TSTP Solution File: GEO040-3 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO040-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun May  5 05:14:44 EDT 2024

% Result   : Unsatisfiable 0.19s 0.46s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :  165
% Syntax   : Number of formulae    :  420 (  61 unt;   0 def)
%            Number of atoms       : 1486 ( 207 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives : 1914 ( 848   ~; 945   |;   0   &)
%                                         ( 121 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :  125 ( 123 usr; 122 prp; 0-4 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-6 aty)
%            Number of variables   : 1073 (1073   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1712,plain,
    $false,
    inference(avatar_sat_refutation,[],[f66,f71,f76,f81,f86,f91,f95,f99,f103,f107,f111,f115,f119,f125,f129,f133,f137,f153,f157,f163,f167,f171,f175,f179,f183,f187,f191,f196,f229,f233,f250,f254,f258,f277,f281,f295,f299,f315,f319,f327,f331,f339,f345,f353,f370,f383,f393,f397,f401,f405,f409,f413,f417,f532,f547,f561,f565,f569,f573,f603,f607,f611,f633,f717,f721,f764,f768,f772,f776,f811,f815,f819,f823,f877,f907,f911,f923,f927,f967,f980,f988,f1010,f1014,f1018,f1022,f1027,f1031,f1035,f1039,f1164,f1168,f1172,f1176,f1255,f1259,f1303,f1307,f1350,f1371,f1406,f1423,f1450,f1475,f1483,f1502,f1506,f1521,f1525,f1552,f1558,f1595,f1614,f1618,f1622,f1626,f1630,f1634,f1639,f1643,f1647,f1711]) ).

fof(f1711,plain,
    ( spl0_1
    | ~ spl0_2
    | ~ spl0_116
    | ~ spl0_121 ),
    inference(avatar_split_clause,[],[f1704,f1645,f1624,f68,f63]) ).

fof(f63,plain,
    ( spl0_1
  <=> u = v ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f68,plain,
    ( spl0_2
  <=> between(u,v,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f1624,plain,
    ( spl0_116
  <=> ! [X0] :
        ( ~ between(u,X0,w)
        | u = inner_pasch(v,u,w,X0,u) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f1645,plain,
    ( spl0_121
  <=> ! [X0] :
        ( ~ between(X0,v,w)
        | v = inner_pasch(v,u,w,v,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f1704,plain,
    ( u = v
    | ~ spl0_2
    | ~ spl0_116
    | ~ spl0_121 ),
    inference(forward_demodulation,[],[f1699,f1676]) ).

fof(f1676,plain,
    ( u = inner_pasch(v,u,w,v,u)
    | ~ spl0_2
    | ~ spl0_116 ),
    inference(resolution,[],[f1625,f70]) ).

fof(f70,plain,
    ( between(u,v,w)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f1625,plain,
    ( ! [X0] :
        ( ~ between(u,X0,w)
        | u = inner_pasch(v,u,w,X0,u) )
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1624]) ).

fof(f1699,plain,
    ( v = inner_pasch(v,u,w,v,u)
    | ~ spl0_2
    | ~ spl0_121 ),
    inference(resolution,[],[f1646,f70]) ).

fof(f1646,plain,
    ( ! [X0] :
        ( ~ between(X0,v,w)
        | v = inner_pasch(v,u,w,v,X0) )
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1645]) ).

fof(f1647,plain,
    ( spl0_121
    | ~ spl0_3
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f754,f719,f73,f1645]) ).

fof(f73,plain,
    ( spl0_3
  <=> between(v,u,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f719,plain,
    ( spl0_66
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | inner_pasch(X1,X3,X2,X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f754,plain,
    ( ! [X0] :
        ( ~ between(X0,v,w)
        | v = inner_pasch(v,u,w,v,X0) )
    | ~ spl0_3
    | ~ spl0_66 ),
    inference(resolution,[],[f720,f75]) ).

fof(f75,plain,
    ( between(v,u,w)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f73]) ).

fof(f720,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X1,X3,X2)
        | ~ between(X0,X1,X2)
        | inner_pasch(X1,X3,X2,X1,X0) = X1 )
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f719]) ).

fof(f1643,plain,
    ( spl0_120
    | ~ spl0_2
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f753,f719,f68,f1641]) ).

fof(f1641,plain,
    ( spl0_120
  <=> ! [X0] :
        ( ~ between(X0,u,w)
        | u = inner_pasch(u,v,w,u,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f753,plain,
    ( ! [X0] :
        ( ~ between(X0,u,w)
        | u = inner_pasch(u,v,w,u,X0) )
    | ~ spl0_2
    | ~ spl0_66 ),
    inference(resolution,[],[f720,f70]) ).

fof(f1639,plain,
    ( spl0_64
    | spl0_119
    | ~ spl0_62
    | ~ spl0_63 ),
    inference(avatar_split_clause,[],[f1383,f626,f609,f1636,f630]) ).

fof(f630,plain,
    ( spl0_64
  <=> v = w ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f1636,plain,
    ( spl0_119
  <=> u = extension(w,v,u,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f609,plain,
    ( spl0_62
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f626,plain,
    ( spl0_63
  <=> u = extension(w,v,v,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f1383,plain,
    ( u = extension(w,v,u,v)
    | v = w
    | ~ spl0_62
    | ~ spl0_63 ),
    inference(superposition,[],[f628,f610]) ).

fof(f610,plain,
    ( ! [X2,X3,X0,X1] :
        ( extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2)
        | X0 = X1 )
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f609]) ).

fof(f628,plain,
    ( u = extension(w,v,v,u)
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f626]) ).

fof(f1634,plain,
    ( spl0_118
    | ~ spl0_28
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f752,f719,f193,f1632]) ).

fof(f1632,plain,
    ( spl0_118
  <=> ! [X0] :
        ( ~ between(X0,w,v)
        | w = inner_pasch(w,u,v,w,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f193,plain,
    ( spl0_28
  <=> between(w,u,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f752,plain,
    ( ! [X0] :
        ( ~ between(X0,w,v)
        | w = inner_pasch(w,u,v,w,X0) )
    | ~ spl0_28
    | ~ spl0_66 ),
    inference(resolution,[],[f720,f195]) ).

fof(f195,plain,
    ( between(w,u,v)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f193]) ).

fof(f1630,plain,
    ( spl0_117
    | ~ spl0_18
    | ~ spl0_66 ),
    inference(avatar_split_clause,[],[f751,f719,f150,f1628]) ).

fof(f1628,plain,
    ( spl0_117
  <=> ! [X0] :
        ( ~ between(X0,w,u)
        | w = inner_pasch(w,v,u,w,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f150,plain,
    ( spl0_18
  <=> between(w,v,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f751,plain,
    ( ! [X0] :
        ( ~ between(X0,w,u)
        | w = inner_pasch(w,v,u,w,X0) )
    | ~ spl0_18
    | ~ spl0_66 ),
    inference(resolution,[],[f720,f152]) ).

fof(f152,plain,
    ( between(w,v,u)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f1626,plain,
    ( spl0_116
    | ~ spl0_3
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f734,f715,f73,f1624]) ).

fof(f715,plain,
    ( spl0_65
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | inner_pasch(X3,X0,X2,X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f734,plain,
    ( ! [X0] :
        ( ~ between(u,X0,w)
        | u = inner_pasch(v,u,w,X0,u) )
    | ~ spl0_3
    | ~ spl0_65 ),
    inference(resolution,[],[f716,f75]) ).

fof(f716,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X3,X0,X2)
        | ~ between(X0,X1,X2)
        | inner_pasch(X3,X0,X2,X1,X0) = X0 )
    | ~ spl0_65 ),
    inference(avatar_component_clause,[],[f715]) ).

fof(f1622,plain,
    ( spl0_115
    | ~ spl0_2
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f733,f715,f68,f1620]) ).

fof(f1620,plain,
    ( spl0_115
  <=> ! [X0] :
        ( ~ between(v,X0,w)
        | v = inner_pasch(u,v,w,X0,v) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f733,plain,
    ( ! [X0] :
        ( ~ between(v,X0,w)
        | v = inner_pasch(u,v,w,X0,v) )
    | ~ spl0_2
    | ~ spl0_65 ),
    inference(resolution,[],[f716,f70]) ).

fof(f1618,plain,
    ( spl0_114
    | ~ spl0_28
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f732,f715,f193,f1616]) ).

fof(f1616,plain,
    ( spl0_114
  <=> ! [X0] :
        ( ~ between(u,X0,v)
        | u = inner_pasch(w,u,v,X0,u) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f732,plain,
    ( ! [X0] :
        ( ~ between(u,X0,v)
        | u = inner_pasch(w,u,v,X0,u) )
    | ~ spl0_28
    | ~ spl0_65 ),
    inference(resolution,[],[f716,f195]) ).

fof(f1614,plain,
    ( spl0_113
    | ~ spl0_18
    | ~ spl0_65 ),
    inference(avatar_split_clause,[],[f731,f715,f150,f1612]) ).

fof(f1612,plain,
    ( spl0_113
  <=> ! [X0] :
        ( ~ between(v,X0,u)
        | v = inner_pasch(w,v,u,X0,v) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f731,plain,
    ( ! [X0] :
        ( ~ between(v,X0,u)
        | v = inner_pasch(w,v,u,X0,v) )
    | ~ spl0_18
    | ~ spl0_65 ),
    inference(resolution,[],[f716,f152]) ).

fof(f1595,plain,
    ( spl0_1
    | spl0_112
    | ~ spl0_55
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f697,f609,f544,f1592,f63]) ).

fof(f1592,plain,
    ( spl0_112
  <=> w = extension(v,u,w,u) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f544,plain,
    ( spl0_55
  <=> w = extension(v,u,u,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f697,plain,
    ( w = extension(v,u,w,u)
    | u = v
    | ~ spl0_55
    | ~ spl0_62 ),
    inference(superposition,[],[f546,f610]) ).

fof(f546,plain,
    ( w = extension(v,u,u,w)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f544]) ).

fof(f1558,plain,
    ( spl0_111
    | ~ spl0_75
    | ~ spl0_110 ),
    inference(avatar_split_clause,[],[f1553,f1549,f874,f1555]) ).

fof(f1555,plain,
    ( spl0_111
  <=> w = extension(w,v,w,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f874,plain,
    ( spl0_75
  <=> u = w ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f1549,plain,
    ( spl0_110
  <=> w = extension(u,v,w,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1553,plain,
    ( w = extension(w,v,w,v)
    | ~ spl0_75
    | ~ spl0_110 ),
    inference(forward_demodulation,[],[f1551,f875]) ).

fof(f875,plain,
    ( u = w
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f874]) ).

fof(f1551,plain,
    ( w = extension(u,v,w,v)
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f1549]) ).

fof(f1552,plain,
    ( spl0_1
    | spl0_110
    | ~ spl0_54
    | ~ spl0_62 ),
    inference(avatar_split_clause,[],[f696,f609,f529,f1549,f63]) ).

fof(f529,plain,
    ( spl0_54
  <=> w = extension(u,v,v,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f696,plain,
    ( w = extension(u,v,w,v)
    | u = v
    | ~ spl0_54
    | ~ spl0_62 ),
    inference(superposition,[],[f531,f610]) ).

fof(f531,plain,
    ( w = extension(u,v,v,w)
    | ~ spl0_54 ),
    inference(avatar_component_clause,[],[f529]) ).

fof(f1525,plain,
    ( spl0_109
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f386,f381,f351,f1523]) ).

fof(f1523,plain,
    ( spl0_109
  <=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | ~ equidistant(X3,X5,X0,continuous(X1,X6,X7,X5,X8,X9))
        | ~ equidistant(X1,X4,X1,X2)
        | ~ equidistant(X3,X1,X0,X1)
        | equidistant(X4,X5,X2,continuous(X1,X6,X7,X5,X8,X9))
        | ~ between(X1,X6,X8)
        | ~ equidistant(X1,X8,X1,X9)
        | ~ equidistant(X1,X6,X1,X7)
        | ~ between(X6,X5,X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f351,plain,
    ( spl0_44
  <=> ! [X6,X10,X9,X0,X5,X3] :
        ( ~ between(X3,X5,X0)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ equidistant(X10,X3,X10,X9)
        | equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f381,plain,
    ( spl0_46
  <=> ! [X2,X3,X9,X0,X8,X6,X1,X7] :
        ( X0 = X1
        | ~ between(X6,X7,X8)
        | ~ between(X0,X1,X2)
        | ~ equidistant(X1,X3,X7,X9)
        | ~ equidistant(X0,X3,X6,X9)
        | ~ equidistant(X1,X2,X7,X8)
        | ~ equidistant(X0,X1,X6,X7)
        | equidistant(X2,X3,X8,X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f386,plain,
    ( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | ~ equidistant(X3,X5,X0,continuous(X1,X6,X7,X5,X8,X9))
        | ~ equidistant(X1,X4,X1,X2)
        | ~ equidistant(X3,X1,X0,X1)
        | equidistant(X4,X5,X2,continuous(X1,X6,X7,X5,X8,X9))
        | ~ between(X1,X6,X8)
        | ~ equidistant(X1,X8,X1,X9)
        | ~ equidistant(X1,X6,X1,X7)
        | ~ between(X6,X5,X8) )
    | ~ spl0_44
    | ~ spl0_46 ),
    inference(resolution,[],[f382,f352]) ).

fof(f352,plain,
    ( ! [X3,X10,X0,X6,X9,X5] :
        ( equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6))
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ equidistant(X10,X3,X10,X9)
        | ~ between(X3,X5,X0) )
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f351]) ).

fof(f382,plain,
    ( ! [X2,X3,X0,X1,X8,X6,X9,X7] :
        ( ~ equidistant(X1,X3,X7,X9)
        | ~ between(X6,X7,X8)
        | ~ between(X0,X1,X2)
        | X0 = X1
        | ~ equidistant(X0,X3,X6,X9)
        | ~ equidistant(X1,X2,X7,X8)
        | ~ equidistant(X0,X1,X6,X7)
        | equidistant(X2,X3,X8,X9) )
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f381]) ).

fof(f1521,plain,
    ( spl0_108
    | ~ spl0_44
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f373,f368,f351,f1519]) ).

fof(f1519,plain,
    ( spl0_108
  <=> ! [X6,X4,X3,X0,X7,X5,X2,X1] :
        ( between(X0,X1,X2)
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | continuous(X0,X3,X4,X5,X6,X7) = X5
        | ~ equidistant(X2,X5,X2,continuous(X0,X3,X4,X5,X6,X7))
        | ~ equidistant(X1,X5,X1,continuous(X0,X3,X4,X5,X6,X7))
        | ~ between(X0,X3,X6)
        | ~ equidistant(X0,X6,X0,X7)
        | ~ equidistant(X0,X3,X0,X4)
        | ~ between(X3,X5,X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f368,plain,
    ( spl0_45
  <=> ! [X2,X3,X0,X5,X1] :
        ( X3 = X5
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | between(X0,X1,X2)
        | ~ equidistant(X2,X5,X2,X3)
        | ~ equidistant(X1,X5,X1,X3)
        | ~ equidistant(X0,X5,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f373,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( between(X0,X1,X2)
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | continuous(X0,X3,X4,X5,X6,X7) = X5
        | ~ equidistant(X2,X5,X2,continuous(X0,X3,X4,X5,X6,X7))
        | ~ equidistant(X1,X5,X1,continuous(X0,X3,X4,X5,X6,X7))
        | ~ between(X0,X3,X6)
        | ~ equidistant(X0,X6,X0,X7)
        | ~ equidistant(X0,X3,X0,X4)
        | ~ between(X3,X5,X6) )
    | ~ spl0_44
    | ~ spl0_45 ),
    inference(resolution,[],[f369,f352]) ).

fof(f369,plain,
    ( ! [X2,X3,X0,X1,X5] :
        ( ~ equidistant(X2,X5,X2,X3)
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | between(X0,X1,X2)
        | X3 = X5
        | ~ equidistant(X1,X5,X1,X3)
        | ~ equidistant(X0,X5,X0,X3) )
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f368]) ).

fof(f1506,plain,
    ( spl0_107
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f365,f351,f343,f1504]) ).

fof(f1504,plain,
    ( spl0_107
  <=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ between(X0,X5,X6)
        | ~ equidistant(X0,X6,X0,X7)
        | ~ between(X5,X8,X6)
        | between(continuous(X0,X1,X4,X5,X2,X3),continuous(X0,X5,continuous(X0,X1,X4,X5,X2,X3),X8,X6,X7),X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f343,plain,
    ( spl0_43
  <=> ! [X6,X10,X9,X0,X5,X3] :
        ( ~ between(X3,X5,X0)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ equidistant(X10,X3,X10,X9)
        | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f365,plain,
    ( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ between(X0,X5,X6)
        | ~ equidistant(X0,X6,X0,X7)
        | ~ between(X5,X8,X6)
        | between(continuous(X0,X1,X4,X5,X2,X3),continuous(X0,X5,continuous(X0,X1,X4,X5,X2,X3),X8,X6,X7),X7) )
    | ~ spl0_43
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f344]) ).

fof(f344,plain,
    ( ! [X3,X10,X0,X6,X9,X5] :
        ( ~ equidistant(X10,X3,X10,X9)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ between(X3,X5,X0)
        | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) )
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f343]) ).

fof(f1502,plain,
    ( spl0_106
    | spl0_75
    | ~ spl0_28
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f282,f227,f193,f874,f1499]) ).

fof(f1499,plain,
    ( spl0_106
  <=> v = extension(w,u,u,v) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f227,plain,
    ( spl0_29
  <=> ! [X5,X3,X10] :
        ( X3 = X10
        | ~ between(X10,X3,X5)
        | extension(X10,X3,X3,X5) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f282,plain,
    ( u = w
    | v = extension(w,u,u,v)
    | ~ spl0_28
    | ~ spl0_29 ),
    inference(resolution,[],[f195,f228]) ).

fof(f228,plain,
    ( ! [X3,X10,X5] :
        ( ~ between(X10,X3,X5)
        | X3 = X10
        | extension(X10,X3,X3,X5) = X5 )
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f227]) ).

fof(f1483,plain,
    ( spl0_105
    | ~ spl0_41
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f364,f351,f329,f1481]) ).

fof(f1481,plain,
    ( spl0_105
  <=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ between(X0,X5,X6)
        | ~ equidistant(X5,X6,continuous(X0,X1,X4,X5,X2,X3),X7)
        | ~ between(X0,continuous(X0,X1,X4,X5,X2,X3),X7)
        | equidistant(X0,X6,X0,X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f329,plain,
    ( spl0_41
  <=> ! [X5,X10,X11,X12,X9,X3] :
        ( ~ between(X11,X9,X12)
        | ~ between(X10,X3,X5)
        | ~ equidistant(X3,X5,X9,X12)
        | ~ equidistant(X10,X3,X11,X9)
        | equidistant(X10,X5,X11,X12) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f364,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ between(X0,X5,X6)
        | ~ equidistant(X5,X6,continuous(X0,X1,X4,X5,X2,X3),X7)
        | ~ between(X0,continuous(X0,X1,X4,X5,X2,X3),X7)
        | equidistant(X0,X6,X0,X7) )
    | ~ spl0_41
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f330]) ).

fof(f330,plain,
    ( ! [X3,X10,X11,X9,X5,X12] :
        ( ~ equidistant(X10,X3,X11,X9)
        | ~ between(X10,X3,X5)
        | ~ equidistant(X3,X5,X9,X12)
        | ~ between(X11,X9,X12)
        | equidistant(X10,X5,X11,X12) )
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f329]) ).

fof(f1475,plain,
    ( spl0_104
    | ~ spl0_36
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f366,f351,f293,f1473]) ).

fof(f1473,plain,
    ( spl0_104
  <=> ! [X5,X6,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | X0 = X6
        | ~ between(X6,X0,X5)
        | ~ between(X6,X0,continuous(X0,X1,X4,X5,X2,X3))
        | continuous(X0,X1,X4,X5,X2,X3) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f293,plain,
    ( spl0_36
  <=> ! [X10,X0,X5,X3] :
        ( X0 = X5
        | X3 = X10
        | ~ between(X10,X3,X5)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X3,X5,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f366,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | X0 = X6
        | ~ between(X6,X0,X5)
        | ~ between(X6,X0,continuous(X0,X1,X4,X5,X2,X3))
        | continuous(X0,X1,X4,X5,X2,X3) = X5 )
    | ~ spl0_36
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f294]) ).

fof(f294,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X3,X5,X3,X0)
        | X3 = X10
        | ~ between(X10,X3,X5)
        | ~ between(X10,X3,X0)
        | X0 = X5 )
    | ~ spl0_36 ),
    inference(avatar_component_clause,[],[f293]) ).

fof(f1450,plain,
    ( spl0_103
    | ~ spl0_29
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f340,f337,f227,f1448]) ).

fof(f1448,plain,
    ( spl0_103
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | euclid1(X3,X0,X1,X2,X4) = X4
        | euclid2(X3,X0,X1,X2,X4) = extension(euclid1(X3,X0,X1,X2,X4),X4,X4,euclid2(X3,X0,X1,X2,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f337,plain,
    ( spl0_42
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f340,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | euclid1(X3,X0,X1,X2,X4) = X4
        | euclid2(X3,X0,X1,X2,X4) = extension(euclid1(X3,X0,X1,X2,X4),X4,X4,euclid2(X3,X0,X1,X2,X4)) )
    | ~ spl0_29
    | ~ spl0_42 ),
    inference(resolution,[],[f338,f228]) ).

fof(f338,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1))
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | X5 = X10 )
    | ~ spl0_42 ),
    inference(avatar_component_clause,[],[f337]) ).

fof(f1423,plain,
    ( spl0_102
    | ~ spl0_19
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f388,f381,f155,f1421]) ).

fof(f1421,plain,
    ( spl0_102
  <=> ! [X3,X4,X0,X7,X6,X5,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X5)
        | X3 = X4
        | ~ equidistant(X3,extension(X6,X4,X1,X7),X0,X7)
        | ~ equidistant(X4,X5,X1,X2)
        | ~ equidistant(X3,X4,X0,X1)
        | equidistant(X5,extension(X6,X4,X1,X7),X2,X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f155,plain,
    ( spl0_19
  <=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f388,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X5)
        | X3 = X4
        | ~ equidistant(X3,extension(X6,X4,X1,X7),X0,X7)
        | ~ equidistant(X4,X5,X1,X2)
        | ~ equidistant(X3,X4,X0,X1)
        | equidistant(X5,extension(X6,X4,X1,X7),X2,X7) )
    | ~ spl0_19
    | ~ spl0_46 ),
    inference(resolution,[],[f382,f156]) ).

fof(f156,plain,
    ( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f155]) ).

fof(f1406,plain,
    ( spl0_101
    | ~ spl0_37
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f363,f351,f297,f1404]) ).

fof(f1404,plain,
    ( spl0_101
  <=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | X6 = X7
        | extension(X7,X6,X0,X5) = extension(X7,X6,X0,continuous(X0,X1,X4,X5,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f297,plain,
    ( spl0_37
  <=> ! [X5,X10,X0,X3,X2,X1] :
        ( X3 = X10
        | ~ equidistant(X5,X0,X1,X2)
        | extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f363,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | X6 = X7
        | extension(X7,X6,X0,X5) = extension(X7,X6,X0,continuous(X0,X1,X4,X5,X2,X3)) )
    | ~ spl0_37
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f298]) ).

fof(f298,plain,
    ( ! [X2,X3,X10,X0,X1,X5] :
        ( ~ equidistant(X5,X0,X1,X2)
        | X3 = X10
        | extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) )
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f297]) ).

fof(f1371,plain,
    ( spl0_100
    | ~ spl0_19
    | ~ spl0_45 ),
    inference(avatar_split_clause,[],[f375,f368,f155,f1369]) ).

fof(f1369,plain,
    ( spl0_100
  <=> ! [X4,X0,X3,X2,X1] :
        ( between(X0,X1,X2)
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | extension(X4,X0,X0,X3) = X3
        | ~ equidistant(X2,extension(X4,X0,X0,X3),X2,X3)
        | ~ equidistant(X1,extension(X4,X0,X0,X3),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f375,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( between(X0,X1,X2)
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | extension(X4,X0,X0,X3) = X3
        | ~ equidistant(X2,extension(X4,X0,X0,X3),X2,X3)
        | ~ equidistant(X1,extension(X4,X0,X0,X3),X1,X3) )
    | ~ spl0_19
    | ~ spl0_45 ),
    inference(resolution,[],[f369,f156]) ).

fof(f1350,plain,
    ( spl0_99
    | ~ spl0_19
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f349,f343,f155,f1348]) ).

fof(f1348,plain,
    ( spl0_99
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,extension(X1,X0,X0,X2),X3)
        | ~ equidistant(X0,X3,X0,X4)
        | ~ between(extension(X1,X0,X0,X2),X5,X3)
        | between(X2,continuous(X0,extension(X1,X0,X0,X2),X2,X5,X3,X4),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f349,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,extension(X1,X0,X0,X2),X3)
        | ~ equidistant(X0,X3,X0,X4)
        | ~ between(extension(X1,X0,X0,X2),X5,X3)
        | between(X2,continuous(X0,extension(X1,X0,X0,X2),X2,X5,X3,X4),X4) )
    | ~ spl0_19
    | ~ spl0_43 ),
    inference(resolution,[],[f344,f156]) ).

fof(f1307,plain,
    ( spl0_98
    | ~ spl0_32
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f362,f351,f252,f1305]) ).

fof(f1305,plain,
    ( spl0_98
  <=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X6,X7)
        | equidistant(X0,X5,X6,X7) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f252,plain,
    ( spl0_32
  <=> ! [X2,X10,X0,X5,X3,X1] :
        ( ~ equidistant(X10,X3,X5,X0)
        | ~ equidistant(X5,X0,X1,X2)
        | equidistant(X10,X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f362,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X6,X7)
        | equidistant(X0,X5,X6,X7) )
    | ~ spl0_32
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f253]) ).

fof(f253,plain,
    ( ! [X2,X3,X10,X0,X1,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | ~ equidistant(X5,X0,X1,X2)
        | equidistant(X10,X3,X1,X2) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f1303,plain,
    ( spl0_97
    | ~ spl0_31
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f361,f351,f248,f1301]) ).

fof(f1301,plain,
    ( spl0_97
  <=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ equidistant(X0,X5,X6,X7)
        | equidistant(X6,X7,X0,continuous(X0,X1,X4,X5,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f248,plain,
    ( spl0_31
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | ~ equidistant(X0,X1,X4,X5)
        | equidistant(X2,X3,X4,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f361,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | ~ equidistant(X0,X5,X6,X7)
        | equidistant(X6,X7,X0,continuous(X0,X1,X4,X5,X2,X3)) )
    | ~ spl0_31
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f249]) ).

fof(f249,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,X1,X4,X5)
        | ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X4,X5) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f248]) ).

fof(f1259,plain,
    ( spl0_96
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f290,f279,f227,f1257]) ).

fof(f1257,plain,
    ( spl0_96
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | inner_pasch(X3,X4,X2,X1,X0) = X1
        | extension(X1,inner_pasch(X3,X4,X2,X1,X0),inner_pasch(X3,X4,X2,X1,X0),X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f279,plain,
    ( spl0_35
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ between(X10,X3,X5)
        | ~ between(X1,X0,X5)
        | between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f290,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | inner_pasch(X3,X4,X2,X1,X0) = X1
        | extension(X1,inner_pasch(X3,X4,X2,X1,X0),inner_pasch(X3,X4,X2,X1,X0),X3) = X3 )
    | ~ spl0_29
    | ~ spl0_35 ),
    inference(resolution,[],[f280,f228]) ).

fof(f280,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X0,inner_pasch(X10,X3,X5,X0,X1),X10)
        | ~ between(X1,X0,X5)
        | ~ between(X10,X3,X5) )
    | ~ spl0_35 ),
    inference(avatar_component_clause,[],[f279]) ).

fof(f1255,plain,
    ( spl0_95
    | ~ spl0_29
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f286,f275,f227,f1253]) ).

fof(f1253,plain,
    ( spl0_95
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | inner_pasch(X3,X4,X2,X1,X0) = X4
        | extension(X4,inner_pasch(X3,X4,X2,X1,X0),inner_pasch(X3,X4,X2,X1,X0),X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f275,plain,
    ( spl0_34
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ between(X10,X3,X5)
        | ~ between(X1,X0,X5)
        | between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f286,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | inner_pasch(X3,X4,X2,X1,X0) = X4
        | extension(X4,inner_pasch(X3,X4,X2,X1,X0),inner_pasch(X3,X4,X2,X1,X0),X0) = X0 )
    | ~ spl0_29
    | ~ spl0_34 ),
    inference(resolution,[],[f276,f228]) ).

fof(f276,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X3,inner_pasch(X10,X3,X5,X0,X1),X1)
        | ~ between(X1,X0,X5)
        | ~ between(X10,X3,X5) )
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f275]) ).

fof(f1176,plain,
    ( spl0_94
    | ~ spl0_10
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f385,f381,f105,f1174]) ).

fof(f1174,plain,
    ( spl0_94
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | ~ equidistant(X3,X5,X0,X5)
        | ~ equidistant(X1,X4,X1,X2)
        | ~ equidistant(X3,X1,X0,X1)
        | equidistant(X4,X5,X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f105,plain,
    ( spl0_10
  <=> ! [X3,X10] : equidistant(X10,X3,X10,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f385,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | ~ equidistant(X3,X5,X0,X5)
        | ~ equidistant(X1,X4,X1,X2)
        | ~ equidistant(X3,X1,X0,X1)
        | equidistant(X4,X5,X2,X5) )
    | ~ spl0_10
    | ~ spl0_46 ),
    inference(resolution,[],[f382,f106]) ).

fof(f106,plain,
    ( ! [X3,X10] : equidistant(X10,X3,X10,X3)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f105]) ).

fof(f1172,plain,
    ( spl0_93
    | ~ spl0_9
    | ~ spl0_46 ),
    inference(avatar_split_clause,[],[f384,f381,f101,f1170]) ).

fof(f1170,plain,
    ( spl0_93
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X5)
        | X3 = X4
        | ~ equidistant(X3,X1,X0,X4)
        | ~ equidistant(X4,X5,X1,X2)
        | ~ equidistant(X3,X4,X0,X1)
        | equidistant(X5,X1,X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f101,plain,
    ( spl0_9
  <=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f384,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X5)
        | X3 = X4
        | ~ equidistant(X3,X1,X0,X4)
        | ~ equidistant(X4,X5,X1,X2)
        | ~ equidistant(X3,X4,X0,X1)
        | equidistant(X5,X1,X2,X4) )
    | ~ spl0_9
    | ~ spl0_46 ),
    inference(resolution,[],[f382,f102]) ).

fof(f102,plain,
    ( ! [X0,X1] : equidistant(X0,X1,X1,X0)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f101]) ).

fof(f1168,plain,
    ( spl0_92
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f322,f317,f227,f1166]) ).

fof(f1166,plain,
    ( spl0_92
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | X2 = X3
        | euclid2(X3,X0,X1,X2,X4) = extension(X3,X2,X2,euclid2(X3,X0,X1,X2,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f317,plain,
    ( spl0_39
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f322,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | X2 = X3
        | euclid2(X3,X0,X1,X2,X4) = extension(X3,X2,X2,euclid2(X3,X0,X1,X2,X4)) )
    | ~ spl0_29
    | ~ spl0_39 ),
    inference(resolution,[],[f318,f228]) ).

fof(f318,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X10,X0,euclid2(X10,X3,X5,X0,X1))
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | X5 = X10 )
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f1164,plain,
    ( spl0_91
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f320,f313,f227,f1162]) ).

fof(f1162,plain,
    ( spl0_91
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | X0 = X3
        | euclid1(X3,X0,X1,X2,X4) = extension(X3,X0,X0,euclid1(X3,X0,X1,X2,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f313,plain,
    ( spl0_38
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f320,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | X0 = X3
        | euclid1(X3,X0,X1,X2,X4) = extension(X3,X0,X0,euclid1(X3,X0,X1,X2,X4)) )
    | ~ spl0_29
    | ~ spl0_38 ),
    inference(resolution,[],[f314,f228]) ).

fof(f314,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X10,X3,euclid1(X10,X3,X5,X0,X1))
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | X5 = X10 )
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f313]) ).

fof(f1039,plain,
    ( spl0_90
    | ~ spl0_26
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f360,f351,f185,f1037]) ).

fof(f1037,plain,
    ( spl0_90
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(continuous(X0,X1,X4,X5,X2,X3),X0,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f185,plain,
    ( spl0_26
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X0,X5,X3,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f360,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(continuous(X0,X1,X4,X5,X2,X3),X0,X5,X0) )
    | ~ spl0_26
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f186]) ).

fof(f186,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X0,X5,X3,X10) )
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f1035,plain,
    ( spl0_89
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f359,f351,f181,f1033]) ).

fof(f1033,plain,
    ( spl0_89
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(continuous(X0,X1,X4,X5,X2,X3),X0,X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f181,plain,
    ( spl0_25
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X0,X5,X10,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f359,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(continuous(X0,X1,X4,X5,X2,X3),X0,X0,X5) )
    | ~ spl0_25
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f182]) ).

fof(f182,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X0,X5,X10,X3) )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f181]) ).

fof(f1031,plain,
    ( spl0_88
    | ~ spl0_24
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f358,f351,f177,f1029]) ).

fof(f1029,plain,
    ( spl0_88
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f177,plain,
    ( spl0_24
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X5,X0,X3,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f358,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X5,X0) )
    | ~ spl0_24
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f178]) ).

fof(f178,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X5,X0,X3,X10) )
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f177]) ).

fof(f1027,plain,
    ( spl0_87
    | ~ spl0_3
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f779,f630,f73,f1024]) ).

fof(f1024,plain,
    ( spl0_87
  <=> between(w,u,w) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f779,plain,
    ( between(w,u,w)
    | ~ spl0_3
    | ~ spl0_64 ),
    inference(superposition,[],[f75,f632]) ).

fof(f632,plain,
    ( v = w
    | ~ spl0_64 ),
    inference(avatar_component_clause,[],[f630]) ).

fof(f1022,plain,
    ( spl0_86
    | ~ spl0_23
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f357,f351,f173,f1020]) ).

fof(f1020,plain,
    ( spl0_86
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X5,X0,continuous(X0,X1,X4,X5,X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f173,plain,
    ( spl0_23
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X3,X10,X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f357,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X5,X0,continuous(X0,X1,X4,X5,X2,X3),X0) )
    | ~ spl0_23
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f174]) ).

fof(f174,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X3,X10,X0,X5) )
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f173]) ).

fof(f1018,plain,
    ( spl0_85
    | ~ spl0_22
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f356,f351,f169,f1016]) ).

fof(f1016,plain,
    ( spl0_85
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,X5,continuous(X0,X1,X4,X5,X2,X3),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f169,plain,
    ( spl0_22
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X10,X3,X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f356,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,X5,continuous(X0,X1,X4,X5,X2,X3),X0) )
    | ~ spl0_22
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f170]) ).

fof(f170,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X10,X3,X0,X5) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f169]) ).

fof(f1014,plain,
    ( spl0_84
    | ~ spl0_21
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f355,f351,f165,f1012]) ).

fof(f1012,plain,
    ( spl0_84
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X5,X0,X0,continuous(X0,X1,X4,X5,X2,X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f165,plain,
    ( spl0_21
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X3,X10,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f355,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X5,X0,X0,continuous(X0,X1,X4,X5,X2,X3)) )
    | ~ spl0_21
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f166]) ).

fof(f166,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X3,X10,X5,X0) )
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f1010,plain,
    ( spl0_83
    | ~ spl0_20
    | ~ spl0_44 ),
    inference(avatar_split_clause,[],[f354,f351,f161,f1008]) ).

fof(f1008,plain,
    ( spl0_83
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X0,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f161,plain,
    ( spl0_20
  <=> ! [X10,X0,X5,X3] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X5,X0,X10,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f354,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ equidistant(X0,X1,X0,X4)
        | ~ between(X1,X5,X2)
        | equidistant(X0,continuous(X0,X1,X4,X5,X2,X3),X0,X5) )
    | ~ spl0_20
    | ~ spl0_44 ),
    inference(resolution,[],[f352,f162]) ).

fof(f162,plain,
    ( ! [X3,X10,X0,X5] :
        ( ~ equidistant(X10,X3,X5,X0)
        | equidistant(X5,X0,X10,X3) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f161]) ).

fof(f988,plain,
    ( spl0_82
    | ~ spl0_19
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f335,f329,f155,f986]) ).

fof(f986,plain,
    ( spl0_82
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,extension(X1,X0,X2,X3),X4)
        | ~ equidistant(extension(X1,X0,X2,X3),X4,X3,X5)
        | ~ between(X2,X3,X5)
        | equidistant(X0,X4,X2,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f335,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,extension(X1,X0,X2,X3),X4)
        | ~ equidistant(extension(X1,X0,X2,X3),X4,X3,X5)
        | ~ between(X2,X3,X5)
        | equidistant(X0,X4,X2,X5) )
    | ~ spl0_19
    | ~ spl0_41 ),
    inference(resolution,[],[f330,f156]) ).

fof(f980,plain,
    ( spl0_81
    | ~ spl0_16
    | ~ spl0_42 ),
    inference(avatar_split_clause,[],[f341,f337,f131,f978]) ).

fof(f978,plain,
    ( spl0_81
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid2(X3,X0,X1,X2,X4),X4,euclid1(X3,X0,X1,X2,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f131,plain,
    ( spl0_16
  <=> ! [X5,X3,X10] :
        ( ~ between(X10,X3,X5)
        | between(X5,X3,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f341,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid2(X3,X0,X1,X2,X4),X4,euclid1(X3,X0,X1,X2,X4)) )
    | ~ spl0_16
    | ~ spl0_42 ),
    inference(resolution,[],[f338,f132]) ).

fof(f132,plain,
    ( ! [X3,X10,X5] :
        ( ~ between(X10,X3,X5)
        | between(X5,X3,X10) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f967,plain,
    ( spl0_80
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(avatar_split_clause,[],[f347,f343,f105,f965]) ).

fof(f965,plain,
    ( spl0_80
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ between(X1,X4,X2)
        | between(X1,continuous(X0,X1,X1,X4,X2,X3),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f347,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X0,X2,X0,X3)
        | ~ between(X1,X4,X2)
        | between(X1,continuous(X0,X1,X1,X4,X2,X3),X3) )
    | ~ spl0_10
    | ~ spl0_43 ),
    inference(resolution,[],[f344,f106]) ).

fof(f927,plain,
    ( spl0_79
    | ~ spl0_19
    | ~ spl0_36 ),
    inference(avatar_split_clause,[],[f303,f293,f155,f925]) ).

fof(f925,plain,
    ( spl0_79
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | ~ between(X1,X0,extension(X2,X0,X0,X3))
        | ~ between(X1,X0,X3)
        | extension(X2,X0,X0,X3) = X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f303,plain,
    ( ! [X2,X3,X0,X1] :
        ( X0 = X1
        | ~ between(X1,X0,extension(X2,X0,X0,X3))
        | ~ between(X1,X0,X3)
        | extension(X2,X0,X0,X3) = X3 )
    | ~ spl0_19
    | ~ spl0_36 ),
    inference(resolution,[],[f294,f156]) ).

fof(f923,plain,
    ( spl0_78
    | ~ spl0_30
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f269,f256,f231,f921]) ).

fof(f921,plain,
    ( spl0_78
  <=> ! [X0,X1] :
        ( extension(extension(X0,X1,X0,X1),X1,X1,extension(X0,X1,X0,X1)) = X0
        | extension(X0,X1,X0,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f231,plain,
    ( spl0_30
  <=> ! [X3,X10] :
        ( X3 = X10
        | extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f256,plain,
    ( spl0_33
  <=> ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f269,plain,
    ( ! [X0,X1] :
        ( extension(extension(X0,X1,X0,X1),X1,X1,extension(X0,X1,X0,X1)) = X0
        | extension(X0,X1,X0,X1) = X1 )
    | ~ spl0_30
    | ~ spl0_33 ),
    inference(superposition,[],[f257,f232]) ).

fof(f232,plain,
    ( ! [X3,X10] :
        ( extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10)
        | X3 = X10 )
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f231]) ).

fof(f257,plain,
    ( ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f911,plain,
    ( spl0_77
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f323,f317,f131,f909]) ).

fof(f909,plain,
    ( spl0_77
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid2(X3,X0,X1,X2,X4),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f323,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid2(X3,X0,X1,X2,X4),X2,X3) )
    | ~ spl0_16
    | ~ spl0_39 ),
    inference(resolution,[],[f318,f132]) ).

fof(f907,plain,
    ( spl0_76
    | ~ spl0_16
    | ~ spl0_38 ),
    inference(avatar_split_clause,[],[f321,f313,f131,f905]) ).

fof(f905,plain,
    ( spl0_76
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid1(X3,X0,X1,X2,X4),X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f321,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X1,X4)
        | X1 = X3
        | between(euclid1(X3,X0,X1,X2,X4),X0,X3) )
    | ~ spl0_16
    | ~ spl0_38 ),
    inference(resolution,[],[f314,f132]) ).

fof(f877,plain,
    ( ~ spl0_75
    | spl0_1
    | ~ spl0_64 ),
    inference(avatar_split_clause,[],[f777,f630,f63,f874]) ).

fof(f777,plain,
    ( u != w
    | spl0_1
    | ~ spl0_64 ),
    inference(superposition,[],[f65,f632]) ).

fof(f65,plain,
    ( u != v
    | spl0_1 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f823,plain,
    ( spl0_74
    | ~ spl0_10
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f333,f329,f105,f821]) ).

fof(f821,plain,
    ( spl0_74
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X1,X2,X1,X3)
        | ~ between(X0,X1,X3)
        | equidistant(X0,X2,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f333,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X1,X2,X1,X3)
        | ~ between(X0,X1,X3)
        | equidistant(X0,X2,X0,X3) )
    | ~ spl0_10
    | ~ spl0_41 ),
    inference(resolution,[],[f330,f106]) ).

fof(f819,plain,
    ( spl0_73
    | ~ spl0_9
    | ~ spl0_41 ),
    inference(avatar_split_clause,[],[f332,f329,f101,f817]) ).

fof(f817,plain,
    ( spl0_73
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X1,X2,X0,X3)
        | ~ between(X1,X0,X3)
        | equidistant(X0,X2,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f332,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ equidistant(X1,X2,X0,X3)
        | ~ between(X1,X0,X3)
        | equidistant(X0,X2,X1,X3) )
    | ~ spl0_9
    | ~ spl0_41 ),
    inference(resolution,[],[f330,f102]) ).

fof(f815,plain,
    ( spl0_72
    | ~ spl0_19
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f310,f297,f155,f813]) ).

fof(f813,plain,
    ( spl0_72
  <=> ! [X2,X3,X4,X0,X5,X1] :
        ( X0 = X1
        | extension(X1,X0,X2,extension(X3,X2,X4,X5)) = extension(X1,X0,X4,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f310,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( X0 = X1
        | extension(X1,X0,X2,extension(X3,X2,X4,X5)) = extension(X1,X0,X4,X5) )
    | ~ spl0_19
    | ~ spl0_37 ),
    inference(resolution,[],[f298,f156]) ).

fof(f811,plain,
    ( spl0_71
    | ~ spl0_30
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f268,f256,f231,f809]) ).

fof(f809,plain,
    ( spl0_71
  <=> ! [X0,X1] :
        ( extension(extension(X0,X1,X1,X0),X1,extension(X0,X1,X1,X0),X1) = X0
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f268,plain,
    ( ! [X0,X1] :
        ( extension(extension(X0,X1,X1,X0),X1,extension(X0,X1,X1,X0),X1) = X0
        | X0 = X1 )
    | ~ spl0_30
    | ~ spl0_33 ),
    inference(superposition,[],[f257,f232]) ).

fof(f776,plain,
    ( spl0_70
    | ~ spl0_16
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f291,f279,f131,f774]) ).

fof(f774,plain,
    ( spl0_70
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | between(X3,inner_pasch(X3,X4,X2,X1,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f291,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | between(X3,inner_pasch(X3,X4,X2,X1,X0),X1) )
    | ~ spl0_16
    | ~ spl0_35 ),
    inference(resolution,[],[f280,f132]) ).

fof(f772,plain,
    ( spl0_69
    | ~ spl0_17
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f288,f279,f135,f770]) ).

fof(f770,plain,
    ( spl0_69
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | between(X4,inner_pasch(X1,X3,X2,X1,X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f135,plain,
    ( spl0_17
  <=> ! [X5,X3,X10] :
        ( ~ between(X10,X5,X10)
        | between(X3,X5,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f288,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | between(X4,inner_pasch(X1,X3,X2,X1,X0),X1) )
    | ~ spl0_17
    | ~ spl0_35 ),
    inference(resolution,[],[f280,f136]) ).

fof(f136,plain,
    ( ! [X3,X10,X5] :
        ( ~ between(X10,X5,X10)
        | between(X3,X5,X10) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f768,plain,
    ( spl0_68
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f287,f275,f131,f766]) ).

fof(f766,plain,
    ( spl0_68
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | between(X0,inner_pasch(X3,X4,X2,X1,X0),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f287,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X2)
        | between(X0,inner_pasch(X3,X4,X2,X1,X0),X4) )
    | ~ spl0_16
    | ~ spl0_34 ),
    inference(resolution,[],[f276,f132]) ).

fof(f764,plain,
    ( spl0_67
    | ~ spl0_17
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f284,f275,f135,f762]) ).

fof(f762,plain,
    ( spl0_67
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | between(X4,inner_pasch(X3,X0,X2,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f284,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | between(X4,inner_pasch(X3,X0,X2,X1,X0),X0) )
    | ~ spl0_17
    | ~ spl0_34 ),
    inference(resolution,[],[f276,f136]) ).

fof(f721,plain,
    ( spl0_66
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(avatar_split_clause,[],[f289,f279,f113,f719]) ).

fof(f113,plain,
    ( spl0_12
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ between(X0,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f289,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | inner_pasch(X1,X3,X2,X1,X0) = X1 )
    | ~ spl0_12
    | ~ spl0_35 ),
    inference(resolution,[],[f280,f114]) ).

fof(f114,plain,
    ( ! [X0,X1] :
        ( ~ between(X0,X1,X0)
        | X0 = X1 )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f113]) ).

fof(f717,plain,
    ( spl0_65
    | ~ spl0_12
    | ~ spl0_34 ),
    inference(avatar_split_clause,[],[f285,f275,f113,f715]) ).

fof(f285,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | inner_pasch(X3,X0,X2,X1,X0) = X0 )
    | ~ spl0_12
    | ~ spl0_34 ),
    inference(resolution,[],[f276,f114]) ).

fof(f633,plain,
    ( spl0_63
    | spl0_64
    | ~ spl0_18
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f238,f227,f150,f630,f626]) ).

fof(f238,plain,
    ( v = w
    | u = extension(w,v,v,u)
    | ~ spl0_18
    | ~ spl0_29 ),
    inference(resolution,[],[f228,f152]) ).

fof(f611,plain,
    ( spl0_62
    | ~ spl0_9
    | ~ spl0_37 ),
    inference(avatar_split_clause,[],[f307,f297,f101,f609]) ).

fof(f307,plain,
    ( ! [X2,X3,X0,X1] :
        ( X0 = X1
        | extension(X1,X0,X2,X3) = extension(X1,X0,X3,X2) )
    | ~ spl0_9
    | ~ spl0_37 ),
    inference(resolution,[],[f298,f102]) ).

fof(f607,plain,
    ( spl0_61
    | ~ spl0_19
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f266,f252,f155,f605]) ).

fof(f605,plain,
    ( spl0_61
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X4,extension(X5,X4,X0,X1),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f266,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X4,extension(X5,X4,X0,X1),X2,X3) )
    | ~ spl0_19
    | ~ spl0_32 ),
    inference(resolution,[],[f253,f156]) ).

fof(f603,plain,
    ( spl0_60
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f262,f248,f155,f601]) ).

fof(f601,plain,
    ( spl0_60
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
        | equidistant(X4,X5,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f262,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
        | equidistant(X4,X5,X2,X3) )
    | ~ spl0_19
    | ~ spl0_31 ),
    inference(resolution,[],[f249,f156]) ).

fof(f573,plain,
    ( spl0_59
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f273,f256,f189,f571]) ).

fof(f571,plain,
    ( spl0_59
  <=> ! [X0,X1] :
        ( X0 != X1
        | extension(X0,X1,X0,X1) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f189,plain,
    ( spl0_27
  <=> ! [X3,X10] :
        ( X3 = X10
        | extension(X10,X3,X10,X3) != X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f273,plain,
    ( ! [X0,X1] :
        ( X0 != X1
        | extension(X0,X1,X0,X1) = X1 )
    | ~ spl0_27
    | ~ spl0_33 ),
    inference(superposition,[],[f190,f257]) ).

fof(f190,plain,
    ( ! [X3,X10] :
        ( extension(X10,X3,X10,X3) != X3
        | X3 = X10 )
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f189]) ).

fof(f569,plain,
    ( spl0_58
    | ~ spl0_11
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f265,f252,f109,f567]) ).

fof(f567,plain,
    ( spl0_58
  <=> ! [X0,X3,X2,X1] :
        ( ~ equidistant(X0,X0,X1,X2)
        | equidistant(X3,X3,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f109,plain,
    ( spl0_11
  <=> ! [X3,X10] : equidistant(X10,X10,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f265,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ equidistant(X0,X0,X1,X2)
        | equidistant(X3,X3,X1,X2) )
    | ~ spl0_11
    | ~ spl0_32 ),
    inference(resolution,[],[f253,f110]) ).

fof(f110,plain,
    ( ! [X3,X10] : equidistant(X10,X10,X3,X3)
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f109]) ).

fof(f565,plain,
    ( spl0_57
    | ~ spl0_11
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f261,f248,f109,f563]) ).

fof(f563,plain,
    ( spl0_57
  <=> ! [X0,X3,X2,X1] :
        ( ~ equidistant(X0,X0,X1,X2)
        | equidistant(X1,X2,X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f261,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ equidistant(X0,X0,X1,X2)
        | equidistant(X1,X2,X3,X3) )
    | ~ spl0_11
    | ~ spl0_31 ),
    inference(resolution,[],[f249,f110]) ).

fof(f561,plain,
    ( spl0_56
    | ~ spl0_27
    | ~ spl0_30 ),
    inference(avatar_split_clause,[],[f246,f231,f189,f559]) ).

fof(f559,plain,
    ( spl0_56
  <=> ! [X0,X1] :
        ( extension(X0,X1,X1,X0) != X1
        | X0 = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f246,plain,
    ( ! [X0,X1] :
        ( extension(X0,X1,X1,X0) != X1
        | X0 = X1 )
    | ~ spl0_27
    | ~ spl0_30 ),
    inference(duplicate_literal_removal,[],[f243]) ).

fof(f243,plain,
    ( ! [X0,X1] :
        ( extension(X0,X1,X1,X0) != X1
        | X0 = X1
        | X0 = X1 )
    | ~ spl0_27
    | ~ spl0_30 ),
    inference(superposition,[],[f190,f232]) ).

fof(f547,plain,
    ( spl0_55
    | spl0_1
    | ~ spl0_3
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f240,f227,f73,f63,f544]) ).

fof(f240,plain,
    ( u = v
    | w = extension(v,u,u,w)
    | ~ spl0_3
    | ~ spl0_29 ),
    inference(resolution,[],[f228,f75]) ).

fof(f532,plain,
    ( spl0_54
    | spl0_1
    | ~ spl0_2
    | ~ spl0_29 ),
    inference(avatar_split_clause,[],[f239,f227,f68,f63,f529]) ).

fof(f239,plain,
    ( u = v
    | w = extension(u,v,v,w)
    | ~ spl0_2
    | ~ spl0_29 ),
    inference(resolution,[],[f228,f70]) ).

fof(f417,plain,
    ( spl0_53
    | ~ spl0_19
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f224,f185,f155,f415]) ).

fof(f415,plain,
    ( spl0_53
  <=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f224,plain,
    ( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X1,X0),X3)
    | ~ spl0_19
    | ~ spl0_26 ),
    inference(resolution,[],[f186,f156]) ).

fof(f413,plain,
    ( spl0_52
    | ~ spl0_19
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f220,f181,f155,f411]) ).

fof(f411,plain,
    ( spl0_52
  <=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f220,plain,
    ( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X1,X0))
    | ~ spl0_19
    | ~ spl0_25 ),
    inference(resolution,[],[f182,f156]) ).

fof(f409,plain,
    ( spl0_51
    | ~ spl0_19
    | ~ spl0_24 ),
    inference(avatar_split_clause,[],[f216,f177,f155,f407]) ).

fof(f407,plain,
    ( spl0_51
  <=> ! [X0,X3,X2,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f216,plain,
    ( ! [X2,X3,X0,X1] : equidistant(X0,X1,extension(X2,X3,X0,X1),X3)
    | ~ spl0_19
    | ~ spl0_24 ),
    inference(resolution,[],[f178,f156]) ).

fof(f405,plain,
    ( spl0_50
    | ~ spl0_19
    | ~ spl0_23 ),
    inference(avatar_split_clause,[],[f212,f173,f155,f403]) ).

fof(f403,plain,
    ( spl0_50
  <=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f212,plain,
    ( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X3,X2)
    | ~ spl0_19
    | ~ spl0_23 ),
    inference(resolution,[],[f174,f156]) ).

fof(f401,plain,
    ( spl0_49
    | ~ spl0_19
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f208,f169,f155,f399]) ).

fof(f399,plain,
    ( spl0_49
  <=> ! [X0,X3,X2,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f208,plain,
    ( ! [X2,X3,X0,X1] : equidistant(X0,extension(X1,X0,X2,X3),X3,X2)
    | ~ spl0_19
    | ~ spl0_22 ),
    inference(resolution,[],[f170,f156]) ).

fof(f397,plain,
    ( spl0_48
    | ~ spl0_19
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f204,f165,f155,f395]) ).

fof(f395,plain,
    ( spl0_48
  <=> ! [X2,X0,X1,X3] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f204,plain,
    ( ! [X2,X3,X0,X1] : equidistant(extension(X0,X1,X2,X3),X1,X2,X3)
    | ~ spl0_19
    | ~ spl0_21 ),
    inference(resolution,[],[f166,f156]) ).

fof(f393,plain,
    ( spl0_47
    | ~ spl0_19
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f200,f161,f155,f391]) ).

fof(f391,plain,
    ( spl0_47
  <=> ! [X0,X3,X2,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f200,plain,
    ( ! [X2,X3,X0,X1] : equidistant(X0,X1,X2,extension(X3,X2,X0,X1))
    | ~ spl0_19
    | ~ spl0_20 ),
    inference(resolution,[],[f162,f156]) ).

fof(f383,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f6,f381]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X8,X6,X9,X7] :
      ( X0 = X1
      | ~ between(X6,X7,X8)
      | ~ between(X0,X1,X2)
      | ~ equidistant(X1,X3,X7,X9)
      | ~ equidistant(X0,X3,X6,X9)
      | ~ equidistant(X1,X2,X7,X8)
      | ~ equidistant(X0,X1,X6,X7)
      | equidistant(X2,X3,X8,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).

fof(f370,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f13,f368]) ).

fof(f13,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X3 = X5
      | between(X2,X0,X1)
      | between(X1,X2,X0)
      | between(X0,X1,X2)
      | ~ equidistant(X2,X5,X2,X3)
      | ~ equidistant(X1,X5,X1,X3)
      | ~ equidistant(X0,X5,X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).

fof(f353,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f18,f351]) ).

fof(f18,axiom,
    ! [X3,X10,X0,X6,X9,X5] :
      ( ~ between(X3,X5,X0)
      | ~ between(X10,X3,X0)
      | ~ equidistant(X10,X0,X10,X6)
      | ~ equidistant(X10,X3,X10,X9)
      | equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).

fof(f345,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f17,f343]) ).

fof(f17,axiom,
    ! [X3,X10,X0,X6,X9,X5] :
      ( ~ between(X3,X5,X0)
      | ~ between(X10,X3,X0)
      | ~ equidistant(X10,X0,X10,X6)
      | ~ equidistant(X10,X3,X10,X9)
      | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).

fof(f339,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f16,f337]) ).

fof(f16,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).

fof(f331,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f37,f329]) ).

fof(f37,axiom,
    ! [X3,X10,X11,X9,X5,X12] :
      ( ~ between(X11,X9,X12)
      | ~ between(X10,X3,X5)
      | ~ equidistant(X3,X5,X9,X12)
      | ~ equidistant(X10,X3,X11,X9)
      | equidistant(X10,X5,X11,X12) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).

fof(f327,plain,
    ( spl0_40
    | ~ spl0_15
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f146,f131,f127,f325]) ).

fof(f325,plain,
    ( spl0_40
  <=> ! [X0,X3,X2,X1] : between(extension(X0,X1,X2,X3),X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f127,plain,
    ( spl0_15
  <=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f146,plain,
    ( ! [X2,X3,X0,X1] : between(extension(X0,X1,X2,X3),X1,X0)
    | ~ spl0_15
    | ~ spl0_16 ),
    inference(resolution,[],[f132,f128]) ).

fof(f128,plain,
    ( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f319,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f15,f317]) ).

fof(f15,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).

fof(f315,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f14,f313]) ).

fof(f14,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).

fof(f299,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f40,f297]) ).

fof(f40,axiom,
    ! [X2,X3,X10,X0,X1,X5] :
      ( X3 = X10
      | ~ equidistant(X5,X0,X1,X2)
      | extension(X10,X3,X5,X0) = extension(X10,X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).

fof(f295,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f38,f293]) ).

fof(f38,axiom,
    ! [X3,X10,X0,X5] :
      ( X0 = X5
      | X3 = X10
      | ~ between(X10,X3,X5)
      | ~ between(X10,X3,X0)
      | ~ equidistant(X3,X5,X3,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).

fof(f281,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f9,f279]) ).

fof(f9,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ between(X10,X3,X5)
      | ~ between(X1,X0,X5)
      | between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).

fof(f277,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f8,f275]) ).

fof(f8,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ between(X10,X3,X5)
      | ~ between(X1,X0,X5)
      | between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).

fof(f258,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f53,f256]) ).

fof(f53,plain,
    ! [X3,X10] : extension(extension(X10,X3,X10,X3),X3,extension(X10,X3,X10,X3),X3) = X10,
    inference(definition_unfolding,[],[f43,f19,f19]) ).

fof(f19,axiom,
    ! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).

fof(f43,axiom,
    ! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).

fof(f254,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f28,f252]) ).

fof(f28,axiom,
    ! [X2,X3,X10,X0,X1,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | ~ equidistant(X5,X0,X1,X2)
      | equidistant(X10,X3,X1,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).

fof(f250,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f2,f248]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ equidistant(X0,X1,X2,X3)
      | ~ equidistant(X0,X1,X4,X5)
      | equidistant(X2,X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

fof(f233,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f41,f231]) ).

fof(f41,axiom,
    ! [X3,X10] :
      ( X3 = X10
      | extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).

fof(f229,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f39,f227]) ).

fof(f39,axiom,
    ! [X3,X10,X5] :
      ( X3 = X10
      | ~ between(X10,X3,X5)
      | extension(X10,X3,X3,X5) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).

fof(f196,plain,
    ( spl0_28
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f143,f131,f73,f193]) ).

fof(f143,plain,
    ( between(w,u,v)
    | ~ spl0_3
    | ~ spl0_16 ),
    inference(resolution,[],[f132,f75]) ).

fof(f191,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f57,f189]) ).

fof(f57,plain,
    ! [X3,X10] :
      ( X3 = X10
      | extension(X10,X3,X10,X3) != X3 ),
    inference(definition_unfolding,[],[f35,f19]) ).

fof(f35,axiom,
    ! [X3,X10] :
      ( X3 = X10
      | reflection(X10,X3) != X3 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).

fof(f187,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f27,f185]) ).

fof(f27,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X0,X5,X3,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).

fof(f183,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f26,f181]) ).

fof(f26,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X0,X5,X10,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).

fof(f179,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f25,f177]) ).

fof(f25,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X5,X0,X3,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).

fof(f175,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f24,f173]) ).

fof(f24,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X3,X10,X0,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).

fof(f171,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f23,f169]) ).

fof(f23,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X10,X3,X0,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).

fof(f167,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f22,f165]) ).

fof(f22,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X3,X10,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).

fof(f163,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f21,f161]) ).

fof(f21,axiom,
    ! [X3,X10,X0,X5] :
      ( ~ equidistant(X10,X3,X5,X0)
      | equidistant(X5,X0,X10,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).

fof(f157,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f5,f155]) ).

fof(f5,axiom,
    ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).

fof(f153,plain,
    ( spl0_18
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f142,f131,f68,f150]) ).

fof(f142,plain,
    ( between(w,v,u)
    | ~ spl0_2
    | ~ spl0_16 ),
    inference(resolution,[],[f132,f70]) ).

fof(f137,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f60,f135]) ).

fof(f60,plain,
    ! [X3,X10,X5] :
      ( ~ between(X10,X5,X10)
      | between(X3,X5,X10) ),
    inference(equality_resolution,[],[f45]) ).

fof(f45,axiom,
    ! [X3,X10,X0,X5] :
      ( X0 != X10
      | ~ between(X10,X5,X0)
      | between(X3,X5,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).

fof(f133,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f46,f131]) ).

fof(f46,axiom,
    ! [X3,X10,X5] :
      ( ~ between(X10,X3,X5)
      | between(X5,X3,X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).

fof(f129,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f4,f127]) ).

fof(f4,axiom,
    ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).

fof(f125,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f3,f123]) ).

fof(f123,plain,
    ( spl0_14
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | ~ equidistant(X0,X1,X2,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ equidistant(X0,X1,X2,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).

fof(f119,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f29,f117]) ).

fof(f117,plain,
    ( spl0_13
  <=> ! [X5,X3,X10] : extension(X10,X3,X5,X5) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f29,axiom,
    ! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).

fof(f115,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f7,f113]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ between(X0,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).

fof(f111,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f36,f109]) ).

fof(f36,axiom,
    ! [X3,X10] : equidistant(X10,X10,X3,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).

fof(f107,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f20,f105]) ).

fof(f20,axiom,
    ! [X3,X10] : equidistant(X10,X3,X10,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).

fof(f103,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f1,f101]) ).

fof(f1,axiom,
    ! [X0,X1] : equidistant(X0,X1,X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

fof(f99,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f47,f97]) ).

fof(f97,plain,
    ( spl0_8
  <=> ! [X3,X10] : between(X10,X10,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f47,axiom,
    ! [X3,X10] : between(X10,X10,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).

fof(f95,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f44,f93]) ).

fof(f93,plain,
    ( spl0_7
  <=> ! [X3,X10] : between(X10,X3,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f44,axiom,
    ! [X3,X10] : between(X10,X3,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).

fof(f91,plain,
    ~ spl0_6,
    inference(avatar_split_clause,[],[f12,f88]) ).

fof(f88,plain,
    ( spl0_6
  <=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f12,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).

fof(f86,plain,
    ~ spl0_5,
    inference(avatar_split_clause,[],[f11,f83]) ).

fof(f83,plain,
    ( spl0_5
  <=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f11,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).

fof(f81,plain,
    ~ spl0_4,
    inference(avatar_split_clause,[],[f10,f78]) ).

fof(f78,plain,
    ( spl0_4
  <=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f10,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).

fof(f76,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f49,f73]) ).

fof(f49,axiom,
    between(v,u,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_between_v_and_w) ).

fof(f71,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f48,f68]) ).

fof(f48,axiom,
    between(u,v,w),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).

fof(f66,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f50,f63]) ).

fof(f50,axiom,
    u != v,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_is_v) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : GEO040-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Fri May  3 22:06:08 EDT 2024
% 0.13/0.34  % CPUTime    : 
% 0.13/0.34  % (31816)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35  % (31819)WARNING: value z3 for option sas not known
% 0.13/0.35  % (31819)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36  % (31817)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36  % (31820)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36  % (31818)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36  % (31821)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36  % (31822)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36  % (31823)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36  TRYING [1]
% 0.13/0.36  TRYING [2]
% 0.13/0.37  TRYING [3]
% 0.13/0.38  TRYING [1]
% 0.13/0.38  TRYING [2]
% 0.19/0.43  TRYING [4]
% 0.19/0.45  % (31821)First to succeed.
% 0.19/0.45  % (31821)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31816"
% 0.19/0.46  % (31821)Refutation found. Thanks to Tanya!
% 0.19/0.46  % SZS status Unsatisfiable for theBenchmark
% 0.19/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.46  % (31821)------------------------------
% 0.19/0.46  % (31821)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.19/0.46  % (31821)Termination reason: Refutation
% 0.19/0.46  
% 0.19/0.46  % (31821)Memory used [KB]: 2132
% 0.19/0.46  % (31821)Time elapsed: 0.098 s
% 0.19/0.46  % (31821)Instructions burned: 165 (million)
% 0.19/0.46  % (31816)Success in time 0.102 s
%------------------------------------------------------------------------------