deps)
+    elif self.is_equal(ab, zw, level):
+      return self.make_equal_pairs30(a, b, z, w, m, n, p, q, x, y, c, d, ab, zw, mn, pq, xy, cd, deps)
+    elif self.is_equal(mn, cd, level):
+      return self.make_equal_pairs30(m, n, c, d, a, b, p, q, x, y, z, w, mn, cd, ab, pq, xy, zw, deps)
+    elif self.is_equal(mn, pq, level):
+      return self.make_equal_pairs30(m, n, p, q, a, b, c, d, x, y, z, w, mn, pq, ab, cd, xy, zw, deps)
+    elif self.is_equal(mn, zw, level):
+      return self.make_equal_pairs30(m, n, z, w, a, b, p, q, x, y, c, d, mn, zw, ab, pq, xy, cd, deps)
+    elif self.is_equal(xy, cd, level):
+      return self.make_equal_pairs30(x, y, c, d, m, n, p, q, a, b, z, w, xy, cd, mn, pq, ab, zw, deps)
+    elif self.is_equal(xy, pq, level):
+      return self.make_equal_pairs30(x, y, p, q, m, n, c, d, a, b, z, w, xy, pq, mn, cd, ab, zw, deps)
+    elif self.is_equal(xy, zw, level):
+      return self.make_equal_pairs30(x, y, z, w, m, n, p, q, a, b, c, d, xy, zw, mn, pq, ab, cd, deps)
+    else:
+      return None
+
+  def _add_eqratio30(
+      self,
+      a: Point,
+      b: Point,
+      c: Point,
+      d: Point,
+      m: Point,
+      n: Point,
+      p: Point,
+      q: Point,
+      x: Point,
+      y: Point,
+      z: Point,
+      w: Point,
+      ab: Segment,
+      cd: Segment,
+      mn: Segment,
+      pq: Segment,
+      xy: Segment,
+      zw: Segment,
+      deps: EmptyDependency,
+  ) -> list[Dependency]:
+    """Add a new eqratio from 12 points (core)."""
+    if deps:
+      deps = deps.copy()
+
+    args = [a, b, c, d, m, n, p, q, x, y, z, w]
+    i = 0
+    for u, v, uv in [(a, b, ab), (c, d, cd), (m, n, mn), (p, q, pq), (x, y, xy), (z, w, zw)]:
+      if {u, v} == set(uv.points):
+        continue
+      u_, v_ = list(uv.points)
+      if deps:
+        deps = deps.extend(self, 'eqratio', list(args), 'cong', [u, v, u_, v_])
+      args[2 * i - 2] = u_
+      args[2 * i - 1] = v_
+
+    add = []
+
+    ab_cd, cd_ab, why1 = self._get_or_create_ratio(ab, cd, deps=None)
+    mnxy_pqzw, pqzw_mnxy, why2 = self._get_or_create_ratio_pro(mn, pq, xy, zw, deps=None)
+
+    why = why1 + why2
+    if why:
+      dep0 = deps.populate('eqratio30', args)
+      deps = EmptyDependency(level=deps.level, rule_name=None)
+      deps.why = [dep0] + why
+
+    lab, lcd = ab_cd._l
+    lpmnxy, lppqzw = mnxy_pqzw._lp
+    lmn, lxy = lpmnxy._l
+    lpq, lzw = lppqzw._l
+
+    a, b = lab._obj.points
+    c, d = lcd._obj.points
+    m, n = lmn._obj.points
+    p, q = lpq._obj.points
+    x, y = lxy._obj.points
+    z, w = lzw._obj.points
+
+    is_eq1 = self.is_equal(ab_cd, pqzw_mnxy)
+    #is_eq1 = self.is_equal(ab_cd, mnxy_pqzw)
+    deps1 = None
+    if deps:
+      deps1 = deps.populate('eqratio30', [a, b, c, d, m, n, p, q, x, y, z, w])
+      deps1.algebra = [ab._val, cd._val, mn._val, pq._val, xy._val, zw._val]
+    if not is_eq1:
+      add += [deps1]
+    self.cache_dep('eqratio30', [a, b, c, d, m, n, p, q, x, y, z, w], deps1)
+    self.make_equal(ab_cd, pqzw_mnxy, deps=deps1)
+    #self.make_equal(ab_cd, mnxy_pqzw, deps=deps1)
+
+    is_eq2 = self.is_equal(cd_ab, mnxy_pqzw)
+    #is_eq2 = self.is_equal(cd_ab, pqzw_mnxy)
+    deps2 = None
+    if deps:
+      deps2 = deps.populate('eqratio30', [c, d, a, b, p, q, m, n, z, w, x, y])
+      deps2.algebra = [cd._val, ab._val, pq._val, mn._val, zw._val, xy._val]
+    if not is_eq2:
+      add += [deps2]
+    self.cache_dep('eqratio30', [c, d, a, b, p, q, m, n, z, w, x, y], deps2)
+    self.make_equal(cd_ab, mnxy_pqzw, deps=deps2)
+    #self.make_equal(cd_ab, pqzw_mnxy, deps=deps2)
+    return add
+
+  def add_eqratio30(
+      self, points: list[Point], deps: EmptyDependency
+  ) -> list[Dependency]:
+    """Add a new eqratio30 from 12 points."""
+    if deps:
+      deps = deps.copy()
+    a, b, c, d, m, n, p, q, x, y, z, w = points
+    ab = self._get_or_create_segment(a, b, deps=None)
+    cd = self._get_or_create_segment(c, d, deps=None)
+    mn = self._get_or_create_segment(m, n, deps=None)
+    pq = self._get_or_create_segment(p, q, deps=None)
+    xy = self._get_or_create_segment(x, y, deps=None)
+    zw = self._get_or_create_segment(z, w, deps=None)
+
+    
+    self.connect_val(ab, deps=None)
+    self.connect_val(cd, deps=None)
+    self.connect_val(mn, deps=None)
+    self.connect_val(pq, deps=None)
+    self.connect_val(xy, deps=None)
+    self.connect_val(zw, deps=None)
+
+    add = self.maybe_make_equal_pairs30(
+        a, b, c, d, m, n, p, q, x, y, z, w, ab, cd, mn, pq, xy, zw, deps
+    )
+
+    if add is not None:
+      return add
+
+    add = []
+
+    _abmn_, why1 = self._get_or_create_length_pro(ab, mn, deps=None)
+    _abxy_, why2 = self._get_or_create_length_pro(ab, xy, deps=None)
+    _mnxy_, why3 = self._get_or_create_length_pro(mn, xy, deps=None)
+    _cdpq_, why4 = self._get_or_create_length_pro(cd, pq, deps=None)
+    _cdzw_, why5 = self._get_or_create_length_pro(cd, zw, deps=None)
+    _pqzw_, why6 = self._get_or_create_length_pro(pq, zw, deps=None)
+
+    self.connect_val(_abmn_, deps=why1)
+    self.connect_val(_abxy_, deps=why2)
+    self.connect_val(_mnxy_, deps=why3)
+    self.connect_val(_cdpq_, deps=why4)
+    self.connect_val(_cdzw_, deps=why5)
+    self.connect_val(_pqzw_, deps=why6)
+
+    add = []
+    add += self._add_eqratio30(a, b, c, d, m, n, p, q, x, y, z, w, ab, cd, mn, pq, xy, zw, deps)
+    add += self._add_eqratio30(a, b, p, q, m, n, c, d, x, y, z, w, ab, pq, mn, cd, xy, zw, deps)
+    add += self._add_eqratio30(a, b, z, w, m, n, p, q, x, y, c, d, ab, zw, mn, pq, xy, cd, deps)
+    add += self._add_eqratio30(m, n, c, d, a, b, p, q, x, y, z, w, mn, cd, ab, pq, xy, zw, deps)
+    add += self._add_eqratio30(m, n, p, q, a, b, c, d, x, y, z, w, mn, pq, ab, cd, xy, zw, deps)
+    add += self._add_eqratio30(m, n, z, w, a, b, c, d, x, y, p, q, mn, zw, ab, cd, xy, pq, deps)
+    add += self._add_eqratio30(x, y, c, d, a, b, p, q, m, n, z, w, xy, cd, ab, pq, mn, zw, deps)
+    add += self._add_eqratio30(x, y, p, q, a, b, c, d, m, n, z, w, xy, pq, ab, cd, mn, zw, deps)
+    add += self._add_eqratio30(x, y, z, w, a, b, c, d, m, n, p, q, xy, zw, ab, cd, mn, pq, deps)
     return add
 
   def check_rconst(self, points: list[Point], verbose: bool = False) -> bool:
@@ -2331,6 +2903,124 @@ def check_eqratio(self, points: list[Point]) -> bool:
           return True
     return False
 
+  def all_equiv_ratio_or_pro(self, rp: Ratio_Pro) -> list[Union(Ratio, Ratio_Pro)]:
+    r2p = []
+    for rt in self.type2nodes[Ratio]:
+      return r2p
+
+  def check_eqratio30(self, points: list[Point]) -> bool:
+    """Check if 12 points make an eqratio30 predicate."""
+
+    a, b, c, d, m, n, p, q, x, y, z, w = points
+
+    if {a, b} == {c, d}:
+      return self.check_eqratio([m, n, p, q, z, w, x, y])
+    if {a, b} == {p, q}:
+      return self.check_eqratio([m, n, c, d, z, w, x, y])
+    if {a, b} == {z, w}:
+      return self.check_eqratio([m, n, p, q, c, d, x, y])
+    if {m, n} == {c, d}:
+      return self.check_eqratio([a, b, p, q, z, w, x, y])
+    if {m, n} == {p, q}:
+      return self.check_eqratio([a, b, c, d, z, w, x, y])
+    if {m, n} == {z, w}:
+      return self.check_eqratio([a, b, p, q, c, d, x, y])     
+    if {x, y} == {c, d}:
+      return self.check_eqratio([a, b, p, q, z, w, m, n])
+    if {x, y} == {p, q}:
+      return self.check_eqratio([a, b, c, d, z, w, m, n])
+    if {x, y} == {z, w}:
+      return self.check_eqratio([a, b, p, q, c, d, m, n])
+
+    ab = self._get_segment(a, b)
+    cd = self._get_segment(c, d)
+    mn = self._get_segment(m, n)
+    pq = self._get_segment(p, q)
+    xy = self._get_segment(x, y)
+    zw = self._get_segment(z, w)
+
+    if not (ab and cd and mn and pq and xy and zw):
+      return False
+    
+    if self.is_equal(ab, cd):
+      return self.check_eqratio([m, n, p, q, z, w, x, y])
+    if self.is_equal(ab, pq):
+      return self.check_eqratio([m, n, c, d, z, w, x, y])
+    if self.is_equal(ab, zw):
+      return self.check_eqratio([m, n, p, q, c, d, x, y])
+    if self.is_equal(mn, cd):
+      return self.check_eqratio([a, b, p, q, z, w, x, y])
+    if self.is_equal(mn, pq):
+      return self.check_eqratio([a, b, c, d, z, w, x, y])
+    if self.is_equal(mn, zw):
+      return self.check_eqratio([a, b, p, q, c, d, x, y])     
+    if self.is_equal(xy, cd):
+      return self.check_eqratio([a, b, p, q, z, w, m, n])
+    if self.is_equal(xy, pq):
+      return self.check_eqratio([a, b, c, d, z, w, m, n])
+    if self.is_equal(xy, zw):
+      return self.check_eqratio([a, b, p, q, c, d, m, n])
+
+    if not (ab.val and cd.val and mn.val and pq.val and xy.val and zw.val):
+      return False
+
+    if Multiset([ab.val, mn.val, xy.val]) == Multiset([cd.val, pq.val, zw.val]):
+      return True
+
+    _abmn_, _ = self._get_or_create_length_pro(ab, mn, deps=None)
+    _abxy_, _ = self._get_or_create_length_pro(ab, xy, deps=None)
+    _mnxy_, _ = self._get_or_create_length_pro(mn, xy, deps=None)
+    _cdpq_, _ = self._get_or_create_length_pro(cd, pq, deps=None)
+    _cdzw_, _ = self._get_or_create_length_pro(cd, zw, deps=None)
+    _pqzw_, _ = self._get_or_create_length_pro(pq, zw, deps=None)
+
+    for rat1, _, _ in gm.all_ratios(ab._val, cd._val):
+      for ratp2, _, _ in gm.all_ratios2(_pqzw_, _mnxy_):
+        if self.is_equal(rat1, ratp2):
+          return True    
+
+    for rat1, _, _ in gm.all_ratios(ab._val, pq._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdzw_, _mnxy_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+
+    for rat1, _, _ in gm.all_ratios(ab._val, zw._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdpq_, _mnxy_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+
+    for rat1, _, _ in gm.all_ratios(mn._val, cd._val):
+      for ratp2, _, _ in gm.all_ratios2(_pqzw_, _abxy_):
+        if self.is_equal(rat1, ratp2):
+          return True    
+
+    for rat1, _, _ in gm.all_ratios(mn._val, pq._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdzw_, _abxy_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+
+    for rat1, _, _ in gm.all_ratios(mn._val, zw._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdpq_, _abxy_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+    
+    for rat1, _, _ in gm.all_ratios(xy._val, cd._val):
+      for ratp2, _, _ in gm.all_ratios2(_pqzw_, _abmn_):
+        if self.is_equal(rat1, ratp2):
+          return True    
+
+    for rat1, _, _ in gm.all_ratios(xy._val, pq._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdzw_, _abmn_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+
+    for rat1, _, _ in gm.all_ratios(xy._val, zw._val):
+      for ratp2, _, _ in gm.all_ratios2(_cdpq_, _abmn_):
+        if self.is_equal(rat1, ratp2):
+          return True   
+
+    return False
+
   def add_simtri_check(
       self, points: list[Point], deps: EmptyDependency
   ) -> list[Dependency]:
@@ -2999,6 +3689,16 @@ def all_cyclics(self) -> Generator[tuple[Point, ...], None, None]:
       for x, y, z, t in utils.perm4(c.neighbors(Point)):
         yield x, y, z, t
 
+  def all_cyclics6(self) -> Generator[tuple[Point, ...], None, None]:
+    for c in self.type2nodes[Circle]:
+      for x, y, z, t, u, v in utils.perm6(c.neighbors(Point)):
+        yield x, y, z, t, u, v
+    
+  def all_cyclics5(self) -> Generator[tuple[Point, ...], None, None]:
+    for c in self.type2nodes[Circle]:
+      for x, y, z, t, u in utils.perm5(c.neighbors(Point)):
+        yield x, y, z, t, u
+
   def all_colls(self) -> Generator[tuple[Point, ...], None, None]:
     for l in self.type2nodes[Line]:
       for x, y, z in utils.perm3(l.neighbors(Point)):
@@ -3031,6 +3731,7 @@ def two_points_of_length(self, l: Length) -> tuple[Point, Point]:
     s = l.neighbors(Segment)[0]
     p1, p2 = s.points
     return p1, p2
+  
 
 
 def create_consts_str(g: Graph, s: str) -> Union[Ratio, Angle]:
diff --git a/graph_utils.py b/graph_utils.py
index f53214b..ba8939c 100644
--- a/graph_utils.py
+++ b/graph_utils.py
@@ -30,6 +30,14 @@ def _cross(elems1, elems2):
 def cross(elems1, elems2):
   return list(_cross(elems1, elems2))
 
+def _cross3(elems1, elems2, elems3):
+  for e1 in elems1:
+    for e2 in elems2:
+      for e3 in elems3:
+        yield e1, e2, e3
+
+def cross3(elems1, elems2, elems3):
+  return list(_cross3(elems1, elems2, elems3))
 
 def _comb2(elems):
   if len(elems) < 2:
@@ -130,3 +138,46 @@ def _perm4(elems):
 
 def perm4(elems):
   return list(_perm4(elems))
+
+def _perm5(elems):
+  for x in elems:
+    for y in elems:
+      if y == x:
+        continue
+      for z in elems:
+        if z in (x, y):
+          continue
+        for t in elems:
+          if t in (x, y, z):
+            continue
+          for u in elems:
+            if u not in (x, y, z, t):
+              yield x, y, z, t, u
+
+def perm5(elems):
+  if len(elems) < 5:
+    return []
+  return list(_perm5(elems))
+
+def _perm6(elems):
+  for x in elems:
+    for y in elems:
+      if y == x:
+        continue
+      for z in elems:
+        if z in (x, y):
+          continue
+        for t in elems:
+          if t in (x, y, z):
+            continue
+          for u in elems:
+            if u in (x, y, z, t):
+              continue
+            for v in elems:
+              if v not in (x, y, z, t, u):
+                yield x, y, z, t, u, v
+
+def perm6(elems):
+  if len(elems) < 6:
+    return []
+  return list(_perm6(elems))
diff --git a/kirine.txt b/kirine.txt
new file mode 100644
index 0000000..32a2a44
--- /dev/null
+++ b/kirine.txt
@@ -0,0 +1,24 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J : Points
+DA = DB [00]
+DB = DC [01]
+DE = DA [02]
+DF = DA [03]
+A,G,B are collinear [04]
+E,F,G are collinear [05]
+C,B,H are collinear [06]
+C,E,I are collinear [07]
+H,I,G are collinear [08]
+J,F,H are collinear [09]
+A,J,I are collinear [10]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. DA = DB [00] & DB = DC [01] ⇒  D is the circumcenter of \Delta ABC [11]
+002. D is the circumcenter of \Delta ABC [11] & DE = DA [02] & DF = DA [03] & A,G,B are collinear [04] & E,F,G are collinear [05] & C,B,H are collinear [06] & J,F,H are collinear [09] & C,E,I are collinear [07] & A,J,I are collinear [10] & H,I,G are collinear [08] ⇒  DA = DJ
+==========================
diff --git a/lines.txt b/lines.txt
new file mode 100644
index 0000000..dc54cae
--- /dev/null
+++ b/lines.txt
@@ -0,0 +1,12 @@
+gcenter
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f ? coll a g d
+hcenter
+a b c = triangle a b c; d = foot d a b c; e = foot e b c a; f = foot f c a b; g = on_line g b e, on_line g c f ? coll a g d
+icenter
+a b c = triangle a b c; d = angle_bisector d a b c, angle_bisector d a c b ? eqangle a b a d a d a c
+ocenter
+a b c = triangle a b c; d = on_bline d a b, on_bline d a c ? cong d b d c 
+radical_axis
+a b = segment a b; o1 = on_bline o1 a b; o2 = on_bline o2 a b; o3 = free; c = on_circle c o1 a; d = on_circle d o1 a, on_circle d o3 c; e = on_circle e o2 a, on_circle e o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
+radical_axis2
+a b c = triangle a b c; e = free; o1 = circle o1 a b c; o2 = circle o2 a b e; o3 = on_bline o3 c e; d = on_circle d o1 a, on_circle d o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
\ No newline at end of file
diff --git a/meliad_lib/meliad b/meliad_lib/meliad
new file mode 160000
index 0000000..e8af054
--- /dev/null
+++ b/meliad_lib/meliad
@@ -0,0 +1 @@
+Subproject commit e8af0543441222c1c4c60d58803511f7cf92908b
diff --git a/newpros.txt b/newpros.txt
new file mode 100644
index 0000000..8dfedf7
--- /dev/null
+++ b/newpros.txt
@@ -0,0 +1,84 @@
+Menelaus_c3
+a b = segment a b; c = on_tline c b a b, on_circle c b a; d = midpoint d b c; e = foot e b a d; f = on_line f b e, on_line f a c; g = midpoint g a f ? cong a g c f
+Menelaus_c22
+a b c = triangle a b c; d = on_line d b c; f = on_line f a c; e = mirror e f d; p = on_line p a d, on_line p b e; m = on_line m a b, on_line m d f; n = on_line n p c, on_line n d f ? cong d m d n
+Menelaus_c32
+a b c = triangle a b c; i = incenter i a b c; d = on_line d a i, on_line d b c; e = on_line e b i, on_line e c a; f = on_tline f c c i, on_line f a b ? coll d e f
+Menelaus_Desargues
+a b c = triangle a b c; d e = segment d e; g = on_line g a d, on_line g b e; f = on_line f g c; l = on_line l a b, on_line l d e; m = on_line m b c, on_line m e f; n = on_line n a c, on_line n d f ? coll l m n
+Menelaus_Pappus
+a b = segment a b; c d = segment c d; e = on_line e a c; f = on_line f b d; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a; j = on_line j c d, on_line j e f; k = on_line k a b, on_line k e f; l = on_line l a b, on_line l c d ? coll g h i
+Menelaus_Newton
+a b c = triangle a b c; d = free; e = on_line e a b, on_line e c d; f = on_line f a d, on_line f b c; g = midpoint g a c; h = midpoint h b d; i = midpoint i e f; j = midpoint j c e; k = midpoint k b c; l = midpoint l b e ? coll g h i
+Menelaus_a2
+a b c = triangle a b c; o = circle o a b c; p = on_line p b c, on_tline p a o a; q = on_line q a c, on_tline q b o b; r = on_line r a b, on_tline r c o c ? coll p q r
+Menelaus_a11
+a b c = triangle a b c; d = on_line d a b; e = on_line e a c; f = midpoint f d e; g = on_line g d e; h = mirror h g f; i = on_line i a b; j = on_line j g i, on_line j a c; k = on_line k a b; l = on_line l k h, on_line l a c; m = on_line m j k, on_line m d e; n = on_line n i l, on_line n d e ? cong f m f n
+Ceva_c2
+a b c = triangle a b c; d = midpoint d b c; e = on_line e a d; f = on_line f a b, on_line f e c; g = on_line g a c, on_line g e b ? para f g b c
+Ceva_c3
+a b c = triangle a b c; o = circle o a b c; d = on_tline d b o b, on_tline d c o c; e = on_tline e a o a, on_tline e c o c; f = on_tline f a o a, on_tline f b o b; g = on_line g a d, on_line g b e ? coll g c f
+Ceva_c5
+a b c = triangle a b c; d = angle_bisector d b a c, on_line d b c; e = on_line e a d, on_tline e b a d; m = midpoint m b c; n = on_line n a m, on_line n b e ? para d n a b
+Ceva_c22
+a b d = triangle a b d; c = angle_bisector c b a d; e = on_line e c d; f = on_line f b e, on_line f a c; g = on_line g d f, on_line g b c; h = on_line h a c, on_line h b d ? eqangle a g a c a c a e
+Ceva_c32
+a b c = triangle a b c; d = on_line d b c; e = angle_bisector e a d c, on_line e a c; f = angle_bisector f a d b, on_line f a b; g = on_line g b e, on_line g c f ? coll g a d
+Ceva_b2
+c d = segment c d; o = on_bline o c d; a = on_tline a d o d; b = on_tline b c o c, on_line b o a; e = on_line e a c, on_line e b d; r = on_line r a d, on_line r b c; f = foot f r a b ? coll r e f
+Menelaus_b3
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; q = on_line q a c, on_line q b d; e = foot e q a b; f = foot f q b c; g = foot g q c d; h = foot h q d a; p = on_line p e h, on_line p b d ? coll p f g
+Menelaus_b6
+a b c = triangle a b c; h = orthocenter h a b c; e = on_line e a b; f = on_line f b c, on_line f e h; d = on_line d a c, on_line d e h; m = on_tline m h e h, on_line m b c; n = on_line n a b, on_line n m h; p = on_line p a c, on_line p m h ? eqratio d e e f p n m n
+Menelaus_b9w
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; j = on_tline j d b c; y = on_circle y j d, on_circle y c d; z = on_circle z j d, on_circle z b d; x = on_line x z b, on_line x y c; p = on_line p b c, on_line p e f ? coll p y z
+Menelaus_b9
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; j = on_tline j d b c; y = on_circle y j d, on_circle y c d; z = on_circle z j d, on_circle z b d; x = on_line x z b, on_line x y c; p = on_line p b c, on_line p e f ? cyclic e f y z
+Menelaus_b10
+a b c = triangle a b c; d = foot d a b c; x e g o1 = excenter2 x e g o1 c a b; y f h o2 = excenter2 y f h o2 b a c; q = on_line q a d, on_line q f h ? coll q e g
+Menelaus_b11
+a b c = triangle a b c; o = circle o a b c; p = on_tline p a o a, on_tline p b o b; d = on_line d p c, on_circle d o a; e = on_pline e c p a, on_line e a b; f = on_line f c e, on_line f a d; k = on_line k c d, on_line k a b; m = on_line m o p, on_line m a b ? cyclic o m c d
+Menelaus_b12
+a b c = triangle a b c; m = midpoint m b c; d = on_line d b c; e = mirror e d m; f = on_line f a b; g = on_line g a c; k = on_line k f e, on_line k g d; v = on_line v f d, on_line v g e; l = on_line l a k, on_line l b c; t = on_line t a v, on_line t b c ? cong d t e l
+Menelaus_b13
+x y = segment x y; p = on_line p x y; a = on_circle a x p; b c = tangent b c a y p; d = on_line d a b, on_circle d x a; e = on_line e a c, on_circle e x a; r = on_line r d e, on_line r b c; q = on_line q p r, on_circle q x a ? coll a q y
+Menelaus_b15
+a b c = triangle a b c; m = midpoint m b c; i = incenter i a b c; d = on_line d m i, on_line d a c; o = circle o a b c; e = on_line e b i, on_circle e o a; f = on_line f b i, on_line f a c ? eqratio e d e i i c i b
+Ceva_a1
+a b c = triangle a b c; d = foot d a b c; h = on_line h a d; e = on_line e a c, on_line e b h; f = on_line f a b, on_line f c h; p = on_pline p a b c, on_line p d f; q = on_line q p a, on_line q d e ? cong a p a q
+tangent
+a b c = triangle a b c; o = circle o a b c; p = on_tline p a o a, on_line p b c ? eqratio30 a b a c a b a c p c p b
+Menelaus_b2a
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f; x = on_pline x g b c, on_line x a b; y = on_line y g x, on_line y a c; p = on_line p b y, on_line p c g; q = on_line q c x, on_line q b g ? eqratio d p a b d q a c
+Menelaus_b2b
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f; x = on_pline x g b c, on_line x a b; y = on_line y g x, on_line y a c; p = on_line p b y, on_line p c g; q = on_line q c x, on_line q b g ? eqratio d p a b p q b c
+Ceva_a4
+a b c = triangle a b c; d = on_circle d c a, on_line d b c; o = circle o a c d; m = midpoint m b c; p = on_circle p o c, on_circle p m c; e = on_line e a c, on_line e b p; f = on_line f a b, on_line f c p ? coll d e f
+Ceva_a7
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a b, on_line e d c; f = on_line f a d, on_line f b c; p = on_circle p o a; r = on_line r p e, on_circle r o a; s = on_line s p f, on_circle s o a; t = on_line t a c, on_line t b d ? eqratio30 a s s d d c r c b r b a
+Circle_a2
+b c = segment b c; a = on_bline a b c; i = incenter i a b c; o = on_bline o b i; p = on_circle p a b, on_circle p o b; q = on_circle q i b, on_circle q o b; r = on_line r i p, on_line r b q ? perp b r c r
+Circle_a5
+a b c = triangle a b c; d e f x = excenter2 d e f x a b c; o1 = circle o1 a e f; p = on_line p b c, on_circle p o1 a; q = on_line q b c, on_circle q o1 a; m = midpoint m a d; o2 = circle o2 m p q; t = on_circle t o2 m, on_circle t x d ? coll o2 x t
+Circle_a6
+a b c = triangle a b c; o = circle o a b c; h = orthocenter h a b c; s = on_circle s o a; p = on_line p b c, on_tline p s a s; o2 = circle o2 a s p; x = on_line x s h, on_circle x o2 a; r = on_line r a b, on_line r o p; q = on_line q a c, on_line q o p; y = foot y q a r; z = foot z r a q ? coll x y z
+Circle_a8
+a b c = triangle a b c; o = circle o a b c; d = on_line d a o, on_line d b c; u = foot u d a c; v = foot v d a b; e = on_tline e a a o, on_line e d u; f = on_tline f a a o, on_line f d v; p = on_line p e c, on_line p f b; x = on_line x b p, on_circle x o a; y = on_line y c p, on_circle y o a ? perp p d b c
+Circle_b4
+a b c = triangle a b c; o = circle o a b c; i = circle i o b c; g = on_circle g i o; x = circle x a b g; y = circle y a c g; e = on_line e a c, on_circle e x a; f = on_line f a b, on_circle f y a; k = on_line k b e, on_line k c f; t = on_line t a k, on_line t b c ? coll t o g
+Circle_b5
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a d, on_line e b c; m = midpoint m a d; n = midpoint n b c; w = circle w e m n; x = on_circle x o a, on_circle x w e; y = on_circle y o a, on_circle y w e; z = on_line z a b, on_line z c d ? coll x y z
+Circle_b7w
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; p = on_line p a d, on_circle p i d; q = on_line q e f, on_tline q p a d; x = on_line x d e, on_line x a q; y = on_line y d f, on_line y a q; u = on_line u d i, on_pline u a b c; v = on_line v d i, on_circle v i d ? cong a x a y
+Circle_b13
+a b c = triangle a b c; d = foot d a b c; e = foot e b c a; m = midpoint a b; o = circle o a b c; f = on_line f d e, on_circle f o a; k = on_line k d e, on_circle k o a; w = circle w m d e; p = on_line p m k, on_circle p w m; q = on_line q m f, on_circle q w m ? cyclic a p q b
+Circle_b15
+a b = segment a b; o = on_bline o a b; p = on_tline p a o a, on_tline p b o b; c = on_circle c o a; d = on_line d p c, on_circle d o a; e = on_pline e c p b, on_circle e o a; f = on_line f a e, on_line f p b; g = on_line g d e, on_line g p b ? cong g f g b
+Circle_c2
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a b, on_line e c d; f = on_line f b c, on_pline f e a d; m = midpoint m o f; g = on_circle g o a, on_circle g m f ? cong f e f g
+Circle_c3
+a b c = triangle a b c; d = angle_bisector d b a c, on_line d b c; m = midpoint m b c; o = circle o a d m; l = on_line l a b, on_circle l o a; n = on_line n a c, on_circle n o a ? cong b l c n
+Pascal_a1
+a b c = triangle a b c; o = circle o a b c; p = free; a1 = on_line a1 a p, on_circle a1 o a; b1 = on_line b1 b p, on_circle b1 o b; c1 = on_line c1 c p, on_circle c1 o c; q = on_circle q o a; x = on_line x q a1, on_line x b c; y = on_line y q b1, on_line y a c; z = on_line z q c1, on_line z a b ? coll x y z
+Pascal_b2
+a c = segment a c; o = midpoint o a c; b = on_circle b o a; d = on_circle d o a; m = on_line m a d, on_line m b c; n = on_tline n b o b, on_tline n d o d; p = on_line p a b, on_line p c d ? perp a c m n
\ No newline at end of file
diff --git a/nothing.txt b/nothing.txt
new file mode 100644
index 0000000..d1b723b
--- /dev/null
+++ b/nothing.txt
@@ -0,0 +1,881 @@
+circle_perp_coll_eqratio
+coll_coll_ncoll_eqratio_cyclic
+cyclic_cyclic_cyclic_coll_coll_coll
+circle_cong_cong_cong_coll_coll_coll_coll_coll_coll_coll
+circle_cong_cong_perp_coll_coll_coll_coll_coll_coll
+circle_cong_perp_coll_coll_coll_perp_coll_coll
+circle_cong_perp_perp_coll_coll_coll_coll_coll
+circle_cong_cong_coll_coll_coll_coll_coll_coll_coll_cong
+
+cyclic A B C D, coll P A B, coll P C D => eqratio P A P C P D P B
+circle O A B C, perp O A A P, coll P B C => eqratio P A P B P C P A
+coll P A B, coll P C D, ncoll A B C D, eqratio P A P C P D P B => cyclic A B C D
+cyclic A B C D, cyclic A B E F, cyclic C D E F, coll P A B, coll P C D => coll P E F
+circle O A B C, cong O A O D, cong O A O E, cong O A O F, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A => coll G H I
+circle O A B C, cong O A O D, cong O A O E, perp O A A G, coll G C D, coll H A B, coll H D E, coll I B C, coll I E A => coll G H I
+circle O A B C, cong O A O D, perp O A A G, coll G B C, coll H A B, coll H C D, perp O B B I, coll I D A => coll G H I
+circle O A B C, cong O A O D, perp O A A G, perp O B B G, coll H A C, coll H B D, coll I C B, coll I D A => coll G H I
+circle O A B C, cong O A O D, cong O A O E, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A, coll G H I => cong O A O F
+
+cyclic A B C D E F, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A => coll G H I
+circle O A B C, cong O A O D, cong O A O E, cong O A O F, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A => coll G H I
+cyclic A B C D, cyclic A B C E => cong A D A E
+
+001. A,F,C are collinear [06] & B,D,C are collinear [03] & A,D,E are collinear [04] & F,B,E are collinear [07] ⇒  (AF:FC) * (CB:BD) * (DE:EA) = 1 [10]
+002. (AF:FC) * (CB:BD) * (DE:EA) = 1 [10] & BC = BA [00] & DB = DC [02] ⇒  (AF:FC) * (AB:AE) * (DE:DC) = 1 [11]
+003. A,D,E are collinear [04] & B,D,C are collinear [03] & BC ⟂ AB [01] & BE ⟂ AD [05] ⇒  ∠BEA = ∠ABD [12]
+004. A,D,E are collinear [04] ⇒  ∠BAE = ∠BAD [13]
+005. ∠BEA = ∠ABD [12] & ∠BAE = ∠BAD [13] ⇒  EB:EA = BD:BA [14]
+006. EB:EA = BD:BA [14] & DB = DC [02] ⇒  BE:AE = DC:AB [15]
+007. A,D,E are collinear [04] & B,D,C are collinear [03] & BC ⟂ AB [01] & BE ⟂ AD [05] ⇒  ∠BED = ∠DBA [16]
+008. D,B,C are collinear [03] & A,D,E are collinear [04] ⇒  ∠BDE = ∠BDA [17]
+009. ∠BED = ∠DBA [16] & ∠BDE = ∠BDA [17] ⇒  EB:ED = BA:BD [18]
+010. EB:ED = BA:BD [18] & DB = DC [02] ⇒  BE:DE = AB:DC [19]
+011. BC = BA [00] & DB = DC [02] & (AF:FC) * (AB:AE) * (DE:DC) = 1 [11] & BE:AE = DC:AB [15] & BE:DE = AB:DC [19] (Ratio chase)⇒  BC:DC = AF:FC [20]
+012. DB = DC [02] (Distance chase)⇒  CD:CB = 1_/2 [21]
+013. GA = GF [09] (Distance chase)⇒  FG:AF = 1_/2 [22]
+014. BC:DC = AF:FC [20] & BC = BA [00] & CD:CB = 1_/2 [21] & FG:AF = 1_/2 [22] & AG = FG [09] ⇒  AG:AF = FC:AF [23]
+015. AG:AF = FC:AF [23] & AF:AC = AF:AC [08] ⇒  AG = FC
+
+001. F,C,A are collinear [04] & D,B,C are collinear [01] & D,A,E are collinear [03] & B,F,E are collinear [05] ⇒  (AF:FC) * (CB:BD) * (DE:EA) = 1 [08]
+002. F,C,A are collinear [04] & D,B,C are collinear [01] & D,A,E are collinear [03] & B,F,E are collinear [05] ⇒  (DC:CB) * (EA:AD) * (BF:FE) = 1 [09]
+003. DB = DC [02] (Distance chase)⇒  CD:CB = 1_/2 [10]
+004. GA = GF [07] (Distance chase)⇒  FG:FA = 1_/2 [11]
+005. (AF:FC) * (CB:BD) * (DE:EA) = 1 [08] & BC = BA [00] & DB = DC [02] & (DC:CB) * (EA:AD) * (BF:FE) = 1 [09] & CD:CB = 1_/2 [10] & FG:FA = 1_/2 [11] ⇒  FG:FA = FC:FA [12]
+006. FG:FA = FC:FA [12] & FA:CA = FA:CA [06] ⇒  FG = FC [13]
+007. FG = FC [13] & GA = GF [07] ⇒  AG = CF
+
+001. C,D,B are collinear [02] & DB = DC [03] ⇒  D is midpoint of CB [10]
+002. G,F,A are collinear [08] & GA = GF [09] ⇒  G is midpoint of FA [11]
+003. D is midpoint of CB [10] & G is midpoint of FA [11] ⇒  DC:CB = GA:AF [12]
+004. D,A,E are collinear [04] & BE ⟂ AD [05] ⇒  ∠DEB = ∠BEA [13]
+005. C,D,B are collinear [02] & BC ⟂ AB [01] ⇒  CD ⟂ AB [14]
+006. F,B,E are collinear [06] & BE ⟂ AD [05] ⇒  EF ⟂ DA [15]
+007. CD ⟂ AB [14] & EF ⟂ DA [15] ⇒  ∠(CD-EF) = ∠BAD [16]
+008. D,C,B are collinear [02] & D,A,E are collinear [04] & ∠(CD-EF) = ∠BAD [16] & E,F,B are collinear [06] ⇒  ∠DBE = ∠BAE [17]
+009. ∠DEB = ∠BEA [13] & ∠DBE = ∠BAE [17] (Similar Triangles)⇒  DE:BE = DB:BA [18]
+010. C,A,F are collinear [07] & E,F,B are collinear [06] & D,A,E are collinear [04] & C,D,B are collinear [02] ⇒  (DE:EB) * (CA:DA) * (FB:CF) = 1 [19]
+011. C,A,F are collinear [07] & E,F,B are collinear [06] & D,A,E are collinear [04] & C,D,B are collinear [02] ⇒  (AF:FC) * (CB:BD) * (DE:EA) = 1 [20]
+012. F,B,E are collinear [06] & D,A,E are collinear [04] & BE ⟂ AD [05] ⇒  FE ⟂ EA [21]
+013. FE ⟂ EA [21] & G is midpoint of FA [11] ⇒  FG = EG [22]
+014. FE ⟂ EA [21] & G is midpoint of FA [11] ⇒  AG = EG [23]
+015. DC:CB = GA:AF [12] & BC = BA [00] & GA = GF [09] & DE:BE = DB:BA [18] & DB = DC [03] & (DE:EB) * (CA:DA) * (FB:CF) = 1 [19] & (AF:FC) * (CB:BD) * (DE:EA) = 1 [20] & GE = GF [22] ⇒  CF:AF = GE:AF [24]
+016. CB = AB [00] ⇒  AF:CB = AF:CB [25]
+017. CF:AF = GE:AF [24] & AF:CB = AF:CB [25] ⇒  CF = GE [26]
+018. CF = GE [26] & AG = EG [23] ⇒  AG = CF
+
+
+cmo23_5
+a b c = triangle a b c; d = on_line d b c; e = on_pline e d a b, on_circle e b d; f = on_pline f d a c, on_circle f c d; g = circle g d e f; h = on_circle h o d, on_line h a d ? eqratio30 a e a f b g b e c f c g
+Traceback (most recent call last):
+  File "/environment/miniconda3/lib/python3.10/runpy.py", line 196, in _run_module_as_main
+    return _run_code(code, main_globals, None,
+  File "/environment/miniconda3/lib/python3.10/runpy.py", line 86, in _run_code
+    exec(code, run_globals)
+  File "/home/featurize/work/alphageometry/alphageometry.py", line 650, in <module>
+    app.run(main)
+  File "/home/featurize/work/alphageometry/lib/python3.10/site-packages/absl/app.py", line 308, in run
+    _run_main(main, args)
+  File "/home/featurize/work/alphageometry/lib/python3.10/site-packages/absl/app.py", line 254, in _run_main
+    sys.exit(main(argv))
+  File "/home/featurize/work/alphageometry/alphageometry.py", line 637, in main
+    run_alphageometry(
+  File "/home/featurize/work/alphageometry/alphageometry.py", line 553, in run_alphageometry
+    translations = [
+  File "/home/featurize/work/alphageometry/alphageometry.py", line 554, in <listcomp>
+    try_translate_constrained_to_construct(o, g)
+  File "/home/featurize/work/alphageometry/alphageometry.py", line 384, in try_translate_constrained_to_construct
+    head, prem_str = string.split(' : ')
+ValueError: not enough values to unpack (expected 2, got 1)
+
+001. C,F,A are collinear [06] & C,D,B are collinear [02] & E,A,D are collinear [04] & E,F,B are collinear [07] ⇒  (AF:FC) * (CB:BD) * (DE:EA) = 1 [10]
+002. C,F,A are collinear [06] & C,D,B are collinear [02] & E,A,D are collinear [04] & E,F,B are collinear [07] ⇒  (ED:EB) * (CA:AD) * (FB:CF) = 1 [11]
+003. E,A,D are collinear [04] & BE ⟂ AD [05] ⇒  ∠AEB = ∠BED [12]
+004. C,D,B are collinear [02] & E,A,D are collinear [04] & BE ⟂ AD [05] & BC ⟂ AB [01] ⇒  ∠DBA = ∠AEB [13]
+005. E,A,D are collinear [04] ⇒  ∠DAB = ∠EAB [14]
+006. ∠DBA = ∠AEB [13] & ∠DAB = ∠EAB [14] ⇒  ∠BDA = ∠ABE [15]
+007. C,D,B are collinear [02] & E,A,D are collinear [04] & ∠BDA = ∠ABE [15] ⇒  ∠ABE = ∠BDE [16]
+008. ∠AEB = ∠BED [12] & ∠ABE = ∠BDE [16] ⇒  BA:DB = BE:DE [17]
+009. DB = DC [03] (Distance chase)⇒  CD:CB = 1_/2 [18]
+010. GA = GF [09] (Distance chase)⇒  AG:AF = 1_/2 [19]
+011. (AF:FC) * (CB:BD) * (DE:EA) = 1 [10] & BC = BA [00] & DB = DC [03] & (ED:EB) * (CA:AD) * (FB:CF) = 1 [11] & BA:DB = BE:DE [17] & CD:CB = 1_/2 [18] & AG:AF = 1_/2 [19] & GA = GF [09] ⇒  AG:FA = CF:FA [20]
+012. AG:FA = CF:FA [20] & FA:CA = FA:CA [08] ⇒  AG = CF
+
+example2_8_1
+a b c = triangle a b c; d = midpoint d a c; e = on_line e b d; f = on_line f a e, on_line f b c; g = on_line g c e, on_line g a b; h = on_pline h f c g, on_line h b d; i = on_circle i e f, on_circle i f e; j = on_circle j e g, on_circle j g e ? cong h i h j
+example2_8_2
+a b c = triangle a b c; d = midpoint d a c; e = on_line e b d; f = on_line f a e, on_line f b c; g = on_line g c e, on_line g a b; h = on_pline h f c g, on_line h b d; i = on_circle i e f, on_circle i f e; j = on_circle j e g, on_circle j g e ? cong h i i j
+example2_7
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a b, on_line e d c; f = on_line f a d, on_line f b c; p = on_circle p o a; r = on_line r p f, on_circle r o a; s = on_line s p e, on_circle s o a; t = on_line t a c, on_line t b d ? eqratio30 a s s d d c r c b r b a
+
+
+==========================
+ * From theorem premises:
+A B C D E F G H J K L M N O : Points
+C,D,B are collinear [00]
+BE = BD [01]
+ED ∥ AB [02]
+CF = CD [03]
+FD ∥ AC [04]
+GE = GD [05]
+GD = GF [06]
+D,H,A are collinear [07]
+GH = GD [08]
+JA = FC [09]
+J,E,A are collinear [10]
+KB = CH [11]
+K,E,B are collinear [12]
+LE = LJ [13]
+LJ = LF [14]
+ME = MK [15]
+MK = MH [16]
+LN = LF [17]
+F,N,A are collinear [18]
+MO = MH [19]
+H,O,B are collinear [20]
+
+ * Auxiliary Constructions:
+Q : Points
+D,Q,H are collinear [21]
+QH = QD [22]
+
+ * Proof steps:
+001. LE = LJ [13] & LJ = LF [14] & LN = LF [17] ⇒  F,J,E,N are concyclic [23]
+002. F,J,E,N are concyclic [23] & F,N,A are collinear [18] & J,E,A are collinear [10] ⇒  FA:JA = EA:NA [24]
+003. ME = MK [15] & MK = MH [16] & MO = MH [19] ⇒  H,E,O,K are concyclic [25]
+004. H,E,O,K are concyclic [25] & H,O,B are collinear [20] & K,E,B are collinear [12] ⇒  BH:BE = BK:BO [26]
+005. BH:BE = BK:BO [26] & BE = BD [01] & KB = CH [11] ⇒  HB:DB = CH:OB [27]
+006. GH = GD [08] & QH = QD [22] ⇒  HD ⟂ GQ [28]
+007. BE = BD [01] & GE = GD [05] ⇒  DE ⟂ BG [29]
+008. D,Q,H are collinear [21] & D,H,A are collinear [07] & HD ⟂ GQ [28] & DE ⟂ BG [29] & DE ∥ AB [02] ⇒  ∠GBA = ∠GQA [30]
+009. ∠GBA = ∠GQA [30] ⇒  A,Q,G,B are concyclic [31]
+010. CF = CD [03] & GD = GF [06] ⇒  DF ⟂ CG [32]
+011. DF ⟂ CG [32] & DF ∥ AC [04] & DE ⟂ BG [29] & DE ∥ AB [02] ⇒  ∠GBA = ∠GCA [33]
+012. ∠GBA = ∠GCA [33] ⇒  C,G,A,B are concyclic [34]
+013. A,Q,G,B are concyclic [31] & C,G,A,B are concyclic [34] ⇒  C,Q,A,B are concyclic [35]
+014. C,Q,A,B are concyclic [35] ⇒  ∠CBA = ∠CQA [36]
+015. C,Q,A,B are concyclic [35] ⇒  ∠CAQ = ∠CBQ [37]
+016. D,C,B are collinear [00] & D,Q,H are collinear [21] & D,H,A are collinear [07] & ∠CBA = ∠CQA [36] ⇒  ∠DBA = ∠CQD [38]
+017. C,D,B are collinear [00] & ∠CBA = ∠CQA [36] & D,Q,H are collinear [21] & D,H,A are collinear [07] ⇒  ∠DAB = ∠QCD [39]
+018. ∠DBA = ∠CQD [38] & ∠DAB = ∠QCD [39] (Similar Triangles)⇒  DB:AB = DQ:CQ [40]
+019. DQ:CQ = DB:AB [40] & HQ = DQ [22] & EB = DB [01] ⇒  QH:QC = BE:BA [41]
+020. BE = BD [01] ⇒  ∠BDE = ∠DEB [42]
+021. C,D,B are collinear [00] & K,E,B are collinear [12] & ∠BDE = ∠DEB [42] ⇒  ∠EDC = ∠KED [43]
+022. C,D,B are collinear [00] & D,A,H are collinear [07] & ∠CBA = ∠CQA [36] & D,Q,H are collinear [21] & AB ∥ DE [02] ⇒  ∠DCQ = ∠EDH [44]
+023. ∠EDC = ∠KED [43] & ∠DCQ = ∠EDH [44] ⇒  ∠(DE-CQ) = ∠(KE-DH) [45]
+024. D,Q,H are collinear [21] & D,H,A are collinear [07] & ∠(DE-CQ) = ∠(KE-DH) [45] & K,E,B are collinear [12] & DE ∥ AB [02] ⇒  ∠HQC = ∠EBA [46]
+025. QH:QC = BE:BA [41] & ∠HQC = ∠EBA [46] (Similar Triangles)⇒  HQ:HC = EB:EA [47]
+026. HQ:HC = EB:EA [47] & QH = QD [22] & BE = BD [01] ⇒  DQ:CH = DB:EA [48]
+027. D,Q,H are collinear [21] & D,H,A are collinear [07] & C,D,B are collinear [00] & ∠CAQ = ∠CBQ [37] ⇒  ∠DQB = ∠ACD [49]
+028. D,C,B are collinear [00] & ∠CAQ = ∠CBQ [37] & D,Q,H are collinear [21] & D,H,A are collinear [07] ⇒  ∠DBQ = ∠CAD [50]
+029. ∠DQB = ∠ACD [49] & ∠DBQ = ∠CAD [50] (Similar Triangles)⇒  QD:QB = CD:CA [51]
+030. QD:QB = CD:CA [51] & JA = FC [09] & CF = CD [03] & HQ = DQ [22] ⇒  QH:QB = CF:CA [52]
+031. CF = CD [03] ⇒  ∠CFD = ∠FDC [53]
+032. C,D,B are collinear [00] & D,A,H are collinear [07] & ∠CAQ = ∠CBQ [37] & D,Q,H are collinear [21] & AC ∥ DF [04] ⇒  ∠(CD-QB) = ∠FDH [54]
+033. ∠CDF = ∠DFC [53] & ∠(CD-QB) = ∠FDH [54] ⇒  ∠(CF-DH) = ∠(DF-QB) [55]
+034. D,Q,H are collinear [21] & D,H,A are collinear [07] & ∠(CF-DH) = ∠(DF-QB) [55] & DF ∥ AC [04] ⇒  ∠HQB = ∠FCA [56]
+035. QH:QB = CF:CA [52] & ∠HQB = ∠FCA [56] (Similar Triangles)⇒  HQ:HB = FC:FA [57]
+036. HQ:HB = FC:FA [57] & QH = QD [22] & JA = FC [09] ⇒  DQ:HB = JA:FA [58]
+037. JA = FC [09] & KB = CH [11] & FA:JA = EA:NA [24] & HB:DB = CH:OB [27] & DQ:CH = DB:EA [48] & DQ:HB = JA:FA [58] (Ratio chase)⇒  NA = OB
+==========================
+
+2_4
+
+
+ * From theorem premises:
+A B C D E F G H I : Points
+C,B,D are collinear [00]
+CA = DC [01]
+EC = ED [02]
+EA = EC [03]
+FB = FC [04]
+C,B,F are collinear [05]
+FG = FC [06]
+EG = EC [07]
+B,G,H are collinear [08]
+A,C,H are collinear [09]
+A,B,I are collinear [10]
+C,G,I are collinear [11]
+
+ * Auxiliary Constructions:
+J : Points
+J,C,H are collinear [12]
+JH = JC [13]
+
+ * Proof steps:
+001. FG = FC [06] & FB = FC [04] ⇒  FB = FG [14]
+002. FG = FC [06] & FB = FC [04] ⇒  F is the circumcenter of \Delta BGC [15]
+003. FB = FG [14] ⇒  ∠FBG = ∠BGF [16]
+004. EG = EC [07] & FG = FC [06] ⇒  GC ⟂ EF [17]
+005. EG = EC [07] & FG = FC [06] (SSS)⇒  ∠GEF = ∠FEC [18]
+006. F is the circumcenter of \Delta BGC [15] & C,B,F are collinear [05] ⇒  BG ⟂ CG [19]
+007. C,B,D are collinear [00] & ∠FBG = ∠BGF [16] & C,B,F are collinear [05] & GC ⟂ EF [17] & BG ⟂ CG [19] ⇒  ∠GBD = ∠GFE [20]
+008. EC = ED [02] & EA = EC [03] ⇒  EA = ED [21]
+009. CD = CA [01] & EA = ED [21] ⇒  AD ⟂ CE [22]
+010. CD = CA [01] & EA = ED [21] (SSS)⇒  ∠ACE = ∠ECD [23]
+011. C,B,F are collinear [05] & FB = FC [04] ⇒  F is midpoint of CB [24]
+012. J,C,H are collinear [12] & JH = JC [13] ⇒  J is midpoint of CH [25]
+013. F is midpoint of CB [24] & J is midpoint of CH [25] ⇒  FJ ∥ BH [26]
+014. BG ⟂ CG [19] & AD ⟂ CE [22] & FJ ∥ BH [26] & B,G,H are collinear [08] ⇒  ∠(CE-AD) = ∠(JF-CG) [27]
+015. EC = ED [02] & EG = EC [07] & EA = EC [03] ⇒  A,C,G,D are concyclic [28]
+016. A,C,G,D are concyclic [28] ⇒  ∠CAD = ∠CGD [29]
+017. A,C,G,D are concyclic [28] ⇒  ∠AGC = ∠ADC [30]
+018. CD = CA [01] ⇒  ∠CAD = ∠ADC [31]
+019. ∠CAD = ∠CGD [29] & ∠CAD = ∠ADC [31] & C,B,D are collinear [00] ⇒  ∠(AD-CB) = ∠CGD [32]
+020. ∠(CE-AD) = ∠(JF-CG) [27] & ∠(AD-CB) = ∠CGD [32] ⇒  ∠(CE-FJ) = ∠(BC-DG) [33]
+021. C,B,D are collinear [00] & ∠GEF = ∠FEC [18] & GC ⟂ EF [17] & BG ⟂ CG [19] & ∠(CE-FJ) = ∠(BC-DG) [33] & FJ ∥ BH [26] & B,G,H are collinear [08] ⇒  ∠GDB = ∠GEF [34]
+022. ∠GBD = ∠GFE [20] & ∠GDB = ∠GEF [34] (Similar Triangles)⇒  BG:FG = BD:FE [35]
+023. BG:FG = BD:FE [35] & FG = FC [06] & BF = CF [04] ⇒  EF:BD = BF:BG [36]
+024. J,C,H are collinear [12] & A,C,H are collinear [09] & C,B,F are collinear [05] & ∠ACE = ∠ECD [23] & C,B,D are collinear [00] ⇒  ∠JCE = ∠ECF [37]
+025. GC ⟂ EF [17] & BG ⟂ CG [19] & FJ ∥ BH [26] & B,G,H are collinear [08] ⇒  FJ ∥ FE [38]
+026. FJ ∥ FE [38] ⇒  J,E,F are collinear [39]
+027. ∠JCE = ∠ECF [37] & J,E,F are collinear [39] ⇒  JE:EF = JC:CF [40]
+028. B,G,H are collinear [08] & CG ⟂ BG [19] ⇒  CG ⟂ GH [41]
+029. CG ⟂ GH [41] & J is midpoint of CH [25] ⇒  CJ = GJ [42]
+030. JE:EF = JC:CF [40] & JG = JC [42] & BF = CF [04] ⇒  JE:EF = JG:BF [43]
+031. J,C,H are collinear [12] & A,C,H are collinear [09] & ∠AGC = ∠ADC [30] & C,B,D are collinear [00] & ∠CAD = ∠ADC [31] ⇒  ∠DAJ = ∠CGA [44]
+032. ∠(CE-AD) = ∠(JF-CG) [27] & ∠DAJ = ∠CGA [44] ⇒  ∠(CE-AJ) = ∠(JF-AG) [45]
+033. J,E,F are collinear [39] & A,C,H are collinear [09] & ∠(CE-AJ) = ∠(JF-AG) [45] & J,C,H are collinear [12] & FJ ∥ BH [26] & B,G,H are collinear [08] & ∠GEF = ∠FEC [18] & GC ⟂ EF [17] & BG ⟂ CG [19] ⇒  ∠GEJ = ∠GAH [46]
+034. C,B,F are collinear [05] & ∠FBG = ∠BGF [16] & FJ ∥ BH [26] & B,G,H are collinear [08] ⇒  ∠GFJ = ∠JFC [47]
+035. FG = FC [06] & ∠GFJ = ∠JFC [47] (SAS)⇒  ∠GJF = ∠FJC [48]
+036. J,E,F are collinear [39] & B,G,H are collinear [08] & A,C,H are collinear [09] & ∠GJF = ∠FJC [48] & J,C,H are collinear [12] & GC ⟂ EF [17] & BG ⟂ CG [19] ⇒  ∠GJE = ∠GHA [49]
+037. ∠GEJ = ∠GAH [46] & ∠GJE = ∠GHA [49] (Similar Triangles)⇒  JG:HG = JE:HA [50]
+038. JE:EF = JG:BF [43] & JG:GH = JE:AH [50] ⇒  BF:GH = EF:AH [51]
+039. EF:BD = BF:BG [36] & EF:AH = BF:GH [51] ⇒  HG:GB = AH:BD [52]
+040. CA = DC [01] & HG:GB = AH:BD [52] ⇒  (HG:GB) * (BD:DC) * (CA:AH) = 1 [53]
+041. B,G,H are collinear [08] & C,B,D are collinear [00] & A,C,H are collinear [09] & A,B,I are collinear [10] & C,G,I are collinear [11] & (HG:GB) * (BD:DC) * (CA:AH) = 1 [53] ⇒  I,H,D are collinear
+
+True
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+
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+C,B,D are collinear [00]
+E,A,D are collinear [01]
+C,A,F are collinear [02]
+B,E,F are collinear [03]
+A,B,G are collinear [04]
+C,E,G are collinear [05]
+HA ∥ BC [06]
+D,G,H are collinear [07]
+I,A,H are collinear [08]
+I,D,F are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. I,A,H are collinear [08] & C,B,D are collinear [00] & AH ∥ BC [06] ⇒  IA ∥ DC [10]
+002. IA ∥ DC [10] & I,D,F are collinear [09] & C,A,F are collinear [02] ⇒  IF:DF = AF:CF [11]
+003. IA ∥ DC [10] & I,D,F are collinear [09] & C,A,F are collinear [02] ⇒  IF:DF = IA:CD [12]
+004. C,B,D are collinear [00] & AH ∥ BC [06] ⇒  AH ∥ BD [13]
+005. AH ∥ BD [13] & A,B,G are collinear [04] & D,G,H are collinear [07] ⇒  AG:BG = AH:BD [14]
+006. C,A,F are collinear [02] & E,A,D are collinear [01] & C,B,D are collinear [00] & B,E,F are collinear [03] (Menelaus)⇒  (CF:AF) * (AE:CB) * (BD:ED) = 1 [15]
+007. A,B,G are collinear [04] & E,A,D are collinear [01] & C,B,D are collinear [00] & C,E,G are collinear [05] (Menelaus)⇒  (BG:AG) * (AE:CB) * (CD:ED) = 1 [16]
+008. IF:DF = AF:CF [11] & IF:DF = IA:CD [12] & AG:BG = AH:BD [14] & (CF:AF) * (AE:CB) * (BD:ED) = 1 [15] & (BG:AG) * (AE:CB) * (CD:ED) = 1 [16] (Ratio chase)⇒  IA = AH
+==========================
+
+Menelaus_a2 v
+a b c = triangle a b c; o = circle o a b c; p = on_line p b c, on_tline p a o a; q = on_line q a c, on_tline q b o b; r = on_line r a b, on_tline r c o c ? coll p q r
+Menelaus_a7 o
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; o = on_bline o a b; m = midpoint m a b; p = on_line p d e, on_circle p o a; q = on_line q d e, on_circle q o a; x = on_line x a b, on_line x d e ? cyclic p q f m
+Menelaus_a9 o
+a b c = triangle a b c; e = midpoint e b c; f = angle_bisector f b a c, on_line f b c; k = on_line k a e, on_pline k f a c; d = on_line d a b, on_line d c k ? cong a d a c
+Menelaus_b2a x
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f; x = on_pline x g b c, on_line x a b; y = on_line y g h, on_line y a c; p = on_line p b y, on_line p c g; q = on_line q c x, on_line q b g ? eqratio m p a b m q a c 
+Menelaus_b2b x
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f; x = on_pline x g b c, on_line x a b; y = on_line y g h, on_line y a c; p = on_line p b y, on_line p c g; q = on_line q c x, on_line q b g ? eqratio m p a b p q b c
+Menelaus_b3 v
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; q = on_line q a c, on_line q b d; e = foot e q a b; f = foot f q b c; g = foot g q c d; h = foot h q d a; p = on_line p e h, on_line p b d ? coll p f g
+Menelaus_b6 v
+a b c = triangle a b c; h = orthocenter h a b c; e = on_line e a b; f = on_line f b c, on_line f e h; d = on_line d a c, on_line d e h; m = on_tline m h e h, on_line m b c; n = on_line n a b, on_line n m h; p = on_line p a c, on_line p m h ? eqratio d e e f p n m n
+Menelaus_b9 v
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; x = on_tline x d b c; i2 = incenter i2 x b c; y = foot y i2 x c; z = foot z i2 x b ? cyclic x y e f
+Menelaus_b9w v
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; x = on_tline x d b c; i2 = incenter i2 x b c; y = foot y i2 x c; z = foot z i2 x b; p = on_line p b c, on_line p e f ? coll p x y
+Menelaus_b10 ?
+a b c = triangle a b c; d = foot d a b c; x e g o1 = excenter2 x e g o1 c a b; y f h o2 = excenter2 y f h o2 b a c; q = on_line q a d, on_line q f h ? coll q e g
+Menelaus_b11 o
+a b c = triangle a b c; o = circle o a b c; p = on_tline p a o a, on_tline p b o b; d = on_line d p c, on_circle d o a; e = on_pline e c p a, on_line e a b; f = on_line f c e, on_line f a d; k = on_line k c d, on_line k a b ? cong e c e f
+Menelaus_b11w o
+a b c = triangle a b c; o = circle o a b c; p = on_tline p a o a, on_tline p b o b; d = on_line d p c, on_circle d o a; e = on_pline e c p a, on_line e a b; f = on_line f c e, on_line f a d; k = on_line k c d, on_line k a b; m = on_line m o p, on_line m a b ? cyclic o m c d
+Menelaus_b12 v
+a b c = triangle a b c; m = midpoint m a b; d = on_line d b c; e = mirror e m d; f = on_line f a b; g = on_line g a c; k = on_line k f e, on_line k g d; v = on_line v f d, on_line v g e; l = on_line l a k, on_line l b c; t = on_line t a v, on_line t b c ? cong d t e l
+Menelaus_b13 v
+x y = segment x y; p = on_line p x y; a = on_circle a x p; b c = tangent b c a y p; d = on_line d a b, on_circle d x a; e = on_line e a c, on_circle e x a; r = on_line r d e, on_line r b c; q = on_line q p r, on_circle q x a ? coll a q y
+Menelaus_b15w v
+a b c = triangle a b c; m = midpoint m b c; i = incenter i a b c; d = on_line d m i, on_line d a c; o = circle o a b c; e = on_line e b i, on_circle e o a; f = on_line f b i, on_line f a c ? eqratio e d e i i c i b
+Menelaus_c3 v
+a b = segment a b; c = on_tline c b a b, on_circle c b a; d = midpoint d b c; e = foot e b a d; f = on_line f b e, on_line f a c; g = midpoint g a f ? cong a g c f
+Menelaus_cDesargues v
+a b c = triangle a b c; d e = segment d e; g = on_line g a d, on_line g b e; f = on_line f g c; l = on_line l a b, on_line l d e; m = on_line m b c, on_line m e f; n = on_line n a c, on_line n d f ? coll l m n
+Menelaus_cNewton x
+a b c = triangle a b c; d = free; e = on_line e a b, on_line e c d; f = on_line f a d, on_line f b c; g = midpoint g a c; h = midpoint h b d; i = midpoint i e f; j = midpoint j c e; k = midpoint k b c; l = midpoint l b e ? coll g h i
+Menelaus_cPappus v
+a b = segment; c = on_line c a b; d e = segment; f = on_line f d e; g = on_line g a e, on_line g b d; h = on_line h a f, on_line h c d; i = on_line i b f, on_line p c e ? coll g h i
+Menelaus_c22 v
+a b c = triangle a b c; d = on_line d a b; f = on_line f a c; e = mirror e d f; p = on_line p a d, on_line p b e; m = on_line m a b, on_line m d f; n = on_line n p c, on_line n d f ? cong d m d n
+Menelaus_c32 v
+a b c = triangle a b c; i = incenter i a b c; d = on_line d a i, on_line d b c; e = on_line e b i, on_line e c a; f = on_tline f c c i, on_line f a b ? coll d e f
+Ceva_c2 v
+a b c = triangle a b c; d = midpoint d b c; e = on_line e a d; f = on_line f a b, on_line f e c; g = on_line g a c, on_line g e b ? perp f g b c
+Ceva_c3 v
+a b c = triangle a b c; o = circle o a b c; d = on_tline d b o b, on_tline d c o c; e = on_tline e a o a, on_tline e c o c; f = on_tline f a o a, on_tline f b o b; g = on_line g a d, on_line g b e ? coll g c f
+Ceva_c5 v
+a b c = triangle a b c; d = angle_bisector d b a c, on_line d b c; e = on_line e a d, on_tline e b a d; m = midpoint m b c; n = on_line n a m, on_line n b e ? perp d n a B
+Ceva_c22 o
+a b d = triangle a b d; c = angle_bisector c b a d; e = on_line e c d; f = on_line f b e, on_line f a c; g = on_line g d f, on_line g b c; h = on_line h a c, on_line h b d ? eqangle a g a c a c a e
+Ceva_c32 v
+a b c = triangle a b c; d = on_line d b c; e = angle_bisector e a d c, on_line e a c; f = angle_bisector f a d b, on_line f a b; g = on_line g b e, on_line g c f ? coll g a d
+Ceva_b2 v
+c d = segment c d; o = midpoint o c d; a = on_line a c d, on_tline a d o d; b = on_line b c d, on_tline b c o c; e = on_line e a c, on_line e b d; r = on_line r a d, on_line r b c; h = foot h r a b ? coll r e h
+
+
+==========================
+ * From theorem premises:
+A B C D E F : Points
+D,B,C are collinear [00]
+D,E,A are collinear [01]
+C,F,A are collinear [02]
+B,E,F are collinear [03]
+
+ * Auxiliary Constructions:
+G H I : Points
+G,C,E are collinear [04]
+G,B,A are collinear [05]
+G,H,D are collinear [06]
+HA ∥ BC [07]
+D,F,I are collinear [08]
+H,I,A are collinear [09]
+
+ * Proof steps:
+001. C,F,A are collinear [02] & D,E,A are collinear [01] & D,B,C are collinear [00] & B,E,F are collinear [03] (Menelaus)⇒  (CF:FA) * (EA:BC) * (BD:DE) = 1 [10]
+002. D,B,C are collinear [00] & C,F,A are collinear [02] & D,E,A are collinear [01] & G,C,E are collinear [04] & G,B,A are collinear [05] & (CF:FA) * (EA:BC) * (BD:DE) = 1 [10] (Ceva)⇒  G,D,F are collinear [11]
+003. B,C,D are collinear [00] & C,F,A are collinear [02] & G,D,F are collinear [11] & G,H,D are collinear [06] & D,F,I are collinear [08] & H,I,A are collinear [09] & AH ∥ BC [07] ⇒  ∠ACD = ∠AFD
+==========================
+
+
+==========================
+ * From theorem premises:
+A B C G D E F H I J L : Points
+∠GAB = ∠CAG [00]
+∠GCA = ∠BCG [01]
+D,B,C are collinear [02]
+DG ⟂ BC [03]
+C,A,E are collinear [04]
+EG ⟂ AC [05]
+B,F,A are collinear [06]
+FG ⟂ AB [07]
+BC ⟂ HD [08]
+HI = HD [09]
+CI = CD [10]
+HJ = HD [11]
+BJ = BD [12]
+B,C,L are collinear [13]
+F,L,E are collinear [14]
+
+ * Auxiliary Constructions:
+K : Points
+K,C,I are collinear [15]
+K,J,B are collinear [16]
+
+ * Proof steps:
+001. HI = HD [09] & HJ = HD [11] ⇒  HJ = HI [17]
+002. HJ = HD [11] & BJ = BD [12] (SSS)⇒  ∠HJB = ∠BDH [18]
+003. K,J,B are collinear [16] & ∠HJB = ∠BDH [18] & D,B,C are collinear [02] & BC ⟂ HD [08] & DG ⟂ BC [03] ⇒  JH ⟂ KJ [19]
+004. HI = HD [09] & CI = CD [10] (SSS)⇒  ∠HDC = ∠CIH [20]
+005. K,C,I are collinear [15] & ∠HDC = ∠CIH [20] & BC ⟂ HD [08] & DG ⟂ BC [03] & D,B,C are collinear [02] ⇒  HI ⟂ IK [21]
+006. HJ = HI [17] & JH ⟂ KJ [19] & HI ⟂ IK [21] (Circle Power)⇒  KI = JK [22]
+007. B,C,L are collinear [13] & B,F,A are collinear [06] & C,A,E are collinear [04] & F,L,E are collinear [14] (Menelaus)⇒  (AE:FA) * (BF:LB) * (CL:EC) = 1 [23]
+008. B,F,A are collinear [06] & C,A,E are collinear [04] & EG ⟂ AC [05] & FG ⟂ AB [07] ⇒  ∠GFA = ∠AEG [24]
+009. B,F,A are collinear [06] & C,A,E are collinear [04] & ∠GAB = ∠CAG [00] ⇒  ∠GAF = ∠EAG [25]
+010. ∠GFA = ∠AEG [24] & ∠GAF = ∠EAG [25] (Similar Triangles)⇒  AF = AE [26]
+
+
+Circle_a2
+b c = segment b c; a = on_bline a b c; i = incenter i a b c; o = on_bline o b i; p = on_circle p a b, on_circle p o b; q = on_circle q i b, on_circle q o b; r = on_line r i p, on_line r b q ? perp b r c r
+Circle_a5
+a b c = triangle a b c; d e f x = excenter2 d e f x a b c; o1 = circle o1 a e f; p = on_line p b c, on_circle p o1 a; q = on_line q b c, on_circle q o1 a; m = midpoint m a d; o2 = circle o2 m p q; t = on_circle t o2 m, on_circle t x d ? coll o2 x t
+Circle_a6
+a b c = triangle a b c; o = circle o a b c; h = orthocenter h a b c; s = on_circle s o a; p = on_line p b c, on_tline p s a s; o2 = circle o2 a s p; x = on_line x s h, on_circle x o2 a; r = on_line r a b, on_line r o p; q = on_line q a c, on_line q o p; y = foot y q a r; z = foot z r a q ? coll x y z
+Circle_a8
+a b c = triangle a b c; o = circle o a b c; d = on_line d a o, on_line d b c; u = foot u d a c; v = foot v d a b; e = on_tline e a a o, on_line e d u; f = on_tline f a a o, on_line f d v; p = on_line p e c, on_line p f b ? perp p d b c
+Circle_b2
+a b c = segment a b c; d = foot d a b c; e = foot e b c a; f = foot f c a b; h = on_line h a d, on_line h b e; p = on_line p b e, on_line p d f; q = on_line q a b, on_tline q p b c; n = on_line n e q, on_line n a d ? cong a n a h
+Circle_b4
+a b c = triangle a b c; o = circle o a b c; i = circle i o b c; g = on_circle g i o; x = circle x a b g; y = circle y a c g; e = on_line e a c, on_circle e x a; f = on_line f a b, on_circle f y a; k = on_line k b e, on_line k c f; t = on_line t a k, on_line t b c ? coll t o g
+Circle_b5
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a d, on_line e b c; m = midpoint m a d; n = midpoint n b c; w = circle w e m n; x = on_circle x o a, on_circle x w e; y = on_circle y o a, on_circle y w e; z = on_line z a b, on_line z c d ? coll x y z
+Circle_b7w
+a b c = triangle a b c; d e f i = incenter2 d e f i a b c; p = on_line p a d, on_circle p i d; q = on_line q e f, on_tline q p a d; x = on_line x d e, on_line x a q; y = on_line y d f, on_line y a q; u = on_line u d i, on_pline u a b c; v = on_line v d i, on_circle v i d ? cong a x a y
+Circle_b13
+a b c = triangle a b c; d = foot d a b c; e = foot e b c a; m = midpoint a b; o = circle o a b c; f = on_line f d e, on_circle f o a; k = on_line k d e, on_circle k o a; w = circle w m d e; p = on_line p m k, on_circle p w m; q = on_line q m f, on_circle q w m ? cyclic a p q b
+Circle_b15
+a b = segment a b; o = on_bline o a b; p = on_tline p a o a, on_tline p b o b; c = on_circle c o a; d = on_line d p c, on_circle d o a; e = on_pline e c p b, on_circle e o a; f = on_line f a e, on_line f p b; g = on_line g d e, on_line g p b ? cong g f g b
+Circle_c2
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a b, on_line e c d; f = on_line f b c, on_pline f e a d; m = midpoint m o f; g = on_circle g o a, on_circle g m f ? cong f e f g
+Circle_c3
+a b c = triangle a b c; d = angle_bisector d b a c, on_line d b c; m = midpoint m b c; o = circle o a d m; l = on_line l a b, on_circle l o a; n = on_line n a c, on_circle n o a ? cong b l c n
+Pascal_a1
+a b c = triangle a b c; o = circle o a b c; p = free; a1 = on_line a1 a p, on_circle a1 o a; b1 = on_line b1 b p, on_circle b1 o b; c1 = on_line c1 c p, on_circle c1 o c; q = on_circle q o a; x = on_line x q a1, on_line x b c; y = on_line y q b1, on_line y a c; z = on_line z q c1, on_line z a b ? coll x y z
+Pascal_b2
+a c = segment a c; o = midpoint o a c; m = on_line m a d, on_line m b c; n = on_tline n b o b, on_tline o d o d ? perp a c m n
\ No newline at end of file
diff --git a/numericals.py b/numericals.py
index e9c092d..63ac926 100644
--- a/numericals.py
+++ b/numericals.py
@@ -27,7 +27,7 @@
 from numpy.random import uniform as unif  # pylint: disable=g-importing-member
 
 
-matplotlib.use('TkAgg')
+matplotlib.use('Agg')
 
 
 ATOM = 1e-12
@@ -401,7 +401,6 @@ def __init__(
         self.center = self.radius = self.r2 = None
         return
         # raise ValueError('Circle without center need p1 p2 p3')
-
       l12 = _perpendicular_bisector(p1, p2)
       l23 = _perpendicular_bisector(p2, p3)
       center = line_line_intersection(l12, l23)
@@ -679,6 +678,20 @@ def check_sameside(points: list[Point]) -> bool:
   yz = y - z
   return ba.dot(bc) * yx.dot(yz) > 0
 
+def check_onseg(points: list[Point]) -> bool:
+  b, a, c = points
+  # whether b(on line ac) is on segment ac 
+  ba = b - a
+  bc = b - c
+  return ba.dot(bc) < 0
+
+def check_offseg(points: list[Point]) -> bool:
+  b, a, c = points
+  # whether b(on line ac) is not on segment ac 
+  ba = b - a
+  bc = b - c
+  return ba.dot(bc) > 0
+
 
 def check_para_or_coll(points: list[Point]) -> bool:
   return check_para(points) or check_coll(points)
@@ -702,7 +715,8 @@ def check_perp(points: list[Point]) -> bool:
 
 def check_cyclic(points: list[Point]) -> bool:
   points = list(set(points))
-  (a, b, c), *ps = points
+  # fixed bug
+  (a, b, c, *ps) = points
   circle = Circle(p1=a, p2=b, p3=c)
   for d in ps:
     if not close_enough(d.distance(circle.center), circle.radius):
@@ -794,6 +808,16 @@ def check_eqratio(points: list[Point]) -> bool:
   gh = g.distance(h)
   return close_enough(ab * gh, cd * ef)
 
+def check_eqratio30(points: list[Point]) -> bool:
+  a, b, c, d, e, f, g, h, x, y, z, w = points
+  ab = a.distance(b)
+  cd = c.distance(d)
+  ef = e.distance(f)
+  gh = g.distance(h)
+  xy = x.distance(y)
+  zw = z.distance(w)
+  return close_enough(ab * ef * xy, cd * gh * zw)
+
 
 def check_cong(points: list[Point]) -> bool:
   a, b, c, d = points
diff --git a/output_new/Desargues.txt b/output_new/Desargues.txt
new file mode 100644
index 0000000..23218da
--- /dev/null
+++ b/output_new/Desargues.txt
@@ -0,0 +1,26 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J : Points
+D,F,A are collinear [00]
+B,F,E are collinear [01]
+F,C,G are collinear [02]
+B,H,A are collinear [03]
+D,H,E are collinear [04]
+B,I,C are collinear [05]
+I,E,G are collinear [06]
+J,C,A are collinear [07]
+D,J,G are collinear [08]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. B,H,A are collinear [03] & D,F,A are collinear [00] & B,F,E are collinear [01] & D,H,E are collinear [04] (Menelaus)⇒  (BH:HA) * (DA:BE) * (FE:DF) = 1 [09]
+002. B,I,C are collinear [05] & B,F,E are collinear [01] & F,C,G are collinear [02] & I,E,G are collinear [06] (Menelaus)⇒  (IC:BI) * (BE:CG) * (FG:FE) = 1 [10]
+003. (BH:HA) * (DA:BE) * (FE:DF) = 1 [09] & (IC:BI) * (BE:CG) * (FG:FE) = 1 [10] (Ratio chase)⇒  (DA:HA) * (FG:BI) * (BH:CG) * (IC:DF) = 1 [11]
+004. J,C,A are collinear [07] & D,F,A are collinear [00] & F,C,G are collinear [02] & D,J,G are collinear [08] (Menelaus)⇒  (CJ:JA) * (DA:CG) * (FG:DF) = 1 [12]
+005. (DA:HA) * (FG:BI) * (BH:CG) * (IC:DF) = 1 [11] & (CJ:JA) * (DA:CG) * (FG:DF) = 1 [12] ⇒  (CJ:JA) * (AH:HB) * (BI:IC) = 1 [13]
+006. J,C,A are collinear [07] & B,H,A are collinear [03] & B,I,C are collinear [05] & (CJ:JA) * (AH:HB) * (BI:IC) = 1 [13] (Menelaus)⇒  I,H,J are collinear
+==========================
diff --git a/output_new/Newton.txt b/output_new/Newton.txt
new file mode 100644
index 0000000..e2d0d79
--- /dev/null
+++ b/output_new/Newton.txt
@@ -0,0 +1,68 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+D,E,C are collinear [00]
+B,A,E are collinear [01]
+B,F,C are collinear [02]
+D,A,F are collinear [03]
+A,C,G are collinear [04]
+GA = GC [05]
+B,D,H are collinear [06]
+HB = HD [07]
+F,I,E are collinear [08]
+IE = IF [09]
+
+ * Auxiliary Constructions:
+J K L : Points
+J,E,C are collinear [10]
+JC = JE [11]
+B,K,C are collinear [12]
+KB = KC [13]
+B,E,L are collinear [14]
+LB = LE [15]
+
+ * Proof steps:
+001. B,K,C are collinear [12] & KB = KC [13] ⇒  K is midpoint of BC [16]
+002. B,D,H are collinear [06] & HB = HD [07] ⇒  H is midpoint of BD [17]
+003. K is midpoint of BC [16] & H is midpoint of BD [17] ⇒  KH ∥ CD [18]
+004. L,B,E are collinear [14] & LB = LE [15] ⇒  L is midpoint of BE [19]
+005. L is midpoint of BE [19] & K is midpoint of BC [16] ⇒  LK ∥ EC [20]
+006. HK ∥ CD [18] & LK ∥ EC [20] & D,E,C are collinear [00] ⇒  KL ∥ KH [21]
+007. KL ∥ KH [21] ⇒  K,H,L are collinear [22]
+008. F,I,E are collinear [08] & IE = IF [09] ⇒  I is midpoint of EF [23]
+009. L is midpoint of BE [19] & I is midpoint of EF [23] ⇒  LI ∥ BF [24]
+010. J,E,C are collinear [10] & JC = JE [11] ⇒  J is midpoint of EC [25]
+011. L is midpoint of BE [19] & J is midpoint of EC [25] ⇒  LJ ∥ BC [26]
+012. LI ∥ BF [24] & B,F,C are collinear [02] & JL ∥ BC [26] ⇒  LJ ∥ LI [27]
+013. LJ ∥ LI [27] ⇒  I,J,L are collinear [28]
+014. A,C,G are collinear [04] & GA = GC [05] ⇒  G is midpoint of CA [29]
+015. K is midpoint of BC [16] & G is midpoint of CA [29] ⇒  KG ∥ BA [30]
+016. J is midpoint of EC [25] & G is midpoint of CA [29] ⇒  JG ∥ EA [31]
+017. GK ∥ AB [30] & JG ∥ EA [31] & B,A,E are collinear [01] ⇒  GJ ∥ GK [32]
+018. GJ ∥ GK [32] ⇒  J,K,G are collinear [33]
+019. J is midpoint of EC [25] & H is midpoint of BD [17] ⇒  JE:EC = HB:BD [34]
+020. JE:EC = HB:BD [34] & HB = HD [07] ⇒  JE:EC = DH:BD [35]
+021. K is midpoint of BC [16] & I is midpoint of EF [23] ⇒  KB:BC = IF:FE [36]
+022. KB:BC = IF:FE [36] & KB = KC [13] ⇒  KC:BC = FI:FE [37]
+023. G is midpoint of CA [29] & H is midpoint of BD [17] ⇒  GA:AC = HB:BD [38]
+024. GA:AC = HB:BD [38] & GA = GC [05] & HB = HD [07] ⇒  CG:AC = DH:BD [39]
+025. G is midpoint of CA [29] & I is midpoint of EF [23] ⇒  GA:AC = IF:FE [40]
+026. GA:AC = IF:FE [40] & GA = GC [05] ⇒  CG:AC = FI:FE [41]
+027. IL ∥ FB [24] & F,I,E are collinear [08] & B,L,E are collinear [14] ⇒  EI:EF = IL:FB [42]
+028. EI:EF = IL:FB [42] & IE = IF [09] ⇒  FI:FE = IL:BF [43]
+029. J is midpoint of EC [25] & I is midpoint of EF [23] ⇒  JI ∥ CF [44]
+030. FC ∥ IJ [44] & F,I,E are collinear [08] & C,J,E are collinear [10] ⇒  EF:EI = FC:IJ [45]
+031. EF:EI = FC:IJ [45] & IE = IF [09] ⇒  FE:FI = FC:IJ [46]
+032. JG ∥ EA [31] & C,J,E are collinear [10] & A,C,G are collinear [04] ⇒  CJ:CE = JG:EA [47]
+033. CJ:CE = JG:EA [47] & JC = JE [11] ⇒  JE:EC = JG:AE [48]
+034. GK ∥ AB [30] & B,K,C are collinear [12] & A,C,G are collinear [04] ⇒  BC:KC = BA:KG [49]
+035. JC = JE [11] & KB = KC [13] & JE:EC = DH:BD [35] & KC:BC = FI:FE [37] & CG:AC = DH:BD [39] & CG:AC = FI:FE [41] & FI:FE = IL:BF [43] & FE:FI = FC:IJ [46] & JE:EC = JG:AE [48] & BC:KC = BA:KG [49] (Ratio chase)⇒  (BA:AE) * (FC:BF) * (JG:KG) * (IL:IJ) = 1 [50]
+036. B,F,C are collinear [02] & B,A,E are collinear [01] & D,E,C are collinear [00] & D,A,F are collinear [03] (Menelaus)⇒  (DC:DE) * (AE:BA) * (BF:FC) = 1 [51]
+037. HK ∥ CD [18] & B,D,H are collinear [06] & B,K,C are collinear [12] ⇒  BH:HK = BD:DC [52]
+038. L is midpoint of BE [19] & H is midpoint of BD [17] ⇒  LH ∥ ED [53]
+039. HL ∥ DE [53] & B,D,H are collinear [06] & B,L,E are collinear [14] ⇒  BH:HL = BD:DE [54]
+040. BD:DC = BH:KH [52] & BD:DE = BH:HL [54] ⇒  KH:HL = DC:DE [55]
+041. (BA:AE) * (FC:BF) * (JG:KG) * (IL:IJ) = 1 [50] & (DC:DE) * (AE:BA) * (BF:FC) = 1 [51] & KH:HL = DC:DE [55] ⇒  (KH:HL) * (LI:IJ) * (JG:GK) = 1 [56]
+042. K,H,L are collinear [22] & I,J,L are collinear [28] & J,K,G are collinear [33] & (KH:HL) * (LI:IJ) * (JG:GK) = 1 [56] (Menelaus)⇒  I,H,G are collinear
+==========================
diff --git a/output_new/Pappus.txt b/output_new/Pappus.txt
new file mode 100644
index 0000000..710d39d
--- /dev/null
+++ b/output_new/Pappus.txt
@@ -0,0 +1,48 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+A,E,C are collinear [00]
+D,B,F are collinear [01]
+A,G,B are collinear [02]
+G,D,E are collinear [03]
+H,B,C are collinear [04]
+E,H,F are collinear [05]
+D,I,C are collinear [06]
+A,I,F are collinear [07]
+
+ * Auxiliary Constructions:
+J K L : Points
+E,F,J are collinear [08]
+D,J,C are collinear [09]
+A,K,B are collinear [10]
+E,K,F are collinear [11]
+D,L,C are collinear [12]
+A,L,B are collinear [13]
+
+ * Proof steps:
+001. L,D,C are collinear [12] & D,I,C are collinear [06] ⇒  D,L,I are collinear [14]
+002. D,L,C are collinear [12] & D,L,I are collinear [14] ⇒  C,I,L are collinear [15]
+003. A,L,B are collinear [13] & A,G,B are collinear [02] ⇒  A,L,G are collinear [16]
+004. A,L,B are collinear [13] & A,L,G are collinear [16] ⇒  L,G,B are collinear [17]
+005. G,D,E are collinear [03] & A,E,C are collinear [00] & A,L,G are collinear [16] & L,D,C are collinear [12] (Menelaus)⇒  (GD:DE) * (AL:AC) * (EC:LG) = 1 [18]
+006. G,D,E are collinear [03] & A,E,C are collinear [00] & A,L,G are collinear [16] & L,D,C are collinear [12] (Menelaus)⇒  (LD:LC) * (AC:AE) * (GE:GD) = 1 [19]
+007. E,H,F are collinear [05] & E,K,F are collinear [11] ⇒  E,K,H are collinear [20]
+008. H,B,C are collinear [04] & A,E,C are collinear [00] & A,K,B are collinear [10] & E,K,H are collinear [20] (Menelaus)⇒  (HB:HC) * (AK:AE) * (EC:KB) = 1 [21]
+009. E,F,J are collinear [08] & E,K,F are collinear [11] ⇒  K,J,E are collinear [22]
+010. A,L,B are collinear [13] & A,K,B are collinear [10] ⇒  A,L,K are collinear [23]
+011. D,L,C are collinear [12] & D,J,C are collinear [09] ⇒  C,L,J are collinear [24]
+012. K,J,E are collinear [22] & A,E,C are collinear [00] & A,L,K are collinear [23] & C,L,J are collinear [24] (Menelaus)⇒  (JK:EJ) * (AL:AC) * (EC:LK) = 1 [25]
+013. K,J,E are collinear [22] & A,E,C are collinear [00] & A,L,K are collinear [23] & C,L,J are collinear [24] (Menelaus)⇒  (LJ:JC) * (AK:AE) * (EC:LK) = 1 [26]
+014. K,J,E are collinear [22] & A,E,C are collinear [00] & A,L,K are collinear [23] & C,L,J are collinear [24] (Menelaus)⇒  (LJ:LC) * (AC:AE) * (EK:JK) = 1 [27]
+015. D,I,C are collinear [06] & D,J,C are collinear [09] ⇒  J,I,C are collinear [28]
+016. J,I,C are collinear [28] & A,E,C are collinear [00] & E,F,J are collinear [08] & A,I,F are collinear [07] (Menelaus)⇒  (IJ:IC) * (AC:AE) * (EF:JF) = 1 [29]
+017. J,I,C are collinear [28] & A,E,C are collinear [00] & E,F,J are collinear [08] & A,I,F are collinear [07] (Menelaus)⇒  (IF:AI) * (AC:EC) * (EJ:JF) = 1 [30]
+018. J,I,C are collinear [28] & A,E,C are collinear [00] & E,F,J are collinear [08] & A,I,F are collinear [07] (Menelaus)⇒  (IF:AF) * (AE:EC) * (JC:IJ) = 1 [31]
+019. A,G,B are collinear [02] & A,K,B are collinear [10] ⇒  B,K,G are collinear [32]
+020. G,D,E are collinear [03] & D,B,F are collinear [01] & B,K,G are collinear [32] & E,K,F are collinear [11] (Menelaus)⇒  (GE:DE) * (KB:BF) * (DF:GK) = 1 [33]
+021. G,D,E are collinear [03] & D,B,F are collinear [01] & B,K,G are collinear [32] & E,K,F are collinear [11] (Menelaus)⇒  (EK:EF) * (GB:DB) * (DF:GK) = 1 [34]
+022. A,I,F are collinear [07] & D,B,F are collinear [01] & L,I,D are collinear [14] & A,L,B are collinear [13] (Menelaus)⇒  (AI:AF) * (BF:DB) * (LD:LI) = 1 [35]
+023. (GD:DE) * (AL:AC) * (EC:LG) = 1 [18] & (HB:HC) * (AK:AE) * (EC:KB) = 1 [21] & (JK:EJ) * (AL:AC) * (EC:LK) = 1 [25] & (LJ:JC) * (AK:AE) * (EC:LK) = 1 [26] & (LD:LC) * (AC:AE) * (GE:GD) = 1 [19] & (LJ:LC) * (AC:AE) * (EK:JK) = 1 [27] & (IJ:IC) * (AC:AE) * (EF:JF) = 1 [29] & (IF:AI) * (AC:EC) * (EJ:JF) = 1 [30] & (IF:AF) * (AE:EC) * (JC:IJ) = 1 [31] & (GE:DE) * (KB:BF) * (DF:GK) = 1 [33] & (EK:EF) * (GB:DB) * (DF:GK) = 1 [34] & (AI:AF) * (BF:DB) * (LD:LI) = 1 [35] (Ratio chase)⇒  (LG:GB) * (HB:HC) * (IC:LI) = 1 [36]
+024. C,I,L are collinear [15] & L,G,B are collinear [17] & H,B,C are collinear [04] & (LG:GB) * (HB:HC) * (IC:LI) = 1 [36] (Menelaus)⇒  G,H,I are collinear
+==========================
diff --git a/output_new/ceva_a1.txt b/output_new/ceva_a1.txt
new file mode 100644
index 0000000..30dec97
--- /dev/null
+++ b/output_new/ceva_a1.txt
@@ -0,0 +1,31 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+C,B,D are collinear [00]
+E,A,D are collinear [01]
+C,A,F are collinear [02]
+B,E,F are collinear [03]
+A,B,G are collinear [04]
+C,E,G are collinear [05]
+HA ∥ BC [06]
+D,G,H are collinear [07]
+I,A,H are collinear [08]
+I,D,F are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. I,A,H are collinear [08] & C,B,D are collinear [00] & AH ∥ BC [06] ⇒  IA ∥ DC [10]
+002. IA ∥ DC [10] & I,D,F are collinear [09] & C,A,F are collinear [02] ⇒  IF:DF = AF:CF [11]
+003. IA ∥ DC [10] & I,D,F are collinear [09] & C,A,F are collinear [02] ⇒  IF:DF = IA:CD [12]
+004. C,B,D are collinear [00] & AH ∥ BC [06] ⇒  AH ∥ BD [13]
+005. AH ∥ BD [13] & A,B,G are collinear [04] & D,G,H are collinear [07] ⇒  AG:BG = AH:BD [14]
+006. C,A,F are collinear [02] & E,A,D are collinear [01] & C,B,D are collinear [00] & B,E,F are collinear [03] (Menelaus)⇒  (CF:AF) * (AE:CB) * (BD:ED) = 1 [15]
+007. A,B,G are collinear [04] & E,A,D are collinear [01] & C,B,D are collinear [00] & C,E,G are collinear [05] (Menelaus)⇒  (BG:AG) * (AE:CB) * (CD:ED) = 1 [16]
+008. IF:DF = AF:CF [11] & IF:DF = IA:CD [12] & AG:BG = AH:BD [14] & (CF:AF) * (AE:CB) * (BD:ED) = 1 [15] & (BG:AG) * (AE:CB) * (CD:ED) = 1 [16] (Ratio chase)⇒  IA = AH
+==========================
+
+
diff --git a/output_new/ceva_a4.txt b/output_new/ceva_a4.txt
new file mode 100644
index 0000000..e69de29
diff --git a/output_new/ceva_a7.txt b/output_new/ceva_a7.txt
new file mode 100644
index 0000000..e27a0c3
--- /dev/null
+++ b/output_new/ceva_a7.txt
@@ -0,0 +1,51 @@
+3 [171.88209223747253, 3241.3160371780396, 25048.504298210144]
+solved
+('eqratio30', 'a', 'b', 'a', 'j', 'c', 'i', 'b', 'i', 'e', 'j', 'c', 'e')
+<problem.Dependency object at 0x7f8048e1e020>
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J : Points
+DA = DB [00]
+DB = DC [01]
+DE = DA [02]
+B,A,F are collinear [03]
+E,C,F are collinear [04]
+E,G,A are collinear [05]
+G,C,B are collinear [06]
+DH = DA [07]
+DI = DA [08]
+I,F,H are collinear [09]
+DJ = DA [10]
+G,H,J are collinear [11]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. E,G,A are collinear [05] & B,A,F are collinear [03] & E,C,F are collinear [04] & G,C,B are collinear [06] (Menelaus)⇒  (EG:GA) * (BA:FB) * (CF:EC) = 1 [12]
+002. E,G,A are collinear [05] & B,A,F are collinear [03] & E,C,F are collinear [04] & G,C,B are collinear [06] (Menelaus)⇒  (GC:GB) * (BA:FA) * (EF:EC) = 1 [13]
+003. DE = DA [02] & DJ = DA [10] & DA = DB [00] & DB = DC [01] & DH = DA [07] ⇒  E,A,H,J are concyclic [14]
+004. E,A,H,J are concyclic [14] & E,G,A are collinear [05] & G,H,J are collinear [11] (Circle Power)⇒  EG:GH = GJ:GA [15]
+005. E,A,H,J are concyclic [14] ⇒  ∠EAJ = ∠EHJ [16]
+006. E,A,H,J are concyclic [14] ⇒  ∠EAH = ∠EJH [17]
+007. E,G,A are collinear [05] & G,H,J are collinear [11] & ∠EAJ = ∠EHJ [16] ⇒  ∠GEH = ∠AJG [18]
+008. G,E,A are collinear [05] & ∠EAJ = ∠EHJ [16] & G,H,J are collinear [11] ⇒  ∠GHE = ∠JAG [19]
+009. ∠GEH = ∠AJG [18] & ∠GHE = ∠JAG [19] (Similar Triangles)⇒  EG:EH = GJ:AJ [20]
+010. E,G,A are collinear [05] & ∠EAH = ∠EJH [17] & G,H,J are collinear [11] ⇒  ∠GEJ = ∠AHG [21]
+011. G,H,J are collinear [11] & G,E,A are collinear [05] & ∠EAH = ∠EJH [17] ⇒  ∠GJE = ∠HAG [22]
+012. ∠GEJ = ∠AHG [21] & ∠GJE = ∠HAG [22] (Similar Triangles)⇒  EG:EJ = GH:HA [23]
+013. DE = DA [02] & DI = DA [08] & DA = DB [00] & DB = DC [01] & DH = DA [07] ⇒  A,H,I,B are concyclic [24]
+014. A,H,I,B are concyclic [24] ⇒  ∠AHI = ∠ABI [25]
+015. A,F,B are collinear [03] & ∠AHI = ∠ABI [25] & I,F,H are collinear [09] ⇒  ∠FBI = ∠AHF [26]
+016. I,H,F are collinear [09] & B,F,A are collinear [03] & ∠AHI = ∠ABI [25] ⇒  ∠FIB = ∠HAF [27]
+017. ∠FBI = ∠AHF [26] & ∠FIB = ∠HAF [27] (Similar Triangles)⇒  FB:IB = FH:HA [28]
+018. DE = DA [02] & DI = DA [08] & DA = DB [00] & DB = DC [01] & DH = DA [07] ⇒  E,C,H,I are concyclic [29]
+019. E,C,H,I are concyclic [29] ⇒  ∠ECI = ∠EHI [30]
+020. I,H,F are collinear [09] & E,C,F are collinear [04] & ∠ECI = ∠EHI [30] ⇒  ∠CIF = ∠FEH [31]
+021. E,C,F are collinear [04] & I,F,H are collinear [09] ⇒  ∠CFI = ∠EFH [32]
+022. ∠CIF = ∠FEH [31] & ∠CFI = ∠EFH [32] (Similar Triangles)⇒  CI:CF = EH:FH [33]
+023. (EG:GA) * (BA:FB) * (CF:EC) = 1 [12] & (GC:GB) * (BA:FA) * (EF:EC) = 1 [13] & EG:GH = GJ:GA [15] & EG:EH = GJ:AJ [20] & EG:EJ = GH:HA [23] & FB:IB = FH:HA [28] & CI:CF = EH:FH [33] (Ratio chase)⇒  (FA:AJ) * (GB:IB) * (CI:GC) * (EJ:EF) = 1 [34]
+024. (FA:AJ) * (GB:IB) * (CI:GC) * (EJ:EF) = 1 [34] & (EC:BA) * (FA:GC) * (GB:EF) = 1 [13] ⇒  (AJ:JE) * (EC:IC) * (BI:BA) = 1
+==========================
\ No newline at end of file
diff --git a/output_new/ceva_b2.txt b/output_new/ceva_b2.txt
new file mode 100644
index 0000000..6c05b9b
--- /dev/null
+++ b/output_new/ceva_b2.txt
@@ -0,0 +1,34 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H : Points
+CA = CB [00]
+BD ⟂ BC [01]
+AE ⟂ AC [02]
+C,E,D are collinear [03]
+B,F,E are collinear [04]
+A,F,D are collinear [05]
+A,G,E are collinear [06]
+B,G,D are collinear [07]
+H,E,D are collinear [08]
+HG ⟂ DE [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. A,G,E are collinear [06] & AC ⟂ AE [02] ⇒  AC ⟂ AG [10]
+002. B,G,D are collinear [07] & BC ⟂ BD [01] ⇒  BC ⟂ BG [11]
+003. CA = CB [00] & AC ⟂ AG [10] & BC ⟂ BG [11] (Circle Power)⇒  GA = BG [12]
+004. H,E,D are collinear [08] & C,E,D are collinear [03] & HG ⟂ DE [09] & AE ⟂ AC [02] ⇒  ∠CAE = ∠EHG [13]
+005. C,E,D are collinear [03] & H,E,D are collinear [08] & A,G,E are collinear [06] ⇒  ∠CEA = ∠HEG [14]
+006. ∠CAE = ∠EHG [13] & ∠CEA = ∠HEG [14] (Similar Triangles)⇒  AC:AE = HG:HE [15]
+007. H,E,D are collinear [08] & C,E,D are collinear [03] & HG ⟂ DE [09] & BD ⟂ BC [01] ⇒  ∠CBD = ∠DHG [16]
+008. H,E,D are collinear [08] & C,E,D are collinear [03] & B,G,D are collinear [07] ⇒  ∠CDB = ∠HDG [17]
+009. ∠CBD = ∠DHG [16] & ∠CDB = ∠HDG [17] (Similar Triangles)⇒  BC:BD = HG:HD [18]
+010. HG:HD = BC:BD [18] & AC = BC [00] ⇒  HG:HD = AC:BD [19]
+011. HG:HE = AC:AE [15] & HG:HD = AC:BD [19] ⇒  EH:AE = HD:DB [20]
+012. GA = BG [12] & EH:AE = HD:DB [20] ⇒  (GA:AE) * (EH:HD) * (DB:BG) = 1 [21]
+013. A,G,E are collinear [06] & E,H,D are collinear [08] & B,G,D are collinear [07] & B,F,E are collinear [04] & A,F,D are collinear [05] & (GA:AE) * (EH:HD) * (DB:BG) = 1 [21] (Ceva)⇒  H,G,F are collinear
+==========================
diff --git a/output_new/ceva_c2.txt b/output_new/ceva_c2.txt
new file mode 100644
index 0000000..e0c6ccd
--- /dev/null
+++ b/output_new/ceva_c2.txt
@@ -0,0 +1,21 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+D,B,C are collinear [00]
+DB = DC [01]
+D,A,E are collinear [02]
+A,B,F are collinear [03]
+E,F,C are collinear [04]
+A,G,C are collinear [05]
+G,B,E are collinear [06]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. A,G,C are collinear [05] & D,B,C are collinear [00] & A,B,F are collinear [03] & E,F,C are collinear [04] & G,B,E are collinear [06] & D,A,E are collinear [02] (Ceva)⇒  (CD:DB) * (AG:GC) * (BF:FA) = 1 [07]
+002. (CD:DB) * (AG:GC) * (BF:FA) = 1 [07] & DB = DC [01] ⇒  AG:GC = FA:BF [08]
+003. AG:GC = FA:BF [08] & A,G,C are collinear [05] & A,B,F are collinear [03] ⇒  GF ∥ CB
+==========================
diff --git a/output_new/ceva_c3.txt b/output_new/ceva_c3.txt
new file mode 100644
index 0000000..1cab7f3
--- /dev/null
+++ b/output_new/ceva_c3.txt
@@ -0,0 +1,30 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H : Points
+DA = DB [00]
+DB = DC [01]
+BE ⟂ BD [02]
+CE ⟂ CD [03]
+DC ⟂ FC [04]
+AF ⟂ AD [05]
+DB ⟂ GB [06]
+DA ⟂ GA [07]
+A,H,E are collinear [08]
+B,H,F are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. DB ⟂ GB [06] & BE ⟂ BD [02] ⇒  B,G,E are collinear [10]
+002. DC ⟂ FC [04] & CE ⟂ CD [03] ⇒  E,F,C are collinear [11]
+003. DA ⟂ GA [07] & AF ⟂ AD [05] ⇒  A,F,G are collinear [12]
+004. DA = DB [00] & DA ⟂ AG [07] & BG ⟂ DB [06] (Circle Power)⇒  GB = AG [13]
+005. DB = DC [01] & CE ⟂ CD [03] & BE ⟂ BD [02] (Circle Power)⇒  EC = BE [14]
+006. DB = DC [01] & DA = DB [00] ⇒  DA = DC [15]
+007. DA = DC [15] & AF ⟂ AD [05] & DC ⟂ CF [04] (Circle Power)⇒  CF = FA [16]
+008. GB = AG [13] & EC = BE [14] & CF = FA [16] ⇒  (GB:BE) * (EC:CF) * (FA:AG) = 1 [17]
+009. B,G,E are collinear [10] & E,F,C are collinear [11] & A,F,G are collinear [12] & A,H,E are collinear [08] & B,H,F are collinear [09] & (GB:BE) * (EC:CF) * (FA:AG) = 1 [17] (Ceva)⇒  G,H,C are collinear
+==========================
diff --git a/output_new/ceva_c32.txt b/output_new/ceva_c32.txt
new file mode 100644
index 0000000..9f05a4f
--- /dev/null
+++ b/output_new/ceva_c32.txt
@@ -0,0 +1,22 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+C,B,D are collinear [00]
+C,A,E are collinear [01]
+∠ADE = ∠EDC [02]
+B,F,A are collinear [03]
+∠ADF = ∠FDB [04]
+G,B,E are collinear [05]
+G,F,C are collinear [06]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. ∠CDE = ∠EDA [02] & C,A,E are collinear [01] ⇒  CE:AE = CD:DA [07]
+002. ∠BDF = ∠FDA [04] & B,F,A are collinear [03] ⇒  FB:FA = DB:DA [08]
+003. CE:AE = CD:DA [07] & FB:FA = DB:DA [08] (Ratio chase)⇒  (AE:FA) * (FB:DB) * (CD:CE) = 1 [09]
+004. B,F,A are collinear [03] & C,B,D are collinear [00] & C,A,E are collinear [01] & G,B,E are collinear [05] & G,F,C are collinear [06] & (AE:FA) * (FB:DB) * (CD:CE) = 1 [09] (Ceva)⇒  G,D,A are collinear
+==========================
diff --git a/output_new/ceva_c5.txt b/output_new/ceva_c5.txt
new file mode 100644
index 0000000..0bc5460
--- /dev/null
+++ b/output_new/ceva_c5.txt
@@ -0,0 +1,33 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+C,D,B are collinear [00]
+∠DAB = ∠CAD [01]
+E,D,A are collinear [02]
+BE ⟂ AD [03]
+C,B,F are collinear [04]
+FB = FC [05]
+G,A,F are collinear [06]
+G,E,B are collinear [07]
+
+ * Auxiliary Constructions:
+H : Points
+B,H,A are collinear [08]
+HB = HA [09]
+
+ * Proof steps:
+001. C,B,F are collinear [04] & C,D,B are collinear [00] ⇒  D,F,B are collinear [10]
+002. E,D,A are collinear [02] & AD ⟂ BE [03] ⇒  AE ⟂ EB [11]
+003. B,H,A are collinear [08] & HB = HA [09] ⇒  H is midpoint of BA [12]
+004. AE ⟂ EB [11] & H is midpoint of BA [12] ⇒  AH = EH [13]
+005. AH = EH [13] ⇒  ∠HAE = ∠AEH [14]
+006. C,B,F are collinear [04] & FB = FC [05] ⇒  F is midpoint of BC [15]
+007. H is midpoint of BA [12] & F is midpoint of BC [15] ⇒  HF ∥ AC [16]
+008. E,D,A are collinear [02] & ∠HAE = ∠AEH [14] & B,H,A are collinear [08] & ∠DAB = ∠CAD [01] & AC ∥ FH [16] ⇒  ∠(HF-ED) = ∠HED [17]
+009. ∠(HF-ED) = ∠HED [17] ⇒  HF ∥ EH [18]
+010. FH ∥ EH [18] ⇒  E,H,F are collinear [19]
+011. G,A,F are collinear [06] & B,H,A are collinear [08] & D,F,B are collinear [10] & E,D,A are collinear [02] & G,E,B are collinear [07] & E,H,F are collinear [19] (Ceva)⇒  (AH:HB) * (FG:GA) * (BD:DF) = 1 [20]
+012. (AH:HB) * (FG:GA) * (BD:DF) = 1 [20] & HB = HA [09] ⇒  FG:GA = DF:BD [21]
+013. FG:GA = DF:BD [21] & G,A,F are collinear [06] & D,F,B are collinear [10] ⇒  GD ∥ AB
+==========================
diff --git a/output_new/circle_b4.txt b/output_new/circle_b4.txt
new file mode 100644
index 0000000..0aed604
--- /dev/null
+++ b/output_new/circle_b4.txt
@@ -0,0 +1,100 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L : Points
+DA = DB [00]
+DB = DC [01]
+ED = EB [02]
+EB = EC [03]
+EF = ED [04]
+GA = GB [05]
+GB = GF [06]
+HA = HC [07]
+HC = HF [08]
+GI = GA [09]
+A,C,I are collinear [10]
+HJ = HA [11]
+A,B,J are collinear [12]
+B,I,K are collinear [13]
+C,K,J are collinear [14]
+B,L,C are collinear [15]
+A,K,L are collinear [16]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. HA = HC [07] & HJ = HA [11] & HC = HF [08] ⇒  A,F,C,J are concyclic [17]
+002. A,F,C,J are concyclic [17] ⇒  ∠FAC = ∠FJC [18]
+003. A,F,C,J are concyclic [17] ⇒  ∠ACF = ∠AJF [19]
+004. A,F,C,J are concyclic [17] ⇒  ∠AFC = ∠AJC [20]
+005. A,F,C,J are concyclic [17] ⇒  ∠AFJ = ∠ACJ [21]
+006. ED = EB [02] & EF = ED [04] & EB = EC [03] ⇒  F,D,B,C are concyclic [22]
+007. F,D,B,C are concyclic [22] ⇒  ∠FDB = ∠FCB [23]
+008. F,D,B,C are concyclic [22] ⇒  ∠FBD = ∠FCD [24]
+009. F,D,B,C are concyclic [22] ⇒  ∠CFD = ∠CBD [25]
+010. F,D,B,C are concyclic [22] ⇒  ∠DFB = ∠DCB [26]
+011. ∠ACF = ∠AJF [19] & A,B,J are collinear [12] ⇒  ∠ACF = ∠(AB-FJ) [27]
+012. DA = DB [00] ⇒  ∠DAB = ∠ABD [28]
+013. DB = DC [01] & DA = DB [00] ⇒  DA = DC [29]
+014. DA = DC [29] ⇒  ∠DAC = ∠ACD [30]
+015. DB = DC [01] ⇒  ∠DBC = ∠BCD [31]
+016. ∠FDB = ∠FCB [23] & ∠ACF = ∠(AB-FJ) [27] & ∠DAB = ∠ABD [28] & ∠DAC = ∠ACD [30] & ∠DBC = ∠BCD [31] (Angle chase)⇒  DF ⟂ FJ [32]
+017. GA = GB [05] & GI = GA [09] & GB = GF [06] ⇒  A,F,B,I are concyclic [33]
+018. GA = GB [05] & GI = GA [09] & GB = GF [06] ⇒  GI = GF [34]
+019. A,F,B,I are concyclic [33] ⇒  ∠ABF = ∠AIF [35]
+020. A,F,B,I are concyclic [33] ⇒  ∠FAB = ∠FIB [36]
+021. A,F,B,I are concyclic [33] ⇒  ∠AFB = ∠AIB [37]
+022. ∠ABF = ∠AIF [35] & A,C,I are collinear [10] ⇒  ∠ABF = ∠(AC-FI) [38]
+023. ∠ABF = ∠AIF [35] & A,C,I are collinear [10] ⇒  ∠BAC = ∠BFI [39]
+024. ∠FBD = ∠FCD [24] & ∠FDB = ∠FCB [23] & ∠ABF = ∠(AC-FI) [38] & ∠DAB = ∠ABD [28] & ∠DAC = ∠ACD [30] & ∠DBC = ∠BCD [31] (Angle chase)⇒  DF ⟂ FI [40]
+025. C,K,J are collinear [14] & ∠FJC = ∠FAC [18] & DF ⟂ FJ [32] & DF ⟂ FI [40] ⇒  ∠(FI-CK) = ∠FAC [41]
+026. ∠(FI-CK) = ∠FAC [41] & ∠FAB = ∠FIB [36] ⇒  ∠(CK-BI) = ∠CAB [42]
+027. I,K,B are collinear [13] & K,J,C are collinear [14] & ∠(CK-BI) = ∠CAB [42] ⇒  ∠BKC = ∠BAC [43]
+028. ∠BKC = ∠BAC [43] ⇒  A,B,K,C are concyclic [44]
+029. B,L,C are collinear [15] & ∠FCB = ∠FDB [23] ⇒  ∠(FC-BL) = ∠FDB [45]
+030. ∠CFD = ∠CBD [25] & ∠CBD = ∠DCB [31] & ∠DFB = ∠DCB [26] ⇒  ∠DFB = ∠CFD [46]
+031. ∠(FC-BL) = ∠FDB [45] & ∠DFB = ∠CFD [46] ⇒  ∠(BL-FD) = ∠DBF [47]
+032. ∠AFB = ∠AIB [37] & A,C,I are collinear [10] ⇒  ∠AFB = ∠(AC-BI) [48]
+033. ∠AFC = ∠AJC [20] & A,B,J are collinear [12] ⇒  ∠AFC = ∠(AB-CJ) [49]
+034. GI = GA [09] & GA = GB [05] ⇒  GB = GI [50]
+035. GB = GI [50] ⇒  ∠GBI = ∠BIG [51]
+036. GB = GF [06] ⇒  ∠GBF = ∠BFG [52]
+037. GI = GF [34] ⇒  ∠GIF = ∠IFG [53]
+038. ∠FBD = ∠FCD [24] & ∠ABF = ∠(AC-FI) [38] & ∠AFB = ∠(AC-BI) [48] & ∠AFC = ∠(AB-CJ) [49] & ∠DAB = ∠ABD [28] & ∠DAC = ∠ACD [30] & ∠GBI = ∠BIG [51] & ∠GBF = ∠BFG [52] & ∠GIF = ∠IFG [53] (Angle chase)⇒  CJ ⟂ GI [54]
+039. C,K,J are collinear [14] & DF ⟂ FI [40] & CJ ⟂ GI [54] ⇒  ∠(IG-CK) = ∠DFI [55]
+040. C,K,J are collinear [14] & ∠ACJ = ∠AFJ [21] ⇒  ∠ACK = ∠AFJ [56]
+041. ∠AFB = ∠(AC-BI) [48] & ∠ACK = ∠AFJ [56] ⇒  ∠(BI-CK) = ∠BFJ [57]
+042. C,K,J are collinear [14] & ∠(BI-CK) = ∠BFJ [57] & DF ⟂ FJ [32] & DF ⟂ FI [40] ⇒  ∠(BI-CK) = ∠BFI [58]
+043. ∠(IG-CK) = ∠DFI [55] & ∠(BI-CK) = ∠BFI [58] ⇒  ∠GIB = ∠DFB [59]
+044. B,L,C are collinear [15] & ∠(BL-FD) = ∠DBF [47] & ∠GIB = ∠DFB [59] & ∠IBG = ∠GIB [51] ⇒  ∠IBG = ∠LBD [60]
+045. DA = DB [00] & GA = GB [05] (SSS)⇒  ∠(AD-BG) = ∠(AG-BD) [61]
+046. DA = DB [00] & GA = GB [05] ⇒  AB ⟂ DG [62]
+047. ∠IBG = ∠LBD [60] & ∠(AD-BG) = ∠(AG-BD) [61] ⇒  ∠(BI-AD) = ∠(BL-AG) [63]
+048. A,B,K,C are concyclic [44] ⇒  ∠AKB = ∠ACB [64]
+049. ∠(BI-AD) = ∠(BL-AG) [63] & B,L,C are collinear [15] & ∠AKB = ∠ACB [64] & B,I,K are collinear [13] ⇒  ∠CAK = ∠GAD [65]
+050. GI = GA [09] ⇒  ∠GIA = ∠IAG [66]
+051. ∠GIA = ∠IAG [66] & A,C,I are collinear [10] ⇒  ∠(GI-AC) = ∠CAG [67]
+052. DA = DC [29] & HA = HC [07] ⇒  AC ⟂ DH [68]
+053. AC ⟂ DH [68] & DF ⟂ FI [40] ⇒  ∠DFI = ∠(AC-DH) [69]
+054. EF = ED [04] & ED = EB [02] ⇒  EB = EF [70]
+055. EB = EF [70] & GB = GF [06] ⇒  BF ⟂ EG [71]
+056. BF ⟂ EG [71] & AB ⟂ DG [62] ⇒  ∠(DG-AB) = ∠(EG-FB) [72]
+057. BF ⟂ EG [71] & AB ⟂ DG [62] ⇒  ∠DGE = ∠ABF [73]
+058. ∠(DG-AB) = ∠(EG-FB) [72] & ∠BAC = ∠BFI [39] ⇒  ∠(DG-AC) = ∠(EG-FI) [74]
+059. AB ⟂ DG [62] & AC ⟂ DH [68] ⇒  ∠(DG-AC) = ∠(AB-DH) [75]
+060. ∠(DG-AC) = ∠(EG-FI) [74] & ∠(DG-AC) = ∠(AB-DH) [75] ⇒  ∠(AB-DH) = ∠(EG-FI) [76]
+061. ∠DFI = ∠(AC-DH) [69] & ∠(AB-DH) = ∠(EG-FI) [76] ⇒  ∠(AC-DF) = ∠(AB-EG) [77]
+062. C,K,J are collinear [14] & AB ⟂ DG [62] & CJ ⟂ GI [54] ⇒  ∠(IG-CK) = ∠(AB-DG) [78]
+063. I,B,K are collinear [13] & K,J,C are collinear [14] & ∠FAC = ∠FJC [18] & ∠AFB = ∠AIB [37] & A,C,I are collinear [10] ⇒  ∠FBK = ∠FJK [79]
+064. ∠FBK = ∠FJK [79] ⇒  F,B,K,J are concyclic [80]
+065. F,B,K,J are concyclic [80] ⇒  ∠FBJ = ∠FKJ [81]
+066. C,K,J are collinear [14] & ∠DGE = ∠ABF [73] & ∠FBJ = ∠FKJ [81] & A,B,J are collinear [12] ⇒  ∠CKF = ∠DGE [82]
+067. ∠(IG-CK) = ∠(AB-DG) [78] & ∠CKF = ∠DGE [82] ⇒  ∠(GI-FK) = ∠(AB-EG) [83]
+068. ∠(AC-DF) = ∠(AB-EG) [77] & ∠(GI-FK) = ∠(AB-EG) [83] ⇒  ∠(IG-FK) = ∠(AC-FD) [84]
+069. ∠(GI-AC) = ∠CAG [67] & ∠(IG-FK) = ∠(AC-FD) [84] ⇒  ∠(AC-FK) = ∠(AG-DF) [85]
+070. ∠CAK = ∠GAD [65] & ∠(AC-FK) = ∠(AG-DF) [85] ⇒  ∠KAD = ∠KFD [86]
+071. ∠KAD = ∠KFD [86] ⇒  A,F,D,K are concyclic [87]
+072. A,B,K,C are concyclic [44] & A,F,D,K are concyclic [87] & F,D,B,C are concyclic [22] & A,K,L are collinear [16] & B,L,C are collinear [15] (Radical Axis) ⇒  F,D,L are collinear
+==========================
diff --git a/output_new/circle_c2.txt b/output_new/circle_c2.txt
new file mode 100644
index 0000000..9f59fe4
--- /dev/null
+++ b/output_new/circle_c2.txt
@@ -0,0 +1,33 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+DA = DB [00]
+DB = DC [01]
+DE = DA [02]
+E,F,C are collinear [03]
+B,F,A are collinear [04]
+B,G,C are collinear [05]
+GF ∥ AE [06]
+HD = HG [07]
+D,H,G are collinear [08]
+DI = DA [09]
+HI = HG [10]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. DA = DB [00] & DE = DA [02] & DB = DC [01] ⇒  E,B,A,C are concyclic [11]
+002. E,B,A,C are concyclic [11] ⇒  ∠BCE = ∠BAE [12]
+003. E,B,A,C are concyclic [11] ⇒  ∠ABC = ∠AEC [13]
+004. B,G,C are collinear [05] & E,F,C are collinear [03] & B,F,A are collinear [04] & ∠BCE = ∠BAE [12] & AE ∥ FG [06] ⇒  ∠GCF = ∠BFG [14]
+005. E,F,C are collinear [03] & B,F,A are collinear [04] & B,G,C are collinear [05] & ∠AEC = ∠ABC [13] & AE ∥ FG [06] ⇒  ∠GFC = ∠FBG [15]
+006. ∠GCF = ∠BFG [14] & ∠GFC = ∠FBG [15] (Similar Triangles)⇒  GC:FG = FG:BG [16]
+007. DI = DA [09] & DA = DB [00] & DB = DC [01] ⇒  D is the circumcenter of \Delta IBC [17]
+008. HI = HG [10] & HD = HG [07] ⇒  H is the circumcenter of \Delta DIG [18]
+009. H is the circumcenter of \Delta DIG [18] & D,H,G are collinear [08] ⇒  DI ⟂ GI [19]
+010. D is the circumcenter of \Delta IBC [17] & DI ⟂ GI [19] & B,G,C are collinear [05] (Circle Power)⇒  IG:BG = GC:IG [20]
+011. GC:FG = FG:BG [16] & IG:BG = GC:IG [20] (Ratio chase)⇒  FG = IG
+==========================
diff --git a/output_new/cricle_c3.txt b/output_new/cricle_c3.txt
new file mode 100644
index 0000000..d17d776
--- /dev/null
+++ b/output_new/cricle_c3.txt
@@ -0,0 +1,31 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H : Points
+B,D,C are collinear [00]
+∠BAD = ∠DAC [01]
+B,E,C are collinear [02]
+EB = EC [03]
+FD = FE [04]
+FA = FD [05]
+FG = FA [06]
+B,G,A are collinear [07]
+FH = FA [08]
+H,C,A are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. FD = FE [04] & FA = FD [05] & FG = FA [06] ⇒  E,D,G,A are concyclic [10]
+002. B,D,C are collinear [00] & B,E,C are collinear [02] ⇒  B,D,E are collinear [11]
+003. B,D,C are collinear [00] & B,E,C are collinear [02] ⇒  C,D,E are collinear [12]
+004. E,D,G,A are concyclic [10] & B,D,E are collinear [11] & B,G,A are collinear [07] (Circle Power)⇒  BD:BA = BG:BE [13]
+005. ∠BAD = ∠DAC [01] & B,D,C are collinear [00] ⇒  BD:BA = DC:CA [14]
+006. FD = FE [04] & FA = FD [05] & FH = FA [08] & FG = FA [06] & E,D,G,A are concyclic [10] ⇒  H,E,D,A are concyclic [15]
+007. H,E,D,A are concyclic [15] & C,D,E are collinear [12] & H,C,A are collinear [09] (Circle Power)⇒  DC:CA = CH:EC [16]
+008. BD:BA = BG:BE [13] & EB = EC [03] & BD:BA = DC:CA [14] & DC:CA = CH:EC [16] ⇒  CH:BE = BG:BE [17]
+009. BE = EC [03] ⇒  BE:BA = BE:BA [18]
+010. CH:BE = BG:BE [17] & BE:BA = BE:BA [18] ⇒  CH = BG
+==========================
diff --git a/output_new/exercise7_13.txt b/output_new/exercise7_13.txt
new file mode 100644
index 0000000..921f695
--- /dev/null
+++ b/output_new/exercise7_13.txt
@@ -0,0 +1,54 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L : Points
+C,B,D are collinear [00]
+AD ⟂ BC [01]
+C,E,A are collinear [02]
+BE ⟂ AC [03]
+B,F,A are collinear [04]
+FA = FB [05]
+GA = GB [06]
+GB = GC [07]
+GH = GA [08]
+E,H,D are collinear [09]
+E,I,D are collinear [10]
+∠DFI = ∠DFI [11]
+GI = GA [12]
+JF = JD [13]
+JD = JE [14]
+K,I,F are collinear [15]
+JK = JF [16]
+H,F,L are collinear [17]
+JL = JF [18]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. C,B,D are collinear [00] & AD ⟂ BC [01] ⇒  AD ⟂ DB [19]
+002. B,F,A are collinear [04] & FA = FB [05] ⇒  F is midpoint of BA [20]
+003. AD ⟂ DB [19] & F is midpoint of BA [20] ⇒  AF = DF [21]
+004. C,E,A are collinear [02] & AC ⟂ BE [03] ⇒  AE ⟂ EB [22]
+005. AE ⟂ EB [22] & F is midpoint of BA [20] ⇒  AF = EF [23]
+006. AF = DF [21] & AF = EF [23] ⇒  FE = FD [24]
+007. FE = FD [24] ⇒  ∠DEF = ∠FDE [25]
+008. JF = JD [13] & JK = JF [16] & JD = JE [14] ⇒  K,E,F,D are concyclic [26]
+009. K,E,F,D are concyclic [26] ⇒  ∠KFE = ∠KDE [27]
+010. K,I,F are collinear [15] & E,I,D are collinear [10] & ∠DEF = ∠FDE [25] & ∠KFE = ∠KDE [27] ⇒  ∠DKF = ∠FDI [28]
+011. K,I,F are collinear [15] & ∠DFI = ∠DFI [11] ⇒  ∠DFK = ∠DFI [29]
+012. ∠DKF = ∠FDI [28] & ∠DFK = ∠DFI [29] (Similar Triangles)⇒  FD:FK = FI:FD [30]
+013. FD:FK = FI:FD [30] & EF = DF [24] & AF = DF [21] & FA = FB [05] & FA = EF [23] ⇒  FB:FI = FK:FA [31]
+014. K,I,F are collinear [15] & B,F,A are collinear [04] & FB:FI = FK:FA [31] ⇒  K,B,I,A are concyclic [32]
+015. JF = JD [13] & JL = JF [18] & JD = JE [14] ⇒  E,F,D,L are concyclic [33]
+016. E,F,D,L are concyclic [33] ⇒  ∠LFD = ∠LED [34]
+017. E,H,D are collinear [09] & ∠DEF = ∠FDE [25] & ∠LFD = ∠LED [34] & H,F,L are collinear [17] ⇒  ∠(HF-EL) = ∠HEF [35]
+018. E,D,F,L are concyclic [33] & K,E,F,D are concyclic [26] ⇒  L,K,F,E are concyclic [36]
+019. L,K,F,E are concyclic [36] ⇒  ∠LKF = ∠LEF [37]
+020. K,I,F are collinear [15] & ∠LKF = ∠LEF [37] ⇒  ∠ELK = ∠(EF-KI) [38]
+021. ∠(HF-EL) = ∠HEF [35] & ∠ELK = ∠(EF-KI) [38] ⇒  ∠(HF-KL) = ∠(EH-KI) [39]
+022. H,F,L are collinear [17] & E,I,D are collinear [10] & E,H,D are collinear [09] & K,I,F are collinear [15] & ∠(HF-KL) = ∠(EH-KI) [39] ⇒  ∠LHI = ∠LKI [40]
+023. ∠LHI = ∠LKI [40] ⇒  K,H,I,L are concyclic [41]
+024. K,B,I,A are concyclic [32] & GA = GB [06] & GI = GA [12] & GB = GC [07] & GH = GA [08] & K,H,I,L are concyclic [41] ⇒  A,K,L,B are concyclic
+==========================
diff --git a/output_new/menelaus_a11.txt b/output_new/menelaus_a11.txt
new file mode 100644
index 0000000..8fa3a33
--- /dev/null
+++ b/output_new/menelaus_a11.txt
@@ -0,0 +1,54 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L M N : Points
+D,A,B are collinear [00]
+E,A,C are collinear [01]
+FD = FE [02]
+D,E,F are collinear [03]
+D,E,G are collinear [04]
+G,H,F are collinear [05]
+B,A,I are collinear [06]
+A,J,C are collinear [07]
+G,J,I are collinear [08]
+K,A,B are collinear [09]
+L,A,C are collinear [10]
+K,L,H are collinear [11]
+K,M,J are collinear [12]
+D,E,M are collinear [13]
+D,N,E are collinear [14]
+N,L,I are collinear [15]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. B,A,I are collinear [06] & D,A,B are collinear [00] ⇒  D,I,A are collinear [16]
+002. L,A,C are collinear [10] & E,A,C are collinear [01] ⇒  L,A,E are collinear [17]
+003. D,N,E are collinear [14] & D,I,A are collinear [16] & A,L,E are collinear [17] & N,L,I are collinear [15] (Menelaus)⇒  (DN:NE) * (AI:LA) * (LE:DI) = 1 [18]
+004. A,J,C are collinear [07] & E,A,C are collinear [01] ⇒  A,J,E are collinear [19]
+005. D,E,G are collinear [04] & D,I,A are collinear [16] & A,J,E are collinear [19] & G,J,I are collinear [08] (Menelaus)⇒  (EG:DG) * (AJ:AI) * (DI:EJ) = 1 [20]
+006. D,E,G are collinear [04] & D,I,A are collinear [16] & A,J,E are collinear [19] & G,J,I are collinear [08] (Menelaus)⇒  (GJ:GI) * (EA:DA) * (DI:EJ) = 1 [21]
+007. D,E,G are collinear [04] & D,I,A are collinear [16] & A,J,E are collinear [19] & G,J,I are collinear [08] (Menelaus)⇒  (GJ:JI) * (AI:DA) * (DE:EG) = 1 [22]
+008. D,A,B are collinear [00] & K,A,B are collinear [09] ⇒  K,A,D are collinear [23]
+009. K,M,J are collinear [12] & D,K,A are collinear [23] & A,J,E are collinear [19] & D,E,M are collinear [13] (Menelaus)⇒  (MJ:KM) * (EA:DA) * (KD:EJ) = 1 [24]
+010. K,M,J are collinear [12] & D,K,A are collinear [23] & A,J,E are collinear [19] & D,E,M are collinear [13] (Menelaus)⇒  (EM:DM) * (AJ:KA) * (KD:EJ) = 1 [25]
+011. K,A,B are collinear [09] & K,A,D are collinear [23] & A,I,B are collinear [06] ⇒  I,K,D are collinear [26]
+012. D,E,M are collinear [13] & D,E,G are collinear [04] ⇒  D,M,G are collinear [27]
+013. G,J,I are collinear [08] & I,K,D are collinear [26] & D,M,G are collinear [27] & K,M,J are collinear [12] (Menelaus)⇒  (GJ:JI) * (DM:KD) * (KI:GM) = 1 [28]
+014. G,J,I are collinear [08] & I,K,D are collinear [26] & D,M,G are collinear [27] & K,M,J are collinear [12] (Menelaus)⇒  (MJ:KJ) * (DG:DI) * (KI:GM) = 1 [29]
+015. G,J,I are collinear [08] & I,K,D are collinear [26] & D,M,G are collinear [27] & K,M,J are collinear [12] (Menelaus)⇒  (KJ:KM) * (DM:DG) * (GI:JI) = 1 [30]
+016. D,N,E are collinear [14] & G,H,F are collinear [05] & D,E,G are collinear [04] & D,E,F are collinear [03] ⇒  D,N,H are collinear [31]
+017. K,L,H are collinear [11] & I,K,D are collinear [26] & D,N,H are collinear [31] & N,L,I are collinear [15] (Menelaus)⇒  (LH:KL) * (DN:DI) * (KI:NH) = 1 [32]
+018. K,L,H are collinear [11] & I,K,D are collinear [26] & D,N,H are collinear [31] & N,L,I are collinear [15] (Menelaus)⇒  (NL:LI) * (DH:KD) * (KI:NH) = 1 [33]
+019. G,H,F are collinear [05] & D,E,G are collinear [04] & D,E,F are collinear [03] ⇒  D,E,H are collinear [34]
+020. K,L,H are collinear [11] & D,K,A are collinear [23] & D,E,H are collinear [34] & A,L,E are collinear [17] (Menelaus)⇒  (LH:KL) * (KA:DA) * (DE:EH) = 1 [35]
+021. D,N,E are collinear [14] & D,E,G are collinear [04] ⇒  E,N,G are collinear [36]
+022. L,A,C are collinear [10] & L,A,E are collinear [17] & A,J,C are collinear [07] ⇒  J,L,E are collinear [37]
+023. N,L,I are collinear [15] & E,N,G are collinear [36] & G,J,I are collinear [08] & J,L,E are collinear [37] (Menelaus)⇒  (LI:NL) * (NE:EG) * (GJ:JI) = 1 [38]
+024. (NE:DN) * (LA:AI) * (DI:LE) = 1 [18] & (EG:DG) * (AJ:AI) * (DI:EJ) = 1 [20] & (GJ:GI) * (EA:DA) * (DI:EJ) = 1 [21] & (MJ:KM) * (EA:DA) * (KD:EJ) = 1 [24] & (GJ:JI) * (DM:KD) * (KI:GM) = 1 [28] & (GJ:JI) * (AI:DA) * (DE:EG) = 1 [22] & (LH:KL) * (DN:DI) * (KI:NH) = 1 [32] & (LH:KL) * (KA:DA) * (DE:EH) = 1 [35] & (MJ:KJ) * (DG:DI) * (KI:GM) = 1 [29] & (NL:LI) * (DH:KD) * (KI:NH) = 1 [33] & (KJ:KM) * (DM:DG) * (GI:JI) = 1 [30] & (LI:NL) * (NE:EG) * (GJ:JI) = 1 [38] (Ratio chase)⇒  (KA:LA) * (EJ:DI) * (AI:AJ) * (LE:KD) = 1 [39]
+025. (DN:NE) * (AI:LA) * (LE:DI) = 1 [18] & (KA:LA) * (EJ:DI) * (AI:AJ) * (LE:KD) = 1 [39] & (EM:DM) * (AJ:KA) * (KD:EJ) = 1 [25] ⇒  ME:MD = ND:NE [40]
+026. ME:MD = ND:NE [40] & D,E,M are collinear [13] & D,N,E are collinear [14] ⇒  ME = ND [41]
+027. FD = FE [02] & ME = ND [41] (Distance chase)⇒  FN = MF
+==========================
diff --git a/output_new/menelaus_a2.txt b/output_new/menelaus_a2.txt
new file mode 100644
index 0000000..0557f02
--- /dev/null
+++ b/output_new/menelaus_a2.txt
@@ -0,0 +1,39 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+DA = DB [00]
+DB = DC [01]
+C,E,B are collinear [02]
+AE ⟂ AD [03]
+A,C,F are collinear [04]
+BF ⟂ BD [05]
+A,G,B are collinear [06]
+CG ⟂ CD [07]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. DA = DB [00] & DB = DC [01] ⇒  D is the circumcenter of \Delta BAC [08]
+002. D is the circumcenter of \Delta BAC [08] & BF ⟂ BD [05] & A,C,F are collinear [04] (Circle Power)⇒  FB:AF = CF:FB [09]
+003. D is the circumcenter of \Delta BAC [08] & AE ⟂ AD [03] & C,E,B are collinear [02] (Circle Power)⇒  AE:EB = CE:AE [10]
+004. D is the circumcenter of \Delta BAC [08] & CG ⟂ CD [07] & A,G,B are collinear [06] (Circle Power)⇒  CG:GB = AG:CG [11]
+005. D is the circumcenter of \Delta BAC [08] & BF ⟂ BD [05] ⇒  ∠FBA = ∠BCA [12]
+006. D is the circumcenter of \Delta BAC [08] & BF ⟂ BD [05] ⇒  ∠CBF = ∠CAB [13]
+007. A,C,F are collinear [04] & ∠FBA = ∠BCA [12] ⇒  ∠FBA = ∠BCF [14]
+008. A,F,C are collinear [04] & ∠CAB = ∠CBF [13] ⇒  ∠FAB = ∠CBF [15]
+009. ∠FBA = ∠BCF [14] & ∠FAB = ∠CBF [15] (Similar Triangles)⇒  FB:AB = CF:CB [16]
+010. D is the circumcenter of \Delta BAC [08] & AE ⟂ AD [03] ⇒  ∠BAE = ∠BCA [17]
+011. C,E,B are collinear [02] & ∠BAE = ∠BCA [17] ⇒  ∠BAE = ∠ECA [18]
+012. C,E,B are collinear [02] ⇒  ∠BEA = ∠CEA [19]
+013. ∠BAE = ∠ECA [18] & ∠BEA = ∠CEA [19] (Similar Triangles)⇒  AB:EB = AC:AE [20]
+014. D is the circumcenter of \Delta BAC [08] & CG ⟂ CD [07] ⇒  ∠BCG = ∠BAC [21]
+015. D is the circumcenter of \Delta BAC [08] & CG ⟂ CD [07] ⇒  ∠GCA = ∠CBA [22]
+016. A,G,B are collinear [06] & ∠BAC = ∠BCG [21] ⇒  ∠GAC = ∠BCG [23]
+017. A,G,B are collinear [06] & ∠GCA = ∠CBA [22] ⇒  ∠GCA = ∠CBG [24]
+018. ∠GAC = ∠BCG [23] & ∠GCA = ∠CBG [24] (Similar Triangles)⇒  AG:AC = CG:CB [25]
+019. FB:AF = CF:FB [09] & AE:EB = CE:AE [10] & CG:GB = AG:CG [11] & FB:AB = CF:CB [16] & AB:EB = AC:AE [20] & AG:AC = CG:CB [25] (Ratio chase)⇒  (GB:AG) * (AF:EB) * (CE:CF) = 1 [26]
+020. A,G,B are collinear [06] & C,E,B are collinear [02] & A,C,F are collinear [04] & (GB:AG) * (AF:EB) * (CE:CF) = 1 [26] (Menelaus)⇒  F,G,E are collinear
+==========================
diff --git a/output_new/menelaus_b10.txt b/output_new/menelaus_b10.txt
new file mode 100644
index 0000000..46d53d8
--- /dev/null
+++ b/output_new/menelaus_b10.txt
@@ -0,0 +1,151 @@
+==========================
+ * From theorem premises:
+A B C D H F G L J K M : Points
+AD ⟂ BC [00]
+C,D,B are collinear [01]
+∠ACH = ∠HCB [02]
+∠HBC = ∠ABH [03]
+C,B,F are collinear [04]
+BC ⟂ HF [05]
+GH ⟂ AC [06]
+C,A,G are collinear [07]
+∠ABL = ∠LBC [08]
+∠LCB = ∠ACL [09]
+C,B,J are collinear [10]
+CB ⟂ LJ [11]
+K,B,A are collinear [12]
+BA ⟂ LK [13]
+D,A,M are collinear [14]
+K,J,M are collinear [15]
+
+ * Auxiliary Constructions:
+E I : Points
+EH ⟂ AB [16]
+B,E,A are collinear [17]
+C,A,I are collinear [18]
+AC ⟂ LI [19]
+
+ * Proof steps:
+001. C,B,J are collinear [10] & K,A,B are collinear [12] & EH ⟂ AB [16] & AD ⟂ BC [00] & CB ⟂ LJ [11] & BA ⟂ LK [13] ⇒  ∠LJB = ∠BKL [20]
+002. C,B,J are collinear [10] & K,A,B are collinear [12] & ∠LBC = ∠ABL [08] ⇒  ∠LBJ = ∠KBL [21]
+003. ∠LJB = ∠BKL [20] & ∠LBJ = ∠KBL [21] (Similar Triangles)⇒  LJ = LK [22]
+004. ∠LJB = ∠BKL [20] & ∠LBJ = ∠KBL [21] (Similar Triangles)⇒  BK = BJ [23]
+005. C,B,J are collinear [10] & C,A,I are collinear [18] & GH ⟂ AC [06] & AD ⟂ BC [00] & CB ⟂ LJ [11] & AC ⟂ LI [19] ⇒  ∠LJC = ∠CIL [24]
+006. C,B,J are collinear [10] & C,A,I are collinear [18] & ∠LCB = ∠ACL [09] ⇒  ∠LCJ = ∠ICL [25]
+007. ∠LJC = ∠CIL [24] & ∠LCJ = ∠ICL [25] (Similar Triangles)⇒  LJ = LI [26]
+008. ∠LJC = ∠CIL [24] & ∠LCJ = ∠ICL [25] (Similar Triangles)⇒  CJ = CI [27]
+009. LJ = LK [22] & LJ = LI [26] ⇒  L is the circumcenter of \Delta IKJ [28]
+010. LJ = LK [22] & LJ = LI [26] ⇒  LI = LK [29]
+011. C,B,J are collinear [10] & C,B,F are collinear [04] ⇒  C,J,F are collinear [30]
+012. C,B,J are collinear [10] & C,B,F are collinear [04] ⇒  B,J,F are collinear [31]
+013. C,B,F are collinear [04] & C,A,G are collinear [07] & GH ⟂ AC [06] & AD ⟂ BC [00] & BC ⟂ HF [05] ⇒  ∠HFC = ∠CGH [32]
+014. C,B,F are collinear [04] & C,A,G are collinear [07] & ∠HCB = ∠ACH [02] ⇒  ∠HCF = ∠GCH [33]
+015. ∠HFC = ∠CGH [32] & ∠HCF = ∠GCH [33] (Similar Triangles)⇒  HF = HG [34]
+016. ∠HFC = ∠CGH [32] & ∠HCF = ∠GCH [33] (Similar Triangles)⇒  CF = CG [35]
+017. HF = HG [34] & CF = CG [35] ⇒  FG ⟂ CH [36]
+018. C,B,J are collinear [10] & C,B,F are collinear [04] & FG ⟂ CH [36] & AD ⟂ BC [00] & BC ⟂ HF [05] ⇒  ∠HFJ = ∠(FG-CH) [37]
+019. C,B,F are collinear [04] & E,A,B are collinear [17] & EH ⟂ AB [16] & AD ⟂ BC [00] & BC ⟂ HF [05] ⇒  ∠HFB = ∠BEH [38]
+020. C,B,F are collinear [04] & E,A,B are collinear [17] & ∠HBC = ∠ABH [03] ⇒  ∠HBF = ∠EBH [39]
+021. ∠HFB = ∠BEH [38] & ∠HBF = ∠EBH [39] (Similar Triangles)⇒  HF = HE [40]
+022. ∠HFB = ∠BEH [38] & ∠HBF = ∠EBH [39] (Similar Triangles)⇒  BF = BE [41]
+023. HF = HE [40] & HF = HG [34] ⇒  H is the circumcenter of \Delta EFG [42]
+024. HF = HE [40] & HF = HG [34] ⇒  HG = HE [43]
+025. K,A,B are collinear [12] & B,E,A are collinear [17] ⇒  B,K,E are collinear [44]
+026. K,A,B are collinear [12] & B,E,A are collinear [17] & EH ⟂ AB [16] ⇒  HE ⟂ EK [45]
+027. H is the circumcenter of \Delta EFG [42] & HE ⟂ EK [45] ⇒  ∠KEF = ∠EGF [46]
+028. LK = LJ [22] & BF = BE [41] ⇒  LK:LJ = BF:BE [47]
+029. LK = LJ [22] & BF = BE [41] ⇒  LK:LJ = BE:BF [48]
+030. K,A,B are collinear [12] & EH ⟂ AB [16] ⇒  EH ⟂ KB [49]
+031. C,B,J are collinear [10] & C,B,F are collinear [04] & FH ⟂ BC [05] ⇒  HF ⟂ JF [50]
+032. EH ⟂ KB [49] & HF ⟂ JF [50] ⇒  ∠EHF = ∠(KB-JF) [51]
+033. E,A,B are collinear [17] & C,B,F are collinear [04] & ∠EHF = ∠(KB-JF) [51] & K,B,A are collinear [12] & C,B,J are collinear [10] & BC ⟂ HF [05] & AD ⟂ BC [00] & BA ⟂ LK [13] & EH ⟂ AB [16] & CB ⟂ LJ [11] ⇒  ∠KLJ = ∠EBF [52]
+034. LK:LJ = BF:BE [47] & ∠KLJ = ∠EBF [52] (Similar Triangles)⇒  ∠KJL = ∠BEF [53]
+035. LI = LK [29] & HG = HE [43] ⇒  LI:LK = HG:HE [54]
+036. AC ⟂ LI [19] & GH ⟂ AC [06] & BA ⟂ LK [13] & EH ⟂ AB [16] ⇒  ∠ILK = ∠GHE [55]
+037. LI:LK = HG:HE [54] & ∠ILK = ∠GHE [55] (Similar Triangles)⇒  ∠(IL-GH) = ∠(IK-EG) [56]
+038. ∠KEF = ∠EGF [46] & K,A,B are collinear [12] & B,E,A are collinear [17] & ∠KJL = ∠BEF [53] & CB ⟂ LJ [11] & AD ⟂ BC [00] & BC ⟂ HF [05] & ∠(IL-GH) = ∠(IK-EG) [56] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠(HF-KJ) = ∠(FG-KI) [57]
+039. ∠HFJ = ∠(FG-CH) [37] & ∠(HF-KJ) = ∠(FG-KI) [57] ⇒  ∠FJK = ∠(CH-KI) [58]
+040. C,A,I are collinear [18] & C,A,G are collinear [07] ⇒  C,I,G are collinear [59]
+041. CJ = CI [27] & CG = CF [35] ⇒  CJ:CI = CG:CF [60]
+042. C,J,F are collinear [30] & C,I,G are collinear [59] & CJ:CI = CG:CF [60] (Circle Power)⇒  I,J,F,G are concyclic [61]
+043. I,J,F,G are concyclic [61] ⇒  ∠IJF = ∠IGF [62]
+044. CI = CJ [27] & HG = HF [34] ⇒  CI:CJ = HG:HF [63]
+045. LI ⟂ CA [19] & HF ⟂ JF [50] ⇒  ∠(LI-HF) = ∠(CA-JF) [64]
+046. C,A,I are collinear [18] & C,B,J are collinear [10] & ∠(LI-HF) = ∠(CA-JF) [64] & C,B,F are collinear [04] & AC ⟂ LI [19] & GH ⟂ AC [06] & BC ⟂ HF [05] & AD ⟂ BC [00] ⇒  ∠ICJ = ∠GHF [65]
+047. CI:CJ = HG:HF [63] & ∠ICJ = ∠GHF [65] (Similar Triangles)⇒  ∠CIJ = ∠HGF [66]
+048. LI = LJ [26] & CG = CF [35] ⇒  LI:LJ = CG:CF [67]
+049. LI = LJ [26] & CG = CF [35] ⇒  LI:LJ = CF:CG [68]
+050. C,A,G are collinear [07] & C,B,F are collinear [04] & ∠(LI-HF) = ∠(CA-JF) [64] & C,B,J are collinear [10] & AC ⟂ LI [19] & GH ⟂ AC [06] & BC ⟂ HF [05] & AD ⟂ BC [00] & CB ⟂ LJ [11] ⇒  ∠ILJ = ∠GCF [69]
+051. LI:LJ = CG:CF [67] & ∠ILJ = ∠GCF [69] (Similar Triangles)⇒  ∠LIJ = ∠CGF [70]
+052. ∠CIJ = ∠HGF [66] & C,A,I are collinear [18] & ∠LIJ = ∠CGF [70] & C,A,G are collinear [07] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  JI ⟂ FG [71]
+053. FG ⟂ CH [36] & JI ⟂ FG [71] ⇒  CH ∥ JI [72]
+054. LJ = LI [26] & CJ = CI [27] ⇒  IJ ⟂ CL [73]
+055. IJ ⟂ CL [73] & JI ⟂ FG [71] ⇒  CL ∥ FG [74]
+056. C,A,I are collinear [18] & C,B,J are collinear [10] & GH ⟂ AC [06] & AD ⟂ BC [00] & AC ⟂ LI [19] & CB ⟂ LJ [11] ⇒  ∠CIL = ∠CJL [75]
+057. ∠CIL = ∠CJL [75] ⇒  C,L,J,I are concyclic [76]
+058. C,L,J,I are concyclic [76] ⇒  ∠CLJ = ∠CIJ [77]
+059. C,L,J,I are concyclic [76] ⇒  ∠CLI = ∠CJI [78]
+060. ∠FJK = ∠(CH-KI) [58] & C,B,J are collinear [10] & C,B,F are collinear [04] & ∠IJF = ∠IGF [62] & C,A,I are collinear [18] & C,A,G are collinear [07] & CH ∥ IJ [72] & CL ∥ FG [74] & ∠CLJ = ∠CIJ [77] & CB ⟂ LJ [11] & AD ⟂ BC [00] ⇒  ∠LJI = ∠JKI [79]
+061. L is the circumcenter of \Delta IKJ [28] & ∠LJI = ∠JKI [79] ⇒  LJ ⟂ JL [80]
+062. C,B,F are collinear [04] & C,A,I are collinear [18] & ∠(LI-HF) = ∠(CA-JF) [64] & C,B,J are collinear [10] ⇒  ∠CFH = ∠CIL [81]
+063. LI:LJ = CF:CG [68] & ∠ILJ = ∠GCF [69] (Similar Triangles)⇒  ∠IJL = ∠CGF [82]
+064. C,B,F are collinear [04] & C,A,G are collinear [07] & GH ⟂ AC [06] & AD ⟂ BC [00] & BC ⟂ HF [05] ⇒  ∠HFC = ∠HGC [83]
+065. ∠HFC = ∠HGC [83] ⇒  C,H,F,G are concyclic [84]
+066. C,H,F,G are concyclic [84] ⇒  ∠CHF = ∠CGF [85]
+067. C,H,F,G are concyclic [84] ⇒  ∠CHG = ∠CFG [86]
+068. C,A,I are collinear [18] & ∠CLJ = ∠CIJ [77] & CB ⟂ LJ [11] & AD ⟂ BC [00] & ∠IJL = ∠CGF [82] & C,A,G are collinear [07] & ∠CHF = ∠CGF [85] & BC ⟂ HF [05] ⇒  ∠CHF = ∠ICL [87]
+069. ∠CFH = ∠CIL [81] & ∠CHF = ∠ICL [87] (Similar Triangles)⇒  ∠FCH = ∠CLI [88]
+070. ∠FCH = ∠CLI [88] & C,B,F are collinear [04] & AC ⟂ LI [19] & GH ⟂ AC [06] & ∠IJF = ∠IGF [62] & C,B,J are collinear [10] & C,A,I are collinear [18] & C,A,G are collinear [07] & CH ∥ IJ [72] & CL ∥ FG [74] ⇒  ∠ACL = ∠ILC [89]
+071. ∠ACL = ∠ILC [89] ⇒  CA ∥ LI [90]
+072. HF = HE [40] & BF = BE [41] ⇒  EF ⟂ BH [91]
+073. FG ⟂ CH [36] & EF ⟂ BH [91] ⇒  ∠(HB-EF) = ∠(CH-FG) [92]
+074. C,A,G are collinear [07] & GH ⟂ AC [06] ⇒  HG ⟂ GC [93]
+075. H is the circumcenter of \Delta EFG [42] & HG ⟂ GC [93] ⇒  ∠CGE = ∠GFE [94]
+076. ∠CGE = ∠GFE [94] & C,A,G are collinear [07] & ∠(IL-GH) = ∠(IK-EG) [56] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠(EF-KI) = ∠(FG-CA) [95]
+077. ∠(HB-EF) = ∠(CH-FG) [92] & ∠(EF-KI) = ∠(FG-CA) [95] ⇒  ∠(BH-IK) = ∠HCA [96]
+078. HE = HF [40] & BK = BJ [23] ⇒  HE:HF = BK:BJ [97]
+079. K,A,B are collinear [12] & C,B,J are collinear [10] & ∠EHF = ∠(KB-JF) [51] & C,B,F are collinear [04] ⇒  ∠EHF = ∠KBJ [98]
+080. HE:HF = BK:BJ [97] & ∠EHF = ∠KBJ [98] (Similar Triangles)⇒  ∠HEF = ∠BKJ [99]
+081. LK:LJ = BE:BF [48] & ∠KLJ = ∠EBF [52] (Similar Triangles)⇒  ∠LKJ = ∠BEF [100]
+082. ∠HEF = ∠BKJ [99] & K,B,A are collinear [12] & ∠LKJ = ∠BEF [100] & B,E,A are collinear [17] & BA ⟂ LK [13] & EH ⟂ AB [16] ⇒  EF ⟂ KJ [101]
+083. EF ⟂ BH [91] & EF ⟂ KJ [101] ⇒  HB ∥ KJ [102]
+084. ∠(BH-IK) = ∠HCA [96] & BH ∥ JK [102] & ∠IJF = ∠IGF [62] & C,B,J are collinear [10] & C,B,F are collinear [04] & C,A,I are collinear [18] & C,A,G are collinear [07] & CH ∥ IJ [72] & CL ∥ FG [74] & ∠CLI = ∠CJI [78] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠LIJ = ∠IKJ [103]
+085. L is the circumcenter of \Delta IKJ [28] & ∠LIJ = ∠IKJ [103] ⇒  LI ⟂ IL [104]
+086. E,B,A are collinear [17] & EH ⟂ AB [16] ⇒  HE ⟂ EA [105]
+087. C,A,G are collinear [07] & GH ⟂ AC [06] ⇒  HG ⟂ GA [106]
+088. HE = HG [43] & HE ⟂ EA [105] & HG ⟂ GA [106] (Circle Power)⇒  AE = AG [107]
+089. HE = HG [43] & AE = AG [107] ⇒  EG ⟂ HA [108]
+090. ∠ACH = ∠HCB [02] & ∠CHG = ∠CFG [86] & C,B,F are collinear [04] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠(LI-FG) = ∠ACH [109]
+091. C,A,I are collinear [18] & K,B,A are collinear [12] & EH ⟂ AB [16] & GH ⟂ AC [06] & AC ⟂ LI [19] & BA ⟂ LK [13] ⇒  ∠AIL = ∠AKL [110]
+092. ∠AIL = ∠AKL [110] ⇒  K,A,L,I are concyclic [111]
+093. K,A,L,I are concyclic [111] ⇒  ∠KLA = ∠KIA [112]
+094. K,A,L,I are concyclic [111] ⇒  ∠KAL = ∠KIL [113]
+095. LI = LK [29] ⇒  ∠LIK = ∠IKL [114]
+096. ∠KLA = ∠KIA [112] & C,A,I are collinear [18] & BA ⟂ LK [13] & EH ⟂ AB [16] & ∠LIK = ∠IKL [114] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠LIK = ∠CAL [115]
+097. ∠(LI-FG) = ∠ACH [109] & ∠LIK = ∠CAL [115] ⇒  ∠(CH-FG) = ∠(AL-IK) [116]
+098. C,A,I are collinear [18] & IL ⟂ AC [19] ⇒  LI ⟂ IC [117]
+099. L is the circumcenter of \Delta IKJ [28] & LI ⟂ IC [117] ⇒  ∠CIK = ∠IJK [118]
+100. K,A,B are collinear [12] & KL ⟂ AB [13] ⇒  LK ⟂ KB [119]
+101. L is the circumcenter of \Delta IKJ [28] & LK ⟂ KB [119] ⇒  ∠BKI = ∠KJI [120]
+102. ∠CIK = ∠IJK [118] & C,A,I are collinear [18] & ∠BKI = ∠KJI [120] & K,B,A are collinear [12] & ∠KAL = ∠KIL [113] & AC ⟂ LI [19] & GH ⟂ AC [06] ⇒  ∠ILA = ∠(CA-KI) [121]
+103. ∠(LI-FG) = ∠ACH [109] & ∠ILA = ∠(CA-KI) [121] ⇒  ∠(CH-FG) = ∠(IK-AL) [122]
+104. LJ = LK [22] & BJ = BK [23] ⇒  JK ⟂ BL [123]
+105. C,B,J are collinear [10] & C,B,F are collinear [04] & JK ⟂ BL [123] & AD ⟂ BC [00] & BC ⟂ HF [05] ⇒  ∠JFH = ∠(BL-KJ) [124]
+106. ∠CLJ = ∠CIJ [77] & C,A,I are collinear [18] & CB ⟂ LJ [11] & AD ⟂ BC [00] & ∠CIK = ∠IJK [118] & BC ⟂ HF [05] ⇒  ∠JKI = ∠(HF-CL) [125]
+107. ∠JFH = ∠(BL-KJ) [124] & ∠JKI = ∠(HF-CL) [125] ⇒  ∠(JF-CL) = ∠(BL-KI) [126]
+108. EF ⟂ KJ [101] & JK ⟂ BL [123] ⇒  EF ∥ BL [127]
+109. ∠(JF-CL) = ∠(BL-KI) [126] & C,B,J are collinear [10] & C,B,F are collinear [04] & EF ∥ BL [127] & ∠(IL-GH) = ∠(IK-EG) [56] & AC ⟂ LI [19] & GH ⟂ AC [06] & ∠IJF = ∠IGF [62] & C,A,I are collinear [18] & C,A,G are collinear [07] & CH ∥ IJ [72] & CL ∥ FG [74] & ∠CHF = ∠CGF [85] & BC ⟂ HF [05] & AD ⟂ BC [00] ⇒  ∠HFG = ∠FEG [128]
+110. H is the circumcenter of \Delta EFG [42] & ∠HFG = ∠FEG [128] ⇒  HF ⟂ FH [129]
+111. BJ = BK [23] & BE = BF [41] ⇒  BJ:BK = BE:BF [130]
+112. B,J,F are collinear [31] & B,K,E are collinear [44] & BJ:BK = BE:BF [130] (Circle Power)⇒  K,E,J,F are concyclic [131]
+113. K,E,J,F are concyclic [131] ⇒  ∠KEF = ∠KJF [132]
+114. A,D,M are collinear [14] & C,B,J are collinear [10] & C,D,B are collinear [01] & K,A,B are collinear [12] & ∠EHF = ∠(KB-JF) [51] & C,B,F are collinear [04] & BC ⟂ HF [05] & AD ⟂ BC [00] & BA ⟂ LK [13] & EH ⟂ AB [16] ⇒  ∠MDJ = ∠LKB [133]
+115. K,A,B are collinear [12] & C,B,J are collinear [10] & ∠EHF = ∠(KB-JF) [51] & C,B,F are collinear [04] & BC ⟂ HF [05] & AD ⟂ BC [00] & BA ⟂ LK [13] & EH ⟂ AB [16] & CB ⟂ LJ [11] ⇒  ∠BKL = ∠BJL [134]
+116. ∠BKL = ∠BJL [134] ⇒  K,L,B,J are concyclic [135]
+117. K,L,B,J are concyclic [135] ⇒  ∠KLB = ∠KJB [136]
+118. K,J,M are collinear [15] & C,B,J are collinear [10] & C,D,B are collinear [01] & ∠KLB = ∠KJB [136] ⇒  ∠MJD = ∠KLB [137]
+119. ∠MDJ = ∠LKB [133] & ∠MJD = ∠KLB [137] (Similar Triangles)⇒  ∠DMJ = ∠LBK [138]
+120. C,B,J are collinear [10] & C,B,F are collinear [04] & ∠KEF = ∠KJF [132] & K,A,B are collinear [12] & B,E,A are collinear [17] & EF ∥ BL [127] & BH ∥ JK [102] & ∠DMJ = ∠LBK [138] & D,A,M are collinear [14] & K,J,M are collinear [15] & BC ⟂ HF [05] & AD ⟂ BC [00] ⇒  ∠FHB = ∠(JF-HB) [139]
+121. ∠FHB = ∠(JF-HB) [139] ⇒  HF ∥ JF [140]
+122. LJ ⟂ JL [80] & AC ⟂ LI [19] & GH ⟂ AC [06] & AC ∥ IL [90] & LI ⟂ IL [104] & C,A,I are collinear [18] & EG ⟂ HA [108] & ∠(CH-FG) = ∠(AL-IK) [116] & CH ∥ IJ [72] & CL ∥ FG [74] & ∠(CH-FG) = ∠(IK-AL) [122] & ∠(IL-GH) = ∠(IK-EG) [56] & HF ⟂ FH [129] & BC ⟂ HF [05] & AD ⟂ BC [00] & HF ∥ JF [140] & C,B,J are collinear [10] & C,B,F are collinear [04] & CB ⟂ LJ [11] & C,J,F are collinear [30] & D,A,M are collinear [14] & C,D,B are collinear [01] & C,A,G are collinear [07] ⇒  M,F,G are collinear
+==========================
\ No newline at end of file
diff --git a/output_new/menelaus_b12.txt b/output_new/menelaus_b12.txt
new file mode 100644
index 0000000..41339d1
--- /dev/null
+++ b/output_new/menelaus_b12.txt
@@ -0,0 +1,36 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L : Points
+D,C,B are collinear [00]
+C,B,E are collinear [01]
+D,F,E are collinear [02]
+A,B,G are collinear [03]
+A,H,C are collinear [04]
+G,F,I are collinear [05]
+I,H,E are collinear [06]
+G,J,E are collinear [07]
+J,F,H are collinear [08]
+K,A,I are collinear [09]
+K,C,B are collinear [10]
+A,J,L are collinear [11]
+C,B,L are collinear [12]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. K,C,B are collinear [10] & D,F,E are collinear [02] & C,B,E are collinear [01] & D,C,B are collinear [00] ⇒  F,K,B are collinear [13]
+002. K,A,I are collinear [09] & F,K,B are collinear [13] & A,B,G are collinear [03] & G,F,I are collinear [05] (Menelaus)⇒  (AI:KI) * (GB:AG) * (KF:FB) = 1 [14]
+003. C,B,L are collinear [12] & C,B,E are collinear [01] ⇒  E,L,B are collinear [15]
+004. A,J,L are collinear [11] & E,L,B are collinear [15] & A,B,G are collinear [03] & G,J,E are collinear [07] (Menelaus)⇒  (AJ:JL) * (GB:AG) * (LE:BE) = 1 [16]
+005. K,C,B are collinear [10] & C,B,E are collinear [01] ⇒  K,C,E are collinear [17]
+006. K,A,I are collinear [09] & E,K,C are collinear [17] & A,H,C are collinear [04] & I,H,E are collinear [06] (Menelaus)⇒  (AI:KI) * (HC:AH) * (KE:CE) = 1 [18]
+007. C,B,L are collinear [12] & D,F,E are collinear [02] & C,B,E are collinear [01] & D,C,B are collinear [00] ⇒  F,L,C are collinear [19]
+008. A,J,L are collinear [11] & F,L,C are collinear [19] & A,H,C are collinear [04] & J,F,H are collinear [08] (Menelaus)⇒  (AJ:JL) * (HC:AH) * (FL:FC) = 1 [20]
+009. (AI:KI) * (GB:AG) * (KF:FB) = 1 [14] & (AJ:JL) * (GB:AG) * (LE:BE) = 1 [16] & (AI:KI) * (HC:AH) * (KE:CE) = 1 [18] & (AJ:JL) * (HC:AH) * (FL:FC) = 1 [20] (Ratio chase)⇒  KF:KE = LE:FL [21]
+010. D,F,E are collinear [02] & C,B,E are collinear [01] & D,C,B are collinear [00] & C,B,L are collinear [12] ⇒  E,L,F are collinear [22]
+011. D,F,E are collinear [02] & C,B,E are collinear [01] & D,C,B are collinear [00] & K,C,B are collinear [10] & K,C,E are collinear [17] ⇒  F,K,E are collinear [23]
+012. KF:KE = LE:FL [21] & E,L,F are collinear [22] & F,K,E are collinear [23] ⇒  LE = KF
+==========================
diff --git a/output_new/menelaus_b13.txt b/output_new/menelaus_b13.txt
new file mode 100644
index 0000000..c7cf4d0
--- /dev/null
+++ b/output_new/menelaus_b13.txt
@@ -0,0 +1,59 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J : Points
+C,A,B are collinear [00]
+AD = AC [01]
+BE = BC [02]
+DE ⟂ BE [03]
+BF = BC [04]
+DF ⟂ BF [05]
+AG = AD [06]
+E,G,D are collinear [07]
+AH = AD [08]
+H,F,D are collinear [09]
+I,E,F are collinear [10]
+I,H,G are collinear [11]
+AJ = AD [12]
+I,C,J are collinear [13]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. BE = BC [02] & BF = BC [04] ⇒  BF = BE [14]
+002. BF = BE [14] & DF ⟂ BF [05] & DE ⟂ BE [03] (Circle Power)⇒  DF = DE [15]
+003. AD = AC [01] & AJ = AD [12] & AG = AD [06] ⇒  C,G,D,J are concyclic [16]
+004. C,G,D,J are concyclic [16] & AD = AC [01] & AH = AD [08] & AG = AD [06] ⇒  J,C,H,D are concyclic [17]
+005. J,C,H,D are concyclic [17] ⇒  ∠JCH = ∠JDH [18]
+006. ∠JCH = ∠JDH [18] & I,C,J are collinear [13] & H,F,D are collinear [09] ⇒  ∠ICH = ∠JDF [19]
+007. I,E,F are collinear [10] & E,G,D are collinear [07] & H,F,D are collinear [09] & I,H,G are collinear [11] (Menelaus)⇒  (IF:IE) * (HD:GD) * (EG:HF) = 1 [20]
+008. I,E,F are collinear [10] & E,G,D are collinear [07] & H,F,D are collinear [09] & I,H,G are collinear [11] (Menelaus)⇒  (IF:EF) * (ED:GD) * (HG:IH) = 1 [21]
+009. I,E,F are collinear [10] & E,G,D are collinear [07] & H,F,D are collinear [09] & I,H,G are collinear [11] (Menelaus)⇒  (IE:EF) * (FD:HD) * (HG:IG) = 1 [22]
+010. (IF:IE) * (HD:GD) * (EG:HF) = 1 [20] & (IF:EF) * (ED:GD) * (HG:IH) = 1 [21] & (IE:EF) * (FD:HD) * (HG:IG) = 1 [22] (Ratio chase)⇒  EG:IG = HF:IH [23]
+011. C,G,D,J are concyclic [16] ⇒  ∠JCG = ∠JDG [24]
+012. ∠JCG = ∠JDG [24] & I,C,J are collinear [13] & E,G,D are collinear [07] ⇒  ∠ICG = ∠JDE [25]
+013. AD = AC [01] ⇒  ∠ADC = ∠DCA [26]
+014. ∠ADC = ∠DCA [26] & C,A,B are collinear [00] ⇒  ∠ADC = ∠(CD-AB) [27]
+015. AJ = AD [12] ⇒  ∠ADJ = ∠DJA [28]
+016. AJ = AD [12] & AD = AC [01] ⇒  AC = AJ [29]
+017. AC = AJ [29] ⇒  ∠ACJ = ∠CJA [30]
+018. ∠ACJ = ∠CJA [30] & C,A,B are collinear [00] & I,C,J are collinear [13] ⇒  ∠(AB-CI) = ∠(CI-AJ) [31]
+019. BE = BC [02] ⇒  ∠BCE = ∠CEB [32]
+020. ∠BCE = ∠CEB [32] & C,A,B are collinear [00] ⇒  ∠(AB-CE) = ∠CEB [33]
+021. DE ⟂ BE [03] & ∠ICG = ∠JDE [25] & ∠ADC = ∠(CD-AB) [27] & ∠ADJ = ∠DJA [28] & ∠(AB-CI) = ∠(CI-AJ) [31] & ∠(AB-CE) = ∠CEB [33] (Angle chase)⇒  ∠GCE = ∠ECD [34]
+022. ∠GCE = ∠ECD [34] & E,G,D are collinear [07] ⇒  EG:CG = ED:CD [35]
+023. BF = BC [04] ⇒  ∠BFC = ∠FCB [36]
+024. ∠BFC = ∠FCB [36] & C,A,B are collinear [00] ⇒  ∠BFC = ∠(CF-AB) [37]
+025. DF ⟂ BF [05] & ∠ICH = ∠JDF [19] & ∠ADC = ∠(CD-AB) [27] & ∠ADJ = ∠DJA [28] & ∠(AB-CI) = ∠(CI-AJ) [31] & ∠BFC = ∠(CF-AB) [37] (Angle chase)⇒  ∠HCF = ∠FCD [38]
+026. ∠HCF = ∠FCD [38] & H,F,D are collinear [09] ⇒  HF:CH = FD:CD [39]
+027. EG:CG = ED:CD [35] & DF = DE [15] & HF:CH = FD:CD [39] ⇒  HF:CH = EG:CG [40]
+028. EG:IG = HF:IH [23] & HF:CH = EG:CG [40] ⇒  IH:IG = CH:CG [41]
+029. IH:IG = CH:CG [41] & I,H,G are collinear [11] ⇒  ∠ICH = ∠GCI [42]
+030. ∠ICH = ∠JDF [19] & ∠ICH = ∠GCI [42] & ∠GCI = ∠EDJ [25] ⇒  ∠EDJ = ∠JDF [43]
+031. DF = DE [15] & ∠EDJ = ∠JDF [43] (SAS)⇒  JE = JF [44]
+032. BF = BE [14] & JE = JF [44] ⇒  FE ⟂ BJ [45]
+033. BF = BE [14] & DF = DE [15] ⇒  EF ⟂ BD [46]
+034. FE ⟂ BJ [45] & EF ⟂ BD [46] ⇒  J,D,B are collinear
+==========================
diff --git a/output_new/menelaus_b15w.txt b/output_new/menelaus_b15w.txt
new file mode 100644
index 0000000..68bbb41
--- /dev/null
+++ b/output_new/menelaus_b15w.txt
@@ -0,0 +1,48 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H : Points
+B,D,C are collinear [00]
+DB = DC [01]
+∠ACE = ∠ECB [02]
+∠BAE = ∠EAC [03]
+F,A,C are collinear [04]
+F,D,E are collinear [05]
+GB = GC [06]
+GA = GB [07]
+GH = GA [08]
+H,B,E are collinear [09]
+
+ * Auxiliary Constructions:
+I : Points
+A,I,C are collinear [10]
+B,I,E are collinear [11]
+
+ * Proof steps:
+001. GB = GC [06] & GA = GB [07] & GH = GA [08] ⇒  H,B,A,C are concyclic [12]
+002. H,B,A,C are concyclic [12] ⇒  ∠HBA = ∠HCA [13]
+003. ∠HBA = ∠HCA [13] & H,B,E are collinear [09] ⇒  ∠EBA = ∠HCA [14]
+004. A,I,C are collinear [10] & ∠BAE = ∠EAC [03] ⇒  ∠BAE = ∠EAI [15]
+005. ∠BAE = ∠EAI [15] & B,I,E are collinear [11] ⇒  BE:BA = IE:AI [16]
+006. ∠BAE = ∠EAI [15] & B,I,E are collinear [11] ⇒  IE:BE = AI:BA [17]
+007. A,I,C are collinear [10] & ∠BCE = ∠ECA [02] ⇒  ∠BCE = ∠ECI [18]
+008. ∠BCE = ∠ECI [18] & B,I,E are collinear [11] ⇒  BE:BC = IE:IC [19]
+009. BE:BA = IE:AI [16] & BE:BC = IE:IC [19] ⇒  AI:IC = BA:BC [20]
+010. AI:IC = BA:BC [20] & A,I,C are collinear [10] ⇒  ∠ABI = ∠IBC [21]
+011. ∠ABI = ∠IBC [21] & B,I,E are collinear [11] ⇒  ∠ABE = ∠EBC [22]
+012. A,I,C are collinear [10] & B,I,E are collinear [11] & ∠HCA = ∠EBA [14] ⇒  ∠HCI = ∠IBA [23]
+013. B,I,E are collinear [11] & H,B,E are collinear [09] & A,I,C are collinear [10] ⇒  ∠HIC = ∠BIA [24]
+014. ∠HCI = ∠IBA [23] & ∠HIC = ∠BIA [24] (Similar Triangles)⇒  HI:HC = AI:BA [25]
+015. A,I,C are collinear [10] & F,A,C are collinear [04] ⇒  C,I,F are collinear [26]
+016. B,I,E are collinear [11] & B,D,C are collinear [00] & C,I,F are collinear [26] & F,D,E are collinear [05] (Menelaus)⇒  (BD:DC) * (IE:EB) * (CF:FI) = 1 [27]
+017. HI:HC = AI:BA [25] & IE:BE = AI:BA [17] & (BD:DC) * (IE:EB) * (CF:FI) = 1 [27] & DB = DC [01] ⇒  FI:FC = HI:HC [28]
+018. FI:FC = HI:HC [28] & C,I,F are collinear [26] ⇒  ∠IHF = ∠FHC [29]
+019. ∠IHF = ∠FHC [29] & B,I,E are collinear [11] & H,B,E are collinear [09] ⇒  ∠(BE-FH) = ∠FHC [30]
+020. ∠ACE = ∠ECB [02] & ∠EBA = ∠HCA [14] & ∠ABE = ∠EBC [22] & ∠(BE-FH) = ∠FHC [30] (Angle chase)⇒  CE ∥ FH [31]
+021. F,A,C are collinear [04] & ∠ACE = ∠ECB [02] & CE ∥ FH [31] ⇒  ∠CFH = ∠ECB [32]
+022. ∠CHF = ∠(FH-BE) [30] & FH ∥ CE [31] ⇒  ∠CHF = ∠CEB [33]
+023. ∠CFH = ∠ECB [32] & ∠CHF = ∠CEB [33] (Similar Triangles)⇒  FH:HC = EC:BE [34]
+024. H,B,E are collinear [09] & ∠CHF = ∠(FH-BE) [30] & FH ∥ CE [31] ⇒  ∠HCE = ∠CEH [35]
+025. ∠HCE = ∠CEH [35] ⇒  HC = HE [36]
+026. FH:HC = EC:BE [34] & HE = HC [36] ⇒  HF:HE = EC:EB
+==========================
diff --git a/output_new/menelaus_b3.txt b/output_new/menelaus_b3.txt
new file mode 100644
index 0000000..65defdd
--- /dev/null
+++ b/output_new/menelaus_b3.txt
@@ -0,0 +1,54 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K : Points
+DA = DB [00]
+DB = DC [01]
+DE = DA [02]
+C,F,A are collinear [03]
+E,F,B are collinear [04]
+G,B,A are collinear [05]
+FG ⟂ AB [06]
+C,H,B are collinear [07]
+FH ⟂ BC [08]
+C,E,I are collinear [09]
+FI ⟂ CE [10]
+J,E,A are collinear [11]
+FJ ⟂ AE [12]
+K,E,B are collinear [13]
+G,K,J are collinear [14]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. J,E,A are collinear [11] & K,E,B are collinear [13] & G,B,A are collinear [05] & G,K,J are collinear [14] (Menelaus)⇒  (JA:EJ) * (GB:GA) * (KE:KB) = 1 [15]
+002. C,B,H are collinear [07] & FH ⟂ BC [08] ⇒  FH ⟂ CH [16]
+003. E,A,J are collinear [11] & FJ ⟂ AE [12] ⇒  FJ ⟂ JE [17]
+004. FH ⟂ CH [16] & FJ ⟂ JE [17] ⇒  ∠(FH-JE) = ∠(CH-FJ) [18]
+005. C,B,H are collinear [07] & E,A,J are collinear [11] & ∠(FH-JE) = ∠(CH-FJ) [18] ⇒  ∠FHC = ∠EJF [19]
+006. DA = DB [00] & DE = DA [02] & DB = DC [01] ⇒  C,E,B,A are concyclic [20]
+007. C,E,B,A are concyclic [20] ⇒  ∠ACB = ∠AEB [21]
+008. C,E,B,A are concyclic [20] ⇒  ∠EBC = ∠EAC [22]
+009. C,E,B,A are concyclic [20] ⇒  ∠BEC = ∠BAC [23]
+010. C,E,B,A are concyclic [20] ⇒  ∠ACE = ∠ABE [24]
+011. C,F,A are collinear [03] & C,B,H are collinear [07] & E,A,J are collinear [11] & E,F,B are collinear [04] & ∠ACB = ∠AEB [21] ⇒  ∠FCH = ∠JEF [25]
+012. ∠FHC = ∠EJF [19] & ∠FCH = ∠JEF [25] (Similar Triangles)⇒  FH:CH = FJ:EJ [26]
+013. C,B,H are collinear [07] & A,E,J are collinear [11] & ∠(FH-JE) = ∠(CH-FJ) [18] ⇒  ∠FHB = ∠AJF [27]
+014. E,F,B are collinear [04] & C,H,B are collinear [07] & J,E,A are collinear [11] & C,F,A are collinear [03] & ∠EBC = ∠EAC [22] ⇒  ∠FBH = ∠JAF [28]
+015. ∠FHB = ∠AJF [27] & ∠FBH = ∠JAF [28] (Similar Triangles)⇒  FH:HB = FJ:JA [29]
+016. G,B,A are collinear [05] & AB ⟂ FG [06] ⇒  GB ⟂ GF [30]
+017. FI ⟂ CE [10] & GB ⟂ GF [30] ⇒  ∠(CE-GF) = ∠(IF-GB) [31]
+018. C,E,I are collinear [09] & G,B,A are collinear [05] & ∠(CE-GF) = ∠(IF-GB) [31] ⇒  ∠FIE = ∠AGF [32]
+019. E,F,B are collinear [04] & C,E,I are collinear [09] & G,B,A are collinear [05] & C,F,A are collinear [03] & ∠BEC = ∠BAC [23] ⇒  ∠FEI = ∠GAF [33]
+020. ∠FIE = ∠AGF [32] & ∠FEI = ∠GAF [33] (Similar Triangles)⇒  IF:EI = GF:GA [34]
+021. (JA:EJ) * (GB:GA) * (KE:KB) = 1 [15] & FH:CH = FJ:EJ [26] & FH:HB = FJ:JA [29] & IF:EI = GF:GA [34] (Ratio chase)⇒  (GB:KB) * (IF:CH) * (HB:EI) * (KE:GF) = 1 [35]
+022. (JA:EJ) * (GB:GA) * (KE:KB) = 1 [15] & IF:EI = GF:GA [34] (Ratio chase)⇒  (JA:EI) * (KE:GF) * (GB:KB) * (IF:EJ) = 1 [36]
+023. C,E,I are collinear [09] & G,B,A are collinear [05] & ∠(CE-GF) = ∠(IF-GB) [31] ⇒  ∠FIC = ∠BGF [37]
+024. C,F,A are collinear [03] & C,E,I are collinear [09] & G,B,A are collinear [05] & E,F,B are collinear [04] & ∠ACE = ∠ABE [24] ⇒  ∠FCI = ∠GBF [38]
+025. ∠FIC = ∠BGF [37] & ∠FCI = ∠GBF [38] (Similar Triangles)⇒  IF:CI = GF:GB [39]
+026. IF:CI = GF:GB [39] & IF:EI = GF:GA [34] ⇒  CI:EI = GB:GA [40]
+027. (GB:KB) * (IF:CH) * (HB:EI) * (KE:GF) = 1 [35] & (JA:EI) * (KE:GF) * (GB:KB) * (IF:EJ) = 1 [36] & (GB:GA) * (JA:KB) * (KE:EJ) = 1 [15] & CI:EI = GB:GA [40] ⇒  (CI:IE) * (EK:KB) * (BH:HC) = 1 [41]
+028. C,E,I are collinear [09] & K,E,B are collinear [13] & C,H,B are collinear [07] & (CI:IE) * (EK:KB) * (BH:HC) = 1 [41] (Menelaus)⇒  K,I,H are collinear
+==========================
diff --git a/output_new/menelaus_b6.txt b/output_new/menelaus_b6.txt
new file mode 100644
index 0000000..2f9fcac
--- /dev/null
+++ b/output_new/menelaus_b6.txt
@@ -0,0 +1,42 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J : Points
+AD ⟂ BC [00]
+BD ⟂ AC [01]
+E,A,B are collinear [02]
+D,F,E are collinear [03]
+C,F,B are collinear [04]
+D,E,G are collinear [05]
+C,A,G are collinear [06]
+C,H,B are collinear [07]
+DH ⟂ DE [08]
+D,H,I are collinear [09]
+I,A,B are collinear [10]
+D,J,H are collinear [11]
+C,J,A are collinear [12]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. D,F,E are collinear [03] & D,E,G are collinear [05] ⇒  F,G,E are collinear [13]
+002. F,G,E are collinear [13] & C,F,B are collinear [04] & C,A,G are collinear [06] & E,A,B are collinear [02] (Menelaus)⇒  (EG:FE) * (CA:AG) * (FB:CB) = 1 [14]
+003. D,J,H are collinear [11] & D,H,I are collinear [09] ⇒  H,J,I are collinear [15]
+004. H,J,I are collinear [15] & C,H,B are collinear [07] & C,J,A are collinear [12] & I,A,B are collinear [10] (Menelaus)⇒  (JI:HI) * (CA:JA) * (HB:CB) = 1 [16]
+005. C,F,B are collinear [04] & AD ⟂ BC [00] ⇒  DA ⟂ CF [17]
+006. D,F,E are collinear [03] & D,J,H are collinear [11] & DE ⟂ DH [08] ⇒  DF ⟂ DJ [18]
+007. DA ⟂ CF [17] & DF ⟂ DJ [18] ⇒  ∠ADF = ∠(CF-DJ) [19]
+008. DA ⟂ CF [17] & DF ⟂ DJ [18] ⇒  ∠ADJ = ∠CFD [20]
+009. D,E,G are collinear [05] & C,H,B are collinear [07] & ∠ADF = ∠(CF-DJ) [19] & D,F,E are collinear [03] & C,F,B are collinear [04] & D,J,H are collinear [11] ⇒  ∠ADG = ∠BHD [21]
+010. C,J,A are collinear [12] & BD ⟂ AC [01] ⇒  DB ⟂ CJ [22]
+011. DF ⟂ DJ [18] & DB ⟂ CJ [22] ⇒  ∠(DF-CJ) = ∠JDB [23]
+012. DF ⟂ DJ [18] & DB ⟂ CJ [22] ⇒  ∠FDB = ∠DJC [24]
+013. C,A,G are collinear [06] & D,E,G are collinear [05] & ∠(DF-CJ) = ∠JDB [23] & D,F,E are collinear [03] & C,J,A are collinear [12] & D,J,H are collinear [11] ⇒  ∠AGD = ∠BDH [25]
+014. ∠ADG = ∠BHD [21] & ∠AGD = ∠BDH [25] (Similar Triangles)⇒  DA:AG = HB:DB [26]
+015. C,F,B are collinear [04] & D,F,E are collinear [03] & D,J,H are collinear [11] & ∠ADJ = ∠CFD [20] ⇒  ∠BFD = ∠ADJ [27]
+016. D,F,E are collinear [03] & C,J,A are collinear [12] & D,J,H are collinear [11] & ∠FDB = ∠DJC [24] ⇒  ∠BDF = ∠AJD [28]
+017. ∠BFD = ∠ADJ [27] & ∠BDF = ∠AJD [28] (Similar Triangles)⇒  FB:DB = DA:JA [29]
+018. (EG:FE) * (CA:AG) * (FB:CB) = 1 [14] & (JI:HI) * (CA:JA) * (HB:CB) = 1 [16] & DA:AG = HB:DB [26] & FB:DB = DA:JA [29] (Ratio chase)⇒  FE:EG = HI:JI
+==========================
diff --git a/output_new/menelaus_b9.txt b/output_new/menelaus_b9.txt
new file mode 100644
index 0000000..505ad8f
--- /dev/null
+++ b/output_new/menelaus_b9.txt
@@ -0,0 +1,64 @@
+
+==========================
+ * From theorem premises:
+A B C G D E F H I J : Points
+∠ACG = ∠GCB [00]
+∠BAG = ∠GAC [01]
+C,B,D are collinear [02]
+DG ⟂ BC [03]
+C,E,A are collinear [04]
+EG ⟂ AC [05]
+B,F,A are collinear [06]
+FG ⟂ AB [07]
+BC ⟂ HD [08]
+CI = CD [09]
+HI = HD [10]
+HJ = HD [11]
+BJ = BD [12]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. D,C,B are collinear [02] & C,E,A are collinear [04] & EG ⟂ AC [05] & DG ⟂ BC [03] ⇒  ∠GDC = ∠CEG [13]
+002. C,B,D are collinear [02] & C,E,A are collinear [04] & ∠GCB = ∠ACG [00] ⇒  ∠GCD = ∠ECG [14]
+003. ∠GDC = ∠CEG [13] & ∠GCD = ∠ECG [14] (Similar Triangles)⇒  CD = CE [15]
+004. ∠GDC = ∠CEG [13] & ∠GCD = ∠ECG [14] (Similar Triangles)⇒  GD = GE [16]
+005. CD = CE [15] & GD = GE [16] ⇒  DE ⟂ CG [17]
+006. HJ = HD [11] & BJ = BD [12] ⇒  DJ ⟂ BH [18]
+007. DE ⟂ CG [17] & DJ ⟂ BH [18] ⇒  ∠(DJ-HB) = ∠(CG-DE) [19]
+008. CI = CD [09] & CD = CE [15] ⇒  C is the circumcenter of \Delta DIE [20]
+009. BC ⟂ HD [08] & DG ⟂ BC [03] & D,C,B are collinear [02] ⇒  HD ⟂ DC [21]
+010. C is the circumcenter of \Delta DIE [20] & HD ⟂ DC [21] ⇒  ∠HDI = ∠DEI [22]
+011. BC ⟂ HD [08] & DG ⟂ BC [03] & DJ ⟂ BH [18] ⇒  ∠(HB-DJ) = ∠(DH-CB) [23]
+012. HI = HD [10] & HJ = HD [11] ⇒  H is the circumcenter of \Delta DIJ [24]
+013. H is the circumcenter of \Delta DIJ [24] & HD ⟂ DC [21] ⇒  ∠CDI = ∠DJI [25]
+014. ∠CDI = ∠DJI [25] & C,B,D are collinear [02] ⇒  ∠(BC-DI) = ∠DJI [26]
+015. ∠(HB-DJ) = ∠(DH-CB) [23] & ∠(BC-DI) = ∠DJI [26] ⇒  ∠(HB-JI) = ∠HDI [27]
+016. ∠HDI = ∠DEI [22] & BC ⟂ HD [08] & DG ⟂ BC [03] & ∠(HB-JI) = ∠HDI [27] ⇒  ∠(HB-JI) = ∠DEI [28]
+017. ∠(DJ-HB) = ∠(CG-DE) [19] & ∠(HB-JI) = ∠DEI [28] ⇒  ∠DJI = ∠(CG-EI) [29]
+018. C,E,A are collinear [04] & B,F,A are collinear [06] & FG ⟂ AB [07] & EG ⟂ AC [05] ⇒  ∠GEA = ∠AFG [30]
+019. C,E,A are collinear [04] & B,F,A are collinear [06] & ∠GAC = ∠BAG [01] ⇒  ∠GAE = ∠FAG [31]
+020. ∠GEA = ∠AFG [30] & ∠GAE = ∠FAG [31] (Similar Triangles)⇒  GE = GF [32]
+021. ∠GEA = ∠AFG [30] & ∠GAE = ∠FAG [31] (Similar Triangles)⇒  AE = AF [33]
+022. GD = GE [16] & GE = GF [32] ⇒  GF = GD [34]
+023. GD = GE [16] & GE = GF [32] ⇒  G is the circumcenter of \Delta FDE [35]
+024. B,F,A are collinear [06] & AB ⟂ FG [07] ⇒  BF ⟂ FG [36]
+025. D,C,B are collinear [02] & DG ⟂ BC [03] ⇒  GD ⟂ DB [37]
+026. GF = GD [34] & BF ⟂ FG [36] & GD ⟂ DB [37] (Circle Power)⇒  BF = BD [38]
+027. BJ = BD [12] & BF = BD [38] ⇒  B is the circumcenter of \Delta DJF [39]
+028. B is the circumcenter of \Delta DJF [39] & BF ⟂ FG [36] ⇒  ∠DFG = ∠DJF [40]
+029. GE = GF [32] & AE = AF [33] ⇒  EF ⟂ AG [41]
+030. DE ⟂ CG [17] & EF ⟂ AG [41] ⇒  ∠(GA-FE) = ∠(DE-CG) [42]
+031. C,E,A are collinear [04] & AC ⟂ EG [05] ⇒  CE ⟂ GE [43]
+032. G is the circumcenter of \Delta FDE [35] & CE ⟂ GE [43] ⇒  ∠CEF = ∠EDF [44]
+033. B,F,A are collinear [06] & C,E,A are collinear [04] & FG ⟂ AB [07] & EG ⟂ AC [05] ⇒  ∠AFG = ∠AEG [45]
+034. ∠AFG = ∠AEG [45] ⇒  G,F,E,A are concyclic [46]
+035. G,F,E,A are concyclic [46] ⇒  ∠GFE = ∠GAE [47]
+036. ∠CEF = ∠EDF [44] & C,E,A are collinear [04] & ∠GFE = ∠GAE [47] ⇒  ∠AGF = ∠EDF [48]
+037. ∠(GA-FE) = ∠(DE-CG) [42] & ∠AGF = ∠EDF [48] ⇒  ∠(CG-EF) = ∠DFG [49]
+038. ∠DFG = ∠DJF [40] & ∠(CG-EF) = ∠DFG [49] ⇒  ∠(CG-FE) = ∠DJF [50]
+039. ∠DJI = ∠(CG-EI) [29] & ∠(CG-FE) = ∠DJF [50] ⇒  ∠EIJ = ∠EFJ [51]
+040. ∠EIJ = ∠EFJ [51] ⇒  J,F,E,I are concyclic
+==========================
diff --git a/output_new/menelaus_b9w.txt b/output_new/menelaus_b9w.txt
new file mode 100644
index 0000000..026aaf5
--- /dev/null
+++ b/output_new/menelaus_b9w.txt
@@ -0,0 +1,97 @@
+
+==========================
+ * From theorem premises:
+A B C G D E F H I J L : Points
+∠GAB = ∠CAG [00]
+∠GCA = ∠BCG [01]
+D,B,C are collinear [02]
+DG ⟂ BC [03]
+C,A,E are collinear [04]
+EG ⟂ AC [05]
+B,F,A are collinear [06]
+FG ⟂ AB [07]
+BC ⟂ HD [08]
+HI = HD [09]
+CI = CD [10]
+HJ = HD [11]
+BJ = BD [12]
+B,C,L are collinear [13]
+F,L,E are collinear [14]
+
+ * Auxiliary Constructions:
+K : Points
+K,C,I are collinear [15]
+K,J,B are collinear [16]
+
+ * Proof steps:
+001. HI = HD [09] & HJ = HD [11] ⇒  HJ = HI [17]
+002. HJ = HD [11] & BJ = BD [12] (SSS)⇒  ∠HJB = ∠BDH [18]
+003. K,J,B are collinear [16] & ∠HJB = ∠BDH [18] & D,B,C are collinear [02] & BC ⟂ HD [08] & DG ⟂ BC [03] ⇒  JH ⟂ KJ [19]
+004. HI = HD [09] & CI = CD [10] (SSS)⇒  ∠HDC = ∠CIH [20]
+005. K,C,I are collinear [15] & ∠HDC = ∠CIH [20] & BC ⟂ HD [08] & DG ⟂ BC [03] & D,B,C are collinear [02] ⇒  HI ⟂ IK [21]
+006. HJ = HI [17] & JH ⟂ KJ [19] & HI ⟂ IK [21] (Circle Power)⇒  KI = JK [22]
+007. B,C,L are collinear [13] & B,F,A are collinear [06] & C,A,E are collinear [04] & F,L,E are collinear [14] (Menelaus)⇒  (AE:FA) * (BF:LB) * (CL:EC) = 1 [23]
+008. B,F,A are collinear [06] & C,A,E are collinear [04] & EG ⟂ AC [05] & FG ⟂ AB [07] ⇒  ∠GFA = ∠AEG [24]
+009. B,F,A are collinear [06] & C,A,E are collinear [04] & ∠GAB = ∠CAG [00] ⇒  ∠GAF = ∠EAG [25]
+010. ∠GFA = ∠AEG [24] & ∠GAF = ∠EAG [25] (Similar Triangles)⇒  AF = AE [26]
+011. ∠GFA = ∠AEG [24] & ∠GAF = ∠EAG [25] (Similar Triangles)⇒  GF = GE [27]
+012. C,A,E are collinear [04] & D,B,C are collinear [02] & DG ⟂ BC [03] & EG ⟂ AC [05] ⇒  ∠GEC = ∠CDG [28]
+013. C,A,E are collinear [04] & D,B,C are collinear [02] & ∠GCA = ∠BCG [01] ⇒  ∠GCE = ∠DCG [29]
+014. ∠GEC = ∠CDG [28] & ∠GCE = ∠DCG [29] (Similar Triangles)⇒  CE = CD [30]
+015. ∠GEC = ∠CDG [28] & ∠GCE = ∠DCG [29] (Similar Triangles)⇒  GE = GD [31]
+016. GF = GE [27] & GE = GD [31] ⇒  GD = GF [32]
+017. D,B,C are collinear [02] & DG ⟂ BC [03] ⇒  DG ⟂ DB [33]
+018. B,F,A are collinear [06] & FG ⟂ AB [07] ⇒  GF ⟂ BF [34]
+019. GD = GF [32] & DG ⟂ DB [33] & GF ⟂ BF [34] (Circle Power)⇒  BD = BF [35]
+020. KI = JK [22] & (AE:FA) * (BF:LB) * (CL:EC) = 1 [23] & AF = AE [26] & CE = CD [30] & CI = CD [10] & BD = BF [35] & BJ = BD [12] ⇒  (KI:IC) * (CL:LB) * (BJ:JK) = 1 [36]
+021. K,C,I are collinear [15] & B,C,L are collinear [13] & K,J,B are collinear [16] & (KI:IC) * (CL:LB) * (BJ:JK) = 1 [36] (Menelaus)⇒  J,I,L are collinear
+==========================
+
+
+
+==========================
+ * From theorem premises:
+A B C G D E F H I J L : Points
+∠GAB = ∠CAG [00]
+∠ACG = ∠GCB [01]
+DG ⟂ BC [02]
+C,B,D are collinear [03]
+C,E,A are collinear [04]
+EG ⟂ AC [05]
+B,F,A are collinear [06]
+FG ⟂ AB [07]
+BC ⟂ HD [08]
+HI = HD [09]
+CI = CD [10]
+HJ = HD [11]
+BJ = BD [12]
+C,B,L are collinear [13]
+F,E,L are collinear [14]
+
+ * Auxiliary Constructions:
+K : Points
+C,K,I are collinear [15]
+B,J,K are collinear [16]
+
+ * Proof steps:
+001. HJ = HD [11] & HI = HD [09] ⇒  HI = HJ [17]
+002. HI = HD [09] & CI = CD [10] (SSS)⇒  ∠HDC = ∠CIH [18]
+003. I,K,C are collinear [15] & ∠HDC = ∠CIH [18] & BC ⟂ HD [08] & DG ⟂ BC [02] & C,B,D are collinear [03] ⇒  HI ⟂ IK [19]
+004. HJ = HD [11] & BJ = BD [12] (SSS)⇒  ∠HDB = ∠BJH [20]
+005. B,K,J are collinear [16] & ∠HDB = ∠BJH [20] & BC ⟂ HD [08] & DG ⟂ BC [02] & C,B,D are collinear [03] ⇒  HJ ⟂ JK [21]
+006. HI = HJ [17] & HI ⟂ IK [19] & HJ ⟂ JK [21] (Circle Power)⇒  KI = JK [22]
+007. C,B,L are collinear [13] & B,F,A are collinear [06] & C,E,A are collinear [04] & F,E,L are collinear [14] (Menelaus)⇒  (AE:FA) * (BF:LB) * (CL:EC) = 1 [23]
+008. B,F,A are collinear [06] & C,E,A are collinear [04] & EG ⟂ AC [05] & FG ⟂ AB [07] ⇒  ∠GFA = ∠AEG [24]
+009. B,F,A are collinear [06] & C,E,A are collinear [04] & ∠GAB = ∠CAG [00] ⇒  ∠GAF = ∠EAG [25]
+010. ∠GFA = ∠AEG [24] & ∠GAF = ∠EAG [25] (Similar Triangles)⇒  AF = AE [26]
+011. ∠GFA = ∠AEG [24] & ∠GAF = ∠EAG [25] (Similar Triangles)⇒  GF = GE [27]
+012. C,B,D are collinear [03] & C,E,A are collinear [04] & EG ⟂ AC [05] & DG ⟂ BC [02] ⇒  ∠GDC = ∠CEG [28]
+013. C,B,D are collinear [03] & C,E,A are collinear [04] & ∠GCB = ∠ACG [01] ⇒  ∠GCD = ∠ECG [29]
+014. ∠GDC = ∠CEG [28] & ∠GCD = ∠ECG [29] (Similar Triangles)⇒  GD = GE [30]
+015. GD = GE [30] & GF = GE [27] ⇒  GF = GD [31]
+016. B,F,A are collinear [06] & FG ⟂ AB [07] ⇒  FG ⟂ BF [32]
+017. C,B,D are collinear [03] & DG ⟂ BC [02] ⇒  GD ⟂ DB [33]
+018. GF = GD [31] & FG ⟂ BF [32] & GD ⟂ DB [33] (Circle Power)⇒  BF = BD [34]
+019. KI = JK [22] & (AE:FA) * (BF:LB) * (CL:EC) = 1 [23] & AF = AE [26] & CI = CD [10] & BF = BD [34] & BJ = BD [12] ⇒  (KI:IC) * (CL:LB) * (BJ:JK) = 1 [35]
+020. C,K,I are collinear [15] & C,B,L are collinear [13] & B,J,K are collinear [16] & (KI:IC) * (CL:LB) * (BJ:JK) = 1 [35] (Menelaus)⇒  I,J,L are collinear
+==========================
diff --git a/output_new/menelaus_c22.txt b/output_new/menelaus_c22.txt
new file mode 100644
index 0000000..e6e4b27
--- /dev/null
+++ b/output_new/menelaus_c22.txt
@@ -0,0 +1,37 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+C,D,B are collinear [00]
+A,E,C are collinear [01]
+E,D,F are collinear [02]
+DE = DF [03]
+G,F,B are collinear [04]
+A,G,D are collinear [05]
+E,D,H are collinear [06]
+A,B,H are collinear [07]
+E,I,D are collinear [08]
+G,I,C are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. E,D,H are collinear [06] & C,D,B are collinear [00] & A,E,C are collinear [01] & A,B,H are collinear [07] (Menelaus)⇒  (EH:DH) * (AC:AE) * (DB:CB) = 1 [10]
+002. E,I,D are collinear [08] & E,D,F are collinear [02] ⇒  D,I,F are collinear [11]
+003. G,F,B are collinear [04] & C,D,B are collinear [00] & D,I,F are collinear [11] & G,I,C are collinear [09] (Menelaus)⇒  (GF:GB) * (CB:DC) * (ID:IF) = 1 [12]
+004. G,F,B are collinear [04] & C,D,B are collinear [00] & D,I,F are collinear [11] & G,I,C are collinear [09] (Menelaus)⇒  (GI:GC) * (CB:DB) * (DF:IF) = 1 [13]
+005. G,F,B are collinear [04] & C,D,B are collinear [00] & D,I,F are collinear [11] & G,I,C are collinear [09] (Menelaus)⇒  (GI:IC) * (FB:DB) * (DC:GF) = 1 [14]
+006. A,G,D are collinear [05] & A,E,C are collinear [01] & E,I,D are collinear [08] & G,I,C are collinear [09] (Menelaus)⇒  (GD:AG) * (AC:EC) * (EI:ID) = 1 [15]
+007. A,G,D are collinear [05] & A,E,C are collinear [01] & E,I,D are collinear [08] & G,I,C are collinear [09] (Menelaus)⇒  (IG:GC) * (CA:AE) * (ED:DI) = 1 [16]
+008. A,G,D are collinear [05] & A,E,C are collinear [01] & E,I,D are collinear [08] & G,I,C are collinear [09] (Menelaus)⇒  (GI:IC) * (AD:AE) * (EC:GD) = 1 [17]
+009. (IG:GC) * (CA:AE) * (ED:DI) = 1 [16] & DE = DF [03] ⇒  (GI:GC) * (AC:AE) * (DF:ID) = 1 [18]
+010. E,D,F are collinear [02] & E,D,H are collinear [06] ⇒  F,H,D are collinear [19]
+011. G,F,B are collinear [04] & F,H,D are collinear [19] & A,G,D are collinear [05] & A,B,H are collinear [07] (Menelaus)⇒  (GB:FB) * (AD:AG) * (FH:DH) = 1 [20]
+012. (GF:GB) * (CB:DC) * (ID:IF) = 1 [12] & (GI:GC) * (CB:DB) * (DF:IF) = 1 [13] & (GI:IC) * (FB:DB) * (DC:GF) = 1 [14] & (GD:AG) * (AC:EC) * (EI:ID) = 1 [15] & (GI:GC) * (AC:AE) * (DF:ID) = 1 [18] & (GI:IC) * (AD:AE) * (EC:GD) = 1 [17] & (GB:FB) * (AD:AG) * (FH:DH) = 1 [20] (Ratio chase)⇒  (AE:AC) * (CB:DB) * (DH:FH) * (EI:IF) = 1 [21]
+013. (GI:GC) * (CB:DB) * (DF:IF) = 1 [13] & (GI:IC) * (FB:DB) * (DC:GF) = 1 [14] & (GD:AG) * (AC:EC) * (EI:ID) = 1 [15] & (GI:GC) * (AC:AE) * (DF:ID) = 1 [18] & (GI:IC) * (AD:AE) * (EC:GD) = 1 [17] & (GB:FB) * (AD:AG) * (FH:DH) = 1 [20] (Ratio chase)⇒  (CB:GB) * (GF:DC) * (DH:FH) * (EI:IF) = 1 [22]
+014. (EH:DH) * (AC:AE) * (DB:CB) = 1 [10] & (AE:AC) * (CB:DB) * (DH:FH) * (EI:IF) = 1 [21] & (CB:GB) * (GF:DC) * (DH:FH) * (EI:IF) = 1 [22] & (IF:ID) * (GB:CB) * (DC:GF) = 1 [12] ⇒  IF:ID = EH:DH [23]
+015. IF:ID = EH:DH [23] & D,I,F are collinear [11] & E,D,H are collinear [06] ⇒  DF:DE = ID:HD [24]
+016. DF:DE = ID:HD [24] & DE = DF [03] ⇒  ID = HD
+==========================
diff --git a/output_new/menelaus_c22w.txt b/output_new/menelaus_c22w.txt
new file mode 100644
index 0000000..0351113
--- /dev/null
+++ b/output_new/menelaus_c22w.txt
@@ -0,0 +1,34 @@
+==========================
+ * From theorem premises:
+A B C D E F G H I : Points
+B,D,C are collinear [00]
+A,C,E are collinear [01]
+F,D,E are collinear [02]
+DE = DF [03]
+F,B,G are collinear [04]
+A,D,G are collinear [05]
+E,D,H are collinear [06]
+B,A,H are collinear [07]
+D,E,I are collinear [08]
+I,C,G are collinear [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. E,D,H are collinear [06] & F,D,E are collinear [02] ⇒  F,H,D are collinear [10]
+002. F,B,G are collinear [04] & F,H,D are collinear [10] & A,D,G are collinear [05] & B,A,H are collinear [07] (Menelaus)⇒  (DH:FH) * (AG:AD) * (FB:BG) = 1 [11]
+003. D,H,E are collinear [06] & B,D,C are collinear [00] & A,C,E are collinear [01] & B,A,H are collinear [07] (Menelaus)⇒  (HE:DH) * (AC:AE) * (BD:BC) = 1 [12]
+004. D,E,I are collinear [08] & F,D,E are collinear [02] ⇒  D,I,F are collinear [13]
+005. F,B,G are collinear [04] & B,D,C are collinear [00] & D,I,F are collinear [13] & I,C,G are collinear [09] (Menelaus)⇒  (FG:BG) * (BC:DC) * (DI:FI) = 1 [14]
+006. F,B,G are collinear [04] & B,D,C are collinear [00] & D,I,F are collinear [13] & I,C,G are collinear [09] (Menelaus)⇒  (IG:CG) * (BC:BD) * (FD:FI) = 1 [15]
+007. F,B,G are collinear [04] & B,D,C are collinear [00] & D,I,F are collinear [13] & I,C,G are collinear [09] (Menelaus)⇒  (IG:CI) * (FB:BD) * (DC:FG) = 1 [16]
+008. A,D,G are collinear [05] & A,C,E are collinear [01] & D,E,I are collinear [08] & I,C,G are collinear [09] (Menelaus)⇒  (DG:AG) * (AC:CE) * (EI:DI) = 1 [17]
+009. A,D,G are collinear [05] & A,C,E are collinear [01] & D,E,I are collinear [08] & I,C,G are collinear [09] (Menelaus)⇒  (IG:GC) * (CA:AE) * (ED:DI) = 1 [18]
+010. A,D,G are collinear [05] & A,C,E are collinear [01] & D,E,I are collinear [08] & I,C,G are collinear [09] (Menelaus)⇒  (IG:CI) * (AD:AE) * (CE:DG) = 1 [19]
+011. (IG:GC) * (CA:AE) * (ED:DI) = 1 [18] & DE = DF [03] ⇒  (IG:CG) * (AC:AE) * (FD:DI) = 1 [20]
+012. (HE:DH) * (AC:AE) * (BD:BC) = 1 [12] & (FG:BG) * (BC:DC) * (DI:FI) = 1 [14] & (IG:CG) * (BC:BD) * (FD:FI) = 1 [15] & (IG:CI) * (FB:BD) * (DC:FG) = 1 [16] & (DG:AG) * (AC:CE) * (EI:DI) = 1 [17] & (IG:CG) * (AC:AE) * (FD:DI) = 1 [20] & (IG:CI) * (AD:AE) * (CE:DG) = 1 [19] (Ratio chase)⇒  (AD:AG) * (BG:FB) * (HE:DH) * (EI:FI) = 1 [21]
+013. (HE:DH) * (AC:AE) * (BD:BC) = 1 [12] & (IG:CG) * (BC:BD) * (FD:FI) = 1 [15] & (DG:AG) * (AC:CE) * (EI:DI) = 1 [17] & (IG:CG) * (AC:AE) * (FD:DI) = 1 [20] (Ratio chase)⇒  (AC:AG) * (DG:CE) * (HE:DH) * (EI:FI) = 1 [22]
+014. (DH:FH) * (AG:AD) * (FB:BG) = 1 [11] & (AD:AG) * (BG:FB) * (HE:DH) * (EI:FI) = 1 [21] & (AC:AG) * (DG:CE) * (HE:DH) * (EI:FI) = 1 [22] & (DI:EI) * (AG:AC) * (CE:DG) = 1 [17] ⇒  DI:EI = DH:FH
+==========================
\ No newline at end of file
diff --git a/output_new/menelaus_c3.txt b/output_new/menelaus_c3.txt
new file mode 100644
index 0000000..8921e73
--- /dev/null
+++ b/output_new/menelaus_c3.txt
@@ -0,0 +1,42 @@
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+BC = BA [00]
+BC ⟂ AB [01]
+D,B,C are collinear [02]
+DB = DC [03]
+E,D,A are collinear [04]
+BE ⟂ AD [05]
+F,C,A are collinear [06]
+E,B,F are collinear [07]
+F,A,G are collinear [08]
+GA = GF [09]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. F,C,A are collinear [06] & D,B,C are collinear [02] & E,D,A are collinear [04] & E,B,F are collinear [07] (Menelaus)⇒  (AF:FC) * (CB:BD) * (DE:EA) = 1 [10]
+002. (AF:FC) * (CB:BD) * (DE:EA) = 1 [10] & BC = BA [00] & DB = DC [03] ⇒  (FC:FA) * (EA:BA) * (DC:ED) = 1 [11]
+003. D,B,C are collinear [02] & E,D,A are collinear [04] & BE ⟂ AD [05] & BC ⟂ AB [01] ⇒  ∠ABD = ∠DEB [12]
+004. D,B,C are collinear [02] & E,D,A are collinear [04] ⇒  ∠ADB = ∠EDB [13]
+005. ∠ABD = ∠DEB [12] & ∠ADB = ∠EDB [13] (Similar Triangles)⇒  BA:BD = EB:ED [14]
+006. ∠ABD = ∠DEB [12] & ∠ADB = ∠EDB [13] (Similar Triangles)⇒  AB:AD = BE:BD [15]
+007. BA:BD = EB:ED [14] & DB = DC [03] ⇒  BA:DC = EB:ED [16]
+008. D,B,C are collinear [02] & BC ⟂ AB [01] ⇒  DB ⟂ BA [17]
+009. DB ⟂ BA [17] & BE ⟂ AD [05] & E,D,A are collinear [04] ⇒  BA:EA = DA:BA [18]
+010. BA:DC = EB:ED [16] & BA:EA = DA:BA [18] (Ratio chase)⇒  (DA:BA) * (EB:ED) * (EA:BA) * (DC:BA) = 1 [19]
+011. AB:AD = BE:BD [15] & DB = DC [03] ⇒  BA:DA = EB:DC [20]
+012. DB = DC [03] & BA:DA = EB:DC [20] & (FA:FC) * (BA:EA) * (ED:DC) = 1 [11] (Ratio chase)⇒  (DA:FA) * (EB:ED) * (EA:BA) * (FC:BA) = 1 [21]
+013. D,B,C are collinear [02] & DB = DC [03] ⇒  D is midpoint of BC [22]
+014. G,F,A are collinear [08] & GA = GF [09] ⇒  G is midpoint of FA [23]
+015. D is midpoint of BC [22] & G is midpoint of FA [23] ⇒  DB:BC = GF:FA [24]
+016. E,B,F are collinear [07] & E,D,A are collinear [04] & BE ⟂ AD [05] ⇒  FE ⟂ EA [25]
+017. FE ⟂ EA [25] & G is midpoint of FA [23] ⇒  FG = EG [26]
+018. FE ⟂ EA [25] & G is midpoint of FA [23] ⇒  AG = EG [27]
+019. (FC:FA) * (EA:BA) * (DC:ED) = 1 [11] & (DA:BA) * (EB:ED) * (EA:BA) * (DC:BA) = 1 [19] & (DA:FA) * (EB:ED) * (EA:BA) * (FC:BA) = 1 [21] & DB:BC = GF:FA [24] & DB = DC [03] & BC = BA [00] & EG = FG [26] ⇒  EG:FA = FC:FA [28]
+020. BC = BA [00] ⇒  FA:BC = FA:BC [29]
+021. EG:FA = FC:FA [28] & FA:BC = FA:BC [29] ⇒  EG = FC [30]
+022. EG = FC [30] & AG = EG [27] ⇒  AG = CF
+==========================
\ No newline at end of file
diff --git a/output_new/menelaus_c32.txt b/output_new/menelaus_c32.txt
new file mode 100644
index 0000000..4e1bda9
--- /dev/null
+++ b/output_new/menelaus_c32.txt
@@ -0,0 +1,33 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+∠DAB = ∠CAD [00]
+∠ACD = ∠DCB [01]
+A,E,D are collinear [02]
+E,C,B are collinear [03]
+F,D,B are collinear [04]
+A,C,F are collinear [05]
+G,A,B are collinear [06]
+CG ⟂ CD [07]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. A,C,F are collinear [05] & ∠CAD = ∠DAB [00] ⇒  ∠FAD = ∠DAB [08]
+002. ∠FAD = ∠DAB [08] & F,D,B are collinear [04] ⇒  FD:DB = AF:AB [09]
+003. A,C,F are collinear [05] & ∠ACD = ∠DCB [01] ⇒  ∠FCD = ∠DCB [10]
+004. ∠FCD = ∠DCB [10] & F,D,B are collinear [04] ⇒  FD:DB = CF:CB [11]
+005. F,D,B are collinear [04] & A,E,D are collinear [02] & A,C,F are collinear [05] & E,C,B are collinear [03] (Menelaus)⇒  (FB:DB) * (AC:AE) * (ED:CF) = 1 [12]
+006. F,D,B are collinear [04] & A,E,D are collinear [02] & A,C,F are collinear [05] & E,C,B are collinear [03] (Menelaus)⇒  (FD:FB) * (AE:AD) * (CB:EC) = 1 [13]
+007. ∠ACD = ∠DCB [01] & CG ⟂ CD [07] (Angle chase)⇒  ∠ACG = ∠GCB [14]
+008. ∠ACG = ∠GCB [14] & G,A,B are collinear [06] ⇒  GA:GB = AC:CB [15]
+009. FD:DB = AF:AB [09] & FD:DB = CF:CB [11] & (FB:DB) * (AC:AE) * (ED:CF) = 1 [12] & GA:GB = AC:CB [15] (Ratio chase)⇒  (AF:AB) * (DB:FB) * (AE:GA) * (GB:ED) = 1 [16]
+010. E,C,B are collinear [03] & ∠ACD = ∠DCB [01] ⇒  ∠ACD = ∠DCE [17]
+011. ∠ACD = ∠DCE [17] & A,E,D are collinear [02] ⇒  AD:ED = AC:EC [18]
+012. AD:ED = AC:EC [18] & FD:DB = AF:AB [09] & FD:DB = CF:CB [11] & (FB:DB) * (AC:AE) * (ED:CF) = 1 [12] (Ratio chase)⇒  (AF:AB) * (DB:FB) * (AE:AD) * (CB:EC) = 1 [19]
+013. (AF:AB) * (DB:FB) * (AE:GA) * (GB:ED) = 1 [16] & (AF:AB) * (DB:FB) * (AE:AD) * (CB:EC) = 1 [19] & (FD:FB) * (AE:AD) * (CB:EC) = 1 [13] ⇒  (DF:FB) * (BG:GA) * (AE:ED) = 1 [20]
+014. F,D,B are collinear [04] & G,A,B are collinear [06] & A,E,D are collinear [02] & (DF:FB) * (BG:GA) * (AE:ED) = 1 [20] (Menelaus)⇒  G,E,F are collinear
+==========================
diff --git a/output_new/pascal_a1.txt b/output_new/pascal_a1.txt
new file mode 100644
index 0000000..bccbb88
--- /dev/null
+++ b/output_new/pascal_a1.txt
@@ -0,0 +1,31 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L : Points
+DB = DC [00]
+DA = DB [01]
+DF = DA [02]
+E,F,A are collinear [03]
+DG = DB [04]
+G,E,B are collinear [05]
+DH = DC [06]
+H,E,C are collinear [07]
+DI = DA [08]
+F,J,I are collinear [09]
+C,J,B are collinear [10]
+C,K,A are collinear [11]
+I,K,G are collinear [12]
+L,B,A are collinear [13]
+H,L,I are collinear [14]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. DH = DC [06] & DB = DC [00] & DA = DB [01] & DI = DA [08] & DG = DB [04] & DF = DA [02] ⇒  C,A,G,B,H,I are concyclic [15]
+002. C,A,G,B,H,I are concyclic [15] & C,K,A are collinear [11] & I,K,G are collinear [12] & L,B,A are collinear [13] & H,L,I are collinear [14] & G,E,B are collinear [05] & H,E,C are collinear [07] (Pascal)⇒  E,L,K are collinear [16]
+003. DH = DC [06] & DB = DC [00] & DA = DB [01] & DI = DA [08] & DG = DB [04] & DF = DA [02] ⇒  C,F,A,G,B,I are concyclic [17]
+004. C,F,A,G,B,I are concyclic [17] & C,K,A are collinear [11] & I,K,G are collinear [12] & E,F,A are collinear [03] & G,E,B are collinear [05] & F,J,I are collinear [09] & C,J,B are collinear [10] (Pascal)⇒  K,E,J are collinear [18]
+005. E,L,K are collinear [16] & K,E,J are collinear [18] ⇒  J,K,L are collinear
+==========================
diff --git a/output_new/pascal_b2.txt b/output_new/pascal_b2.txt
new file mode 100644
index 0000000..6537506
--- /dev/null
+++ b/output_new/pascal_b2.txt
@@ -0,0 +1,35 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G : Points
+CA = CB [00]
+B,C,A are collinear [01]
+CD = CA [02]
+CE = CA [03]
+B,F,D are collinear [04]
+E,F,A are collinear [05]
+DG ⟂ CD [06]
+EG ⟂ CE [07]
+
+ * Auxiliary Constructions:
+H : Points
+B,E,H are collinear [08]
+H,D,A are collinear [09]
+
+ * Proof steps:
+001. CE = CA [03] & CD = CA [02] & CA = CB [00] ⇒  C is the circumcenter of \Delta DEB [10]
+002. CE = CA [03] & CD = CA [02] & CA = CB [00] ⇒  B,D,E,A are concyclic [11]
+003. C is the circumcenter of \Delta DEB [10] & CD = CA [02] & DG ⟂ CD [06] & EG ⟂ CE [07] & B,F,D are collinear [04] & E,F,A are collinear [05] & B,E,H are collinear [08] & H,D,A are collinear [09] (Pascal)⇒  H,G,F are collinear [12]
+004. B,D,E,A are concyclic [11] ⇒  ∠DEB = ∠DAB [13]
+005. CA = CB [00] & CD = CA [02] ⇒  C is the circumcenter of \Delta DBA [14]
+006. C is the circumcenter of \Delta DBA [14] & B,C,A are collinear [01] ⇒  BD ⟂ AD [15]
+007. CA = CB [00] & CE = CA [03] ⇒  C is the circumcenter of \Delta EBA [16]
+008. C is the circumcenter of \Delta EBA [16] & B,C,A are collinear [01] ⇒  BE ⟂ AE [17]
+009. H,E,B are collinear [08] & E,F,A are collinear [05] & H,D,A are collinear [09] & B,F,D are collinear [04] & BD ⟂ AD [15] & BE ⟂ AE [17] ⇒  ∠HEF = ∠HDF [18]
+010. ∠HEF = ∠HDF [18] ⇒  H,E,F,D are concyclic [19]
+011. H,E,F,D are concyclic [19] ⇒  ∠HED = ∠HFD [20]
+012. B,F,D are collinear [04] & H,G,F are collinear [12] & H,D,A are collinear [09] & B,C,A are collinear [01] & ∠DEB = ∠DAB [13] & ∠HED = ∠HFD [20] & B,E,H are collinear [08] ⇒  ∠(BF-HG) = ∠(HD-BC) [21]
+013. H,D,A are collinear [09] & B,F,D are collinear [04] & AD ⟂ BD [15] ⇒  HD ⟂ BF [22]
+014. ∠(BF-HG) = ∠(HD-BC) [21] & HD ⟂ BF [22] ⇒  BC ⟂ HG [23]
+015. BC ⟂ HG [23] & B,C,A are collinear [01] & H,G,F are collinear [12] ⇒  AB ⟂ FG
+==========================
diff --git a/output_old/example6_3.txt b/output_old/example6_3.txt
new file mode 100644
index 0000000..6fda53a
--- /dev/null
+++ b/output_old/example6_3.txt
@@ -0,0 +1,133 @@
+
+==========================
+ * From theorem premises:
+A B C D E F G H I J K L : Points
+D,C,B are collinear [00]
+AD ⟂ BC [01]
+E,C,A are collinear [02]
+BE ⟂ AC [03]
+∠(AD-BE) = ∠(AD-BE) [04]
+F,A,B are collinear [05]
+CF ⟂ AB [06]
+G,D,A are collinear [07]
+G,E,B are collinear [08]
+AE = AH [09]
+DE = DH [10]
+AF = AI [11]
+DF = DI [12]
+J,I,B are collinear [13]
+J,C,H are collinear [14]
+K,C,I are collinear [15]
+H,K,B are collinear [16]
+G,K,L are collinear [17]
+J,A,L are collinear [18]
+
+ * Auxiliary Constructions:
+: Points
+
+
+ * Proof steps:
+001. AE = AH [09] & DE = DH [10] ⇒  AD ⟂ EH [19]
+002. AE = AH [09] & DE = DH [10] (SSS)⇒  ∠ADE = ∠HDA [20]
+003. AE = AH [09] & DE = DH [10] (SSS)⇒  ∠EAD = ∠DAH [21]
+004. F,A,B are collinear [05] & C,D,B are collinear [00] & AD ⟂ BC [01] & CF ⟂ AB [06] ⇒  ∠AFC = ∠ADC [22]
+005. ∠AFC = ∠ADC [22] ⇒  F,D,C,A are concyclic [23]
+006. F,D,C,A are concyclic [23] ⇒  ∠FDC = ∠FAC [24]
+007. F,D,C,A are concyclic [23] ⇒  ∠ADF = ∠ACF [25]
+008. E,C,A are collinear [02] & D,C,B are collinear [00] & F,A,B are collinear [05] & ∠FDC = ∠FAC [24] ⇒  ∠ECD = ∠BFD [26]
+009. AF = AI [11] & DF = DI [12] ⇒  AD ⟂ FI [27]
+010. AF = AI [11] & DF = DI [12] (SSS)⇒  ∠ADF = ∠IDA [28]
+011. AF = AI [11] & DF = DI [12] (SSS)⇒  ∠AFD = ∠DIA [29]
+012. C,D,B are collinear [00] & E,C,A are collinear [02] & BE ⟂ AC [03] & AD ⟂ BC [01] ⇒  ∠ADB = ∠AEB [30]
+013. ∠ADB = ∠AEB [30] ⇒  E,D,A,B are concyclic [31]
+014. E,D,A,B are concyclic [31] ⇒  ∠EDB = ∠EAB [32]
+015. E,D,A,B are concyclic [31] ⇒  ∠EDA = ∠EBA [33]
+016. C,D,B are collinear [00] & ∠FDC = ∠FAC [24] & F,A,B are collinear [05] & AD ⟂ FI [27] & AD ⟂ EH [19] & AD ⟂ BC [01] & ∠EDB = ∠EAB [32] & E,C,A are collinear [02] ⇒  ∠EDC = ∠BDF [34]
+017. ∠ECD = ∠BFD [26] & ∠EDC = ∠BDF [34] (Similar Triangles)⇒  DE:DC = DB:DF [35]
+018. ∠ECD = ∠BFD [26] & ∠EDC = ∠BDF [34] (Similar Triangles)⇒  DE:DB = DC:DF [36]
+019. DE:DC = DB:DF [35] & DE = DH [10] & DF = DI [12] ⇒  DH:DC = DB:DI [37]
+020. DE = DH [10] ⇒  ∠HED = ∠DHE [38]
+021. E,C,A are collinear [02] & G,E,B are collinear [08] & AC ⟂ BE [03] ⇒  EC ⟂ GE [39]
+022. F,A,B are collinear [05] & CF ⟂ AB [06] ⇒  FC ⟂ FA [40]
+023. EC ⟂ GE [39] & FC ⟂ FA [40] ⇒  ∠ECF = ∠(GE-FA) [41]
+024. ∠ECF = ∠(GE-FA) [41] & E,C,A are collinear [02] & G,E,B are collinear [08] & F,A,B are collinear [05] ⇒  ∠ACF = ∠EBA [42]
+025. G,D,A are collinear [07] & ∠EDA = ∠EBA [33] & ∠ACF = ∠EBA [42] & ∠ADF = ∠ACF [25] & ∠ADF = ∠IDA [28] ⇒  ∠IDG = ∠EDG [43]
+026. ∠IDG = ∠EDG [43] ⇒  DI ∥ ED [44]
+027. C,D,B are collinear [00] & ∠DHE = ∠HED [38] & AD ⟂ EH [19] & AD ⟂ BC [01] & DE ∥ DI [44] ⇒  ∠HDC = ∠BDI [45]
+028. C,D,B are collinear [00] & ∠DHE = ∠HED [38] & AD ⟂ EH [19] & AD ⟂ BC [01] & DE ∥ DI [44] ⇒  ∠CDI = ∠HDB [46]
+029. DH:DC = DB:DI [37] & ∠HDC = ∠BDI [45] (Similar Triangles)⇒  ∠DHC = ∠DBI [47]
+030. G,D,A are collinear [07] & ∠ADE = ∠HDA [20] & ∠ADE = ∠ABE [33] & ∠FCA = ∠ABE [42] & ∠FDA = ∠FCA [25] ⇒  ∠FDG = ∠HDG [48]
+031. ∠FDG = ∠HDG [48] ⇒  FD ∥ DH [49]
+032. DF ∥ DH [49] ⇒  F,D,H are collinear [50]
+033. AE = AH [09] (SSS)⇒  ∠AEH = ∠EHA [51]
+034. ∠AEH = ∠EHA [51] & E,C,A are collinear [02] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] & ∠FDC = ∠FAC [24] & D,C,B are collinear [00] & F,A,B are collinear [05] & ∠AFD = ∠DIA [29] ⇒  ∠DIA = ∠EHA [52]
+035. DF = DI [12] ⇒  ∠DFI = ∠FID [53]
+036. ∠FID = ∠DFI [53] & AD ⟂ FI [27] & AD ⟂ EH [19] ⇒  ∠(EH-DI) = ∠(FD-EH) [54]
+037. ∠DIA = ∠EHA [52] & ∠(EH-DI) = ∠(FD-EH) [54] ⇒  ∠IAH = ∠(EH-DF) [55]
+038. J,I,B are collinear [13] & C,J,H are collinear [14] & ∠DHC = ∠DBI [47] & F,D,H are collinear [50] & D,C,B are collinear [00] & DF ∥ DH [49] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] & ∠IAH = ∠(EH-DF) [55] ⇒  ∠IAH = ∠IJH [56]
+039. ∠IAH = ∠IJH [56] ⇒  J,I,A,H are concyclic [57]
+040. AF = AI [11] (SSS)⇒  ∠AFI = ∠FIA [58]
+041. F,A,B are collinear [05] & E,C,A are collinear [02] & BE ⟂ AC [03] & CF ⟂ AB [06] ⇒  ∠BFC = ∠BEC [59]
+042. ∠BFC = ∠BEC [59] ⇒  F,E,C,B are concyclic [60]
+043. F,E,C,B are concyclic [60] ⇒  ∠FEC = ∠FBC [61]
+044. E,C,A are collinear [02] & ∠AFI = ∠FIA [58] & F,A,B are collinear [05] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] & ∠FEC = ∠FBC [61] ⇒  ∠AEF = ∠AIF [62]
+045. ∠AEF = ∠AIF [62] ⇒  F,E,I,A are concyclic [63]
+046. C,D,B are collinear [00] & G,D,A are collinear [07] & BC ⟂ AD [01] ⇒  DC ⟂ GD [64]
+047. EC ⟂ GE [39] & DC ⟂ GD [64] ⇒  ∠ECD = ∠EGD [65]
+048. G,E,B are collinear [08] & G,D,A are collinear [07] & F,A,B are collinear [05] & ∠FEC = ∠FBC [61] & E,C,A are collinear [02] & ∠ECD = ∠EGD [65] & D,C,B are collinear [00] ⇒  ∠EGA = ∠EFA [66]
+049. ∠EGA = ∠EFA [66] ⇒  G,E,A,F are concyclic [67]
+050. G,E,B are collinear [08] & G,D,A are collinear [07] & ∠AEH = ∠EHA [51] & E,C,A are collinear [02] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] & ∠ECD = ∠EGD [65] & D,C,B are collinear [00] ⇒  ∠EGA = ∠EHA [68]
+051. ∠EGA = ∠EHA [68] ⇒  G,E,A,H are concyclic [69]
+052. J,I,A,H are concyclic [57] & F,E,I,A are concyclic [63] & G,E,A,F are concyclic [67] & G,E,A,H are concyclic [69] ⇒  J,A,G,E are concyclic [70]
+053. J,A,G,E are concyclic [70] ⇒  ∠JAE = ∠JGE [71]
+054. G,D,A are collinear [07] & ∠JAE = ∠JGE [71] & E,C,A are collinear [02] & G,E,B are collinear [08] & BE ⟂ AC [03] & AD ⟂ BC [01] & AD ⟂ EH [19] ⇒  ∠(EH-GD) = ∠GJA [72]
+055. DE:DB = DC:DF [36] & DE = DH [10] & DF = DI [12] ⇒  DH:DB = DC:DI [73]
+056. DH:DB = DC:DI [73] & ∠CDI = ∠HDB [46] (Similar Triangles)⇒  ∠DCI = ∠DHB [74]
+057. K,C,I are collinear [15] & K,B,H are collinear [16] & C,D,B are collinear [00] & F,D,H are collinear [50] & ∠DCI = ∠DHB [74] ⇒  ∠CKH = ∠CDH [75]
+058. ∠CKH = ∠CDH [75] ⇒  K,D,C,H are concyclic [76]
+059. K,D,C,H are concyclic [76] ⇒  ∠KDC = ∠KHC [77]
+060. F,A,B are collinear [05] & E,C,A are collinear [02] & BE ⟂ AC [03] & CF ⟂ AB [06] ⇒  ∠AFC = ∠BEA [78]
+061. ∠AFC = ∠BEA [78] & ∠ACF = ∠EBA [42] (Similar Triangles)⇒  AE:AB = AF:AC [79]
+062. AE:AB = AF:AC [79] & AE = AH [09] & AF = AI [11] ⇒  AH:AB = IA:CA [80]
+063. F,A,B are collinear [05] & ∠FEC = ∠FBC [61] & E,C,A are collinear [02] & ∠AEH = ∠EHA [51] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] ⇒  ∠EHA = ∠EFA [81]
+064. E,C,A are collinear [02] & ∠AFI = ∠FIA [58] & F,A,B are collinear [05] & AD ⟂ EH [19] & AD ⟂ BC [01] & AD ⟂ FI [27] & ∠FEC = ∠FBC [61] ⇒  ∠FEC = ∠(EH-IA) [82]
+065. ∠EHA = ∠EFA [81] & ∠FEC = ∠(EH-IA) [82] ⇒  ∠(FA-EC) = ∠HAI [83]
+066. ∠(FA-EC) = ∠HAI [83] & F,A,B are collinear [05] & E,C,A are collinear [02] ⇒  ∠BAH = ∠CAI [84]
+067. AH:AB = IA:CA [80] & ∠BAH = ∠CAI [84] (Similar Triangles)⇒  ∠(CI-BH) = ∠IAH [85]
+068. C,K,I are collinear [15] & K,B,H are collinear [16] & ∠IAH = ∠(CI-BH) [85] ⇒  ∠IAH = ∠IKH [86]
+069. ∠IAH = ∠IKH [86] ⇒  K,I,A,H are concyclic [87]
+070. J,I,A,H are concyclic [57] & F,E,I,A are concyclic [63] & G,E,A,F are concyclic [67] & G,E,A,H are concyclic [69] & K,I,A,H are concyclic [87] ⇒  J,H,K,G are concyclic [88]
+071. J,H,K,G are concyclic [88] ⇒  ∠JHK = ∠JGK [89]
+072. ∠KDC = ∠KHC [77] & D,C,B are collinear [00] & H,K,B are collinear [16] & AD ⟂ FI [27] & AD ⟂ EH [19] & AD ⟂ BC [01] & ∠JHK = ∠JGK [89] & J,C,H are collinear [14] ⇒  ∠JGK = ∠(EH-KD) [90]
+073. ∠(EH-GD) = ∠GJA [72] & ∠JGK = ∠(EH-KD) [90] ⇒  ∠(JA-GK) = ∠GDK [91]
+074. G,K,L are collinear [17] & J,A,L are collinear [18] & ∠(JA-GK) = ∠GDK [91] & G,D,A are collinear [07] ⇒  ∠KLA = ∠KDA [92]
+075. ∠KLA = ∠KDA [92] ⇒  K,D,A,L are concyclic [93]
+076. K,D,A,L are concyclic [93] ⇒  ∠KAD = ∠KLD [94]
+077. J,I,A,H are concyclic [57] & F,E,I,A are concyclic [63] & G,E,A,F are concyclic [67] & G,E,A,H are concyclic [69] & K,I,A,H are concyclic [87] ⇒  J,K,A,G are concyclic [95]
+078. J,K,A,G are concyclic [95] ⇒  ∠GJA = ∠GKA [96]
+079. G,D,A are collinear [07] & C,D,B are collinear [00] & E,C,A are collinear [02] & G,E,B are collinear [08] & BE ⟂ AC [03] & AD ⟂ BC [01] ⇒  ∠GDB = ∠AEG [97]
+080. G,D,A are collinear [07] & G,E,B are collinear [08] & ∠(AD-BE) = ∠(AD-BE) [04] ⇒  ∠AGE = ∠DGB [98]
+081. ∠GDB = ∠AEG [97] & ∠AGE = ∠DGB [98] (Similar Triangles)⇒  EA:EG = DB:DG [99]
+082. ∠GDB = ∠AEG [97] & ∠AGE = ∠DGB [98] (Similar Triangles)⇒  GA:GE = GB:GD [100]
+083. E,C,A are collinear [02] & G,D,A are collinear [07] & ∠EAD = ∠DAH [21] ⇒  ∠EAG = ∠GAH [101]
+084. AE = AH [09] & ∠EAG = ∠GAH [101] (SAS)⇒  GE = GH [102]
+085. EA:EG = DB:DG [99] & AE = AH [09] & GE = GH [102] ⇒  AH:GH = DB:GD [103]
+086. GA:GE = GB:GD [100] & GE = GH [102] ⇒  GA:GH = GB:GD [104]
+087. AH:GH = DB:GD [103] & GA:GH = GB:GD [104] (Similar Triangles)⇒  ∠BDG = ∠AHG [105]
+088. K,I,A,H are concyclic [87] & F,E,I,A are concyclic [63] & G,E,A,F are concyclic [67] & G,E,A,H are concyclic [69] ⇒  H,K,A,G are concyclic [106]
+089. H,K,A,G are concyclic [106] ⇒  ∠GHA = ∠GKA [107]
+090. G,D,A are collinear [07] & ∠BDG = ∠AHG [105] & D,C,B are collinear [00] & ∠GHA = ∠GKA [107] & AD ⟂ EH [19] & AD ⟂ BC [01] ⇒  ∠GKA = ∠(GD-EH) [108]
+091. J,I,B are collinear [13] & C,J,H are collinear [14] & C,D,B are collinear [00] & F,D,H are collinear [50] & ∠DHC = ∠DBI [47] ⇒  ∠BJH = ∠BDH [109]
+092. ∠BJH = ∠BDH [109] ⇒  H,J,D,B are concyclic [110]
+093. H,J,D,B are concyclic [110] ⇒  ∠HJD = ∠HBD [111]
+094. J,I,A,H are concyclic [57] & F,E,I,A are concyclic [63] & G,E,A,F are concyclic [67] & G,E,A,H are concyclic [69] & K,I,A,H are concyclic [87] ⇒  J,H,K,A are concyclic [112]
+095. J,H,K,A are concyclic [112] ⇒  ∠JHK = ∠JAK [113]
+096. ∠HJD = ∠HBD [111] & J,C,H are collinear [14] & D,C,B are collinear [00] & AD ⟂ FI [27] & AD ⟂ EH [19] & AD ⟂ BC [01] & ∠JHK = ∠JAK [113] & H,K,B are collinear [16] ⇒  ∠KAJ = ∠(EH-JD) [114]
+097. ∠GKA = ∠(GD-EH) [108] & ∠KAJ = ∠(EH-JD) [114] ⇒  ∠(GK-JA) = ∠GDJ [115]
+098. G,D,A are collinear [07] & G,K,L are collinear [17] & J,A,L are collinear [18] & ∠(GK-JA) = ∠GDJ [115] ⇒  ∠GDJ = ∠GLJ [116]
+099. ∠GDJ = ∠GLJ [116] ⇒  G,J,D,L are concyclic [117]
+100. G,J,D,L are concyclic [117] ⇒  ∠GJL = ∠GDL [118]
+101. C,D,B are collinear [00] & AD ⟂ EH [19] & ∠KAD = ∠KLD [94] & G,K,L are collinear [17] & ∠GJA = ∠GKA [96] & ∠GJL = ∠GDL [118] & J,A,L are collinear [18] & G,D,A are collinear [07] & AD ⟂ BC [01] ⇒  DC ∥ DL [119]
+102. DC ∥ DL [119] ⇒  C,D,L are collinear [120]
+103. C,D,L are collinear [120] & D,C,B are collinear [00] ⇒  C,L,B are collinear
+==========================
diff --git a/pretty.py b/pretty.py
index d794fd8..8d598a0 100644
--- a/pretty.py
+++ b/pretty.py
@@ -115,6 +115,10 @@ def pretty_nl(name: str, args: list[str]) -> str:
     return f'{pretty_angle(a, b, c, d)} = {pretty_angle(e, f, g, h)}'
   if name in ['eqratio', 'eqratio6', '/']:
     return '{}{}:{}{} = {}{}:{}{}'.format(*args)
+  if name == 'eqratio30':
+    return '({}{}:{}{}) * ({}{}:{}{}) * ({}{}:{}{}) = 1'.format(*args)
+  if name == 'eqratio40':
+    return '({}{}:{}{}) * ({}{}:{}{}) * ({}{}:{}{}) * ({}{}:{}{}) = 1'.format(*args)
   if name == 'eqratio3':
     a, b, c, d, o, o = args  # pylint: disable=redeclared-assigned-name
     return f'S {o} {a} {b} {o} {c} {d}'
diff --git a/problem.py b/problem.py
index 9108837..adc64cc 100644
--- a/problem.py
+++ b/problem.py
@@ -456,52 +456,52 @@ def conclusion_name_args(
 
 
 def why_eqratio(
-    d1: gm.Direction,
-    d2: gm.Direction,
-    d3: gm.Direction,
-    d4: gm.Direction,
+    l1: gm.Length,
+    l2: gm.Length,
+    l3: gm.Length,
+    l4: gm.Length,
     level: int,
 ) -> list[Dependency]:
   """Why two ratios are equal, returns a Dependency objects."""
-  all12 = list(gm.all_ratios(d1, d2, level))
-  all34 = list(gm.all_ratios(d3, d4, level))
+  all12 = list(gm.all_ratios(l1, l2, level))
+  all34 = list(gm.all_ratios(l3, l4, level))
 
   min_why = None
-  for ang12, d1s, d2s in all12:
-    for ang34, d3s, d4s in all34:
-      why0 = gm.why_equal(ang12, ang34, level)
+  for rat12, l1s, l2s in all12:
+    for rat34, l3s, l4s in all34:
+      why0 = gm.why_equal(rat12, rat34, level)
       if why0 is None:
         continue
-      d1_, d2_ = ang12._l
-      d3_, d4_ = ang34._l
-      why1 = gm.bfs_backtrack(d1, [d1_], d1s)
-      why2 = gm.bfs_backtrack(d2, [d2_], d2s)
-      why3 = gm.bfs_backtrack(d3, [d3_], d3s)
-      why4 = gm.bfs_backtrack(d4, [d4_], d4s)
+      l1_, l2_ = rat12._l
+      l3_, l4_ = rat34._l
+      why1 = gm.bfs_backtrack(l1, [l1_], l1s)
+      why2 = gm.bfs_backtrack(l2, [l2_], l2s)
+      why3 = gm.bfs_backtrack(l3, [l3_], l3s)
+      why4 = gm.bfs_backtrack(l4, [l4_], l4s)
       why = why0 + why1 + why2 + why3 + why4
       if min_why is None or len(why) < len(min_why[0]):
-        min_why = why, ang12, ang34, why0, why1, why2, why3, why4
+        min_why = why, rat12, rat34, why0, why1, why2, why3, why4
 
   if min_why is None:
     return None
 
-  _, ang12, ang34, why0, why1, why2, why3, why4 = min_why
-  d1_, d2_ = ang12._l
-  d3_, d4_ = ang34._l
+  _, rat12, rat34, why0, why1, why2, why3, why4 = min_why
+  l1_, l2_ = rat12._l
+  l3_, l4_ = rat34._l
 
-  if d1 == d1_ and d2 == d2_ and d3 == d3_ and d4 == d4_:
+  if l1 == l1_ and l2 == l2_ and l3 == l3_ and l4 == l4_:
     return why0
 
-  (a_, b_), (c_, d_) = d1_._obj.points, d2_._obj.points
-  (e_, f_), (g_, h_) = d3_._obj.points, d4_._obj.points
+  (a_, b_), (c_, d_) = l1_._obj.points, l2_._obj.points
+  (e_, f_), (g_, h_) = l3_._obj.points, l4_._obj.points
   deps = []
   if why0:
     dep = Dependency('eqratio', [a_, b_, c_, d_, e_, f_, g_, h_], '', level)
     dep.why = why0
     deps.append(dep)
 
-  (a, b), (c, d) = d1._obj.points, d2._obj.points
-  (e, f), (g, h) = d3._obj.points, d4._obj.points
+  (a, b), (c, d) = l1._obj.points, l2._obj.points
+  (e, f), (g, h) = l3._obj.points, l4._obj.points
   for why, (x, y), (x_, y_) in zip(
       [why1, why2, why3, why4],
       [(a, b), (c, d), (e, f), (g, h)],
@@ -514,6 +514,80 @@ def why_eqratio(
 
   return deps
 
+def why_eqratio30(
+    l1: gm.Length,
+    l2: gm.Length,
+    lp35: gm.Length_Pro,
+    lp46: gm.Length_Pro,
+    level: int,
+) -> list[Dependency]:
+  """Why two ratios are equal, returns a Dependency objects."""
+  all12 = list(gm.all_ratios(l1, l2, level))
+  all43 = list(gm.all_ratios2(lp46, lp35, level))
+  #print(all12,all43)
+  min_why = None
+  for rat12, l1s, l2s in all12:
+    for ratp43, lp4s, lp3s in all43:
+      why0 = gm.why_equal(rat12, ratp43, level)
+      if why0 is None:
+        continue
+      l1_, l2_ = rat12._l
+      lp46_, lp35_ = ratp43._lp
+      why1 = gm.bfs_backtrack(l1, [l1_], l1s)
+      why2 = gm.bfs_backtrack(l2, [l2_], l2s)
+      why3 = gm.bfs_backtrack(lp35, [lp35_], lp3s)
+      why4 = gm.bfs_backtrack(lp46, [lp46_], lp4s)
+      why = why0 + why1 + why2 + why3 + why4
+      if min_why is None or len(why) < len(min_why[0]):
+        min_why = why, rat12, ratp43, why0, why1, why2, why3, why4
+
+  if min_why is None:
+    return None
+
+  _, rat12, ratp43, why0, why1, why2, why3, why4 = min_why
+  l1_, l2_ = rat12._l
+  lp46_, lp35_ = ratp43._lp
+
+  if l1 == l1_ and l2 == l2_ and lp35 == lp35_ and lp46 == lp46_:
+    return why0
+  
+  l3_, l5_ = lp35._l
+  l4_, l6_ = lp46._l
+
+  (a_, b_), (c_, d_) = l1_._obj.points, l2_._obj.points
+  (m_, n_), (p_, q_) = l3_._obj.points, l4_._obj.points
+  (x_, y_), (z_, w_) = l5_._obj.points, l6_._obj.points
+  deps = []
+  if why0:
+    dep = Dependency('eqratio30', [a_, b_, c_, d_, m_, n_, p_, q_, x_, y_, z_, w_], '', level)
+    dep.why = why0
+    deps.append(dep)
+
+  l3, l5 = lp35._l
+  l4, l6 = lp46._l
+
+  (a, b), (c, d) = l1._obj.points, l2._obj.points
+  (m, n), (p, q) = l3._obj.points, l4._obj.points
+  (x, y), (z, w) = l5._obj.points, l6._obj.points
+
+  if why1:
+    dep = Dependency('cong', [a, b, a_, b_], '', level)
+    dep.why = why1
+    deps.append(dep)
+  if why2:
+    dep = Dependency('cong', [c, d, c_, d_], '', level)
+    dep.why = why2
+    deps.append(dep)
+  if why3:
+    dep = Dependency('eqratio', [m, n, m_, n_, x_, y_, x, y], '', level)
+    dep.why = why3
+    deps.append(dep)
+  if why4:
+    dep = Dependency('eqratio', [p, q, p_, q_, z_, w_, z, w], '', level)
+    dep.why = why4
+    deps.append(dep)
+  return deps
+
 
 def why_eqangle(
     d1: gm.Direction,
@@ -688,6 +762,7 @@ def __init__(
     self.trace = None
 
   def _find(self, dep_hashed: tuple[str, ...]) -> Dependency:
+    #self.why = [w for w in self.why if type(w) is not EmptyDependency]
     for w in self.why:
       f = w._find(dep_hashed)
       if f:
@@ -969,6 +1044,131 @@ def why_me(self, g: Any, level: int) -> None:
         elif ab._val and cd._val and mn._val and pq._val:
           self.why = why_eqangle(ab._val, cd._val, mn._val, pq._val, level)
 
+    elif self.name == 'eqratio30':
+      a, b, c, d, m, n, p, q, x, y, z, w = self.args
+      ab = g._get_segment(a, b)
+      cd = g._get_segment(c, d)
+      mn = g._get_segment(m, n)
+      pq = g._get_segment(p, q)
+      xy = g._get_segment(x, y)
+      zw = g._get_segment(z, w)
+      if ab is None or cd is None or mn is None or pq is None or xy is None or zw is None:
+        if {a, b} == {c, d}:
+          dp = Dependency('eqratio', [m, n, p, q, z, w, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {a, b} == {p, q}:
+          dp = Dependency('eqratio', [m, n, c, d, z, w, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {a, b} == {z, w}:
+          dp = Dependency('eqratio', [m, n, p, q, c, d, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]  
+        if {m, n} == {c, d}:
+          dp = Dependency('eqratio', [a, b, p, q, z, w, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {m, n} == {p, q}:
+          dp = Dependency('eqratio', [a, b, c, d, z, w, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {m, n} == {z, w}:
+          dp = Dependency('eqratio', [a, b, p, q, c, d, x, y], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]  
+        if {x, y} == {c, d}:
+          dp = Dependency('eqratio', [a, b, p, q, z, w, m, n], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {x, y} == {p, q}:
+          dp = Dependency('eqratio', [a, b, c, d, z, w, m, n], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]
+        if {x, y} == {z, w}:
+          dp = Dependency('eqratio', [a, b, p, q, c, d, m, n], None, level)
+          self.why = [dp.why_me_or_cache(g, level)]  
+        return
+      
+      ab_mn, _ = g._get_or_create_length_pro(ab, mn, deps=None)
+      ab_xy, _ = g._get_or_create_length_pro(ab, xy, deps=None)
+      mn_xy, _ = g._get_or_create_length_pro(mn, xy, deps=None)
+      cd_pq, _ = g._get_or_create_length_pro(cd, pq, deps=None)
+      cd_zw, _ = g._get_or_create_length_pro(cd, zw, deps=None)
+      pq_zw, _ = g._get_or_create_length_pro(pq, zw, deps=None)
+
+      self.why = []
+      if g.is_equal(ab, cd) or g.is_equal(mn_xy, pq_zw):
+        dep1 = Dependency('cong', [a, b, c, d], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [m, n, p, q, z, w, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(ab, pq) or g.is_equal(mn_xy, cd_zw):
+        dep1 = Dependency('cong', [a, b, p, q], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [m, n, c, d, z, w, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(ab, zw) or g.is_equal(mn_xy, cd_pq):
+        dep1 = Dependency('cong', [a, b, z, w], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [m, n, c, d, p, q, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(mn, cd) or g.is_equal(ab_xy, pq_zw):
+        dep1 = Dependency('cong', [m, n, c, d], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, p, q, z, w, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(mn, pq) or g.is_equal(ab_xy, cd_zw):
+        dep1 = Dependency('cong', [m, n, p, q], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, c, d, z, w, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(mn, zw) or g.is_equal(ab_xy, cd_pq):
+        dep1 = Dependency('cong', [m, n, z, w], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, c, d, p, q, x, y], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(xy, cd) or g.is_equal(ab_mn, pq_zw):
+        dep1 = Dependency('cong', [x, y, c, d], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, p, q, z, w, m, n], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(xy, pq) or g.is_equal(ab_mn, cd_zw):
+        dep1 = Dependency('cong', [x, y, p, q], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, c, d, z, w, m, n], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      elif g.is_equal(xy, zw) or g.is_equal(ab_mn, cd_pq):
+        dep1 = Dependency('cong', [x, y, z, w], None, level)
+        dep1.why_me(g, level)
+        dep2 = Dependency('eqratio', [a, b, c, d, p, q, m, n], None, level)
+        dep2.why_me(g, level)
+        self.why += [dep1, dep2]
+      else:
+        self.why = None
+
+      if self.why is None:
+        self.why = why_eqratio30(ab._val, cd._val, mn_xy, pq_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(ab._val, pq._val, mn_xy, cd_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(ab._val, zw._val, mn_xy, cd_pq, level)
+      if self.why is None:
+        self.why = why_eqratio30(mn._val, cd._val, ab_xy, pq_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(mn._val, pq._val, ab_xy, cd_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(mn._val, zw._val, ab_xy, cd_pq, level)
+      if self.why is None:
+        self.why = why_eqratio30(xy._val, cd._val, ab_mn, pq_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(xy._val, pq._val, ab_mn, cd_zw, level)
+      if self.why is None:
+        self.why = why_eqratio30(xy._val, zw._val, ab_mn, cd_pq, level)
+      if self.why is None:
+        self.why = []
+
+
     elif self.name in ['diff', 'npara', 'nperp', 'ncoll', 'sameside']:
       self.why = []
 
@@ -1129,5 +1329,55 @@ def hashed_txt(name: str, args: list[str]) -> tuple[str, ...]:
 
   if name in ['sameside', 's_angle']:
     return (name,) + tuple(args)
+  
+  if name in ['eqratio30']:
+    a, b, c, d, e, f, g, h, i, j, k, l = args
+    a, b = sorted([a, b])
+    c, d = sorted([c, d])
+    e, f = sorted([e, f])
+    g, h = sorted([g, h])
+    i, j = sorted([i, j])
+    k, l = sorted([k, l])
+    ratios1 = [(a, b),(e, f),(i, j)]
+    ratios1.sort()
+    ratios2 = [(c, d),(g, h),(k, l)]
+    ratios2.sort()
+    if ratios1 > ratios2:
+      ratios1, ratios2 = ratios2, ratios1
+    a, b = ratios1[0]
+    e, f = ratios1[1]
+    i, j = ratios1[2]
+    c, d = ratios2[0]
+    g, h = ratios2[1]
+    k, l = ratios2[2]
+    
+    return (name, a, b, c, d, e, f, g, h, i, j, k, l)
+  
+  if name in ['eqratio40']:
+    a, b, c, d, e, f, g, h, i, j, k, l, x, y, z, w = args
+    a, b = sorted([a, b])
+    c, d = sorted([c, d])
+    e, f = sorted([e, f])
+    g, h = sorted([g, h])
+    i, j = sorted([i, j])
+    k, l = sorted([k, l])
+    x, y = sorted([x, y])
+    z, w = sorted([z, w])
+    ratios1 = [(a, b),(e, f),(i, j),(x, y)]
+    ratios1.sort()
+    ratios2 = [(c, d),(g, h),(k, l),(z, w)]
+    ratios2.sort()
+    if ratios1 > ratios2:
+      ratios1, ratios2 = ratios2, ratios1
+    a, b = ratios1[0]
+    e, f = ratios1[1]
+    i, j = ratios1[2]
+    x, y = ratios1[3]
+    c, d = ratios2[0]
+    g, h = ratios2[1]
+    k, l = ratios2[2]
+    z, w = ratios2[3]
+    
+    return (name, a, b, c, d, e, f, g, h, i, j, k, l, x, y, z, w)
 
   raise ValueError(f'Not recognize {name} to hash.')
diff --git a/pros2.txt b/pros2.txt
new file mode 100644
index 0000000..8dbee47
--- /dev/null
+++ b/pros2.txt
@@ -0,0 +1,66 @@
+test_circle
+a b c = triangle a b c; o = circle o a b c; d = on_tline d a b c, on_circle d o a ? cyclic a b c a
+test_ccc2p
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; p = on_line p a b, on_line p c d ? eqratio p a p c p d p b
+test_ccc2pt1
+a b c = triangle a b c; o = circle o a b c; p = on_line p b c, on_tline p a o a; d = on_circle d o a; e = on_line e p d, on_circle e o a ? eqratio p a p b p c p a
+test_ccc2pt2
+a b c = triangle a b c; o = circle o a b c; p = on_line p b c, on_tline p a o a; d = on_circle d o a; e = on_line e p d, on_circle e o a ? eqratio p a p d p e p a
+test_ccc2pt3
+a b c = triangle a b c; o = circle o a b c; p = on_line p b a, on_tline p c o c; d = on_circle d o a; e = on_line e p d, on_circle e o a ? eqratio p c p b p a p c
+test_ccc2pt4
+a b c = triangle a b c; o = circle o a b c; p = on_line p b a, on_tline p c o c; d = on_circle d o a; e = on_line e p d, on_circle e o a ? eqratio p c p d p e p c
+test_pascal61
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a ? coll g h i
+test_pascal62
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a; a1 b1 c1 = triangle a1 b1 c1; o1 = circle o1 a1 b1 c1; d1 = on_circle d1 o1 a1; e1 = on_circle e1 o1 a1; f1 = on_circle f1 o1 a1 ? coll g h i
+test_pascal63
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a; a1 = free; b1 = free; c1 = free; o1 = circle o1 a1 b1 c1; d1 = on_circle d1 o1 a1; e1 = on_circle e1 o1 a1; f1 = on_circle f1 o1 a1 ? coll g h i
+test_circle2
+a b c = triangle a b c; o = circle o a b c; d = free; w = circle w a b d ? cong o a w a
+test_pascal5
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; g = on_tline g a o a, on_line g c d; h = on_line h a b, on_line h d e; i = on_line i b c, on_line i e a ? coll g h i
+test_pascal41
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; g = on_tline g a o a, on_line g b c; h = on_line h a b, on_line h c d; i = on_tline i b o b, on_line i d a ? coll g h i
+test_pascal42
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; g = on_tline g a o a, on_tline g b o b; h = on_line h a c, on_line h b d; i = on_line i c b, on_line i d a ? coll g h i
+test_pascal6_rev
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; g = on_line g a b, on_line g d e; h = on_line h b c; i = on_line i g h, on_line i c d; f = on_line f h e, on_line f a i ? cong o a o f
+test_p2ccc
+a b = segment a b; o = on_bline o a b; w = on_bline w a b; c = on_circle c o a; d = on_circle d o a; p = on_line p a b, on_line p c d; e = on_circle e w a; f = on_circle f w a, on_line f p e ? cyclic c d e f
+test_radical_axis1
+a b = segment a b; o1 = on_bline o1 a b; o2 = on_bline o2 a b; o3 = free; c = on_circle c o1 a; d = on_circle d o1 a, on_circle d o3 c; e = on_circle e o2 a, on_circle e o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
+test_radical_axis2
+a b c = triangle a b c; e = free; o1 = circle o1 a b c; o2 = circle o2 a b e; o3 = on_bline o3 c e; d = on_circle d o1 a, on_circle d o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
+test_radical_axis_rev
+a b c = triangle a b c; d = on_line a b; o1 = circle o1 a b c; e = on_line e c d, on_circle e o1 a; o2 = on_bline o2 c e; f = on_circle f o2 c; g = on_circle g o2 c, on_line g d f ? cyclic a b f g
+test_gcenter1
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; g = on_line g b e, on_line g a d; f = on_line f a b, on_line f c g ? cong f a f b
+test_gcenter2
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f ? coll a g d
+test_icenter1
+a b c = triangle a b c; d = angle_bisector d b a c, on_line d b c; e = angle_bisector e a b c, on_line e a c; i = on_line i a d, on_line i b e; f = on_line f c i, on_line f a b ? eqangle c a c f c f c b
+example2_1
+a b c = triangle a b c; d = foot d a b c; h = on_line h a d; e = on_line e a c, on_line e b h; f = on_line f a b, on_line f c h; p = on_pline p a b c, on_line p d f; q = on_line q p a, on_line q d e ? cong a p a q
+test_menelaus
+a b c = triangle a b c; d = midpoint d b c; e = on_line e c a; f = on_line f a b, on_line f d e ? eqratio c e e a b f f a
+exercise20_2
+a b = segment a b; c = on_tline c b a b, on_circle c b a; d = midpoint d b c; e = foot e b a d; f = on_line f b e, on_line f a c; g = midpoint g a f ? cong a g c f
+example1_11
+a b c = triangle a b c; d = on_line d a b; e = on_line e a c; f = midpoint f d e; g = on_line g d e; h = mirror h g f; i = on_line i a b; j = on_line j g i, on_line j a c; k = on_line k a b; l = on_line l k h, on_line l a c; m = on_line m j k, on_line m d e; n = on_line n i l, on_line n d e ? cong f m f n
+cmo23_5
+a b c = triangle a b c; d = on_line d b c; e = on_pline e d a b, on_circle e b d; f = on_pline f d a c, on_circle f c d; g = circle g d e f; h = on_circle h g d, on_line h a d ? eqratio30 a e a f b h b e c f c h
+reduced_cmo_2023_p5_b
+a b c = triangle a b c; k = on_line k b c; p = on_pline p k a b, on_circle p b k; q = on_pline q k a c, on_circle q c k; y = circle p k q; t = on_circle t y k, on_line t a k; z1 = on_line z1 p q; d = on_line d a p, eqdistance d a q c; f = on_line f p b, eqdistance f b c t; y1 = circle p d q; y2 = circle p f t; e = on_circle e y1 q, on_line q a; g = on_circle g y2 t, on_line g t b ? cong a e b g
+example2_8_1
+a b c = triangle a b c; d = midpoint d a c; e = on_line e b d; f = on_line f a e, on_line f b c; g = on_line g c e, on_line g a b; h = on_pline h f c e, on_line h b d; i = on_circle i e f, on_circle i f e; j = on_circle j e g, on_circle j g e ? cong h i h j
+example2_8_2
+a b c = triangle a b c; d = midpoint d a c; e = on_line e b d; f = on_line f a e, on_line f b c; g = on_line g c e, on_line g a b; h = on_pline h f c e, on_line h b d; i = on_circle i e f, on_circle i f e; j = on_circle j e g, on_circle j g e ? cong h i i j
+example2_7
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_line e a b, on_line e d c; f = on_line f a d, on_line f b c; p = on_circle p o a; r = on_line r p f, on_circle r o a; s = on_line s p e, on_circle s o a; t = on_line t a c, on_line t b d ? eqratio30 a s s d d c r c b r b a
+example2_4
+a b c = triangle a b c; d = on_circle d c a, on_line d b c; o = circle o a c d; m = midpoint m b c; p = on_circle p o c, on_circle p m c; e = on_line e a c, on_line e b p; f = on_line f a b, on_line f c p ? coll d e f
+test_anglebi
+a b c = triangle a b c; i = incenter i a b c; d = on_line d a i, on_line d b c; e = on_tline e a a i, on_line e b c ? eqratio b d c d b e c e
+test_413
+a b = segment a b; c = on_circle c a b; d = midpoint d b c; e = foot e d a c; f = midpoint f d e; g = on_line g a f, on_line g b e ? perp a f b e
\ No newline at end of file
diff --git a/pyvenv.cfg b/pyvenv.cfg
new file mode 100644
index 0000000..ff7177d
--- /dev/null
+++ b/pyvenv.cfg
@@ -0,0 +1,8 @@
+home = /environment/miniconda3/bin
+implementation = CPython
+version_info = 3.10.12.final.0
+virtualenv = 20.29.2
+include-system-site-packages = false
+base-prefix = /environment/miniconda3
+base-exec-prefix = /environment/miniconda3
+base-executable = /environment/miniconda3/bin/python3.10
diff --git a/rules.txt b/rules.txt
index f329f76..8e6d4ab 100644
--- a/rules.txt
+++ b/rules.txt
@@ -41,3 +41,20 @@ eqratio6 B A B C Q P Q R, eqangle6 B A B C Q P Q R, ncoll A B C => simtri* A B C
 eqratio6 B A B C Q P Q R, eqratio6 C A C B R P R Q, ncoll A B C, cong A B P Q => contri* A B C P Q R
 para a b c d, coll m a d, coll n b c, eqratio6 m a m d n b n c, sameside m a d n b c => para m n a b
 para a b c d, coll m a d, coll n b c, para m n a b => eqratio6 m a m d n b n c
+coll A F B, coll B D C, coll C E A, coll D E F => eqratio30 A F F B B D D C C E E A
+coll A F B, coll B D C, coll C E A, eqratio30 A F F B B D D C C E E A => coll D E F
+coll A F B, coll B D C, coll C E A, coll B P E, coll C P F, coll A P D => eqratio30 A F F B B D D C C E E A
+coll A F B, coll B D C, coll C E A, coll B P E, coll C P F, eqratio30 A F F B B D D C C E E A => coll A P D
+cyclic A B C D, coll P A B, coll P C D => eqratio P A P C P D P B
+circle O A B C, perp O A A P, coll P B C => eqratio P A P B P C P A
+cong O A O B, perp O A A P, perp O B B P => cong P A P B
+coll P A B, coll P C D, ncoll A B C D, eqratio P A P C P D P B => cyclic A B C D
+cyclic A B C D, cyclic A B E F, cyclic C D E F, coll P A B, coll P C D => coll P E F
+cyclic A B C D E F, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A => coll G H I
+circle O A B C, cong O A O D, cong O A O E, perp O A A G, coll G C D, coll H A B, coll H D E, coll I B C, coll I E A => coll G H I
+circle O A B C, cong O A O D, perp O A A G, coll G B C, coll H A B, coll H C D, perp O B B I, coll I D A => coll G H I
+circle O A B C, cong O A O D, perp O A A G, perp O B B G, coll H A C, coll H B D, coll I C B, coll I D A => coll G H I
+circle O A B C, cong O A O D, cong O A O E, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A, coll G H I => cong O A O F
+perp A B A C, perp A D B C, coll B C D => eqratio B A B D B C B A
+perp A B A C, coll B C D, perp A D B C => eqratio D A D B D C D A
+eqratio6 B A B C Q P Q R, coll A B C, coll P Q R => eqratio B A A C Q P P R
\ No newline at end of file
diff --git a/rules1.txt b/rules1.txt
new file mode 100644
index 0000000..139dfae
--- /dev/null
+++ b/rules1.txt
@@ -0,0 +1 @@
+circle O A B C, cong O A O D, cong O A O E, coll G A B, coll G D E, coll H B C, coll H E F, coll I C D, coll I F A, coll G H I => cong O A O F
\ No newline at end of file
diff --git a/rules2.txt b/rules2.txt
new file mode 100644
index 0000000..1c87686
--- /dev/null
+++ b/rules2.txt
@@ -0,0 +1,6 @@
+cong O A O B, cong O B O C, cong O C O D => cyclic A B C D
+A A B B C D
+AA BC / AB CD / BB DA
+
+A A C B B D
+AA BB / AC BD / CB DA
\ No newline at end of file
diff --git a/run.sh b/run.sh
index 330d1fe..83f9561 100644
--- a/run.sh
+++ b/run.sh
@@ -14,20 +14,15 @@
 # ==============================================================================
 
 # !/bin/bash
-set -e
-set -x
 
 virtualenv -p python3 .
 source ./bin/activate
 
 pip install --require-hashes -r requirements.txt
 
-gdown --folder https://bit.ly/alphageometry
 DATA=ag_ckpt_vocab
 
 MELIAD_PATH=meliad_lib/meliad
-mkdir -p $MELIAD_PATH
-git clone https://github.com/google-research/meliad $MELIAD_PATH
 export PYTHONPATH=$PYTHONPATH:$MELIAD_PATH
 
 DDAR_ARGS=(
@@ -70,3 +65,5 @@ python -m alphageometry \
 "${DDAR_ARGS[@]}" \
 "${SEARCH_ARGS[@]}" \
 "${LM_ARGS[@]}"
+set -e
+set -x
diff --git a/run_tests.sh b/run_tests.sh
index 7005644..04095e5 100644
--- a/run_tests.sh
+++ b/run_tests.sh
@@ -13,6 +13,8 @@
 # limitations under the License.
 # ==============================================================================
 
+source ./bin/activate
+
 DATA=ag_ckpt_vocab
 MELIAD_PATH=meliad_lib/meliad
 export PYTHONPATH=$PYTHONPATH:$MELIAD_PATH
diff --git a/share/man/man1/ttx.1 b/share/man/man1/ttx.1
new file mode 100644
index 0000000..bba23b5
--- /dev/null
+++ b/share/man/man1/ttx.1
@@ -0,0 +1,225 @@
+.Dd May 18, 2004
+.\" ttx is not specific to any OS, but contrary to what groff_mdoc(7)
+.\" seems to imply, entirely omitting the .Os macro causes 'BSD' to
+.\" be used, so I give a zero-width space as its argument.
+.Os \&
+.\" The "FontTools Manual" argument apparently has no effect in
+.\" groff 1.18.1. I think it is a bug in the -mdoc groff package.
+.Dt TTX 1 "FontTools Manual"
+.Sh NAME
+.Nm ttx
+.Nd tool for manipulating TrueType and OpenType fonts
+.Sh SYNOPSIS
+.Nm
+.Bk
+.Op Ar option ...
+.Ek
+.Bk
+.Ar file ...
+.Ek
+.Sh DESCRIPTION
+.Nm
+is a tool for manipulating TrueType and OpenType fonts.  It can convert
+TrueType and OpenType fonts to and from an
+.Tn XML Ns -based format called
+.Tn TTX .
+.Tn TTX
+files have a
+.Ql .ttx
+extension.
+.Pp
+For each
+.Ar file
+argument it is given,
+.Nm
+detects whether it is a
+.Ql .ttf ,
+.Ql .otf
+or
+.Ql .ttx
+file and acts accordingly: if it is a
+.Ql .ttf
+or
+.Ql .otf
+file, it generates a
+.Ql .ttx
+file; if it is a
+.Ql .ttx
+file, it generates a
+.Ql .ttf
+or
+.Ql .otf
+file.
+.Pp
+By default, every output file is created in the same directory as the
+corresponding input file and with the same name except for the
+extension, which is substituted appropriately.
+.Nm
+never overwrites existing files; if necessary, it appends a suffix to
+the output file name before the extension, as in
+.Pa Arial#1.ttf .
+.Ss "General options"
+.Bl -tag -width ".Fl t Ar table"
+.It Fl h
+Display usage information.
+.It Fl d Ar dir
+Write the output files to directory
+.Ar dir
+instead of writing every output file to the same directory as the
+corresponding input file.
+.It Fl o Ar file
+Write the output to
+.Ar file
+instead of writing it to the same directory as the
+corresponding input file.
+.It Fl v
+Be verbose.  Write more messages to the standard output describing what
+is being done.
+.It Fl a
+Allow virtual glyphs ID's on compile or decompile.
+.El
+.Ss "Dump options"
+The following options control the process of dumping font files
+(TrueType or OpenType) to
+.Tn TTX
+files.
+.Bl -tag -width ".Fl t Ar table"
+.It Fl l
+List table information.  Instead of dumping the font to a
+.Tn TTX
+file, display minimal information about each table.
+.It Fl t Ar table
+Dump table
+.Ar table .
+This option may be given multiple times to dump several tables at
+once.  When not specified, all tables are dumped.
+.It Fl x Ar table
+Exclude table
+.Ar table
+from the list of tables to dump.  This option may be given multiple
+times to exclude several tables from the dump.  The
+.Fl t
+and
+.Fl x
+options are mutually exclusive.
+.It Fl s
+Split tables.  Dump each table to a separate
+.Tn TTX
+file and write (under the name that would have been used for the output
+file if the
+.Fl s
+option had not been given) one small
+.Tn TTX
+file containing references to the individual table dump files.  This
+file can be used as input to
+.Nm
+as long as the referenced files can be found in the same directory.
+.It Fl i
+.\" XXX: I suppose OpenType programs (exist and) are also affected.
+Don't disassemble TrueType instructions.  When this option is specified,
+all TrueType programs (glyph programs, the font program and the
+pre-program) are written to the
+.Tn TTX
+file as hexadecimal data instead of
+assembly.  This saves some time and results in smaller
+.Tn TTX
+files.
+.It Fl y Ar n
+When decompiling a TrueType Collection (TTC) file,
+decompile font number
+.Ar n ,
+starting from 0.
+.El
+.Ss "Compilation options"
+The following options control the process of compiling
+.Tn TTX
+files into font files (TrueType or OpenType):
+.Bl -tag -width ".Fl t Ar table"
+.It Fl m Ar fontfile
+Merge the input
+.Tn TTX
+file
+.Ar file
+with
+.Ar fontfile .
+No more than one
+.Ar file
+argument can be specified when this option is used.
+.It Fl b
+Don't recalculate glyph bounding boxes.  Use the values in the
+.Tn TTX
+file as is.
+.El
+.Sh "THE TTX FILE FORMAT"
+You can find some information about the
+.Tn TTX
+file format in
+.Pa documentation.html .
+In particular, you will find in that file the list of tables understood by
+.Nm
+and the relations between TrueType GlyphIDs and the glyph names used in
+.Tn TTX
+files.
+.Sh EXAMPLES
+In the following examples, all files are read from and written to the
+current directory.  Additionally, the name given for the output file
+assumes in every case that it did not exist before
+.Nm
+was invoked.
+.Pp
+Dump the TrueType font contained in
+.Pa FreeSans.ttf
+to
+.Pa FreeSans.ttx :
+.Pp
+.Dl ttx FreeSans.ttf
+.Pp
+Compile
+.Pa MyFont.ttx
+into a TrueType or OpenType font file:
+.Pp
+.Dl ttx MyFont.ttx
+.Pp
+List the tables in
+.Pa FreeSans.ttf
+along with some information:
+.Pp
+.Dl ttx -l FreeSans.ttf
+.Pp
+Dump the
+.Sq cmap
+table from
+.Pa FreeSans.ttf
+to
+.Pa FreeSans.ttx :
+.Pp
+.Dl ttx -t cmap FreeSans.ttf
+.Sh NOTES
+On MS\-Windows and MacOS,
+.Nm
+is available as a graphical application to which files can be dropped.
+.Sh SEE ALSO
+.Pa documentation.html
+.Pp
+.Xr fontforge 1 ,
+.Xr ftinfo 1 ,
+.Xr gfontview 1 ,
+.Xr xmbdfed 1 ,
+.Xr Font::TTF 3pm
+.Sh AUTHORS
+.Nm
+was written by
+.An -nosplit
+.An "Just van Rossum" Aq just@letterror.com .
+.Pp
+This manual page was written by
+.An "Florent Rougon" Aq f.rougon@free.fr
+for the Debian GNU/Linux system based on the existing FontTools
+documentation.  It may be freely used, modified and distributed without
+restrictions.
+.\" For Emacs:
+.\" Local Variables:
+.\" fill-column: 72
+.\" sentence-end: "[.?!][]\"')}]*\\($\\| $\\|   \\|  \\)[   \n]*"
+.\" sentence-end-double-space: t
+.\" End:
\ No newline at end of file
diff --git a/speed.txt b/speed.txt
new file mode 100644
index 0000000..9366b02
--- /dev/null
+++ b/speed.txt
@@ -0,0 +1,30 @@
+test_ccc2p
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; p = on_line p a b, on_line p c d ? eqratio p a p c p d p b
+test_ccc2pt
+a b c = triangle a b c; o = circle o a b c; p = on_line p b c, on_tline p a o a; d = on_circle d o a; e = on_line e p d, on_circle e o a ? eqratio p a p b p c p a
+test_p2ccc
+a b = segment a b; o = on_bline o a b; w = on_bline w a b; c = on_circle c o a; d = on_circle d o a; p = on_line p a b, on_line p c d; e = on_circle e w a; f = on_circle f w a, on_line f p e ? cyclic c d e f
+test_radical_axis1
+a b = segment a b; o1 = on_bline o1 a b; o2 = on_bline o2 a b; o3 = free; c = on_circle c o1 a; d = on_circle d o1 a, on_circle d o3 c; e = on_circle e o2 a, on_circle e o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
+test_radical_axis2
+a b c = triangle a b c; e = free; o1 = circle o1 a b c; o2 = circle o2 a b e; o3 = on_bline o3 c e; d = on_circle d o1 a, on_circle d o3 c; f = on_circle f o2 a, on_circle f o3 c; g = on_line g c d, on_line g e f ? coll g a b
+test_pascal61
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a ? coll g h i
+test_pascal62
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a; a1 b1 c1 = triangle a1 b1 c1; o1 = circle o1 a1 b1 c1; d1 = on_circle d1 o1 a1; e1 = on_circle e1 o1 a1; f1 = on_circle f1 o1 a1 ? coll g h i
+test_pascal63
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; f = on_circle f o a; g = on_line g a b, on_line g d e; h = on_line h b c, on_line h e f; i = on_line i c d, on_line i f a; a1 = free; b1 = free; c1 = free; o1 = circle o1 a1 b1 c1; d1 = on_circle d1 o1 a1; e1 = on_circle e1 o1 a1; f1 = on_circle f1 o1 a1 ? coll g h i
+test_pascal5
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; g = on_tline g a o a, on_line g c d; h = on_line h a b, on_line h d e; i = on_line i b c, on_line i e a ? coll g h i
+test_pascal41
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; g = on_tline g a o a, on_line g b c; h = on_line h a b, on_line h c d; i = on_tline i b o b, on_line i d a ? coll g h i
+test_pascal42
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; g = on_tline g a o a, on_tline g b o b; h = on_line h a c, on_line h b d; i = on_line i c b, on_line i d a ? coll g h i
+test_pascal6_rev
+a b c = triangle a b c; o = circle o a b c; d = on_circle d o a; e = on_circle e o a; g = on_line g a b, on_line g d e; h = on_line h b c; i = on_line i g h, on_line i c d; f = on_line f h e, on_line f a i ? cong o a o f
+test_gcenter1
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; g = on_line g b e, on_line g a d; f = on_line f a b, on_line f c g ? cong f a f b
+test_gcenter2
+a b c = triangle a b c; d = midpoint d b c; e = midpoint e c a; f = midpoint f a b; g = on_line g b e, on_line g c f ? coll a g d
+test_menelaus
+a b c = triangle a b c; d = midpoint d b c; e = on_line e c a; f = on_line f a b, on_line f d e ? eqratio c e e a b f f a
\ No newline at end of file
diff --git a/test.py b/test.py
new file mode 100644
index 0000000..f013588
--- /dev/null
+++ b/test.py
@@ -0,0 +1,5 @@
+import random
+
+for _ in range(10): 
+    a = random.randint(1,50)
+    print(a)
\ No newline at end of file
diff --git a/test.sh b/test.sh
new file mode 100644
index 0000000..00e0165
--- /dev/null
+++ b/test.sh
@@ -0,0 +1,7 @@
+# !/bin/bash
+virtualenv -p python3 .
+source ./bin/activate
+
+export TF_CPP_MIN_LOG_LEVEL=0 
+
+python test.py
\ No newline at end of file
diff --git a/trace_back.py b/trace_back.py
index 2543918..06eb5f5 100644
--- a/trace_back.py
+++ b/trace_back.py
@@ -279,7 +279,9 @@ def get_logs(
     set[gm.Point],
 ]:
   """Given a DAG and conclusion N, return the premise, aux, proof."""
+  print(query.hashed())
   query = query.why_me_or_cache(g, query.level)
+  print(query)
   log = recursive_traceback(query)
   log, setup, aux_setup, setup_points, _ = separate_dependency_difference(
       query, log