TSTP Solution File: GEO045-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GEO045-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n019.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 : Fri Sep 1 14:41:57 EDT 2023
% Result : Unsatisfiable 0.20s 0.58s
% Output : Refutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 266
% Syntax : Number of formulae : 716 ( 75 unt; 0 def)
% Number of atoms : 2486 ( 293 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 3182 (1412 ~;1558 |; 0 &)
% ( 212 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 216 ( 214 usr; 213 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-6 aty)
% Number of variables : 1653 (;1653 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3433,plain,
$false,
inference(avatar_sat_refutation,[],[f65,f70,f75,f80,f85,f90,f95,f99,f103,f107,f111,f115,f119,f123,f128,f132,f136,f140,f150,f154,f158,f162,f166,f178,f188,f192,f202,f206,f210,f214,f218,f223,f227,f231,f270,f275,f279,f283,f287,f307,f311,f330,f341,f345,f349,f370,f380,f398,f402,f420,f424,f448,f457,f467,f479,f496,f505,f515,f527,f532,f541,f545,f549,f553,f557,f561,f565,f569,f573,f689,f693,f706,f710,f714,f718,f739,f743,f747,f751,f755,f759,f763,f767,f771,f860,f905,f924,f930,f956,f960,f964,f1020,f1025,f1036,f1055,f1059,f1073,f1077,f1081,f1140,f1144,f1148,f1152,f1215,f1284,f1296,f1300,f1304,f1385,f1386,f1397,f1401,f1440,f1444,f1448,f1534,f1538,f1558,f1562,f1584,f1604,f1608,f1612,f1616,f1660,f1672,f1710,f1714,f1718,f1722,f1726,f1737,f1755,f1759,f1763,f1801,f1806,f1810,f1814,f1818,f1822,f1826,f1830,f1834,f1838,f1850,f1854,f1858,f2026,f2030,f2034,f2038,f2133,f2156,f2160,f2164,f2168,f2228,f2233,f2237,f2286,f2290,f2341,f2345,f2349,f2397,f2422,f2451,f2485,f2531,f2541,f2562,f2584,f2588,f2601,f2623,f2627,f2633,f2637,f2641,f2645,f2654,f2717,f2721,f2735,f2766,f2792,f2797,f2822,f2827,f2852,f2886,f2890,f2894,f2965,f2979,f3041,f3043,f3047,f3062,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3432]) ).
fof(f3432,plain,
( spl0_1
| ~ spl0_23
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f3118,f3074,f164,f62]) ).
fof(f62,plain,
( spl0_1
<=> between(u,v,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f164,plain,
( spl0_23
<=> ! [X5,X3,X10] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f3074,plain,
( spl0_202
<=> between(x,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f3118,plain,
( between(u,v,x)
| ~ spl0_23
| ~ spl0_202 ),
inference(resolution,[],[f3076,f165]) ).
fof(f165,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f3076,plain,
( between(x,v,u)
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f3074]) ).
fof(f3117,plain,
( spl0_212
| ~ spl0_64
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1180,f1142,f543,f3115]) ).
fof(f3115,plain,
( spl0_212
<=> ! [X54,X52,X53,X55] : equidistant(reflection(extension(X52,X53,X54,X55),X53),X53,X54,X55) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f543,plain,
( spl0_64
<=> ! [X0,X1] : equidistant(X1,X0,reflection(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1142,plain,
( spl0_103
<=> ! [X17,X14,X13,X12,X16,X15] :
( ~ equidistant(X12,extension(X13,X12,X14,X15),X16,X17)
| equidistant(X16,X17,X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1180,plain,
( ! [X54,X55,X52,X53] : equidistant(reflection(extension(X52,X53,X54,X55),X53),X53,X54,X55)
| ~ spl0_64
| ~ spl0_103 ),
inference(resolution,[],[f1143,f544]) ).
fof(f544,plain,
( ! [X0,X1] : equidistant(X1,X0,reflection(X0,X1),X1)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f1143,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ equidistant(X12,extension(X13,X12,X14,X15),X16,X17)
| equidistant(X16,X17,X14,X15) )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f3113,plain,
( spl0_211
| ~ spl0_70
| ~ spl0_103 ),
inference(avatar_split_clause,[],[f1173,f1142,f567,f3111]) ).
fof(f3111,plain,
( spl0_211
<=> ! [X18,X17,X16,X19] : equidistant(X16,reflection(extension(X17,X16,X18,X19),X16),X18,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f567,plain,
( spl0_70
<=> ! [X11,X10] : equidistant(X10,X11,X10,reflection(X11,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1173,plain,
( ! [X18,X19,X16,X17] : equidistant(X16,reflection(extension(X17,X16,X18,X19),X16),X18,X19)
| ~ spl0_70
| ~ spl0_103 ),
inference(resolution,[],[f1143,f568]) ).
fof(f568,plain,
( ! [X10,X11] : equidistant(X10,X11,X10,reflection(X11,X10))
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f3109,plain,
( spl0_210
| ~ spl0_69
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1113,f1075,f563,f3107]) ).
fof(f3107,plain,
( spl0_210
<=> ! [X36,X37] : equidistant(reflection(X36,reflection(X37,X36)),reflection(X37,X36),X37,X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f563,plain,
( spl0_69
<=> ! [X11,X10] : equidistant(X10,X11,reflection(X10,X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1075,plain,
( spl0_100
<=> ! [X18,X19,X20,X21] :
( ~ equidistant(X18,reflection(X19,X18),X20,X21)
| equidistant(X20,X21,X19,X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1113,plain,
( ! [X36,X37] : equidistant(reflection(X36,reflection(X37,X36)),reflection(X37,X36),X37,X36)
| ~ spl0_69
| ~ spl0_100 ),
inference(resolution,[],[f1076,f564]) ).
fof(f564,plain,
( ! [X10,X11] : equidistant(X10,X11,reflection(X10,X11),X11)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f1076,plain,
( ! [X21,X18,X19,X20] :
( ~ equidistant(X18,reflection(X19,X18),X20,X21)
| equidistant(X20,X21,X19,X18) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f3105,plain,
( spl0_209
| ~ spl0_84
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1111,f1075,f761,f3103]) ).
fof(f3103,plain,
( spl0_209
<=> ! [X30,X32,X31,X33] : equidistant(extension(X30,X31,reflection(X32,X33),X33),X31,X32,X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f761,plain,
( spl0_84
<=> ! [X9,X7,X6,X8] : equidistant(X6,X7,extension(X8,X9,X7,X6),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1111,plain,
( ! [X31,X32,X30,X33] : equidistant(extension(X30,X31,reflection(X32,X33),X33),X31,X32,X33)
| ~ spl0_84
| ~ spl0_100 ),
inference(resolution,[],[f1076,f762]) ).
fof(f762,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,extension(X8,X9,X7,X6),X9)
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f761]) ).
fof(f3101,plain,
( spl0_208
| ~ spl0_82
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1110,f1075,f753,f3099]) ).
fof(f3099,plain,
( spl0_208
<=> ! [X29,X27,X28,X26] : equidistant(extension(X26,X27,X28,reflection(X29,X28)),X27,X29,X28) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f753,plain,
( spl0_82
<=> ! [X9,X7,X6,X8] : equidistant(X6,X7,extension(X8,X9,X6,X7),X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1110,plain,
( ! [X28,X29,X26,X27] : equidistant(extension(X26,X27,X28,reflection(X29,X28)),X27,X29,X28)
| ~ spl0_82
| ~ spl0_100 ),
inference(resolution,[],[f1076,f754]) ).
fof(f754,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,extension(X8,X9,X6,X7),X9)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f3097,plain,
( spl0_207
| ~ spl0_83
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1109,f1075,f757,f3095]) ).
fof(f3095,plain,
( spl0_207
<=> ! [X24,X23,X25,X22] : equidistant(X22,extension(X23,X22,reflection(X24,X25),X25),X24,X25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f757,plain,
( spl0_83
<=> ! [X9,X7,X6,X8] : equidistant(X6,X7,X8,extension(X9,X8,X7,X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1109,plain,
( ! [X24,X22,X25,X23] : equidistant(X22,extension(X23,X22,reflection(X24,X25),X25),X24,X25)
| ~ spl0_83
| ~ spl0_100 ),
inference(resolution,[],[f1076,f758]) ).
fof(f758,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,X8,extension(X9,X8,X7,X6))
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f3093,plain,
( spl0_206
| ~ spl0_78
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1108,f1075,f737,f3091]) ).
fof(f3091,plain,
( spl0_206
<=> ! [X18,X19,X20,X21] : equidistant(X18,extension(X19,X18,X20,reflection(X21,X20)),X21,X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f737,plain,
( spl0_78
<=> ! [X9,X7,X6,X8] : equidistant(X6,X7,X8,extension(X9,X8,X6,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1108,plain,
( ! [X21,X18,X19,X20] : equidistant(X18,extension(X19,X18,X20,reflection(X21,X20)),X21,X20)
| ~ spl0_78
| ~ spl0_100 ),
inference(resolution,[],[f1076,f738]) ).
fof(f738,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,X8,extension(X9,X8,X6,X7))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f3089,plain,
( spl0_205
| ~ spl0_65
| ~ spl0_100 ),
inference(avatar_split_clause,[],[f1107,f1075,f547,f3087]) ).
fof(f3087,plain,
( spl0_205
<=> ! [X16,X17] : equidistant(reflection(X16,X17),reflection(X17,reflection(X16,X17)),X16,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f547,plain,
( spl0_65
<=> ! [X11,X10] : equidistant(X10,X11,X11,reflection(X10,X11)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1107,plain,
( ! [X16,X17] : equidistant(reflection(X16,X17),reflection(X17,reflection(X16,X17)),X16,X17)
| ~ spl0_65
| ~ spl0_100 ),
inference(resolution,[],[f1076,f548]) ).
fof(f548,plain,
( ! [X10,X11] : equidistant(X10,X11,X11,reflection(X10,X11))
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f3085,plain,
( spl0_204
| ~ spl0_39
| ~ spl0_75 ),
inference(avatar_split_clause,[],[f722,f708,f285,f3083]) ).
fof(f3083,plain,
( spl0_204
<=> ! [X17,X14,X16,X15] :
( X14 = X15
| ~ between(extension(X14,X15,X16,X17),X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f285,plain,
( spl0_39
<=> ! [X5,X3,X10] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f708,plain,
( spl0_75
<=> ! [X9,X7,X6,X8] : between(extension(X6,X7,X8,X9),X7,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f722,plain,
( ! [X16,X14,X17,X15] :
( X14 = X15
| ~ between(extension(X14,X15,X16,X17),X14,X15) )
| ~ spl0_39
| ~ spl0_75 ),
inference(resolution,[],[f709,f286]) ).
fof(f286,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X5,X3)
| X3 = X5
| ~ between(X10,X3,X5) )
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f709,plain,
( ! [X8,X6,X9,X7] : between(extension(X6,X7,X8,X9),X7,X6)
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f3081,plain,
( spl0_203
| ~ spl0_24
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f435,f281,f176,f3079]) ).
fof(f3079,plain,
( spl0_203
<=> ! [X11,X10] :
( ~ between(X10,reflection(X11,X10),X11)
| reflection(X11,X10) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f176,plain,
( spl0_24
<=> ! [X2,X3] : between(reflection(X2,X3),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f281,plain,
( spl0_38
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f435,plain,
( ! [X10,X11] :
( ~ between(X10,reflection(X11,X10),X11)
| reflection(X11,X10) = X10 )
| ~ spl0_24
| ~ spl0_38 ),
inference(resolution,[],[f177,f282]) ).
fof(f282,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| ~ between(X3,X10,X5)
| X3 = X10 )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f177,plain,
( ! [X2,X3] : between(reflection(X2,X3),X3,X2)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f3077,plain,
( spl0_202
| ~ spl0_32
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f3063,f3060,f220,f3074]) ).
fof(f220,plain,
( spl0_32
<=> between(w,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f3060,plain,
( spl0_201
<=> ! [X0] :
( ~ between(w,v,X0)
| between(x,v,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f3063,plain,
( between(x,v,u)
| ~ spl0_32
| ~ spl0_201 ),
inference(resolution,[],[f3061,f222]) ).
fof(f222,plain,
( between(w,v,u)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f3061,plain,
( ! [X0] :
( ~ between(w,v,X0)
| between(x,v,X0) )
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f3060]) ).
fof(f3062,plain,
( spl0_201
| spl0_2
| ~ spl0_36
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f371,f347,f272,f67,f3060]) ).
fof(f67,plain,
( spl0_2
<=> v = w ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f272,plain,
( spl0_36
<=> between(x,w,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f347,plain,
( spl0_45
<=> ! [X10,X0,X5,X3] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f371,plain,
( ! [X0] :
( v = w
| ~ between(w,v,X0)
| between(x,v,X0) )
| ~ spl0_36
| ~ spl0_45 ),
inference(resolution,[],[f274,f348]) ).
fof(f348,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| X3 = X5
| ~ between(X3,X5,X0)
| between(X10,X5,X0) )
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f347]) ).
fof(f274,plain,
( between(x,w,v)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f3047,plain,
( spl0_200
| ~ spl0_35
| ~ spl0_90 ),
inference(avatar_split_clause,[],[f3015,f927,f268,f3045]) ).
fof(f3045,plain,
( spl0_200
<=> ! [X0] :
( x != X0
| between(u,w,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f268,plain,
( spl0_35
<=> ! [X5,X10,X0,X3,X1] :
( between(X10,X3,X1)
| extension(X10,X3,X5,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f927,plain,
( spl0_90
<=> x = extension(u,w,w,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f3015,plain,
( ! [X0] :
( x != X0
| between(u,w,X0) )
| ~ spl0_35
| ~ spl0_90 ),
inference(superposition,[],[f269,f929]) ).
fof(f929,plain,
( x = extension(u,w,w,x)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f269,plain,
( ! [X3,X10,X0,X1,X5] :
( extension(X10,X3,X5,X0) != X1
| between(X10,X3,X1) )
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f3043,plain,
( ~ spl0_9
| spl0_199 ),
inference(avatar_contradiction_clause,[],[f3042]) ).
fof(f3042,plain,
( $false
| ~ spl0_9
| spl0_199 ),
inference(resolution,[],[f3040,f102]) ).
fof(f102,plain,
( ! [X3,X10] : between(X10,X10,X3)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f101]) ).
fof(f101,plain,
( spl0_9
<=> ! [X3,X10] : between(X10,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f3040,plain,
( ~ between(u,u,x)
| spl0_199 ),
inference(avatar_component_clause,[],[f3038]) ).
fof(f3038,plain,
( spl0_199
<=> between(u,u,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f3041,plain,
( ~ spl0_199
| spl0_1
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f906,f498,f62,f3038]) ).
fof(f498,plain,
( spl0_57
<=> u = v ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f906,plain,
( ~ between(u,u,x)
| spl0_1
| ~ spl0_57 ),
inference(superposition,[],[f64,f500]) ).
fof(f500,plain,
( u = v
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f498]) ).
fof(f64,plain,
( ~ between(u,v,x)
| spl0_1 ),
inference(avatar_component_clause,[],[f62]) ).
fof(f2979,plain,
( spl0_198
| ~ spl0_14
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2973,f2963,f121,f2976]) ).
fof(f2976,plain,
( spl0_198
<=> between(w,u,reflection(v,u)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f121,plain,
( spl0_14
<=> ! [X3,X10] : between(X10,X3,reflection(X10,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f2963,plain,
( spl0_197
<=> ! [X16] :
( ~ between(v,u,X16)
| between(w,u,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2973,plain,
( between(w,u,reflection(v,u))
| ~ spl0_14
| ~ spl0_197 ),
inference(resolution,[],[f2964,f122]) ).
fof(f122,plain,
( ! [X3,X10] : between(X10,X3,reflection(X10,X3))
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f121]) ).
fof(f2964,plain,
( ! [X16] :
( ~ between(v,u,X16)
| between(w,u,X16) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2963]) ).
fof(f2965,plain,
( spl0_197
| spl0_57
| ~ spl0_32
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f366,f347,f220,f498,f2963]) ).
fof(f366,plain,
( ! [X16] :
( u = v
| ~ between(v,u,X16)
| between(w,u,X16) )
| ~ spl0_32
| ~ spl0_45 ),
inference(resolution,[],[f348,f222]) ).
fof(f2894,plain,
( spl0_196
| ~ spl0_19
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1119,f1079,f148,f2892]) ).
fof(f2892,plain,
( spl0_196
<=> ! [X6,X4,X5] :
( ~ equidistant(X4,X5,X6,X6)
| reflection(X4,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f148,plain,
( spl0_19
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1079,plain,
( spl0_101
<=> ! [X18,X19,X20,X21] :
( ~ equidistant(X18,X19,X20,X21)
| equidistant(X19,reflection(X18,X19),X20,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1119,plain,
( ! [X6,X4,X5] :
( ~ equidistant(X4,X5,X6,X6)
| reflection(X4,X5) = X5 )
| ~ spl0_19
| ~ spl0_101 ),
inference(resolution,[],[f1080,f149]) ).
fof(f149,plain,
( ! [X2,X0,X1] :
( ~ equidistant(X0,X1,X2,X2)
| X0 = X1 )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f1080,plain,
( ! [X21,X18,X19,X20] :
( equidistant(X19,reflection(X18,X19),X20,X21)
| ~ equidistant(X18,X19,X20,X21) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f2890,plain,
( spl0_195
| ~ spl0_23
| ~ spl0_91 ),
inference(avatar_split_clause,[],[f974,f954,f164,f2888]) ).
fof(f2888,plain,
( spl0_195
<=> ! [X27,X28,X26] :
( ~ between(X26,X27,X28)
| between(reflection(X26,X28),X28,X27) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f954,plain,
( spl0_91
<=> ! [X9,X8,X10] :
( ~ between(X8,X9,X10)
| between(X9,X10,reflection(X8,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f974,plain,
( ! [X28,X26,X27] :
( ~ between(X26,X27,X28)
| between(reflection(X26,X28),X28,X27) )
| ~ spl0_23
| ~ spl0_91 ),
inference(resolution,[],[f955,f165]) ).
fof(f955,plain,
( ! [X10,X8,X9] :
( between(X9,X10,reflection(X8,X10))
| ~ between(X8,X9,X10) )
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f2886,plain,
( spl0_194
| ~ spl0_24
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f433,f305,f176,f2884]) ).
fof(f2884,plain,
( spl0_194
<=> ! [X6,X5,X7] :
( ~ between(reflection(X5,X6),X7,X6)
| between(X7,X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f305,plain,
( spl0_40
<=> ! [X10,X0,X5,X3] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f433,plain,
( ! [X6,X7,X5] :
( ~ between(reflection(X5,X6),X7,X6)
| between(X7,X6,X5) )
| ~ spl0_24
| ~ spl0_40 ),
inference(resolution,[],[f177,f306]) ).
fof(f306,plain,
( ! [X3,X10,X0,X5] :
( ~ between(X10,X5,X0)
| ~ between(X10,X3,X5)
| between(X3,X5,X0) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f2852,plain,
( spl0_193
| ~ spl0_91
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1393,f1034,f954,f2850]) ).
fof(f2850,plain,
( spl0_193
<=> ! [X11] :
( between(v,x,reflection(X11,x))
| ~ between(X11,w,x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1034,plain,
( spl0_96
<=> ! [X15] :
( ~ between(w,x,X15)
| between(v,x,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1393,plain,
( ! [X11] :
( between(v,x,reflection(X11,x))
| ~ between(X11,w,x) )
| ~ spl0_91
| ~ spl0_96 ),
inference(resolution,[],[f1035,f955]) ).
fof(f1035,plain,
( ! [X15] :
( ~ between(w,x,X15)
| between(v,x,X15) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f2827,plain,
( spl0_2
| spl0_192
| ~ spl0_89
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1264,f1150,f921,f2824,f67]) ).
fof(f2824,plain,
( spl0_192
<=> x = extension(v,w,x,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f921,plain,
( spl0_89
<=> x = extension(v,w,w,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1150,plain,
( spl0_105
<=> ! [X5,X4,X7,X6] :
( X4 = X5
| extension(X5,X4,X6,X7) = extension(X5,X4,X7,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1264,plain,
( x = extension(v,w,x,w)
| v = w
| ~ spl0_89
| ~ spl0_105 ),
inference(superposition,[],[f923,f1151]) ).
fof(f1151,plain,
( ! [X6,X7,X4,X5] :
( extension(X5,X4,X6,X7) = extension(X5,X4,X7,X6)
| X4 = X5 )
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f923,plain,
( x = extension(v,w,w,x)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f921]) ).
fof(f2822,plain,
( spl0_183
| ~ spl0_191
| spl0_90
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1263,f1150,f927,f2819,f2647]) ).
fof(f2647,plain,
( spl0_183
<=> u = w ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2819,plain,
( spl0_191
<=> x = extension(u,w,x,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1263,plain,
( x != extension(u,w,x,w)
| u = w
| spl0_90
| ~ spl0_105 ),
inference(superposition,[],[f928,f1151]) ).
fof(f928,plain,
( x != extension(u,w,w,x)
| spl0_90 ),
inference(avatar_component_clause,[],[f927]) ).
fof(f2797,plain,
( spl0_57
| spl0_190
| ~ spl0_88
| ~ spl0_105 ),
inference(avatar_split_clause,[],[f1262,f1150,f902,f2794,f498]) ).
fof(f2794,plain,
( spl0_190
<=> w = extension(u,v,w,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f902,plain,
( spl0_88
<=> w = extension(u,v,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1262,plain,
( w = extension(u,v,w,v)
| u = v
| ~ spl0_88
| ~ spl0_105 ),
inference(superposition,[],[f904,f1151]) ).
fof(f904,plain,
( w = extension(u,v,v,w)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f2792,plain,
( spl0_189
| ~ spl0_91
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1032,f1018,f954,f2790]) ).
fof(f2790,plain,
( spl0_189
<=> ! [X8] :
( between(u,w,reflection(X8,w))
| ~ between(X8,v,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1018,plain,
( spl0_94
<=> ! [X14] :
( ~ between(v,w,X14)
| between(u,w,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1032,plain,
( ! [X8] :
( between(u,w,reflection(X8,w))
| ~ between(X8,v,w) )
| ~ spl0_91
| ~ spl0_94 ),
inference(resolution,[],[f1019,f955]) ).
fof(f1019,plain,
( ! [X14] :
( ~ between(v,w,X14)
| between(u,w,X14) )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f2766,plain,
( spl0_188
| spl0_63
| ~ spl0_36
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f372,f328,f272,f538,f2763]) ).
fof(f2763,plain,
( spl0_188
<=> v = extension(x,w,w,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f538,plain,
( spl0_63
<=> w = x ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f328,plain,
( spl0_42
<=> ! [X5,X3,X10] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f372,plain,
( w = x
| v = extension(x,w,w,v)
| ~ spl0_36
| ~ spl0_42 ),
inference(resolution,[],[f274,f329]) ).
fof(f329,plain,
( ! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| X3 = X10
| extension(X10,X3,X3,X5) = X5 )
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f328]) ).
fof(f2735,plain,
( spl0_187
| spl0_2
| ~ spl0_32
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f337,f328,f220,f67,f2732]) ).
fof(f2732,plain,
( spl0_187
<=> u = extension(w,v,v,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f337,plain,
( v = w
| u = extension(w,v,v,u)
| ~ spl0_32
| ~ spl0_42 ),
inference(resolution,[],[f329,f222]) ).
fof(f2721,plain,
( spl0_186
| ~ spl0_18
| ~ spl0_85 ),
inference(avatar_split_clause,[],[f895,f765,f138,f2719]) ).
fof(f2719,plain,
( spl0_186
<=> ! [X4,X2,X3] :
( X2 != X4
| between(reflection(X2,X3),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f138,plain,
( spl0_18
<=> ! [X3,X10] : reflection(reflection(X10,X3),X3) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f765,plain,
( spl0_85
<=> ! [X6,X4,X5] :
( reflection(X4,X5) != X6
| between(X4,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f895,plain,
( ! [X2,X3,X4] :
( X2 != X4
| between(reflection(X2,X3),X3,X4) )
| ~ spl0_18
| ~ spl0_85 ),
inference(superposition,[],[f766,f139]) ).
fof(f139,plain,
( ! [X3,X10] : reflection(reflection(X10,X3),X3) = X10
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f766,plain,
( ! [X6,X4,X5] :
( reflection(X4,X5) != X6
| between(X4,X5,X6) )
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f765]) ).
fof(f2717,plain,
( spl0_185
| ~ spl0_24
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f434,f285,f176,f2715]) ).
fof(f2715,plain,
( spl0_185
<=> ! [X9,X8] :
( X8 = X9
| ~ between(reflection(X8,X9),X8,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f434,plain,
( ! [X8,X9] :
( X8 = X9
| ~ between(reflection(X8,X9),X8,X9) )
| ~ spl0_24
| ~ spl0_39 ),
inference(resolution,[],[f177,f286]) ).
fof(f2654,plain,
( spl0_183
| ~ spl0_184
| ~ spl0_38
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1450,f1212,f281,f2651,f2647]) ).
fof(f2651,plain,
( spl0_184
<=> between(w,u,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1212,plain,
( spl0_106
<=> between(u,w,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1450,plain,
( ~ between(w,u,x)
| u = w
| ~ spl0_38
| ~ spl0_106 ),
inference(resolution,[],[f1214,f282]) ).
fof(f1214,plain,
( between(u,w,x)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f2645,plain,
( spl0_182
| ~ spl0_20
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1388,f1034,f152,f2643]) ).
fof(f2643,plain,
( spl0_182
<=> ! [X0,X1] : between(v,x,extension(w,x,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f152,plain,
( spl0_20
<=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1388,plain,
( ! [X0,X1] : between(v,x,extension(w,x,X0,X1))
| ~ spl0_20
| ~ spl0_96 ),
inference(resolution,[],[f1035,f153]) ).
fof(f153,plain,
( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f152]) ).
fof(f2641,plain,
( spl0_181
| ~ spl0_20
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1028,f1018,f152,f2639]) ).
fof(f2639,plain,
( spl0_181
<=> ! [X0,X1] : between(u,w,extension(v,w,X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1028,plain,
( ! [X0,X1] : between(u,w,extension(v,w,X0,X1))
| ~ spl0_20
| ~ spl0_94 ),
inference(resolution,[],[f1019,f153]) ).
fof(f2637,plain,
( spl0_180
| ~ spl0_36
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f373,f305,f272,f2635]) ).
fof(f2635,plain,
( spl0_180
<=> ! [X1] :
( ~ between(x,X1,w)
| between(X1,w,v) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f373,plain,
( ! [X1] :
( ~ between(x,X1,w)
| between(X1,w,v) )
| ~ spl0_36
| ~ spl0_40 ),
inference(resolution,[],[f274,f306]) ).
fof(f2633,plain,
( spl0_179
| ~ spl0_32
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f318,f305,f220,f2631]) ).
fof(f2631,plain,
( spl0_179
<=> ! [X0] :
( ~ between(w,X0,v)
| between(X0,v,u) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f318,plain,
( ! [X0] :
( ~ between(w,X0,v)
| between(X0,v,u) )
| ~ spl0_32
| ~ spl0_40 ),
inference(resolution,[],[f222,f306]) ).
fof(f2627,plain,
( spl0_178
| ~ spl0_35
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f944,f921,f268,f2625]) ).
fof(f2625,plain,
( spl0_178
<=> ! [X0] :
( x != X0
| between(v,w,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f944,plain,
( ! [X0] :
( x != X0
| between(v,w,X0) )
| ~ spl0_35
| ~ spl0_89 ),
inference(superposition,[],[f269,f923]) ).
fof(f2623,plain,
( spl0_177
| ~ spl0_35
| ~ spl0_88 ),
inference(avatar_split_clause,[],[f933,f902,f268,f2621]) ).
fof(f2621,plain,
( spl0_177
<=> ! [X0] :
( w != X0
| between(u,v,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f933,plain,
( ! [X0] :
( w != X0
| between(u,v,X0) )
| ~ spl0_35
| ~ spl0_88 ),
inference(superposition,[],[f269,f904]) ).
fof(f2601,plain,
( spl0_63
| ~ spl0_176
| ~ spl0_36
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f375,f281,f272,f2598,f538]) ).
fof(f2598,plain,
( spl0_176
<=> between(w,x,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f375,plain,
( ~ between(w,x,v)
| w = x
| ~ spl0_36
| ~ spl0_38 ),
inference(resolution,[],[f274,f282]) ).
fof(f2588,plain,
( spl0_175
| ~ spl0_55
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f519,f513,f477,f2586]) ).
fof(f2586,plain,
( spl0_175
<=> ! [X21,X18,X19,X26,X27,X24,X22,X25,X23,X20] :
( ~ between(X18,X19,X20)
| ~ between(X21,X19,X22)
| X19 = X21
| ~ equidistant(X21,X23,X18,continuous(X19,X24,X25,X23,X26,X27))
| ~ equidistant(X19,X22,X19,X20)
| ~ equidistant(X21,X19,X18,X19)
| equidistant(X22,X23,X20,continuous(X19,X24,X25,X23,X26,X27))
| ~ between(X19,X24,X26)
| ~ equidistant(X19,X26,X19,X27)
| ~ equidistant(X19,X24,X19,X25)
| ~ between(X24,X23,X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f477,plain,
( spl0_55
<=> ! [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_55])]) ).
fof(f513,plain,
( spl0_59
<=> ! [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_59])]) ).
fof(f519,plain,
( ! [X21,X18,X19,X26,X27,X24,X22,X25,X23,X20] :
( ~ between(X18,X19,X20)
| ~ between(X21,X19,X22)
| X19 = X21
| ~ equidistant(X21,X23,X18,continuous(X19,X24,X25,X23,X26,X27))
| ~ equidistant(X19,X22,X19,X20)
| ~ equidistant(X21,X19,X18,X19)
| equidistant(X22,X23,X20,continuous(X19,X24,X25,X23,X26,X27))
| ~ between(X19,X24,X26)
| ~ equidistant(X19,X26,X19,X27)
| ~ equidistant(X19,X24,X19,X25)
| ~ between(X24,X23,X26) )
| ~ spl0_55
| ~ spl0_59 ),
inference(resolution,[],[f514,f478]) ).
fof(f478,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_55 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f514,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_59 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f2584,plain,
( spl0_174
| ~ spl0_55
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f509,f494,f477,f2582]) ).
fof(f2582,plain,
( spl0_174
<=> ! [X17,X10,X16,X11,X14,X13,X12,X15] :
( between(X10,X11,X12)
| between(X12,X10,X11)
| between(X11,X12,X10)
| continuous(X10,X13,X14,X15,X16,X17) = X15
| ~ equidistant(X12,X15,X12,continuous(X10,X13,X14,X15,X16,X17))
| ~ equidistant(X11,X15,X11,continuous(X10,X13,X14,X15,X16,X17))
| ~ between(X10,X13,X16)
| ~ equidistant(X10,X16,X10,X17)
| ~ equidistant(X10,X13,X10,X14)
| ~ between(X13,X15,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f494,plain,
( spl0_56
<=> ! [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_56])]) ).
fof(f509,plain,
( ! [X10,X11,X16,X14,X17,X15,X12,X13] :
( between(X10,X11,X12)
| between(X12,X10,X11)
| between(X11,X12,X10)
| continuous(X10,X13,X14,X15,X16,X17) = X15
| ~ equidistant(X12,X15,X12,continuous(X10,X13,X14,X15,X16,X17))
| ~ equidistant(X11,X15,X11,continuous(X10,X13,X14,X15,X16,X17))
| ~ between(X10,X13,X16)
| ~ equidistant(X10,X16,X10,X17)
| ~ equidistant(X10,X13,X10,X14)
| ~ between(X13,X15,X16) )
| ~ spl0_55
| ~ spl0_56 ),
inference(resolution,[],[f495,f478]) ).
fof(f495,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_56 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f2562,plain,
( spl0_173
| ~ spl0_54
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f491,f477,f465,f2560]) ).
fof(f2560,plain,
( spl0_173
<=> ! [X82,X80,X78,X81,X79,X76,X77,X74,X75] :
( ~ between(X74,X75,X76)
| ~ equidistant(X74,X76,X74,X77)
| ~ equidistant(X74,X75,X74,X78)
| ~ between(X75,X79,X76)
| ~ between(X74,X79,X80)
| ~ equidistant(X74,X80,X74,X81)
| ~ between(X79,X82,X80)
| between(continuous(X74,X75,X78,X79,X76,X77),continuous(X74,X79,continuous(X74,X75,X78,X79,X76,X77),X82,X80,X81),X81) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f465,plain,
( spl0_54
<=> ! [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_54])]) ).
fof(f491,plain,
( ! [X82,X80,X78,X81,X79,X76,X77,X74,X75] :
( ~ between(X74,X75,X76)
| ~ equidistant(X74,X76,X74,X77)
| ~ equidistant(X74,X75,X74,X78)
| ~ between(X75,X79,X76)
| ~ between(X74,X79,X80)
| ~ equidistant(X74,X80,X74,X81)
| ~ between(X79,X82,X80)
| between(continuous(X74,X75,X78,X79,X76,X77),continuous(X74,X79,continuous(X74,X75,X78,X79,X76,X77),X82,X80,X81),X81) )
| ~ spl0_54
| ~ spl0_55 ),
inference(resolution,[],[f478,f466]) ).
fof(f466,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_54 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f2541,plain,
( spl0_172
| ~ spl0_52
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f490,f477,f446,f2539]) ).
fof(f2539,plain,
( spl0_172
<=> ! [X72,X70,X68,X73,X71,X69,X67,X66] :
( ~ between(X66,X67,X68)
| ~ equidistant(X66,X68,X66,X69)
| ~ equidistant(X66,X67,X66,X70)
| ~ between(X67,X71,X68)
| ~ between(X66,X71,X72)
| ~ equidistant(X71,X72,continuous(X66,X67,X70,X71,X68,X69),X73)
| ~ between(X66,continuous(X66,X67,X70,X71,X68,X69),X73)
| equidistant(X66,X72,X66,X73) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f446,plain,
( spl0_52
<=> ! [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_52])]) ).
fof(f490,plain,
( ! [X72,X70,X73,X71,X68,X69,X66,X67] :
( ~ between(X66,X67,X68)
| ~ equidistant(X66,X68,X66,X69)
| ~ equidistant(X66,X67,X66,X70)
| ~ between(X67,X71,X68)
| ~ between(X66,X71,X72)
| ~ equidistant(X71,X72,continuous(X66,X67,X70,X71,X68,X69),X73)
| ~ between(X66,continuous(X66,X67,X70,X71,X68,X69),X73)
| equidistant(X66,X72,X66,X73) )
| ~ spl0_52
| ~ spl0_55 ),
inference(resolution,[],[f478,f447]) ).
fof(f447,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_52 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f2531,plain,
( spl0_171
| ~ spl0_48
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f492,f477,f396,f2529]) ).
fof(f2529,plain,
( spl0_171
<=> ! [X85,X88,X83,X84,X87,X89,X86] :
( ~ between(X83,X84,X85)
| ~ equidistant(X83,X85,X83,X86)
| ~ equidistant(X83,X84,X83,X87)
| ~ between(X84,X88,X85)
| X83 = X89
| ~ between(X89,X83,X88)
| ~ between(X89,X83,continuous(X83,X84,X87,X88,X85,X86))
| continuous(X83,X84,X87,X88,X85,X86) = X88 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f396,plain,
( spl0_48
<=> ! [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_48])]) ).
fof(f492,plain,
( ! [X83,X88,X86,X89,X87,X84,X85] :
( ~ between(X83,X84,X85)
| ~ equidistant(X83,X85,X83,X86)
| ~ equidistant(X83,X84,X83,X87)
| ~ between(X84,X88,X85)
| X83 = X89
| ~ between(X89,X83,X88)
| ~ between(X89,X83,continuous(X83,X84,X87,X88,X85,X86))
| continuous(X83,X84,X87,X88,X85,X86) = X88 )
| ~ spl0_48
| ~ spl0_55 ),
inference(resolution,[],[f478,f397]) ).
fof(f397,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X3,X5,X3,X0)
| X3 = X10
| ~ between(X10,X3,X5)
| ~ between(X10,X3,X0)
| X0 = X5 )
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f2485,plain,
( spl0_170
| ~ spl0_45
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f458,f455,f347,f2483]) ).
fof(f2483,plain,
( spl0_170
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid2(X3,X0,X1,X2,X4) = X4
| ~ between(X4,euclid2(X3,X0,X1,X2,X4),X5)
| between(euclid1(X3,X0,X1,X2,X4),euclid2(X3,X0,X1,X2,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f455,plain,
( spl0_53
<=> ! [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_53])]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid2(X3,X0,X1,X2,X4) = X4
| ~ between(X4,euclid2(X3,X0,X1,X2,X4),X5)
| between(euclid1(X3,X0,X1,X2,X4),euclid2(X3,X0,X1,X2,X4),X5) )
| ~ spl0_45
| ~ spl0_53 ),
inference(resolution,[],[f456,f348]) ).
fof(f456,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_53 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f2451,plain,
( spl0_169
| ~ spl0_42
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f459,f455,f328,f2449]) ).
fof(f2449,plain,
( spl0_169
<=> ! [X10,X9,X7,X6,X8] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| euclid1(X9,X6,X7,X8,X10) = X10
| euclid2(X9,X6,X7,X8,X10) = extension(euclid1(X9,X6,X7,X8,X10),X10,X10,euclid2(X9,X6,X7,X8,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f459,plain,
( ! [X10,X8,X6,X9,X7] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| euclid1(X9,X6,X7,X8,X10) = X10
| euclid2(X9,X6,X7,X8,X10) = extension(euclid1(X9,X6,X7,X8,X10),X10,X10,euclid2(X9,X6,X7,X8,X10)) )
| ~ spl0_42
| ~ spl0_53 ),
inference(resolution,[],[f456,f329]) ).
fof(f2422,plain,
( spl0_168
| ~ spl0_25
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f520,f513,f186,f2420]) ).
fof(f2420,plain,
( spl0_168
<=> ! [X31,X33,X32,X34,X29,X35,X28,X30] :
( ~ between(X28,X29,X30)
| ~ between(X31,X32,X33)
| X31 = X32
| ~ equidistant(X31,extension(X34,X32,X29,X35),X28,X35)
| ~ equidistant(X32,X33,X29,X30)
| ~ equidistant(X31,X32,X28,X29)
| equidistant(X33,extension(X34,X32,X29,X35),X30,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f186,plain,
( spl0_25
<=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f520,plain,
( ! [X31,X28,X29,X34,X35,X32,X30,X33] :
( ~ between(X28,X29,X30)
| ~ between(X31,X32,X33)
| X31 = X32
| ~ equidistant(X31,extension(X34,X32,X29,X35),X28,X35)
| ~ equidistant(X32,X33,X29,X30)
| ~ equidistant(X31,X32,X28,X29)
| equidistant(X33,extension(X34,X32,X29,X35),X30,X35) )
| ~ spl0_25
| ~ spl0_59 ),
inference(resolution,[],[f514,f187]) ).
fof(f187,plain,
( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f2397,plain,
( spl0_167
| ~ spl0_49
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f489,f477,f400,f2395]) ).
fof(f2395,plain,
( spl0_167
<=> ! [X65,X61,X58,X64,X63,X59,X62,X60] :
( ~ between(X58,X59,X60)
| ~ equidistant(X58,X60,X58,X61)
| ~ equidistant(X58,X59,X58,X62)
| ~ between(X59,X63,X60)
| X64 = X65
| extension(X65,X64,X58,X63) = extension(X65,X64,X58,continuous(X58,X59,X62,X63,X60,X61)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f400,plain,
( spl0_49
<=> ! [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_49])]) ).
fof(f489,plain,
( ! [X65,X58,X59,X62,X63,X60,X61,X64] :
( ~ between(X58,X59,X60)
| ~ equidistant(X58,X60,X58,X61)
| ~ equidistant(X58,X59,X58,X62)
| ~ between(X59,X63,X60)
| X64 = X65
| extension(X65,X64,X58,X63) = extension(X65,X64,X58,continuous(X58,X59,X62,X63,X60,X61)) )
| ~ spl0_49
| ~ spl0_55 ),
inference(resolution,[],[f478,f401]) ).
fof(f401,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_49 ),
inference(avatar_component_clause,[],[f400]) ).
fof(f2349,plain,
( spl0_166
| ~ spl0_25
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f510,f494,f186,f2347]) ).
fof(f2347,plain,
( spl0_166
<=> ! [X18,X19,X20,X22,X21] :
( between(X18,X19,X20)
| between(X20,X18,X19)
| between(X19,X20,X18)
| extension(X22,X18,X18,X21) = X21
| ~ equidistant(X20,extension(X22,X18,X18,X21),X20,X21)
| ~ equidistant(X19,extension(X22,X18,X18,X21),X19,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f510,plain,
( ! [X21,X18,X19,X22,X20] :
( between(X18,X19,X20)
| between(X20,X18,X19)
| between(X19,X20,X18)
| extension(X22,X18,X18,X21) = X21
| ~ equidistant(X20,extension(X22,X18,X18,X21),X20,X21)
| ~ equidistant(X19,extension(X22,X18,X18,X21),X19,X21) )
| ~ spl0_25
| ~ spl0_56 ),
inference(resolution,[],[f495,f187]) ).
fof(f2345,plain,
( spl0_165
| ~ spl0_45
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f439,f422,f347,f2343]) ).
fof(f2343,plain,
( spl0_165
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid2(X3,X0,X1,X2,X4) = X2
| ~ between(X2,euclid2(X3,X0,X1,X2,X4),X5)
| between(X3,euclid2(X3,X0,X1,X2,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f422,plain,
( spl0_51
<=> ! [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_51])]) ).
fof(f439,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid2(X3,X0,X1,X2,X4) = X2
| ~ between(X2,euclid2(X3,X0,X1,X2,X4),X5)
| between(X3,euclid2(X3,X0,X1,X2,X4),X5) )
| ~ spl0_45
| ~ spl0_51 ),
inference(resolution,[],[f423,f348]) ).
fof(f423,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_51 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f2341,plain,
( spl0_164
| ~ spl0_45
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f425,f418,f347,f2339]) ).
fof(f2339,plain,
( spl0_164
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid1(X3,X0,X1,X2,X4) = X0
| ~ between(X0,euclid1(X3,X0,X1,X2,X4),X5)
| between(X3,euclid1(X3,X0,X1,X2,X4),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f418,plain,
( spl0_50
<=> ! [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_50])]) ).
fof(f425,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ between(X0,X1,X2)
| ~ between(X3,X1,X4)
| X1 = X3
| euclid1(X3,X0,X1,X2,X4) = X0
| ~ between(X0,euclid1(X3,X0,X1,X2,X4),X5)
| between(X3,euclid1(X3,X0,X1,X2,X4),X5) )
| ~ spl0_45
| ~ spl0_50 ),
inference(resolution,[],[f419,f348]) ).
fof(f419,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_50 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f2290,plain,
( spl0_163
| ~ spl0_17
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f521,f513,f134,f2288]) ).
fof(f2288,plain,
( spl0_163
<=> ! [X38,X41,X40,X36,X39,X37] :
( ~ between(X36,X37,X38)
| ~ between(X39,X40,X41)
| X39 = X40
| ~ equidistant(X39,reflection(X37,X40),X36,X40)
| ~ equidistant(X40,X41,X37,X38)
| ~ equidistant(X39,X40,X36,X37)
| equidistant(X41,reflection(X37,X40),X38,X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f134,plain,
( spl0_17
<=> ! [X3,X10] : equidistant(X3,reflection(X10,X3),X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f521,plain,
( ! [X40,X38,X41,X39,X36,X37] :
( ~ between(X36,X37,X38)
| ~ between(X39,X40,X41)
| X39 = X40
| ~ equidistant(X39,reflection(X37,X40),X36,X40)
| ~ equidistant(X40,X41,X37,X38)
| ~ equidistant(X39,X40,X36,X37)
| equidistant(X41,reflection(X37,X40),X38,X40) )
| ~ spl0_17
| ~ spl0_59 ),
inference(resolution,[],[f514,f135]) ).
fof(f135,plain,
( ! [X3,X10] : equidistant(X3,reflection(X10,X3),X10,X3)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f134]) ).
fof(f2286,plain,
( spl0_162
| ~ spl0_25
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f471,f465,f186,f2284]) ).
fof(f2284,plain,
( spl0_162
<=> ! [X17,X18,X13,X14,X16,X15] :
( ~ between(X13,extension(X14,X13,X13,X15),X16)
| ~ equidistant(X13,X16,X13,X17)
| ~ between(extension(X14,X13,X13,X15),X18,X16)
| between(X15,continuous(X13,extension(X14,X13,X13,X15),X15,X18,X16,X17),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f471,plain,
( ! [X18,X16,X14,X17,X15,X13] :
( ~ between(X13,extension(X14,X13,X13,X15),X16)
| ~ equidistant(X13,X16,X13,X17)
| ~ between(extension(X14,X13,X13,X15),X18,X16)
| between(X15,continuous(X13,extension(X14,X13,X13,X15),X15,X18,X16,X17),X17) )
| ~ spl0_25
| ~ spl0_54 ),
inference(resolution,[],[f466,f187]) ).
fof(f2237,plain,
( spl0_161
| ~ spl0_44
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f488,f477,f343,f2235]) ).
fof(f2235,plain,
( spl0_161
<=> ! [X55,X56,X51,X53,X54,X50,X57,X52] :
( ~ between(X50,X51,X52)
| ~ equidistant(X50,X52,X50,X53)
| ~ equidistant(X50,X51,X50,X54)
| ~ between(X51,X55,X52)
| ~ equidistant(X50,continuous(X50,X51,X54,X55,X52,X53),X56,X57)
| equidistant(X50,X55,X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f343,plain,
( spl0_44
<=> ! [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_44])]) ).
fof(f488,plain,
( ! [X50,X51,X56,X54,X57,X55,X52,X53] :
( ~ between(X50,X51,X52)
| ~ equidistant(X50,X52,X50,X53)
| ~ equidistant(X50,X51,X50,X54)
| ~ between(X51,X55,X52)
| ~ equidistant(X50,continuous(X50,X51,X54,X55,X52,X53),X56,X57)
| equidistant(X50,X55,X56,X57) )
| ~ spl0_44
| ~ spl0_55 ),
inference(resolution,[],[f478,f344]) ).
fof(f344,plain,
( ! [X2,X3,X10,X0,X1,X5] :
( ~ equidistant(X10,X3,X5,X0)
| ~ equidistant(X5,X0,X1,X2)
| equidistant(X10,X3,X1,X2) )
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f343]) ).
fof(f2233,plain,
( spl0_160
| ~ spl0_23
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1966,f1803,f164,f2230]) ).
fof(f2230,plain,
( spl0_160
<=> between(reflection(w,x),x,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1803,plain,
( spl0_138
<=> between(v,x,reflection(w,x)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1966,plain,
( between(reflection(w,x),x,v)
| ~ spl0_23
| ~ spl0_138 ),
inference(resolution,[],[f1805,f165]) ).
fof(f1805,plain,
( between(v,x,reflection(w,x))
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1803]) ).
fof(f2228,plain,
( spl0_159
| ~ spl0_43
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f487,f477,f339,f2226]) ).
fof(f2226,plain,
( spl0_159
<=> ! [X44,X43,X42,X46,X49,X48,X45,X47] :
( ~ between(X42,X43,X44)
| ~ equidistant(X42,X44,X42,X45)
| ~ equidistant(X42,X43,X42,X46)
| ~ between(X43,X47,X44)
| ~ equidistant(X42,X47,X48,X49)
| equidistant(X48,X49,X42,continuous(X42,X43,X46,X47,X44,X45)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f339,plain,
( spl0_43
<=> ! [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_43])]) ).
fof(f487,plain,
( ! [X48,X46,X49,X47,X44,X45,X42,X43] :
( ~ between(X42,X43,X44)
| ~ equidistant(X42,X44,X42,X45)
| ~ equidistant(X42,X43,X42,X46)
| ~ between(X43,X47,X44)
| ~ equidistant(X42,X47,X48,X49)
| equidistant(X48,X49,X42,continuous(X42,X43,X46,X47,X44,X45)) )
| ~ spl0_43
| ~ spl0_55 ),
inference(resolution,[],[f478,f340]) ).
fof(f340,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ equidistant(X0,X1,X4,X5)
| ~ equidistant(X0,X1,X2,X3)
| equidistant(X2,X3,X4,X5) )
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f2168,plain,
( spl0_158
| ~ spl0_38
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f462,f455,f281,f2166]) ).
fof(f2166,plain,
( spl0_158
<=> ! [X24,X23,X25,X22,X26] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X26,euclid1(X25,X22,X23,X24,X26),euclid2(X25,X22,X23,X24,X26))
| euclid1(X25,X22,X23,X24,X26) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f462,plain,
( ! [X26,X24,X22,X25,X23] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X26,euclid1(X25,X22,X23,X24,X26),euclid2(X25,X22,X23,X24,X26))
| euclid1(X25,X22,X23,X24,X26) = X26 )
| ~ spl0_38
| ~ spl0_53 ),
inference(resolution,[],[f456,f282]) ).
fof(f2164,plain,
( spl0_157
| ~ spl0_39
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f461,f455,f285,f2162]) ).
fof(f2162,plain,
( spl0_157
<=> ! [X18,X19,X17,X21,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid2(X20,X17,X18,X19,X21) = X21
| ~ between(euclid1(X20,X17,X18,X19,X21),euclid2(X20,X17,X18,X19,X21),X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f461,plain,
( ! [X21,X18,X19,X17,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid2(X20,X17,X18,X19,X21) = X21
| ~ between(euclid1(X20,X17,X18,X19,X21),euclid2(X20,X17,X18,X19,X21),X21) )
| ~ spl0_39
| ~ spl0_53 ),
inference(resolution,[],[f456,f286]) ).
fof(f2160,plain,
( spl0_156
| ~ spl0_42
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f390,f378,f328,f2158]) ).
fof(f2158,plain,
( spl0_156
<=> ! [X10,X11,X14,X13,X12] :
( ~ between(X10,X11,X12)
| ~ between(X13,X14,X12)
| inner_pasch(X13,X14,X12,X11,X10) = X11
| extension(X11,inner_pasch(X13,X14,X12,X11,X10),inner_pasch(X13,X14,X12,X11,X10),X13) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f378,plain,
( spl0_47
<=> ! [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_47])]) ).
fof(f390,plain,
( ! [X10,X11,X14,X12,X13] :
( ~ between(X10,X11,X12)
| ~ between(X13,X14,X12)
| inner_pasch(X13,X14,X12,X11,X10) = X11
| extension(X11,inner_pasch(X13,X14,X12,X11,X10),inner_pasch(X13,X14,X12,X11,X10),X13) = X13 )
| ~ spl0_42
| ~ spl0_47 ),
inference(resolution,[],[f379,f329]) ).
fof(f379,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_47 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f2156,plain,
( spl0_155
| ~ spl0_42
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f383,f368,f328,f2154]) ).
fof(f2154,plain,
( spl0_155
<=> ! [X10,X11,X14,X13,X12] :
( ~ between(X10,X11,X12)
| ~ between(X13,X14,X12)
| inner_pasch(X13,X14,X12,X11,X10) = X14
| extension(X14,inner_pasch(X13,X14,X12,X11,X10),inner_pasch(X13,X14,X12,X11,X10),X10) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f368,plain,
( spl0_46
<=> ! [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_46])]) ).
fof(f383,plain,
( ! [X10,X11,X14,X12,X13] :
( ~ between(X10,X11,X12)
| ~ between(X13,X14,X12)
| inner_pasch(X13,X14,X12,X11,X10) = X14
| extension(X14,inner_pasch(X13,X14,X12,X11,X10),inner_pasch(X13,X14,X12,X11,X10),X10) = X10 )
| ~ spl0_42
| ~ spl0_46 ),
inference(resolution,[],[f369,f329]) ).
fof(f369,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_46 ),
inference(avatar_component_clause,[],[f368]) ).
fof(f2133,plain,
( spl0_154
| ~ spl0_23
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1839,f1734,f164,f2130]) ).
fof(f2130,plain,
( spl0_154
<=> between(reflection(v,w),w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1734,plain,
( spl0_133
<=> between(u,w,reflection(v,w)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1839,plain,
( between(reflection(v,w),w,u)
| ~ spl0_23
| ~ spl0_133 ),
inference(resolution,[],[f1736,f165]) ).
fof(f1736,plain,
( between(u,w,reflection(v,w))
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1734]) ).
fof(f2038,plain,
( spl0_153
| ~ spl0_11
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f518,f513,f109,f2036]) ).
fof(f2036,plain,
( spl0_153
<=> ! [X17,X13,X14,X12,X16,X15] :
( ~ between(X12,X13,X14)
| ~ between(X15,X13,X16)
| X13 = X15
| ~ equidistant(X15,X17,X12,X17)
| ~ equidistant(X13,X16,X13,X14)
| ~ equidistant(X15,X13,X12,X13)
| equidistant(X16,X17,X14,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f109,plain,
( spl0_11
<=> ! [X3,X10] : equidistant(X10,X3,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f518,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ between(X12,X13,X14)
| ~ between(X15,X13,X16)
| X13 = X15
| ~ equidistant(X15,X17,X12,X17)
| ~ equidistant(X13,X16,X13,X14)
| ~ equidistant(X15,X13,X12,X13)
| equidistant(X16,X17,X14,X17) )
| ~ spl0_11
| ~ spl0_59 ),
inference(resolution,[],[f514,f110]) ).
fof(f110,plain,
( ! [X3,X10] : equidistant(X10,X3,X10,X3)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f109]) ).
fof(f2034,plain,
( spl0_152
| ~ spl0_10
| ~ spl0_59 ),
inference(avatar_split_clause,[],[f517,f513,f105,f2032]) ).
fof(f2032,plain,
( spl0_152
<=> ! [X10,X9,X11,X6,X8,X7] :
( ~ between(X6,X7,X8)
| ~ between(X9,X10,X11)
| X9 = X10
| ~ equidistant(X9,X7,X6,X10)
| ~ equidistant(X10,X11,X7,X8)
| ~ equidistant(X9,X10,X6,X7)
| equidistant(X11,X7,X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f105,plain,
( spl0_10
<=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f517,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( ~ between(X6,X7,X8)
| ~ between(X9,X10,X11)
| X9 = X10
| ~ equidistant(X9,X7,X6,X10)
| ~ equidistant(X10,X11,X7,X8)
| ~ equidistant(X9,X10,X6,X7)
| equidistant(X11,X7,X8,X10) )
| ~ spl0_10
| ~ spl0_59 ),
inference(resolution,[],[f514,f106]) ).
fof(f106,plain,
( ! [X0,X1] : equidistant(X0,X1,X1,X0)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f105]) ).
fof(f2030,plain,
( spl0_151
| ~ spl0_42
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f440,f422,f328,f2028]) ).
fof(f2028,plain,
( spl0_151
<=> ! [X10,X9,X7,X6,X8] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| X8 = X9
| euclid2(X9,X6,X7,X8,X10) = extension(X9,X8,X8,euclid2(X9,X6,X7,X8,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f440,plain,
( ! [X10,X8,X6,X9,X7] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| X8 = X9
| euclid2(X9,X6,X7,X8,X10) = extension(X9,X8,X8,euclid2(X9,X6,X7,X8,X10)) )
| ~ spl0_42
| ~ spl0_51 ),
inference(resolution,[],[f423,f329]) ).
fof(f2026,plain,
( spl0_150
| ~ spl0_42
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f426,f418,f328,f2024]) ).
fof(f2024,plain,
( spl0_150
<=> ! [X10,X9,X7,X6,X8] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| X6 = X9
| euclid1(X9,X6,X7,X8,X10) = extension(X9,X6,X6,euclid1(X9,X6,X7,X8,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f426,plain,
( ! [X10,X8,X6,X9,X7] :
( ~ between(X6,X7,X8)
| ~ between(X9,X7,X10)
| X7 = X9
| X6 = X9
| euclid1(X9,X6,X7,X8,X10) = extension(X9,X6,X6,euclid1(X9,X6,X7,X8,X10)) )
| ~ spl0_42
| ~ spl0_50 ),
inference(resolution,[],[f419,f329]) ).
fof(f1858,plain,
( spl0_149
| ~ spl0_34
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f486,f477,f229,f1856]) ).
fof(f1856,plain,
( spl0_149
<=> ! [X38,X41,X40,X36,X39,X37] :
( ~ between(X36,X37,X38)
| ~ equidistant(X36,X38,X36,X39)
| ~ equidistant(X36,X37,X36,X40)
| ~ between(X37,X41,X38)
| equidistant(continuous(X36,X37,X40,X41,X38,X39),X36,X41,X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f229,plain,
( spl0_34
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f486,plain,
( ! [X40,X38,X41,X39,X36,X37] :
( ~ between(X36,X37,X38)
| ~ equidistant(X36,X38,X36,X39)
| ~ equidistant(X36,X37,X36,X40)
| ~ between(X37,X41,X38)
| equidistant(continuous(X36,X37,X40,X41,X38,X39),X36,X41,X36) )
| ~ spl0_34
| ~ spl0_55 ),
inference(resolution,[],[f478,f230]) ).
fof(f230,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) )
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f1854,plain,
( spl0_148
| ~ spl0_33
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f485,f477,f225,f1852]) ).
fof(f1852,plain,
( spl0_148
<=> ! [X31,X34,X33,X35,X32,X30] :
( ~ between(X30,X31,X32)
| ~ equidistant(X30,X32,X30,X33)
| ~ equidistant(X30,X31,X30,X34)
| ~ between(X31,X35,X32)
| equidistant(continuous(X30,X31,X34,X35,X32,X33),X30,X30,X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f225,plain,
( spl0_33
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f485,plain,
( ! [X31,X34,X35,X32,X30,X33] :
( ~ between(X30,X31,X32)
| ~ equidistant(X30,X32,X30,X33)
| ~ equidistant(X30,X31,X30,X34)
| ~ between(X31,X35,X32)
| equidistant(continuous(X30,X31,X34,X35,X32,X33),X30,X30,X35) )
| ~ spl0_33
| ~ spl0_55 ),
inference(resolution,[],[f478,f226]) ).
fof(f226,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f1850,plain,
( spl0_147
| ~ spl0_31
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f484,f477,f216,f1848]) ).
fof(f1848,plain,
( spl0_147
<=> ! [X28,X24,X29,X27,X25,X26] :
( ~ between(X24,X25,X26)
| ~ equidistant(X24,X26,X24,X27)
| ~ equidistant(X24,X25,X24,X28)
| ~ between(X25,X29,X26)
| equidistant(X24,continuous(X24,X25,X28,X29,X26,X27),X29,X24) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f216,plain,
( spl0_31
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f484,plain,
( ! [X28,X29,X26,X27,X24,X25] :
( ~ between(X24,X25,X26)
| ~ equidistant(X24,X26,X24,X27)
| ~ equidistant(X24,X25,X24,X28)
| ~ between(X25,X29,X26)
| equidistant(X24,continuous(X24,X25,X28,X29,X26,X27),X29,X24) )
| ~ spl0_31
| ~ spl0_55 ),
inference(resolution,[],[f478,f217]) ).
fof(f217,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f1838,plain,
( spl0_146
| ~ spl0_30
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f483,f477,f212,f1836]) ).
fof(f1836,plain,
( spl0_146
<=> ! [X18,X19,X20,X22,X23,X21] :
( ~ between(X18,X19,X20)
| ~ equidistant(X18,X20,X18,X21)
| ~ equidistant(X18,X19,X18,X22)
| ~ between(X19,X23,X20)
| equidistant(X23,X18,continuous(X18,X19,X22,X23,X20,X21),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f212,plain,
( spl0_30
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f483,plain,
( ! [X21,X18,X19,X22,X23,X20] :
( ~ between(X18,X19,X20)
| ~ equidistant(X18,X20,X18,X21)
| ~ equidistant(X18,X19,X18,X22)
| ~ between(X19,X23,X20)
| equidistant(X23,X18,continuous(X18,X19,X22,X23,X20,X21),X18) )
| ~ spl0_30
| ~ spl0_55 ),
inference(resolution,[],[f478,f213]) ).
fof(f213,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f1834,plain,
( spl0_145
| ~ spl0_29
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f482,f477,f208,f1832]) ).
fof(f1832,plain,
( spl0_145
<=> ! [X16,X13,X14,X12,X17,X15] :
( ~ between(X12,X13,X14)
| ~ equidistant(X12,X14,X12,X15)
| ~ equidistant(X12,X13,X12,X16)
| ~ between(X13,X17,X14)
| equidistant(X12,X17,continuous(X12,X13,X16,X17,X14,X15),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f208,plain,
( spl0_29
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f482,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ between(X12,X13,X14)
| ~ equidistant(X12,X14,X12,X15)
| ~ equidistant(X12,X13,X12,X16)
| ~ between(X13,X17,X14)
| equidistant(X12,X17,continuous(X12,X13,X16,X17,X14,X15),X12) )
| ~ spl0_29
| ~ spl0_55 ),
inference(resolution,[],[f478,f209]) ).
fof(f209,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f1830,plain,
( spl0_144
| ~ spl0_28
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f481,f477,f204,f1828]) ).
fof(f1828,plain,
( spl0_144
<=> ! [X10,X11,X9,X7,X6,X8] :
( ~ between(X6,X7,X8)
| ~ equidistant(X6,X8,X6,X9)
| ~ equidistant(X6,X7,X6,X10)
| ~ between(X7,X11,X8)
| equidistant(X11,X6,X6,continuous(X6,X7,X10,X11,X8,X9)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f204,plain,
( spl0_28
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f481,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( ~ between(X6,X7,X8)
| ~ equidistant(X6,X8,X6,X9)
| ~ equidistant(X6,X7,X6,X10)
| ~ between(X7,X11,X8)
| equidistant(X11,X6,X6,continuous(X6,X7,X10,X11,X8,X9)) )
| ~ spl0_28
| ~ spl0_55 ),
inference(resolution,[],[f478,f205]) ).
fof(f205,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f1826,plain,
( spl0_143
| ~ spl0_27
| ~ spl0_55 ),
inference(avatar_split_clause,[],[f480,f477,f200,f1824]) ).
fof(f1824,plain,
( spl0_143
<=> ! [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_143])]) ).
fof(f200,plain,
( spl0_27
<=> ! [X10,X0,X5,X3] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f480,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_27
| ~ spl0_55 ),
inference(resolution,[],[f478,f201]) ).
fof(f201,plain,
( ! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f1822,plain,
( spl0_142
| ~ spl0_40
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f460,f455,f305,f1820]) ).
fof(f1820,plain,
( spl0_142
<=> ! [X16,X11,X13,X14,X12,X15] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(euclid1(X14,X11,X12,X13,X15),X16,X15)
| between(X16,X15,euclid2(X14,X11,X12,X13,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f460,plain,
( ! [X11,X16,X14,X15,X12,X13] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(euclid1(X14,X11,X12,X13,X15),X16,X15)
| between(X16,X15,euclid2(X14,X11,X12,X13,X15)) )
| ~ spl0_40
| ~ spl0_53 ),
inference(resolution,[],[f456,f306]) ).
fof(f1818,plain,
( spl0_141
| ~ spl0_45
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f389,f378,f347,f1816]) ).
fof(f1816,plain,
( spl0_141
<=> ! [X5,X4,X9,X7,X6,X8] :
( ~ between(X4,X5,X6)
| ~ between(X7,X8,X6)
| inner_pasch(X7,X8,X6,X5,X4) = X7
| ~ between(inner_pasch(X7,X8,X6,X5,X4),X7,X9)
| between(X5,X7,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f389,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( ~ between(X4,X5,X6)
| ~ between(X7,X8,X6)
| inner_pasch(X7,X8,X6,X5,X4) = X7
| ~ between(inner_pasch(X7,X8,X6,X5,X4),X7,X9)
| between(X5,X7,X9) )
| ~ spl0_45
| ~ spl0_47 ),
inference(resolution,[],[f379,f348]) ).
fof(f1814,plain,
( spl0_140
| ~ spl0_45
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f382,f368,f347,f1812]) ).
fof(f1812,plain,
( spl0_140
<=> ! [X5,X4,X9,X7,X6,X8] :
( ~ between(X4,X5,X6)
| ~ between(X7,X8,X6)
| inner_pasch(X7,X8,X6,X5,X4) = X4
| ~ between(inner_pasch(X7,X8,X6,X5,X4),X4,X9)
| between(X8,X4,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f382,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( ~ between(X4,X5,X6)
| ~ between(X7,X8,X6)
| inner_pasch(X7,X8,X6,X5,X4) = X4
| ~ between(inner_pasch(X7,X8,X6,X5,X4),X4,X9)
| between(X8,X4,X9) )
| ~ spl0_45
| ~ spl0_46 ),
inference(resolution,[],[f369,f348]) ).
fof(f1810,plain,
( spl0_139
| ~ spl0_39
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f442,f422,f285,f1808]) ).
fof(f1808,plain,
( spl0_139
<=> ! [X18,X19,X17,X21,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid2(X20,X17,X18,X19,X21) = X19
| ~ between(X20,euclid2(X20,X17,X18,X19,X21),X19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f442,plain,
( ! [X21,X18,X19,X17,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid2(X20,X17,X18,X19,X21) = X19
| ~ between(X20,euclid2(X20,X17,X18,X19,X21),X19) )
| ~ spl0_39
| ~ spl0_51 ),
inference(resolution,[],[f423,f286]) ).
fof(f1806,plain,
( spl0_138
| ~ spl0_14
| ~ spl0_96 ),
inference(avatar_split_clause,[],[f1392,f1034,f121,f1803]) ).
fof(f1392,plain,
( between(v,x,reflection(w,x))
| ~ spl0_14
| ~ spl0_96 ),
inference(resolution,[],[f1035,f122]) ).
fof(f1801,plain,
( spl0_137
| ~ spl0_39
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f428,f418,f285,f1799]) ).
fof(f1799,plain,
( spl0_137
<=> ! [X18,X19,X17,X21,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid1(X20,X17,X18,X19,X21) = X17
| ~ between(X20,euclid1(X20,X17,X18,X19,X21),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f428,plain,
( ! [X21,X18,X19,X17,X20] :
( ~ between(X17,X18,X19)
| ~ between(X20,X18,X21)
| X18 = X20
| euclid1(X20,X17,X18,X19,X21) = X17
| ~ between(X20,euclid1(X20,X17,X18,X19,X21),X17) )
| ~ spl0_39
| ~ spl0_50 ),
inference(resolution,[],[f419,f286]) ).
fof(f1763,plain,
( spl0_136
| ~ spl0_25
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f452,f446,f186,f1761]) ).
fof(f1761,plain,
( spl0_136
<=> ! [X17,X14,X13,X12,X16,X15] :
( ~ between(X12,extension(X13,X12,X14,X15),X16)
| ~ equidistant(extension(X13,X12,X14,X15),X16,X15,X17)
| ~ between(X14,X15,X17)
| equidistant(X12,X16,X14,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f452,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ between(X12,extension(X13,X12,X14,X15),X16)
| ~ equidistant(extension(X13,X12,X14,X15),X16,X15,X17)
| ~ between(X14,X15,X17)
| equidistant(X12,X16,X14,X17) )
| ~ spl0_25
| ~ spl0_52 ),
inference(resolution,[],[f447,f187]) ).
fof(f1759,plain,
( spl0_135
| ~ spl0_40
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f391,f378,f305,f1757]) ).
fof(f1757,plain,
( spl0_135
<=> ! [X15,X17,X20,X18,X16,X19] :
( ~ between(X15,X16,X17)
| ~ between(X18,X19,X17)
| ~ between(X16,X20,inner_pasch(X18,X19,X17,X16,X15))
| between(X20,inner_pasch(X18,X19,X17,X16,X15),X18) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f391,plain,
( ! [X18,X19,X16,X17,X15,X20] :
( ~ between(X15,X16,X17)
| ~ between(X18,X19,X17)
| ~ between(X16,X20,inner_pasch(X18,X19,X17,X16,X15))
| between(X20,inner_pasch(X18,X19,X17,X16,X15),X18) )
| ~ spl0_40
| ~ spl0_47 ),
inference(resolution,[],[f379,f306]) ).
fof(f1755,plain,
( spl0_134
| ~ spl0_40
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f384,f368,f305,f1753]) ).
fof(f1753,plain,
( spl0_134
<=> ! [X15,X17,X20,X18,X16,X19] :
( ~ between(X15,X16,X17)
| ~ between(X18,X19,X17)
| ~ between(X19,X20,inner_pasch(X18,X19,X17,X16,X15))
| between(X20,inner_pasch(X18,X19,X17,X16,X15),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f384,plain,
( ! [X18,X19,X16,X17,X15,X20] :
( ~ between(X15,X16,X17)
| ~ between(X18,X19,X17)
| ~ between(X19,X20,inner_pasch(X18,X19,X17,X16,X15))
| between(X20,inner_pasch(X18,X19,X17,X16,X15),X15) )
| ~ spl0_40
| ~ spl0_46 ),
inference(resolution,[],[f369,f306]) ).
fof(f1737,plain,
( spl0_133
| ~ spl0_14
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1031,f1018,f121,f1734]) ).
fof(f1031,plain,
( between(u,w,reflection(v,w))
| ~ spl0_14
| ~ spl0_94 ),
inference(resolution,[],[f1019,f122]) ).
fof(f1726,plain,
( spl0_132
| ~ spl0_23
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f463,f455,f164,f1724]) ).
fof(f1724,plain,
( spl0_132
<=> ! [X31,X29,X27,X28,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid2(X30,X27,X28,X29,X31),X31,euclid1(X30,X27,X28,X29,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f463,plain,
( ! [X31,X28,X29,X27,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid2(X30,X27,X28,X29,X31),X31,euclid1(X30,X27,X28,X29,X31)) )
| ~ spl0_23
| ~ spl0_53 ),
inference(resolution,[],[f456,f165]) ).
fof(f1722,plain,
( spl0_131
| ~ spl0_38
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f393,f378,f281,f1720]) ).
fof(f1720,plain,
( spl0_131
<=> ! [X26,X29,X27,X28,X30] :
( ~ between(X26,X27,X28)
| ~ between(X29,X30,X28)
| ~ between(inner_pasch(X29,X30,X28,X27,X26),X27,X29)
| inner_pasch(X29,X30,X28,X27,X26) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f393,plain,
( ! [X28,X29,X26,X27,X30] :
( ~ between(X26,X27,X28)
| ~ between(X29,X30,X28)
| ~ between(inner_pasch(X29,X30,X28,X27,X26),X27,X29)
| inner_pasch(X29,X30,X28,X27,X26) = X27 )
| ~ spl0_38
| ~ spl0_47 ),
inference(resolution,[],[f379,f282]) ).
fof(f1718,plain,
( spl0_130
| ~ spl0_39
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f392,f378,f285,f1716]) ).
fof(f1716,plain,
( spl0_130
<=> ! [X24,X21,X23,X25,X22] :
( ~ between(X21,X22,X23)
| ~ between(X24,X25,X23)
| inner_pasch(X24,X25,X23,X22,X21) = X24
| ~ between(X22,X24,inner_pasch(X24,X25,X23,X22,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f392,plain,
( ! [X21,X24,X22,X25,X23] :
( ~ between(X21,X22,X23)
| ~ between(X24,X25,X23)
| inner_pasch(X24,X25,X23,X22,X21) = X24
| ~ between(X22,X24,inner_pasch(X24,X25,X23,X22,X21)) )
| ~ spl0_39
| ~ spl0_47 ),
inference(resolution,[],[f379,f286]) ).
fof(f1714,plain,
( spl0_129
| ~ spl0_38
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f386,f368,f281,f1712]) ).
fof(f1712,plain,
( spl0_129
<=> ! [X26,X29,X27,X28,X30] :
( ~ between(X26,X27,X28)
| ~ between(X29,X30,X28)
| ~ between(inner_pasch(X29,X30,X28,X27,X26),X30,X26)
| inner_pasch(X29,X30,X28,X27,X26) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f386,plain,
( ! [X28,X29,X26,X27,X30] :
( ~ between(X26,X27,X28)
| ~ between(X29,X30,X28)
| ~ between(inner_pasch(X29,X30,X28,X27,X26),X30,X26)
| inner_pasch(X29,X30,X28,X27,X26) = X30 )
| ~ spl0_38
| ~ spl0_46 ),
inference(resolution,[],[f369,f282]) ).
fof(f1710,plain,
( spl0_128
| ~ spl0_39
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f385,f368,f285,f1708]) ).
fof(f1708,plain,
( spl0_128
<=> ! [X24,X21,X23,X25,X22] :
( ~ between(X21,X22,X23)
| ~ between(X24,X25,X23)
| inner_pasch(X24,X25,X23,X22,X21) = X21
| ~ between(X25,X21,inner_pasch(X24,X25,X23,X22,X21)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f385,plain,
( ! [X21,X24,X22,X25,X23] :
( ~ between(X21,X22,X23)
| ~ between(X24,X25,X23)
| inner_pasch(X24,X25,X23,X22,X21) = X21
| ~ between(X25,X21,inner_pasch(X24,X25,X23,X22,X21)) )
| ~ spl0_39
| ~ spl0_46 ),
inference(resolution,[],[f369,f286]) ).
fof(f1672,plain,
( spl0_127
| ~ spl0_40
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f441,f422,f305,f1670]) ).
fof(f1670,plain,
( spl0_127
<=> ! [X16,X11,X13,X14,X12,X15] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(X14,X16,X13)
| between(X16,X13,euclid2(X14,X11,X12,X13,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f441,plain,
( ! [X11,X16,X14,X15,X12,X13] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(X14,X16,X13)
| between(X16,X13,euclid2(X14,X11,X12,X13,X15)) )
| ~ spl0_40
| ~ spl0_51 ),
inference(resolution,[],[f423,f306]) ).
fof(f1660,plain,
( spl0_126
| ~ spl0_40
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f427,f418,f305,f1658]) ).
fof(f1658,plain,
( spl0_126
<=> ! [X16,X11,X13,X14,X12,X15] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(X14,X16,X11)
| between(X16,X11,euclid1(X14,X11,X12,X13,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f427,plain,
( ! [X11,X16,X14,X15,X12,X13] :
( ~ between(X11,X12,X13)
| ~ between(X14,X12,X15)
| X12 = X14
| ~ between(X14,X16,X11)
| between(X16,X11,euclid1(X14,X11,X12,X13,X15)) )
| ~ spl0_40
| ~ spl0_50 ),
inference(resolution,[],[f419,f306]) ).
fof(f1616,plain,
( spl0_125
| ~ spl0_11
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f470,f465,f109,f1614]) ).
fof(f1614,plain,
( spl0_125
<=> ! [X10,X11,X12,X9,X8] :
( ~ between(X8,X9,X10)
| ~ equidistant(X8,X10,X8,X11)
| ~ between(X9,X12,X10)
| between(X9,continuous(X8,X9,X9,X12,X10,X11),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f470,plain,
( ! [X10,X11,X8,X9,X12] :
( ~ between(X8,X9,X10)
| ~ equidistant(X8,X10,X8,X11)
| ~ between(X9,X12,X10)
| between(X9,continuous(X8,X9,X9,X12,X10,X11),X11) )
| ~ spl0_11
| ~ spl0_54 ),
inference(resolution,[],[f466,f110]) ).
fof(f1612,plain,
( spl0_124
| ~ spl0_38
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f443,f422,f281,f1610]) ).
fof(f1610,plain,
( spl0_124
<=> ! [X24,X23,X25,X22,X26] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X24,X25,euclid2(X25,X22,X23,X24,X26))
| X24 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f443,plain,
( ! [X26,X24,X22,X25,X23] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X24,X25,euclid2(X25,X22,X23,X24,X26))
| X24 = X25 )
| ~ spl0_38
| ~ spl0_51 ),
inference(resolution,[],[f423,f282]) ).
fof(f1608,plain,
( spl0_123
| ~ spl0_38
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f429,f418,f281,f1606]) ).
fof(f1606,plain,
( spl0_123
<=> ! [X24,X23,X25,X22,X26] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X22,X25,euclid1(X25,X22,X23,X24,X26))
| X22 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f429,plain,
( ! [X26,X24,X22,X25,X23] :
( ~ between(X22,X23,X24)
| ~ between(X25,X23,X26)
| X23 = X25
| ~ between(X22,X25,euclid1(X25,X22,X23,X24,X26))
| X22 = X25 )
| ~ spl0_38
| ~ spl0_50 ),
inference(resolution,[],[f419,f282]) ).
fof(f1604,plain,
( spl0_122
| ~ spl0_20
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f363,f347,f152,f1602]) ).
fof(f1602,plain,
( spl0_122
<=> ! [X10,X11,X13,X12,X9] :
( extension(X10,X9,X11,X12) = X9
| ~ between(X9,extension(X10,X9,X11,X12),X13)
| between(X10,extension(X10,X9,X11,X12),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f363,plain,
( ! [X10,X11,X9,X12,X13] :
( extension(X10,X9,X11,X12) = X9
| ~ between(X9,extension(X10,X9,X11,X12),X13)
| between(X10,extension(X10,X9,X11,X12),X13) )
| ~ spl0_20
| ~ spl0_45 ),
inference(resolution,[],[f348,f153]) ).
fof(f1584,plain,
( spl0_121
| ~ spl0_23
| ~ spl0_106 ),
inference(avatar_split_clause,[],[f1449,f1212,f164,f1581]) ).
fof(f1581,plain,
( spl0_121
<=> between(x,w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1449,plain,
( between(x,w,u)
| ~ spl0_23
| ~ spl0_106 ),
inference(resolution,[],[f1214,f165]) ).
fof(f1562,plain,
( spl0_120
| ~ spl0_17
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f453,f446,f134,f1560]) ).
fof(f1560,plain,
( spl0_120
<=> ! [X18,X19,X20,X21] :
( ~ between(X18,reflection(X19,X18),X20)
| ~ equidistant(reflection(X19,X18),X20,X18,X21)
| ~ between(X19,X18,X21)
| equidistant(X18,X20,X19,X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f453,plain,
( ! [X21,X18,X19,X20] :
( ~ between(X18,reflection(X19,X18),X20)
| ~ equidistant(reflection(X19,X18),X20,X18,X21)
| ~ between(X19,X18,X21)
| equidistant(X18,X20,X19,X21) )
| ~ spl0_17
| ~ spl0_52 ),
inference(resolution,[],[f447,f135]) ).
fof(f1558,plain,
( spl0_119
| ~ spl0_25
| ~ spl0_48 ),
inference(avatar_split_clause,[],[f406,f396,f186,f1556]) ).
fof(f1556,plain,
( spl0_119
<=> ! [X10,X7,X9,X8] :
( X7 = X8
| ~ between(X8,X7,extension(X9,X7,X7,X10))
| ~ between(X8,X7,X10)
| extension(X9,X7,X7,X10) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f406,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| ~ between(X8,X7,extension(X9,X7,X7,X10))
| ~ between(X8,X7,X10)
| extension(X9,X7,X7,X10) = X10 )
| ~ spl0_25
| ~ spl0_48 ),
inference(resolution,[],[f397,f187]) ).
fof(f1538,plain,
( spl0_118
| ~ spl0_23
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f444,f422,f164,f1536]) ).
fof(f1536,plain,
( spl0_118
<=> ! [X31,X29,X27,X28,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid2(X30,X27,X28,X29,X31),X29,X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f444,plain,
( ! [X31,X28,X29,X27,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid2(X30,X27,X28,X29,X31),X29,X30) )
| ~ spl0_23
| ~ spl0_51 ),
inference(resolution,[],[f423,f165]) ).
fof(f1534,plain,
( spl0_117
| ~ spl0_23
| ~ spl0_50 ),
inference(avatar_split_clause,[],[f430,f418,f164,f1532]) ).
fof(f1532,plain,
( spl0_117
<=> ! [X31,X29,X27,X28,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid1(X30,X27,X28,X29,X31),X27,X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f430,plain,
( ! [X31,X28,X29,X27,X30] :
( ~ between(X27,X28,X29)
| ~ between(X30,X28,X31)
| X28 = X30
| between(euclid1(X30,X27,X28,X29,X31),X27,X30) )
| ~ spl0_23
| ~ spl0_50 ),
inference(resolution,[],[f419,f165]) ).
fof(f1448,plain,
( spl0_116
| ~ spl0_11
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f451,f446,f109,f1446]) ).
fof(f1446,plain,
( spl0_116
<=> ! [X10,X11,X9,X8] :
( ~ between(X8,X9,X10)
| ~ equidistant(X9,X10,X9,X11)
| ~ between(X8,X9,X11)
| equidistant(X8,X10,X8,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f451,plain,
( ! [X10,X11,X8,X9] :
( ~ between(X8,X9,X10)
| ~ equidistant(X9,X10,X9,X11)
| ~ between(X8,X9,X11)
| equidistant(X8,X10,X8,X11) )
| ~ spl0_11
| ~ spl0_52 ),
inference(resolution,[],[f447,f110]) ).
fof(f1444,plain,
( spl0_115
| ~ spl0_10
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f450,f446,f105,f1442]) ).
fof(f1442,plain,
( spl0_115
<=> ! [X5,X4,X7,X6] :
( ~ between(X4,X5,X6)
| ~ equidistant(X5,X6,X4,X7)
| ~ between(X5,X4,X7)
| equidistant(X4,X6,X5,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f450,plain,
( ! [X6,X7,X4,X5] :
( ~ between(X4,X5,X6)
| ~ equidistant(X5,X6,X4,X7)
| ~ between(X5,X4,X7)
| equidistant(X4,X6,X5,X7) )
| ~ spl0_10
| ~ spl0_52 ),
inference(resolution,[],[f447,f106]) ).
fof(f1440,plain,
( spl0_114
| ~ spl0_25
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f414,f400,f186,f1438]) ).
fof(f1438,plain,
( spl0_114
<=> ! [X17,X13,X14,X12,X16,X15] :
( X12 = X13
| extension(X13,X12,X14,extension(X15,X14,X16,X17)) = extension(X13,X12,X16,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f414,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( X12 = X13
| extension(X13,X12,X14,extension(X15,X14,X16,X17)) = extension(X13,X12,X16,X17) )
| ~ spl0_25
| ~ spl0_49 ),
inference(resolution,[],[f401,f187]) ).
fof(f1401,plain,
( spl0_113
| ~ spl0_23
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f394,f378,f164,f1399]) ).
fof(f1399,plain,
( spl0_113
<=> ! [X35,X34,X31,X33,X32] :
( ~ between(X31,X32,X33)
| ~ between(X34,X35,X33)
| between(X34,inner_pasch(X34,X35,X33,X32,X31),X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f394,plain,
( ! [X31,X34,X35,X32,X33] :
( ~ between(X31,X32,X33)
| ~ between(X34,X35,X33)
| between(X34,inner_pasch(X34,X35,X33,X32,X31),X32) )
| ~ spl0_23
| ~ spl0_47 ),
inference(resolution,[],[f379,f165]) ).
fof(f1397,plain,
( spl0_112
| ~ spl0_23
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f387,f368,f164,f1395]) ).
fof(f1395,plain,
( spl0_112
<=> ! [X35,X34,X31,X33,X32] :
( ~ between(X31,X32,X33)
| ~ between(X34,X35,X33)
| between(X31,inner_pasch(X34,X35,X33,X32,X31),X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f387,plain,
( ! [X31,X34,X35,X32,X33] :
( ~ between(X31,X32,X33)
| ~ between(X34,X35,X33)
| between(X31,inner_pasch(X34,X35,X33,X32,X31),X35) )
| ~ spl0_23
| ~ spl0_46 ),
inference(resolution,[],[f369,f165]) ).
fof(f1386,plain,
( spl0_1
| ~ spl0_3
| ~ spl0_63 ),
inference(avatar_split_clause,[],[f1037,f538,f72,f62]) ).
fof(f72,plain,
( spl0_3
<=> between(u,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1037,plain,
( between(u,v,x)
| ~ spl0_3
| ~ spl0_63 ),
inference(superposition,[],[f74,f540]) ).
fof(f540,plain,
( w = x
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f74,plain,
( between(u,v,w)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f72]) ).
fof(f1385,plain,
( spl0_111
| ~ spl0_14
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f362,f347,f121,f1383]) ).
fof(f1383,plain,
( spl0_111
<=> ! [X6,X7,X8] :
( reflection(X7,X6) = X6
| ~ between(X6,reflection(X7,X6),X8)
| between(X7,reflection(X7,X6),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f362,plain,
( ! [X8,X6,X7] :
( reflection(X7,X6) = X6
| ~ between(X6,reflection(X7,X6),X8)
| between(X7,reflection(X7,X6),X8) )
| ~ spl0_14
| ~ spl0_45 ),
inference(resolution,[],[f348,f122]) ).
fof(f1304,plain,
( spl0_110
| ~ spl0_17
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f415,f400,f134,f1302]) ).
fof(f1302,plain,
( spl0_110
<=> ! [X18,X19,X20,X21] :
( X18 = X19
| extension(X19,X18,X20,reflection(X21,X20)) = extension(X19,X18,X21,X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f415,plain,
( ! [X21,X18,X19,X20] :
( X18 = X19
| extension(X19,X18,X20,reflection(X21,X20)) = extension(X19,X18,X21,X20) )
| ~ spl0_17
| ~ spl0_49 ),
inference(resolution,[],[f401,f135]) ).
fof(f1300,plain,
( spl0_109
| ~ spl0_15
| ~ spl0_47 ),
inference(avatar_split_clause,[],[f388,f378,f126,f1298]) ).
fof(f1298,plain,
( spl0_109
<=> ! [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_109])]) ).
fof(f126,plain,
( spl0_15
<=> ! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f388,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X1,X3,X2)
| inner_pasch(X1,X3,X2,X1,X0) = X1 )
| ~ spl0_15
| ~ spl0_47 ),
inference(resolution,[],[f379,f127]) ).
fof(f127,plain,
( ! [X0,X1] :
( ~ between(X0,X1,X0)
| X0 = X1 )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f126]) ).
fof(f1296,plain,
( spl0_108
| ~ spl0_15
| ~ spl0_46 ),
inference(avatar_split_clause,[],[f381,f368,f126,f1294]) ).
fof(f1294,plain,
( spl0_108
<=> ! [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_108])]) ).
fof(f381,plain,
( ! [X2,X3,X0,X1] :
( ~ between(X0,X1,X2)
| ~ between(X3,X0,X2)
| inner_pasch(X3,X0,X2,X1,X0) = X0 )
| ~ spl0_15
| ~ spl0_46 ),
inference(resolution,[],[f369,f127]) ).
fof(f1284,plain,
( spl0_107
| ~ spl0_20
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f303,f285,f152,f1282]) ).
fof(f1282,plain,
( spl0_107
<=> ! [X9,X7,X6,X8] :
( extension(X6,X7,X8,X9) = X7
| ~ between(X6,extension(X6,X7,X8,X9),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f303,plain,
( ! [X8,X6,X9,X7] :
( extension(X6,X7,X8,X9) = X7
| ~ between(X6,extension(X6,X7,X8,X9),X7) )
| ~ spl0_20
| ~ spl0_39 ),
inference(resolution,[],[f286,f153]) ).
fof(f1215,plain,
( spl0_106
| ~ spl0_4
| ~ spl0_94 ),
inference(avatar_split_clause,[],[f1026,f1018,f77,f1212]) ).
fof(f77,plain,
( spl0_4
<=> between(v,w,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1026,plain,
( between(u,w,x)
| ~ spl0_4
| ~ spl0_94 ),
inference(resolution,[],[f1019,f79]) ).
fof(f79,plain,
( between(v,w,x)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f1152,plain,
( spl0_105
| ~ spl0_10
| ~ spl0_49 ),
inference(avatar_split_clause,[],[f412,f400,f105,f1150]) ).
fof(f412,plain,
( ! [X6,X7,X4,X5] :
( X4 = X5
| extension(X5,X4,X6,X7) = extension(X5,X4,X7,X6) )
| ~ spl0_10
| ~ spl0_49 ),
inference(resolution,[],[f401,f106]) ).
fof(f1148,plain,
( spl0_104
| ~ spl0_25
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f358,f343,f186,f1146]) ).
fof(f1146,plain,
( spl0_104
<=> ! [X16,X13,X14,X12,X17,X15] :
( ~ equidistant(X12,X13,X14,X15)
| equidistant(X16,extension(X17,X16,X12,X13),X14,X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f358,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ equidistant(X12,X13,X14,X15)
| equidistant(X16,extension(X17,X16,X12,X13),X14,X15) )
| ~ spl0_25
| ~ spl0_44 ),
inference(resolution,[],[f344,f187]) ).
fof(f1144,plain,
( spl0_103
| ~ spl0_25
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f353,f339,f186,f1142]) ).
fof(f353,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( ~ equidistant(X12,extension(X13,X12,X14,X15),X16,X17)
| equidistant(X16,X17,X14,X15) )
| ~ spl0_25
| ~ spl0_43 ),
inference(resolution,[],[f340,f187]) ).
fof(f1140,plain,
( spl0_102
| ~ spl0_14
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f333,f328,f121,f1138]) ).
fof(f1138,plain,
( spl0_102
<=> ! [X4,X5] :
( X4 = X5
| reflection(X5,X4) = extension(X5,X4,X4,reflection(X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f333,plain,
( ! [X4,X5] :
( X4 = X5
| reflection(X5,X4) = extension(X5,X4,X4,reflection(X5,X4)) )
| ~ spl0_14
| ~ spl0_42 ),
inference(resolution,[],[f329,f122]) ).
fof(f1081,plain,
( spl0_101
| ~ spl0_17
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f359,f343,f134,f1079]) ).
fof(f359,plain,
( ! [X21,X18,X19,X20] :
( ~ equidistant(X18,X19,X20,X21)
| equidistant(X19,reflection(X18,X19),X20,X21) )
| ~ spl0_17
| ~ spl0_44 ),
inference(resolution,[],[f344,f135]) ).
fof(f1077,plain,
( spl0_100
| ~ spl0_17
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f354,f339,f134,f1075]) ).
fof(f354,plain,
( ! [X21,X18,X19,X20] :
( ~ equidistant(X18,reflection(X19,X18),X20,X21)
| equidistant(X20,X21,X19,X18) )
| ~ spl0_17
| ~ spl0_43 ),
inference(resolution,[],[f340,f135]) ).
fof(f1073,plain,
( spl0_99
| ~ spl0_20
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f317,f305,f152,f1071]) ).
fof(f1071,plain,
( spl0_99
<=> ! [X11,X13,X14,X12,X15] :
( ~ between(X11,X12,X13)
| between(X12,X13,extension(X11,X13,X14,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f317,plain,
( ! [X11,X14,X15,X12,X13] :
( ~ between(X11,X12,X13)
| between(X12,X13,extension(X11,X13,X14,X15)) )
| ~ spl0_20
| ~ spl0_40 ),
inference(resolution,[],[f306,f153]) ).
fof(f1059,plain,
( spl0_98
| ~ spl0_14
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f302,f285,f121,f1057]) ).
fof(f1057,plain,
( spl0_98
<=> ! [X4,X5] :
( reflection(X4,X5) = X5
| ~ between(X4,reflection(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f302,plain,
( ! [X4,X5] :
( reflection(X4,X5) = X5
| ~ between(X4,reflection(X4,X5),X5) )
| ~ spl0_14
| ~ spl0_39 ),
inference(resolution,[],[f286,f122]) ).
fof(f1055,plain,
( spl0_97
| ~ spl0_20
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f297,f281,f152,f1053]) ).
fof(f1053,plain,
( spl0_97
<=> ! [X9,X7,X6,X8] :
( ~ between(X6,X7,extension(X7,X6,X8,X9))
| X6 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f297,plain,
( ! [X8,X6,X9,X7] :
( ~ between(X6,X7,extension(X7,X6,X8,X9))
| X6 = X7 )
| ~ spl0_20
| ~ spl0_38 ),
inference(resolution,[],[f282,f153]) ).
fof(f1036,plain,
( spl0_96
| spl0_63
| ~ spl0_4
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f365,f347,f77,f538,f1034]) ).
fof(f365,plain,
( ! [X15] :
( w = x
| ~ between(w,x,X15)
| between(v,x,X15) )
| ~ spl0_4
| ~ spl0_45 ),
inference(resolution,[],[f348,f79]) ).
fof(f1025,plain,
( ~ spl0_95
| spl0_2
| ~ spl0_36
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f374,f285,f272,f67,f1022]) ).
fof(f1022,plain,
( spl0_95
<=> between(x,v,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f374,plain,
( v = w
| ~ between(x,v,w)
| ~ spl0_36
| ~ spl0_39 ),
inference(resolution,[],[f274,f286]) ).
fof(f1020,plain,
( spl0_94
| spl0_2
| ~ spl0_3
| ~ spl0_45 ),
inference(avatar_split_clause,[],[f364,f347,f72,f67,f1018]) ).
fof(f364,plain,
( ! [X14] :
( v = w
| ~ between(v,w,X14)
| between(u,w,X14) )
| ~ spl0_3
| ~ spl0_45 ),
inference(resolution,[],[f348,f74]) ).
fof(f964,plain,
( spl0_93
| ~ spl0_13
| ~ spl0_44 ),
inference(avatar_split_clause,[],[f355,f343,f117,f962]) ).
fof(f962,plain,
( spl0_93
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f117,plain,
( spl0_13
<=> ! [X3,X10] : equidistant(X10,X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f355,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X3,X3,X1,X2) )
| ~ spl0_13
| ~ spl0_44 ),
inference(resolution,[],[f344,f118]) ).
fof(f118,plain,
( ! [X3,X10] : equidistant(X10,X10,X3,X3)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f117]) ).
fof(f960,plain,
( spl0_92
| ~ spl0_13
| ~ spl0_43 ),
inference(avatar_split_clause,[],[f350,f339,f117,f958]) ).
fof(f958,plain,
( spl0_92
<=> ! [X0,X3,X2,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f350,plain,
( ! [X2,X3,X0,X1] :
( ~ equidistant(X0,X0,X1,X2)
| equidistant(X1,X2,X3,X3) )
| ~ spl0_13
| ~ spl0_43 ),
inference(resolution,[],[f340,f118]) ).
fof(f956,plain,
( spl0_91
| ~ spl0_14
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f316,f305,f121,f954]) ).
fof(f316,plain,
( ! [X10,X8,X9] :
( ~ between(X8,X9,X10)
| between(X9,X10,reflection(X8,X10)) )
| ~ spl0_14
| ~ spl0_40 ),
inference(resolution,[],[f306,f122]) ).
fof(f930,plain,
( spl0_90
| ~ spl0_57
| ~ spl0_89 ),
inference(avatar_split_clause,[],[f925,f921,f498,f927]) ).
fof(f925,plain,
( x = extension(u,w,w,x)
| ~ spl0_57
| ~ spl0_89 ),
inference(forward_demodulation,[],[f923,f500]) ).
fof(f924,plain,
( spl0_89
| spl0_2
| ~ spl0_4
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f336,f328,f77,f67,f921]) ).
fof(f336,plain,
( v = w
| x = extension(v,w,w,x)
| ~ spl0_4
| ~ spl0_42 ),
inference(resolution,[],[f329,f79]) ).
fof(f905,plain,
( spl0_88
| spl0_57
| ~ spl0_3
| ~ spl0_42 ),
inference(avatar_split_clause,[],[f335,f328,f72,f498,f902]) ).
fof(f335,plain,
( u = v
| w = extension(u,v,v,w)
| ~ spl0_3
| ~ spl0_42 ),
inference(resolution,[],[f329,f74]) ).
fof(f860,plain,
( spl0_2
| ~ spl0_87
| ~ spl0_32
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f320,f281,f220,f857,f67]) ).
fof(f857,plain,
( spl0_87
<=> between(v,w,u) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f320,plain,
( ~ between(v,w,u)
| v = w
| ~ spl0_32
| ~ spl0_38 ),
inference(resolution,[],[f222,f282]) ).
fof(f771,plain,
( spl0_86
| ~ spl0_14
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f296,f281,f121,f769]) ).
fof(f769,plain,
( spl0_86
<=> ! [X4,X5] :
( ~ between(X4,X5,reflection(X5,X4))
| X4 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f296,plain,
( ! [X4,X5] :
( ~ between(X4,X5,reflection(X5,X4))
| X4 = X5 )
| ~ spl0_14
| ~ spl0_38 ),
inference(resolution,[],[f282,f122]) ).
fof(f767,plain,
( spl0_85
| ~ spl0_26
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f289,f268,f190,f765]) ).
fof(f190,plain,
( spl0_26
<=> ! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f289,plain,
( ! [X6,X4,X5] :
( reflection(X4,X5) != X6
| between(X4,X5,X6) )
| ~ spl0_26
| ~ spl0_35 ),
inference(superposition,[],[f269,f191]) ).
fof(f191,plain,
( ! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f763,plain,
( spl0_84
| ~ spl0_25
| ~ spl0_34 ),
inference(avatar_split_clause,[],[f265,f229,f186,f761]) ).
fof(f265,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,extension(X8,X9,X7,X6),X9)
| ~ spl0_25
| ~ spl0_34 ),
inference(resolution,[],[f230,f187]) ).
fof(f759,plain,
( spl0_83
| ~ spl0_25
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f260,f225,f186,f757]) ).
fof(f260,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,X8,extension(X9,X8,X7,X6))
| ~ spl0_25
| ~ spl0_33 ),
inference(resolution,[],[f226,f187]) ).
fof(f755,plain,
( spl0_82
| ~ spl0_25
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f255,f216,f186,f753]) ).
fof(f255,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,extension(X8,X9,X6,X7),X9)
| ~ spl0_25
| ~ spl0_31 ),
inference(resolution,[],[f217,f187]) ).
fof(f751,plain,
( spl0_81
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f250,f212,f186,f749]) ).
fof(f749,plain,
( spl0_81
<=> ! [X6,X9,X8,X7] : equidistant(extension(X6,X7,X8,X9),X7,X9,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f250,plain,
( ! [X8,X6,X9,X7] : equidistant(extension(X6,X7,X8,X9),X7,X9,X8)
| ~ spl0_25
| ~ spl0_30 ),
inference(resolution,[],[f213,f187]) ).
fof(f747,plain,
( spl0_80
| ~ spl0_25
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f245,f208,f186,f745]) ).
fof(f745,plain,
( spl0_80
<=> ! [X9,X7,X6,X8] : equidistant(X6,extension(X7,X6,X8,X9),X9,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f245,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,extension(X7,X6,X8,X9),X9,X8)
| ~ spl0_25
| ~ spl0_29 ),
inference(resolution,[],[f209,f187]) ).
fof(f743,plain,
( spl0_79
| ~ spl0_25
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f240,f204,f186,f741]) ).
fof(f741,plain,
( spl0_79
<=> ! [X6,X9,X8,X7] : equidistant(extension(X6,X7,X8,X9),X7,X8,X9) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f240,plain,
( ! [X8,X6,X9,X7] : equidistant(extension(X6,X7,X8,X9),X7,X8,X9)
| ~ spl0_25
| ~ spl0_28 ),
inference(resolution,[],[f205,f187]) ).
fof(f739,plain,
( spl0_78
| ~ spl0_25
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f235,f200,f186,f737]) ).
fof(f235,plain,
( ! [X8,X6,X9,X7] : equidistant(X6,X7,X8,extension(X9,X8,X6,X7))
| ~ spl0_25
| ~ spl0_27 ),
inference(resolution,[],[f201,f187]) ).
fof(f718,plain,
( spl0_77
| ~ spl0_9
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f315,f305,f101,f716]) ).
fof(f716,plain,
( spl0_77
<=> ! [X6,X5,X7] :
( ~ between(X5,X6,X5)
| between(X6,X5,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f315,plain,
( ! [X6,X7,X5] :
( ~ between(X5,X6,X5)
| between(X6,X5,X7) )
| ~ spl0_9
| ~ spl0_40 ),
inference(resolution,[],[f306,f102]) ).
fof(f714,plain,
( spl0_76
| ~ spl0_37 ),
inference(avatar_split_clause,[],[f291,f277,f712]) ).
fof(f712,plain,
( spl0_76
<=> ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f277,plain,
( spl0_37
<=> ! [X5,X0,X3,X10] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f291,plain,
( ! [X2,X0,X1] :
( ~ between(X0,X1,X0)
| between(X2,X1,X0) )
| ~ spl0_37 ),
inference(equality_resolution,[],[f278]) ).
fof(f278,plain,
( ! [X3,X10,X0,X5] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f710,plain,
( spl0_75
| ~ spl0_20
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f184,f164,f152,f708]) ).
fof(f184,plain,
( ! [X8,X6,X9,X7] : between(extension(X6,X7,X8,X9),X7,X6)
| ~ spl0_20
| ~ spl0_23 ),
inference(resolution,[],[f165,f153]) ).
fof(f706,plain,
( ~ spl0_74
| spl0_57
| ~ spl0_32
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f319,f285,f220,f498,f703]) ).
fof(f703,plain,
( spl0_74
<=> between(w,u,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f319,plain,
( u = v
| ~ between(w,u,v)
| ~ spl0_32
| ~ spl0_39 ),
inference(resolution,[],[f222,f286]) ).
fof(f693,plain,
( spl0_73
| ~ spl0_4
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f313,f305,f77,f691]) ).
fof(f691,plain,
( spl0_73
<=> ! [X1] :
( ~ between(v,X1,w)
| between(X1,w,x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f313,plain,
( ! [X1] :
( ~ between(v,X1,w)
| between(X1,w,x) )
| ~ spl0_4
| ~ spl0_40 ),
inference(resolution,[],[f306,f79]) ).
fof(f689,plain,
( spl0_72
| ~ spl0_3
| ~ spl0_40 ),
inference(avatar_split_clause,[],[f312,f305,f72,f687]) ).
fof(f687,plain,
( spl0_72
<=> ! [X0] :
( ~ between(u,X0,v)
| between(X0,v,w) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f312,plain,
( ! [X0] :
( ~ between(u,X0,v)
| between(X0,v,w) )
| ~ spl0_3
| ~ spl0_40 ),
inference(resolution,[],[f306,f74]) ).
fof(f573,plain,
( spl0_71
| ~ spl0_16
| ~ spl0_35 ),
inference(avatar_split_clause,[],[f288,f268,f130,f571]) ).
fof(f571,plain,
( spl0_71
<=> ! [X0,X1,X3] :
( X1 != X3
| between(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f130,plain,
( spl0_16
<=> ! [X5,X3,X10] : extension(X10,X3,X5,X5) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f288,plain,
( ! [X3,X0,X1] :
( X1 != X3
| between(X0,X1,X3) )
| ~ spl0_16
| ~ spl0_35 ),
inference(superposition,[],[f269,f131]) ).
fof(f131,plain,
( ! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f130]) ).
fof(f569,plain,
( spl0_70
| ~ spl0_17
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f261,f225,f134,f567]) ).
fof(f261,plain,
( ! [X10,X11] : equidistant(X10,X11,X10,reflection(X11,X10))
| ~ spl0_17
| ~ spl0_33 ),
inference(resolution,[],[f226,f135]) ).
fof(f565,plain,
( spl0_69
| ~ spl0_17
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f256,f216,f134,f563]) ).
fof(f256,plain,
( ! [X10,X11] : equidistant(X10,X11,reflection(X10,X11),X11)
| ~ spl0_17
| ~ spl0_31 ),
inference(resolution,[],[f217,f135]) ).
fof(f561,plain,
( spl0_68
| ~ spl0_17
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f251,f212,f134,f559]) ).
fof(f559,plain,
( spl0_68
<=> ! [X11,X10] : equidistant(reflection(X10,X11),X11,X11,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f251,plain,
( ! [X10,X11] : equidistant(reflection(X10,X11),X11,X11,X10)
| ~ spl0_17
| ~ spl0_30 ),
inference(resolution,[],[f213,f135]) ).
fof(f557,plain,
( spl0_67
| ~ spl0_17
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f246,f208,f134,f555]) ).
fof(f555,plain,
( spl0_67
<=> ! [X11,X10] : equidistant(X10,reflection(X11,X10),X10,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f246,plain,
( ! [X10,X11] : equidistant(X10,reflection(X11,X10),X10,X11)
| ~ spl0_17
| ~ spl0_29 ),
inference(resolution,[],[f209,f135]) ).
fof(f553,plain,
( spl0_66
| ~ spl0_17
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f241,f204,f134,f551]) ).
fof(f551,plain,
( spl0_66
<=> ! [X11,X10] : equidistant(reflection(X10,X11),X11,X10,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f241,plain,
( ! [X10,X11] : equidistant(reflection(X10,X11),X11,X10,X11)
| ~ spl0_17
| ~ spl0_28 ),
inference(resolution,[],[f205,f135]) ).
fof(f549,plain,
( spl0_65
| ~ spl0_17
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f236,f200,f134,f547]) ).
fof(f236,plain,
( ! [X10,X11] : equidistant(X10,X11,X11,reflection(X10,X11))
| ~ spl0_17
| ~ spl0_27 ),
inference(resolution,[],[f201,f135]) ).
fof(f545,plain,
( spl0_64
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f145,f138,f134,f543]) ).
fof(f145,plain,
( ! [X0,X1] : equidistant(X1,X0,reflection(X0,X1),X1)
| ~ spl0_17
| ~ spl0_18 ),
inference(superposition,[],[f135,f139]) ).
fof(f541,plain,
( ~ spl0_62
| spl0_63
| ~ spl0_4
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f299,f285,f77,f538,f534]) ).
fof(f534,plain,
( spl0_62
<=> between(v,x,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f299,plain,
( w = x
| ~ between(v,x,w)
| ~ spl0_4
| ~ spl0_39 ),
inference(resolution,[],[f286,f79]) ).
fof(f532,plain,
( ~ spl0_61
| spl0_2
| ~ spl0_3
| ~ spl0_39 ),
inference(avatar_split_clause,[],[f298,f285,f72,f67,f529]) ).
fof(f529,plain,
( spl0_61
<=> between(u,w,v) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f298,plain,
( v = w
| ~ between(u,w,v)
| ~ spl0_3
| ~ spl0_39 ),
inference(resolution,[],[f286,f74]) ).
fof(f527,plain,
( spl0_2
| ~ spl0_60
| ~ spl0_4
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f293,f281,f77,f524,f67]) ).
fof(f524,plain,
( spl0_60
<=> between(w,v,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f293,plain,
( ~ between(w,v,x)
| v = w
| ~ spl0_4
| ~ spl0_38 ),
inference(resolution,[],[f282,f79]) ).
fof(f515,plain,
spl0_59,
inference(avatar_split_clause,[],[f6,f513]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',outer_five_segment) ).
fof(f505,plain,
( spl0_57
| ~ spl0_58
| ~ spl0_3
| ~ spl0_38 ),
inference(avatar_split_clause,[],[f292,f281,f72,f502,f498]) ).
fof(f502,plain,
( spl0_58
<=> between(v,u,w) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f292,plain,
( ~ between(v,u,w)
| u = v
| ~ spl0_3
| ~ spl0_38 ),
inference(resolution,[],[f282,f74]) ).
fof(f496,plain,
spl0_56,
inference(avatar_split_clause,[],[f13,f494]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',upper_dimension) ).
fof(f479,plain,
spl0_55,
inference(avatar_split_clause,[],[f18,f477]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',continuity2) ).
fof(f467,plain,
spl0_54,
inference(avatar_split_clause,[],[f17,f465]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',continuity1) ).
fof(f457,plain,
spl0_53,
inference(avatar_split_clause,[],[f16,f455]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',euclid3) ).
fof(f448,plain,
spl0_52,
inference(avatar_split_clause,[],[f37,f446]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d8) ).
fof(f424,plain,
spl0_51,
inference(avatar_split_clause,[],[f15,f422]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',euclid2) ).
fof(f420,plain,
spl0_50,
inference(avatar_split_clause,[],[f14,f418]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',euclid1) ).
fof(f402,plain,
spl0_49,
inference(avatar_split_clause,[],[f40,f400]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d10_2) ).
fof(f398,plain,
spl0_48,
inference(avatar_split_clause,[],[f38,f396]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d9) ).
fof(f380,plain,
spl0_47,
inference(avatar_split_clause,[],[f9,f378]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',inner_pasch2) ).
fof(f370,plain,
spl0_46,
inference(avatar_split_clause,[],[f8,f368]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',inner_pasch1) ).
fof(f349,plain,
spl0_45,
inference(avatar_split_clause,[],[f54,f347]) ).
fof(f54,axiom,
! [X3,X10,X0,X5] :
( X3 = X5
| ~ between(X10,X3,X5)
| ~ between(X3,X5,X0)
| between(X10,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b6) ).
fof(f345,plain,
spl0_44,
inference(avatar_split_clause,[],[f28,f343]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d5) ).
fof(f341,plain,
spl0_43,
inference(avatar_split_clause,[],[f2,f339]) ).
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/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',transitivity_for_equidistance) ).
fof(f330,plain,
spl0_42,
inference(avatar_split_clause,[],[f39,f328]) ).
fof(f39,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X10,X3,X5)
| extension(X10,X3,X3,X5) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d10_1) ).
fof(f311,plain,
spl0_41,
inference(avatar_split_clause,[],[f60,f309]) ).
fof(f309,plain,
( spl0_41
<=> ! [X3,X10] :
( reflection(X10,X3) = extension(X10,X3,X3,X10)
| X3 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f60,plain,
! [X3,X10] :
( reflection(X10,X3) = extension(X10,X3,X3,X10)
| X3 = X10 ),
inference(forward_demodulation,[],[f41,f19]) ).
fof(f19,axiom,
! [X3,X10] : reflection(X10,X3) = extension(X10,X3,X10,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',reflection) ).
fof(f41,axiom,
! [X3,X10] :
( X3 = X10
| extension(X10,X3,X10,X3) = extension(X10,X3,X3,X10) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d10_3) ).
fof(f307,plain,
spl0_40,
inference(avatar_split_clause,[],[f53,f305]) ).
fof(f53,axiom,
! [X3,X10,X0,X5] :
( ~ between(X10,X3,X5)
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b5) ).
fof(f287,plain,
spl0_39,
inference(avatar_split_clause,[],[f49,f285]) ).
fof(f49,axiom,
! [X3,X10,X5] :
( X3 = X5
| ~ between(X10,X5,X3)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b3) ).
fof(f283,plain,
spl0_38,
inference(avatar_split_clause,[],[f48,f281]) ).
fof(f48,axiom,
! [X3,X10,X5] :
( X3 = X10
| ~ between(X3,X10,X5)
| ~ between(X10,X3,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b2) ).
fof(f279,plain,
spl0_37,
inference(avatar_split_clause,[],[f45,f277]) ).
fof(f45,axiom,
! [X3,X10,X0,X5] :
( X0 != X10
| ~ between(X10,X5,X0)
| between(X3,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b1) ).
fof(f275,plain,
( spl0_36
| ~ spl0_4
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f180,f164,f77,f272]) ).
fof(f180,plain,
( between(x,w,v)
| ~ spl0_4
| ~ spl0_23 ),
inference(resolution,[],[f165,f79]) ).
fof(f270,plain,
spl0_35,
inference(avatar_split_clause,[],[f30,f268]) ).
fof(f30,axiom,
! [X3,X10,X0,X1,X5] :
( between(X10,X3,X1)
| extension(X10,X3,X5,X0) != X1 ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',b0) ).
fof(f231,plain,
spl0_34,
inference(avatar_split_clause,[],[f27,f229]) ).
fof(f27,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X3,X10) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d4_5) ).
fof(f227,plain,
spl0_33,
inference(avatar_split_clause,[],[f26,f225]) ).
fof(f26,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X0,X5,X10,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d4_4) ).
fof(f223,plain,
( spl0_32
| ~ spl0_3
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f179,f164,f72,f220]) ).
fof(f179,plain,
( between(w,v,u)
| ~ spl0_3
| ~ spl0_23 ),
inference(resolution,[],[f165,f74]) ).
fof(f218,plain,
spl0_31,
inference(avatar_split_clause,[],[f25,f216]) ).
fof(f25,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X3,X10) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d4_3) ).
fof(f214,plain,
spl0_30,
inference(avatar_split_clause,[],[f24,f212]) ).
fof(f24,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X0,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d4_2) ).
fof(f210,plain,
spl0_29,
inference(avatar_split_clause,[],[f23,f208]) ).
fof(f23,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X10,X3,X0,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d4_1) ).
fof(f206,plain,
spl0_28,
inference(avatar_split_clause,[],[f22,f204]) ).
fof(f22,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X3,X10,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d3) ).
fof(f202,plain,
spl0_27,
inference(avatar_split_clause,[],[f21,f200]) ).
fof(f21,axiom,
! [X3,X10,X0,X5] :
( ~ equidistant(X10,X3,X5,X0)
| equidistant(X5,X0,X10,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d2) ).
fof(f192,plain,
spl0_26,
inference(avatar_split_clause,[],[f19,f190]) ).
fof(f188,plain,
spl0_25,
inference(avatar_split_clause,[],[f5,f186]) ).
fof(f5,axiom,
! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',segment_construction2) ).
fof(f178,plain,
( spl0_24
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f146,f138,f121,f176]) ).
fof(f146,plain,
( ! [X2,X3] : between(reflection(X2,X3),X3,X2)
| ~ spl0_14
| ~ spl0_18 ),
inference(superposition,[],[f122,f139]) ).
fof(f166,plain,
spl0_23,
inference(avatar_split_clause,[],[f46,f164]) ).
fof(f46,axiom,
! [X3,X10,X5] :
( ~ between(X10,X3,X5)
| between(X5,X3,X10) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',t1) ).
fof(f162,plain,
spl0_22,
inference(avatar_split_clause,[],[f35,f160]) ).
fof(f160,plain,
( spl0_22
<=> ! [X3,X10] :
( X3 = X10
| reflection(X10,X3) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f35,axiom,
! [X3,X10] :
( X3 = X10
| reflection(X10,X3) != X3 ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r4) ).
fof(f158,plain,
spl0_21,
inference(avatar_split_clause,[],[f33,f156]) ).
fof(f156,plain,
( spl0_21
<=> ! [X3,X10] :
( X3 != X10
| reflection(X10,X3) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f33,axiom,
! [X3,X10] :
( X3 != X10
| reflection(X10,X3) = X3 ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r3_1) ).
fof(f154,plain,
spl0_20,
inference(avatar_split_clause,[],[f4,f152]) ).
fof(f4,axiom,
! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',segment_construction1) ).
fof(f150,plain,
spl0_19,
inference(avatar_split_clause,[],[f3,f148]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( X0 = X1
| ~ equidistant(X0,X1,X2,X2) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',identity_for_equidistance) ).
fof(f140,plain,
spl0_18,
inference(avatar_split_clause,[],[f43,f138]) ).
fof(f43,axiom,
! [X3,X10] : reflection(reflection(X10,X3),X3) = X10,
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r6) ).
fof(f136,plain,
spl0_17,
inference(avatar_split_clause,[],[f32,f134]) ).
fof(f32,axiom,
! [X3,X10] : equidistant(X3,reflection(X10,X3),X10,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r2_2) ).
fof(f132,plain,
spl0_16,
inference(avatar_split_clause,[],[f29,f130]) ).
fof(f29,axiom,
! [X3,X10,X5] : extension(X10,X3,X5,X5) = X3,
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',e1) ).
fof(f128,plain,
spl0_15,
inference(avatar_split_clause,[],[f7,f126]) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ between(X0,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',identity_for_betweeness) ).
fof(f123,plain,
spl0_14,
inference(avatar_split_clause,[],[f31,f121]) ).
fof(f31,axiom,
! [X3,X10] : between(X10,X3,reflection(X10,X3)),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r2_1) ).
fof(f119,plain,
spl0_13,
inference(avatar_split_clause,[],[f36,f117]) ).
fof(f36,axiom,
! [X3,X10] : equidistant(X10,X10,X3,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d7) ).
fof(f115,plain,
spl0_12,
inference(avatar_split_clause,[],[f34,f113]) ).
fof(f113,plain,
( spl0_12
<=> ! [X10] : reflection(X10,X10) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f34,axiom,
! [X10] : reflection(X10,X10) = X10,
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',r3_2) ).
fof(f111,plain,
spl0_11,
inference(avatar_split_clause,[],[f20,f109]) ).
fof(f20,axiom,
! [X3,X10] : equidistant(X10,X3,X10,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',d1) ).
fof(f107,plain,
spl0_10,
inference(avatar_split_clause,[],[f1,f105]) ).
fof(f1,axiom,
! [X0,X1] : equidistant(X0,X1,X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',reflexivity_for_equidistance) ).
fof(f103,plain,
spl0_9,
inference(avatar_split_clause,[],[f47,f101]) ).
fof(f47,axiom,
! [X3,X10] : between(X10,X10,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',t2) ).
fof(f99,plain,
spl0_8,
inference(avatar_split_clause,[],[f44,f97]) ).
fof(f97,plain,
( spl0_8
<=> ! [X3,X10] : between(X10,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f44,axiom,
! [X3,X10] : between(X10,X3,X3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',t3) ).
fof(f95,plain,
~ spl0_7,
inference(avatar_split_clause,[],[f12,f92]) ).
fof(f92,plain,
( spl0_7
<=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f12,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',lower_dimension3) ).
fof(f90,plain,
~ spl0_6,
inference(avatar_split_clause,[],[f11,f87]) ).
fof(f87,plain,
( spl0_6
<=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f11,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',lower_dimension2) ).
fof(f85,plain,
~ spl0_5,
inference(avatar_split_clause,[],[f10,f82]) ).
fof(f82,plain,
( spl0_5
<=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f10,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',lower_dimension1) ).
fof(f80,plain,
spl0_4,
inference(avatar_split_clause,[],[f56,f77]) ).
fof(f56,axiom,
between(v,w,x),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',w_between_v_and_x) ).
fof(f75,plain,
spl0_3,
inference(avatar_split_clause,[],[f55,f72]) ).
fof(f55,axiom,
between(u,v,w),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',v_between_u_and_w) ).
fof(f70,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f57,f67]) ).
fof(f57,axiom,
v != w,
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',v_not_w) ).
fof(f65,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f58,f62]) ).
fof(f58,axiom,
~ between(u,v,x),
file('/export/starexec/sandbox2/tmp/tmp.GlZZxrUfaL/Vampire---4.8_9635',prove_v_between_u_and_x) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO045-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 30 18:14:27 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.40 % (9775)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.41 % (9777)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.20/0.41 % (9776)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.20/0.41 % (9779)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.20/0.41 % (9778)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 Vampire---4 for (569ds/0Mi)
% 0.20/0.41 % (9780)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 Vampire---4 for (531ds/0Mi)
% 0.20/0.41 % (9781)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 Vampire---4 for (522ds/0Mi)
% 0.20/0.41 % (9782)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 Vampire---4 for (497ds/0Mi)
% 0.20/0.41 TRYING [1]
% 0.20/0.41 TRYING [2]
% 0.20/0.42 TRYING [3]
% 0.20/0.43 TRYING [1]
% 0.20/0.44 TRYING [2]
% 0.20/0.44 TRYING [1]
% 0.20/0.44 TRYING [2]
% 0.20/0.45 TRYING [3]
% 0.20/0.49 TRYING [4]
% 0.20/0.53 TRYING [4]
% 0.20/0.55 TRYING [3]
% 0.20/0.58 % (9780)First to succeed.
% 0.20/0.58 % (9780)Refutation found. Thanks to Tanya!
% 0.20/0.58 % SZS status Unsatisfiable for Vampire---4
% 0.20/0.58 % SZS output start Proof for Vampire---4
% See solution above
% 1.14/0.59 % (9780)------------------------------
% 1.14/0.59 % (9780)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 1.14/0.59 % (9780)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 1.14/0.59 % (9780)Termination reason: Refutation
% 1.14/0.59
% 1.14/0.59 % (9780)Memory used [KB]: 9722
% 1.14/0.59 % (9780)Time elapsed: 0.173 s
% 1.14/0.59 % (9780)------------------------------
% 1.14/0.59 % (9780)------------------------------
% 1.14/0.59 % (9775)Success in time 0.234 s
% 1.14/0.59 % Vampire---4.8 exiting
%------------------------------------------------------------------------------