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