TSTP Solution File: NUM494+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% 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 : n025.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 : Thu Aug 31 12:10:09 EDT 2023
% Result : Theorem 0.22s 0.53s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 156
% Syntax : Number of formulae : 617 ( 66 unt; 0 def)
% Number of atoms : 2012 ( 213 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 2357 ( 962 ~;1050 |; 184 &)
% ( 128 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 134 ( 132 usr; 123 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-2 aty)
% Number of variables : 231 (; 204 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1283,plain,
$false,
inference(avatar_smt_refutation,[],[f380,f384,f388,f392,f396,f400,f404,f408,f412,f416,f420,f424,f428,f432,f436,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f480,f484,f488,f492,f510,f514,f518,f522,f526,f530,f534,f538,f542,f546,f563,f568,f575,f582,f587,f594,f601,f608,f615,f622,f636,f639,f642,f645,f648,f651,f654,f664,f668,f672,f676,f680,f694,f699,f725,f741,f755,f765,f771,f779,f803,f808,f835,f844,f869,f878,f885,f905,f916,f940,f949,f958,f981,f994,f1002,f1007,f1031,f1047,f1052,f1060,f1081,f1086,f1090,f1109,f1118,f1129,f1132,f1135,f1150,f1154,f1174,f1189,f1193,f1202,f1207,f1215,f1228,f1254,f1263,f1278,f1282]) ).
fof(f1282,plain,
( ~ spl19_102
| ~ spl19_103
| spl19_122
| spl19_121 ),
inference(avatar_split_clause,[],[f1273,f1261,f1280,f1076,f1073]) ).
fof(f1073,plain,
( spl19_102
<=> aNaturalNumber0(sdtpldt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_102])]) ).
fof(f1076,plain,
( spl19_103
<=> aNaturalNumber0(sdtpldt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_103])]) ).
fof(f1280,plain,
( spl19_122
<=> sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_122])]) ).
fof(f1261,plain,
( spl19_121
<=> sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_121])]) ).
fof(f1273,plain,
( sdtlseqdt0(sdtpldt0(xn,xm),sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl19_121 ),
inference(resolution,[],[f1262,f248]) ).
fof(f248,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mLETotal) ).
fof(f1262,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| spl19_121 ),
inference(avatar_component_clause,[],[f1261]) ).
fof(f1278,plain,
( spl19_79
| ~ spl19_6
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10
| spl19_121 ),
inference(avatar_split_clause,[],[f1277,f1261,f410,f406,f402,f394,f864]) ).
fof(f864,plain,
( spl19_79
<=> sQ18_eqProxy(xr,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_79])]) ).
fof(f394,plain,
( spl19_6
<=> aNaturalNumber0(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_6])]) ).
fof(f402,plain,
( spl19_8
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_8])]) ).
fof(f406,plain,
( spl19_9
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_9])]) ).
fof(f410,plain,
( spl19_10
<=> sdtlseqdt0(xr,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_10])]) ).
fof(f1277,plain,
( sQ18_eqProxy(xr,xn)
| ~ spl19_6
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10
| spl19_121 ),
inference(subsumption_resolution,[],[f1276,f395]) ).
fof(f395,plain,
( aNaturalNumber0(xr)
| ~ spl19_6 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f1276,plain,
( sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ spl19_8
| ~ spl19_9
| ~ spl19_10
| spl19_121 ),
inference(subsumption_resolution,[],[f1275,f407]) ).
fof(f407,plain,
( aNaturalNumber0(xn)
| ~ spl19_9 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f1275,plain,
( sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ spl19_8
| ~ spl19_10
| spl19_121 ),
inference(subsumption_resolution,[],[f1274,f411]) ).
fof(f411,plain,
( sdtlseqdt0(xr,xn)
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f1274,plain,
( ~ sdtlseqdt0(xr,xn)
| sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ spl19_8
| spl19_121 ),
inference(subsumption_resolution,[],[f1272,f403]) ).
fof(f403,plain,
( aNaturalNumber0(xm)
| ~ spl19_8 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f1272,plain,
( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xr,xn)
| sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| spl19_121 ),
inference(resolution,[],[f1262,f349]) ).
fof(f349,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| sQ18_eqProxy(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f260,f299]) ).
fof(f299,plain,
! [X0,X1] :
( sQ18_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(equality_proxy_definition,[new_symbols(naming,[sQ18_eqProxy])]) ).
fof(f260,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mMonAdd) ).
fof(f1263,plain,
( ~ spl19_103
| ~ spl19_102
| spl19_105
| ~ spl19_121
| spl19_2
| ~ spl19_7 ),
inference(avatar_split_clause,[],[f1259,f398,f378,f1261,f1084,f1073,f1076]) ).
fof(f1084,plain,
( spl19_105
<=> sQ18_eqProxy(sdtpldt0(xr,xm),sdtpldt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_105])]) ).
fof(f378,plain,
( spl19_2
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_2])]) ).
fof(f398,plain,
( spl19_7
<=> aNaturalNumber0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_7])]) ).
fof(f1259,plain,
( ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sQ18_eqProxy(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| spl19_2
| ~ spl19_7 ),
inference(subsumption_resolution,[],[f1255,f399]) ).
fof(f399,plain,
( aNaturalNumber0(xp)
| ~ spl19_7 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f1255,plain,
( ~ aNaturalNumber0(xp)
| ~ sdtlseqdt0(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| sQ18_eqProxy(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| spl19_2 ),
inference(resolution,[],[f349,f379]) ).
fof(f379,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| spl19_2 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f1254,plain,
( spl19_120
| ~ spl19_113 ),
inference(avatar_split_clause,[],[f1250,f1187,f1252]) ).
fof(f1252,plain,
( spl19_120
<=> sQ18_eqProxy(xr,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_120])]) ).
fof(f1187,plain,
( spl19_113
<=> sQ18_eqProxy(sz00,xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_113])]) ).
fof(f1250,plain,
( sQ18_eqProxy(xr,sz00)
| ~ spl19_113 ),
inference(resolution,[],[f1188,f372]) ).
fof(f372,plain,
! [X0,X1] :
( ~ sQ18_eqProxy(X0,X1)
| sQ18_eqProxy(X1,X0) ),
inference(equality_proxy_axiom,[],[f299]) ).
fof(f1188,plain,
( sQ18_eqProxy(sz00,xr)
| ~ spl19_113 ),
inference(avatar_component_clause,[],[f1187]) ).
fof(f1228,plain,
( spl19_119
| ~ spl19_111 ),
inference(avatar_split_clause,[],[f1224,f1169,f1226]) ).
fof(f1226,plain,
( spl19_119
<=> sQ18_eqProxy(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_119])]) ).
fof(f1169,plain,
( spl19_111
<=> sQ18_eqProxy(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_111])]) ).
fof(f1224,plain,
( sQ18_eqProxy(xm,sz00)
| ~ spl19_111 ),
inference(resolution,[],[f1170,f372]) ).
fof(f1170,plain,
( sQ18_eqProxy(sz00,xm)
| ~ spl19_111 ),
inference(avatar_component_clause,[],[f1169]) ).
fof(f1215,plain,
( ~ spl19_87
| spl19_117
| spl19_118
| ~ spl19_7
| ~ spl19_88 ),
inference(avatar_split_clause,[],[f1208,f911,f398,f1213,f1210,f908]) ).
fof(f908,plain,
( spl19_87
<=> aNaturalNumber0(sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_87])]) ).
fof(f1210,plain,
( spl19_117
<=> sQ18_eqProxy(xp,sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_117])]) ).
fof(f1213,plain,
( spl19_118
<=> iLess0(xp,sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_118])]) ).
fof(f911,plain,
( spl19_88
<=> sdtlseqdt0(xp,sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_88])]) ).
fof(f1208,plain,
( iLess0(xp,sdtasdt0(xr,xm))
| sQ18_eqProxy(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ spl19_7
| ~ spl19_88 ),
inference(subsumption_resolution,[],[f1197,f399]) ).
fof(f1197,plain,
( iLess0(xp,sdtasdt0(xr,xm))
| sQ18_eqProxy(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_88 ),
inference(resolution,[],[f912,f348]) ).
fof(f348,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X0,X1)
| iLess0(X0,X1)
| sQ18_eqProxy(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f256,f299]) ).
fof(f256,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( iLess0(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> iLess0(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mIH_03) ).
fof(f912,plain,
( sdtlseqdt0(xp,sdtasdt0(xr,xm))
| ~ spl19_88 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f1207,plain,
( ~ spl19_87
| ~ spl19_116
| spl19_78
| ~ spl19_7
| ~ spl19_88 ),
inference(avatar_split_clause,[],[f1203,f911,f398,f842,f1205,f908]) ).
fof(f1205,plain,
( spl19_116
<=> sdtlseqdt0(sdtasdt0(xr,xm),xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_116])]) ).
fof(f842,plain,
( spl19_78
<=> sQ18_eqProxy(sdtasdt0(xr,xm),xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_78])]) ).
fof(f1203,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),xp)
| ~ sdtlseqdt0(sdtasdt0(xr,xm),xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ spl19_7
| ~ spl19_88 ),
inference(subsumption_resolution,[],[f1196,f399]) ).
fof(f1196,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),xp)
| ~ sdtlseqdt0(sdtasdt0(xr,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ spl19_88 ),
inference(resolution,[],[f912,f358]) ).
fof(f358,plain,
! [X0,X1] :
( ~ sdtlseqdt0(X1,X0)
| sQ18_eqProxy(X0,X1)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f266,f299]) ).
fof(f266,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mLEAsym) ).
fof(f1202,plain,
( ~ spl19_87
| spl19_115
| ~ spl19_7
| ~ spl19_88 ),
inference(avatar_split_clause,[],[f1198,f911,f398,f1200,f908]) ).
fof(f1200,plain,
( spl19_115
<=> ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_115])]) ).
fof(f1198,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xr,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X0) )
| ~ spl19_7
| ~ spl19_88 ),
inference(subsumption_resolution,[],[f1195,f399]) ).
fof(f1195,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xr,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) )
| ~ spl19_88 ),
inference(resolution,[],[f912,f284]) ).
fof(f284,plain,
! [X2,X0,X1] :
( ~ sdtlseqdt0(X1,X2)
| sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mLETran) ).
fof(f1193,plain,
( spl19_114
| ~ spl19_89 ),
inference(avatar_split_clause,[],[f1183,f914,f1191]) ).
fof(f1191,plain,
( spl19_114
<=> sQ18_eqProxy(sdtasdt0(xr,xm),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_114])]) ).
fof(f914,plain,
( spl19_89
<=> sQ18_eqProxy(sz00,sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_89])]) ).
fof(f1183,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),sz00)
| ~ spl19_89 ),
inference(resolution,[],[f915,f372]) ).
fof(f915,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xr,xm))
| ~ spl19_89 ),
inference(avatar_component_clause,[],[f914]) ).
fof(f1189,plain,
( spl19_111
| spl19_113
| ~ spl19_6
| ~ spl19_8
| ~ spl19_89 ),
inference(avatar_split_clause,[],[f1185,f914,f402,f394,f1187,f1169]) ).
fof(f1185,plain,
( sQ18_eqProxy(sz00,xr)
| sQ18_eqProxy(sz00,xm)
| ~ spl19_6
| ~ spl19_8
| ~ spl19_89 ),
inference(subsumption_resolution,[],[f1184,f395]) ).
fof(f1184,plain,
( sQ18_eqProxy(sz00,xr)
| sQ18_eqProxy(sz00,xm)
| ~ aNaturalNumber0(xr)
| ~ spl19_8
| ~ spl19_89 ),
inference(subsumption_resolution,[],[f1182,f403]) ).
fof(f1182,plain,
( sQ18_eqProxy(sz00,xr)
| sQ18_eqProxy(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| ~ spl19_89 ),
inference(resolution,[],[f915,f345]) ).
fof(f345,plain,
! [X0,X1] :
( ~ sQ18_eqProxy(sz00,sdtasdt0(X0,X1))
| sQ18_eqProxy(sz00,X0)
| sQ18_eqProxy(sz00,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f253,f299,f299,f299]) ).
fof(f253,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mZeroMul) ).
fof(f1174,plain,
( spl19_111
| spl19_112
| ~ spl19_8
| ~ spl19_9
| ~ spl19_86 ),
inference(avatar_split_clause,[],[f1167,f903,f406,f402,f1172,f1169]) ).
fof(f1172,plain,
( spl19_112
<=> sQ18_eqProxy(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_112])]) ).
fof(f903,plain,
( spl19_86
<=> sQ18_eqProxy(sz00,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_86])]) ).
fof(f1167,plain,
( sQ18_eqProxy(sz00,xn)
| sQ18_eqProxy(sz00,xm)
| ~ spl19_8
| ~ spl19_9
| ~ spl19_86 ),
inference(subsumption_resolution,[],[f1166,f407]) ).
fof(f1166,plain,
( sQ18_eqProxy(sz00,xn)
| sQ18_eqProxy(sz00,xm)
| ~ aNaturalNumber0(xn)
| ~ spl19_8
| ~ spl19_86 ),
inference(subsumption_resolution,[],[f1164,f403]) ).
fof(f1164,plain,
( sQ18_eqProxy(sz00,xn)
| sQ18_eqProxy(sz00,xm)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ spl19_86 ),
inference(resolution,[],[f904,f345]) ).
fof(f904,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xn,xm))
| ~ spl19_86 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f1154,plain,
( ~ spl19_106
| ~ spl19_107
| spl19_1
| spl19_110
| ~ spl19_108 ),
inference(avatar_split_clause,[],[f1146,f1127,f1152,f375,f1124,f1121]) ).
fof(f1121,plain,
( spl19_106
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_106])]) ).
fof(f1124,plain,
( spl19_107
<=> aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_107])]) ).
fof(f375,plain,
( spl19_1
<=> sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_1])]) ).
fof(f1152,plain,
( spl19_110
<=> iLess0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_110])]) ).
fof(f1127,plain,
( spl19_108
<=> sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_108])]) ).
fof(f1146,plain,
( iLess0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl19_108 ),
inference(resolution,[],[f1128,f348]) ).
fof(f1128,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ spl19_108 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f1150,plain,
( ~ spl19_106
| ~ spl19_107
| spl19_109
| ~ spl19_108 ),
inference(avatar_split_clause,[],[f1144,f1127,f1148,f1124,f1121]) ).
fof(f1148,plain,
( spl19_109
<=> ! [X0] :
( sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_109])]) ).
fof(f1144,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ sdtlseqdt0(X0,sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ aNaturalNumber0(X0) )
| ~ spl19_108 ),
inference(resolution,[],[f1128,f284]) ).
fof(f1135,plain,
( ~ spl19_103
| ~ spl19_7
| spl19_107 ),
inference(avatar_split_clause,[],[f1134,f1124,f398,f1076]) ).
fof(f1134,plain,
( ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ spl19_7
| spl19_107 ),
inference(subsumption_resolution,[],[f1133,f399]) ).
fof(f1133,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| spl19_107 ),
inference(resolution,[],[f1125,f244]) ).
fof(f244,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mSortsB) ).
fof(f1125,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| spl19_107 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f1132,plain,
( ~ spl19_102
| ~ spl19_7
| spl19_106 ),
inference(avatar_split_clause,[],[f1131,f1121,f398,f1073]) ).
fof(f1131,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ spl19_7
| spl19_106 ),
inference(subsumption_resolution,[],[f1130,f399]) ).
fof(f1130,plain,
( ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl19_106 ),
inference(resolution,[],[f1122,f244]) ).
fof(f1122,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| spl19_106 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f1129,plain,
( ~ spl19_106
| ~ spl19_107
| spl19_108
| spl19_2 ),
inference(avatar_split_clause,[],[f1119,f378,f1127,f1124,f1121]) ).
fof(f1119,plain,
( sdtlseqdt0(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ aNaturalNumber0(sdtpldt0(sdtpldt0(xn,xm),xp))
| spl19_2 ),
inference(resolution,[],[f379,f248]) ).
fof(f1118,plain,
( ~ spl19_6
| ~ spl19_8
| ~ spl19_9
| spl19_13
| ~ spl19_104 ),
inference(avatar_contradiction_clause,[],[f1117]) ).
fof(f1117,plain,
( $false
| ~ spl19_6
| ~ spl19_8
| ~ spl19_9
| spl19_13
| ~ spl19_104 ),
inference(subsumption_resolution,[],[f1116,f403]) ).
fof(f1116,plain,
( ~ aNaturalNumber0(xm)
| ~ spl19_6
| ~ spl19_9
| spl19_13
| ~ spl19_104 ),
inference(subsumption_resolution,[],[f1115,f407]) ).
fof(f1115,plain,
( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl19_6
| spl19_13
| ~ spl19_104 ),
inference(subsumption_resolution,[],[f1114,f395]) ).
fof(f1114,plain,
( ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| spl19_13
| ~ spl19_104 ),
inference(subsumption_resolution,[],[f1112,f423]) ).
fof(f423,plain,
( ~ sQ18_eqProxy(xn,xr)
| spl19_13 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f422,plain,
( spl19_13
<=> sQ18_eqProxy(xn,xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_13])]) ).
fof(f1112,plain,
( sQ18_eqProxy(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ spl19_104 ),
inference(resolution,[],[f1080,f369]) ).
fof(f369,plain,
! [X2,X0,X1] :
( ~ sQ18_eqProxy(sdtpldt0(X1,X0),sdtpldt0(X2,X0))
| sQ18_eqProxy(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f286,f299,f299]) ).
fof(f286,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mAddCanc) ).
fof(f1080,plain,
( sQ18_eqProxy(sdtpldt0(xn,xm),sdtpldt0(xr,xm))
| ~ spl19_104 ),
inference(avatar_component_clause,[],[f1079]) ).
fof(f1079,plain,
( spl19_104
<=> sQ18_eqProxy(sdtpldt0(xn,xm),sdtpldt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_104])]) ).
fof(f1109,plain,
( ~ spl19_6
| ~ spl19_8
| spl19_103 ),
inference(avatar_contradiction_clause,[],[f1108]) ).
fof(f1108,plain,
( $false
| ~ spl19_6
| ~ spl19_8
| spl19_103 ),
inference(subsumption_resolution,[],[f1107,f395]) ).
fof(f1107,plain,
( ~ aNaturalNumber0(xr)
| ~ spl19_8
| spl19_103 ),
inference(subsumption_resolution,[],[f1106,f403]) ).
fof(f1106,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| spl19_103 ),
inference(resolution,[],[f1077,f244]) ).
fof(f1077,plain,
( ~ aNaturalNumber0(sdtpldt0(xr,xm))
| spl19_103 ),
inference(avatar_component_clause,[],[f1076]) ).
fof(f1090,plain,
( ~ spl19_8
| ~ spl19_9
| spl19_102 ),
inference(avatar_contradiction_clause,[],[f1089]) ).
fof(f1089,plain,
( $false
| ~ spl19_8
| ~ spl19_9
| spl19_102 ),
inference(subsumption_resolution,[],[f1088,f407]) ).
fof(f1088,plain,
( ~ aNaturalNumber0(xn)
| ~ spl19_8
| spl19_102 ),
inference(subsumption_resolution,[],[f1087,f403]) ).
fof(f1087,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl19_102 ),
inference(resolution,[],[f1074,f244]) ).
fof(f1074,plain,
( ~ aNaturalNumber0(sdtpldt0(xn,xm))
| spl19_102 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1086,plain,
( ~ spl19_103
| ~ spl19_102
| spl19_105
| ~ spl19_7
| ~ spl19_58 ),
inference(avatar_split_clause,[],[f1082,f662,f398,f1084,f1073,f1076]) ).
fof(f662,plain,
( spl19_58
<=> sQ18_eqProxy(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_58])]) ).
fof(f1082,plain,
( sQ18_eqProxy(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ spl19_7
| ~ spl19_58 ),
inference(subsumption_resolution,[],[f1062,f399]) ).
fof(f1062,plain,
( sQ18_eqProxy(sdtpldt0(xr,xm),sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_58 ),
inference(resolution,[],[f369,f663]) ).
fof(f663,plain,
( sQ18_eqProxy(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl19_58 ),
inference(avatar_component_clause,[],[f662]) ).
fof(f1081,plain,
( ~ spl19_102
| ~ spl19_103
| spl19_104
| ~ spl19_1
| ~ spl19_7 ),
inference(avatar_split_clause,[],[f1071,f398,f375,f1079,f1076,f1073]) ).
fof(f1071,plain,
( sQ18_eqProxy(sdtpldt0(xn,xm),sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ spl19_1
| ~ spl19_7 ),
inference(subsumption_resolution,[],[f1061,f399]) ).
fof(f1061,plain,
( sQ18_eqProxy(sdtpldt0(xn,xm),sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xr,xm))
| ~ aNaturalNumber0(sdtpldt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_1 ),
inference(resolution,[],[f369,f376]) ).
fof(f376,plain,
( sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f1060,plain,
( ~ spl19_84
| spl19_100
| spl19_101
| ~ spl19_7
| ~ spl19_85 ),
inference(avatar_split_clause,[],[f1053,f900,f398,f1058,f1055,f897]) ).
fof(f897,plain,
( spl19_84
<=> aNaturalNumber0(sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_84])]) ).
fof(f1055,plain,
( spl19_100
<=> sQ18_eqProxy(xp,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_100])]) ).
fof(f1058,plain,
( spl19_101
<=> iLess0(xp,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_101])]) ).
fof(f900,plain,
( spl19_85
<=> sdtlseqdt0(xp,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_85])]) ).
fof(f1053,plain,
( iLess0(xp,sdtasdt0(xn,xm))
| sQ18_eqProxy(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl19_7
| ~ spl19_85 ),
inference(subsumption_resolution,[],[f1042,f399]) ).
fof(f1042,plain,
( iLess0(xp,sdtasdt0(xn,xm))
| sQ18_eqProxy(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_85 ),
inference(resolution,[],[f901,f348]) ).
fof(f901,plain,
( sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ spl19_85 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f1052,plain,
( ~ spl19_84
| ~ spl19_99
| spl19_76
| ~ spl19_7
| ~ spl19_85 ),
inference(avatar_split_clause,[],[f1048,f900,f398,f833,f1050,f897]) ).
fof(f1050,plain,
( spl19_99
<=> sdtlseqdt0(sdtasdt0(xn,xm),xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_99])]) ).
fof(f833,plain,
( spl19_76
<=> sQ18_eqProxy(sdtasdt0(xn,xm),xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_76])]) ).
fof(f1048,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl19_7
| ~ spl19_85 ),
inference(subsumption_resolution,[],[f1041,f399]) ).
fof(f1041,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),xp)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl19_85 ),
inference(resolution,[],[f901,f358]) ).
fof(f1047,plain,
( ~ spl19_84
| spl19_98
| ~ spl19_7
| ~ spl19_85 ),
inference(avatar_split_clause,[],[f1043,f900,f398,f1045,f897]) ).
fof(f1045,plain,
( spl19_98
<=> ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ sdtlseqdt0(X0,xp) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_98])]) ).
fof(f1043,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) )
| ~ spl19_7
| ~ spl19_85 ),
inference(subsumption_resolution,[],[f1040,f399]) ).
fof(f1040,plain,
( ! [X0] :
( sdtlseqdt0(X0,sdtasdt0(xn,xm))
| ~ sdtlseqdt0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) )
| ~ spl19_85 ),
inference(resolution,[],[f901,f284]) ).
fof(f1031,plain,
( spl19_97
| ~ spl19_86 ),
inference(avatar_split_clause,[],[f1027,f903,f1029]) ).
fof(f1029,plain,
( spl19_97
<=> sQ18_eqProxy(sdtasdt0(xn,xm),sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_97])]) ).
fof(f1027,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),sz00)
| ~ spl19_86 ),
inference(resolution,[],[f904,f372]) ).
fof(f1007,plain,
( ~ spl19_87
| spl19_96
| ~ spl19_7
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f1003,f462,f398,f1005,f908]) ).
fof(f1005,plain,
( spl19_96
<=> ! [X1] :
( doDivides0(X1,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X1)
| ~ doDivides0(X1,xp) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_96])]) ).
fof(f462,plain,
( spl19_23
<=> doDivides0(xp,sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_23])]) ).
fof(f1003,plain,
( ! [X1] :
( doDivides0(X1,sdtasdt0(xr,xm))
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(X1) )
| ~ spl19_7
| ~ spl19_23 ),
inference(subsumption_resolution,[],[f983,f399]) ).
fof(f983,plain,
( ! [X1] :
( doDivides0(X1,sdtasdt0(xr,xm))
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X1) )
| ~ spl19_23 ),
inference(resolution,[],[f281,f463]) ).
fof(f463,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f281,plain,
! [X2,X0,X1] :
( ~ doDivides0(X1,X2)
| doDivides0(X0,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mDivTrans) ).
fof(f1002,plain,
( ~ spl19_6
| ~ spl19_8
| spl19_87 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
fof(f1001,plain,
( $false
| ~ spl19_6
| ~ spl19_8
| spl19_87 ),
inference(subsumption_resolution,[],[f1000,f395]) ).
fof(f1000,plain,
( ~ aNaturalNumber0(xr)
| ~ spl19_8
| spl19_87 ),
inference(subsumption_resolution,[],[f999,f403]) ).
fof(f999,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xr)
| spl19_87 ),
inference(resolution,[],[f909,f243]) ).
fof(f243,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mSortsB_02) ).
fof(f909,plain,
( ~ aNaturalNumber0(sdtasdt0(xr,xm))
| spl19_87 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f994,plain,
( ~ spl19_84
| spl19_95
| ~ spl19_7
| ~ spl19_14 ),
inference(avatar_split_clause,[],[f990,f426,f398,f992,f897]) ).
fof(f992,plain,
( spl19_95
<=> ! [X0] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0)
| ~ doDivides0(X0,xp) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_95])]) ).
fof(f426,plain,
( spl19_14
<=> doDivides0(xp,sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_14])]) ).
fof(f990,plain,
( ! [X0] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(X0) )
| ~ spl19_7
| ~ spl19_14 ),
inference(subsumption_resolution,[],[f982,f399]) ).
fof(f982,plain,
( ! [X0] :
( doDivides0(X0,sdtasdt0(xn,xm))
| ~ doDivides0(X0,xp)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(X0) )
| ~ spl19_14 ),
inference(resolution,[],[f281,f427]) ).
fof(f427,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
| ~ spl19_14 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f981,plain,
( ~ spl19_8
| ~ spl19_9
| spl19_84 ),
inference(avatar_contradiction_clause,[],[f980]) ).
fof(f980,plain,
( $false
| ~ spl19_8
| ~ spl19_9
| spl19_84 ),
inference(subsumption_resolution,[],[f979,f407]) ).
fof(f979,plain,
( ~ aNaturalNumber0(xn)
| ~ spl19_8
| spl19_84 ),
inference(subsumption_resolution,[],[f978,f403]) ).
fof(f978,plain,
( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| spl19_84 ),
inference(resolution,[],[f898,f243]) ).
fof(f898,plain,
( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| spl19_84 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f958,plain,
( ~ spl19_93
| spl19_94
| ~ spl19_7
| ~ spl19_28
| ~ spl19_67 ),
inference(avatar_split_clause,[],[f951,f739,f482,f398,f956,f953]) ).
fof(f953,plain,
( spl19_93
<=> sdtlseqdt0(xp,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_93])]) ).
fof(f956,plain,
( spl19_94
<=> sQ18_eqProxy(xp,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_94])]) ).
fof(f482,plain,
( spl19_28
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_28])]) ).
fof(f739,plain,
( spl19_67
<=> sdtlseqdt0(sz10,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_67])]) ).
fof(f951,plain,
( sQ18_eqProxy(xp,sz10)
| ~ sdtlseqdt0(xp,sz10)
| ~ spl19_7
| ~ spl19_28
| ~ spl19_67 ),
inference(subsumption_resolution,[],[f950,f399]) ).
fof(f950,plain,
( sQ18_eqProxy(xp,sz10)
| ~ sdtlseqdt0(xp,sz10)
| ~ aNaturalNumber0(xp)
| ~ spl19_28
| ~ spl19_67 ),
inference(subsumption_resolution,[],[f927,f483]) ).
fof(f483,plain,
( aNaturalNumber0(sz10)
| ~ spl19_28 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f927,plain,
( sQ18_eqProxy(xp,sz10)
| ~ sdtlseqdt0(xp,sz10)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xp)
| ~ spl19_67 ),
inference(resolution,[],[f358,f740]) ).
fof(f740,plain,
( sdtlseqdt0(sz10,xp)
| ~ spl19_67 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f949,plain,
( ~ spl19_91
| spl19_92
| ~ spl19_7
| ~ spl19_9
| ~ spl19_20 ),
inference(avatar_split_clause,[],[f942,f450,f406,f398,f947,f944]) ).
fof(f944,plain,
( spl19_91
<=> sdtlseqdt0(xn,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_91])]) ).
fof(f947,plain,
( spl19_92
<=> sQ18_eqProxy(xn,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_92])]) ).
fof(f450,plain,
( spl19_20
<=> sdtlseqdt0(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_20])]) ).
fof(f942,plain,
( sQ18_eqProxy(xn,xp)
| ~ sdtlseqdt0(xn,xp)
| ~ spl19_7
| ~ spl19_9
| ~ spl19_20 ),
inference(subsumption_resolution,[],[f941,f407]) ).
fof(f941,plain,
( sQ18_eqProxy(xn,xp)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xn)
| ~ spl19_7
| ~ spl19_20 ),
inference(subsumption_resolution,[],[f926,f399]) ).
fof(f926,plain,
( sQ18_eqProxy(xn,xp)
| ~ sdtlseqdt0(xn,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(xn)
| ~ spl19_20 ),
inference(resolution,[],[f358,f451]) ).
fof(f451,plain,
( sdtlseqdt0(xp,xn)
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f940,plain,
( ~ spl19_90
| ~ spl19_6
| ~ spl19_9
| ~ spl19_10
| spl19_13 ),
inference(avatar_split_clause,[],[f936,f422,f410,f406,f394,f938]) ).
fof(f938,plain,
( spl19_90
<=> sdtlseqdt0(xn,xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_90])]) ).
fof(f936,plain,
( ~ sdtlseqdt0(xn,xr)
| ~ spl19_6
| ~ spl19_9
| ~ spl19_10
| spl19_13 ),
inference(subsumption_resolution,[],[f935,f407]) ).
fof(f935,plain,
( ~ sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xn)
| ~ spl19_6
| ~ spl19_10
| spl19_13 ),
inference(subsumption_resolution,[],[f934,f395]) ).
fof(f934,plain,
( ~ sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ spl19_10
| spl19_13 ),
inference(subsumption_resolution,[],[f925,f423]) ).
fof(f925,plain,
( sQ18_eqProxy(xn,xr)
| ~ sdtlseqdt0(xn,xr)
| ~ aNaturalNumber0(xr)
| ~ aNaturalNumber0(xn)
| ~ spl19_10 ),
inference(resolution,[],[f358,f411]) ).
fof(f916,plain,
( ~ spl19_87
| spl19_88
| spl19_89
| ~ spl19_7
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f906,f462,f398,f914,f911,f908]) ).
fof(f906,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xr,xm))
| sdtlseqdt0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ spl19_7
| ~ spl19_23 ),
inference(subsumption_resolution,[],[f887,f399]) ).
fof(f887,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xr,xm))
| sdtlseqdt0(xp,sdtasdt0(xr,xm))
| ~ aNaturalNumber0(sdtasdt0(xr,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_23 ),
inference(resolution,[],[f357,f463]) ).
fof(f357,plain,
! [X0,X1] :
( ~ doDivides0(X0,X1)
| sQ18_eqProxy(sz00,X1)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f265,f299]) ).
fof(f265,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1] :
( sdtlseqdt0(X0,X1)
| sz00 = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sz00 != X1
& doDivides0(X0,X1) )
=> sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mDivLE) ).
fof(f905,plain,
( ~ spl19_84
| spl19_85
| spl19_86
| ~ spl19_7
| ~ spl19_14 ),
inference(avatar_split_clause,[],[f895,f426,f398,f903,f900,f897]) ).
fof(f895,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xn,xm))
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ spl19_7
| ~ spl19_14 ),
inference(subsumption_resolution,[],[f886,f399]) ).
fof(f886,plain,
( sQ18_eqProxy(sz00,sdtasdt0(xn,xm))
| sdtlseqdt0(xp,sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xp)
| ~ spl19_14 ),
inference(resolution,[],[f357,f427]) ).
fof(f885,plain,
( spl19_83
| ~ spl19_7
| spl19_18
| ~ spl19_28
| ~ spl19_67 ),
inference(avatar_split_clause,[],[f881,f739,f482,f442,f398,f883]) ).
fof(f883,plain,
( spl19_83
<=> iLess0(sz10,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_83])]) ).
fof(f442,plain,
( spl19_18
<=> sQ18_eqProxy(sz10,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_18])]) ).
fof(f881,plain,
( iLess0(sz10,xp)
| ~ spl19_7
| spl19_18
| ~ spl19_28
| ~ spl19_67 ),
inference(subsumption_resolution,[],[f880,f483]) ).
fof(f880,plain,
( iLess0(sz10,xp)
| ~ aNaturalNumber0(sz10)
| ~ spl19_7
| spl19_18
| ~ spl19_67 ),
inference(subsumption_resolution,[],[f879,f399]) ).
fof(f879,plain,
( iLess0(sz10,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| spl19_18
| ~ spl19_67 ),
inference(subsumption_resolution,[],[f854,f443]) ).
fof(f443,plain,
( ~ sQ18_eqProxy(sz10,xp)
| spl19_18 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f854,plain,
( iLess0(sz10,xp)
| sQ18_eqProxy(sz10,xp)
| ~ aNaturalNumber0(xp)
| ~ aNaturalNumber0(sz10)
| ~ spl19_67 ),
inference(resolution,[],[f348,f740]) ).
fof(f878,plain,
( spl19_81
| spl19_82
| ~ spl19_7
| ~ spl19_9
| ~ spl19_20 ),
inference(avatar_split_clause,[],[f871,f450,f406,f398,f876,f873]) ).
fof(f873,plain,
( spl19_81
<=> sQ18_eqProxy(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_81])]) ).
fof(f876,plain,
( spl19_82
<=> iLess0(xp,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_82])]) ).
fof(f871,plain,
( iLess0(xp,xn)
| sQ18_eqProxy(xp,xn)
| ~ spl19_7
| ~ spl19_9
| ~ spl19_20 ),
inference(subsumption_resolution,[],[f870,f399]) ).
fof(f870,plain,
( iLess0(xp,xn)
| sQ18_eqProxy(xp,xn)
| ~ aNaturalNumber0(xp)
| ~ spl19_9
| ~ spl19_20 ),
inference(subsumption_resolution,[],[f853,f407]) ).
fof(f853,plain,
( iLess0(xp,xn)
| sQ18_eqProxy(xp,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xp)
| ~ spl19_20 ),
inference(resolution,[],[f348,f451]) ).
fof(f869,plain,
( spl19_79
| spl19_80
| ~ spl19_6
| ~ spl19_9
| ~ spl19_10 ),
inference(avatar_split_clause,[],[f862,f410,f406,f394,f867,f864]) ).
fof(f867,plain,
( spl19_80
<=> iLess0(xr,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_80])]) ).
fof(f862,plain,
( iLess0(xr,xn)
| sQ18_eqProxy(xr,xn)
| ~ spl19_6
| ~ spl19_9
| ~ spl19_10 ),
inference(subsumption_resolution,[],[f861,f395]) ).
fof(f861,plain,
( iLess0(xr,xn)
| sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xr)
| ~ spl19_9
| ~ spl19_10 ),
inference(subsumption_resolution,[],[f852,f407]) ).
fof(f852,plain,
( iLess0(xr,xn)
| sQ18_eqProxy(xr,xn)
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xr)
| ~ spl19_10 ),
inference(resolution,[],[f348,f411]) ).
fof(f844,plain,
( ~ spl19_77
| spl19_78
| ~ spl19_7
| spl19_18
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f837,f462,f442,f398,f842,f839]) ).
fof(f839,plain,
( spl19_77
<=> sP4(sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_77])]) ).
fof(f837,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),xp)
| ~ sP4(sdtasdt0(xr,xm))
| ~ spl19_7
| spl19_18
| ~ spl19_23 ),
inference(subsumption_resolution,[],[f836,f399]) ).
fof(f836,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ sP4(sdtasdt0(xr,xm))
| spl19_18
| ~ spl19_23 ),
inference(subsumption_resolution,[],[f821,f443]) ).
fof(f821,plain,
( sQ18_eqProxy(sz10,xp)
| sQ18_eqProxy(sdtasdt0(xr,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ sP4(sdtasdt0(xr,xm))
| ~ spl19_23 ),
inference(resolution,[],[f336,f463]) ).
fof(f336,plain,
! [X2,X0] :
( ~ doDivides0(X2,X0)
| sQ18_eqProxy(sz10,X2)
| sQ18_eqProxy(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ sP4(X0) ),
inference(equality_proxy_replacement,[],[f234,f299,f299]) ).
fof(f234,plain,
! [X2,X0] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0] :
( ( sP4(X0)
| ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& aNaturalNumber0(sK14(X0)) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f156,f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( sK14(X0) != X0
& sz10 != sK14(X0)
& doDivides0(sK14(X0),X0)
& aNaturalNumber0(sK14(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f156,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X2] :
( X0 = X2
| sz10 = X2
| ~ doDivides0(X2,X0)
| ~ aNaturalNumber0(X2) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(rectify,[],[f155]) ).
fof(f155,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ( sP4(X0)
| ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0 )
& ( ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( sP4(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f835,plain,
( ~ spl19_75
| spl19_76
| ~ spl19_7
| ~ spl19_14
| spl19_18 ),
inference(avatar_split_clause,[],[f828,f442,f426,f398,f833,f830]) ).
fof(f830,plain,
( spl19_75
<=> sP4(sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_75])]) ).
fof(f828,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),xp)
| ~ sP4(sdtasdt0(xn,xm))
| ~ spl19_7
| ~ spl19_14
| spl19_18 ),
inference(subsumption_resolution,[],[f827,f399]) ).
fof(f827,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ sP4(sdtasdt0(xn,xm))
| ~ spl19_14
| spl19_18 ),
inference(subsumption_resolution,[],[f820,f443]) ).
fof(f820,plain,
( sQ18_eqProxy(sz10,xp)
| sQ18_eqProxy(sdtasdt0(xn,xm),xp)
| ~ aNaturalNumber0(xp)
| ~ sP4(sdtasdt0(xn,xm))
| ~ spl19_14 ),
inference(resolution,[],[f336,f427]) ).
fof(f808,plain,
( spl19_74
| ~ spl19_72 ),
inference(avatar_split_clause,[],[f804,f798,f806]) ).
fof(f806,plain,
( spl19_74
<=> sQ18_eqProxy(sK15(xp),xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_74])]) ).
fof(f798,plain,
( spl19_72
<=> sQ18_eqProxy(xp,sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_72])]) ).
fof(f804,plain,
( sQ18_eqProxy(sK15(xp),xp)
| ~ spl19_72 ),
inference(resolution,[],[f799,f372]) ).
fof(f799,plain,
( sQ18_eqProxy(xp,sK15(xp))
| ~ spl19_72 ),
inference(avatar_component_clause,[],[f798]) ).
fof(f803,plain,
( spl19_72
| spl19_73
| ~ spl19_7
| spl19_18
| spl19_19
| ~ spl19_69 ),
inference(avatar_split_clause,[],[f796,f763,f446,f442,f398,f801,f798]) ).
fof(f801,plain,
( spl19_73
<=> sQ18_eqProxy(sz10,sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_73])]) ).
fof(f446,plain,
( spl19_19
<=> sQ18_eqProxy(sz00,xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_19])]) ).
fof(f763,plain,
( spl19_69
<=> aNaturalNumber0(sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_69])]) ).
fof(f796,plain,
( sQ18_eqProxy(sz10,sK15(xp))
| sQ18_eqProxy(xp,sK15(xp))
| ~ spl19_7
| spl19_18
| spl19_19
| ~ spl19_69 ),
inference(subsumption_resolution,[],[f795,f764]) ).
fof(f764,plain,
( aNaturalNumber0(sK15(xp))
| ~ spl19_69 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f795,plain,
( sQ18_eqProxy(sz10,sK15(xp))
| sQ18_eqProxy(xp,sK15(xp))
| ~ aNaturalNumber0(sK15(xp))
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f794,f399]) ).
fof(f794,plain,
( ~ aNaturalNumber0(xp)
| sQ18_eqProxy(sz10,sK15(xp))
| sQ18_eqProxy(xp,sK15(xp))
| ~ aNaturalNumber0(sK15(xp))
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f793,f447]) ).
fof(f447,plain,
( ~ sQ18_eqProxy(sz00,xp)
| spl19_19 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f793,plain,
( sQ18_eqProxy(sz00,xp)
| ~ aNaturalNumber0(xp)
| sQ18_eqProxy(sz10,sK15(xp))
| sQ18_eqProxy(xp,sK15(xp))
| ~ aNaturalNumber0(sK15(xp))
| spl19_18 ),
inference(subsumption_resolution,[],[f792,f443]) ).
fof(f792,plain,
( sQ18_eqProxy(sz10,xp)
| sQ18_eqProxy(sz00,xp)
| ~ aNaturalNumber0(xp)
| sQ18_eqProxy(sz10,sK15(xp))
| sQ18_eqProxy(xp,sK15(xp))
| ~ aNaturalNumber0(sK15(xp)) ),
inference(resolution,[],[f338,f307]) ).
fof(f307,plain,
! [X1] :
( ~ doDivides0(X1,xp)
| sQ18_eqProxy(sz10,X1)
| sQ18_eqProxy(xp,X1)
| ~ aNaturalNumber0(X1) ),
inference(equality_proxy_replacement,[],[f188,f299,f299]) ).
fof(f188,plain,
! [X1] :
( xp = X1
| sz10 = X1
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7)
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f54,f131]) ).
fof(f131,plain,
( ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xn,xm) = sdtasdt0(xp,sK7)
& aNaturalNumber0(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( xp = X1
| sz10 = X1
| ( ~ doDivides0(X1,xp)
& ! [X2] :
( sdtasdt0(X1,X2) != xp
| ~ aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1) )
& sz10 != xp
& sz00 != xp ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X1] :
( ( ( doDivides0(X1,xp)
| ? [X2] :
( sdtasdt0(X1,X2) = xp
& aNaturalNumber0(X2) ) )
& aNaturalNumber0(X1) )
=> ( xp = X1
| sz10 = X1 ) )
& sz10 != xp
& sz00 != xp ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [X0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,X0)
& aNaturalNumber0(X0) )
& isPrime0(xp)
& ! [X0] :
( ( ( doDivides0(X0,xp)
| ? [X1] :
( sdtasdt0(X0,X1) = xp
& aNaturalNumber0(X1) ) )
& aNaturalNumber0(X0) )
=> ( xp = X0
| sz10 = X0 ) )
& sz10 != xp
& sz00 != xp ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1860) ).
fof(f338,plain,
! [X0] :
( doDivides0(sK15(X0),X0)
| sQ18_eqProxy(sz10,X0)
| sQ18_eqProxy(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f241,f299,f299]) ).
fof(f241,plain,
! [X0] :
( doDivides0(sK15(X0),X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,plain,
! [X0] :
( ( isPrime0(sK15(X0))
& doDivides0(sK15(X0),X0)
& aNaturalNumber0(sK15(X0)) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f68,f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( isPrime0(sK15(X0))
& doDivides0(sK15(X0),X0)
& aNaturalNumber0(sK15(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ( sz10 != X0
& sz00 != X0
& aNaturalNumber0(X0) )
=> ? [X1] :
( isPrime0(X1)
& doDivides0(X1,X0)
& aNaturalNumber0(X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mPrimDiv) ).
fof(f779,plain,
( spl19_71
| ~ spl19_68
| ~ spl19_70 ),
inference(avatar_split_clause,[],[f775,f769,f753,f777]) ).
fof(f777,plain,
( spl19_71
<=> sP4(sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_71])]) ).
fof(f753,plain,
( spl19_68
<=> isPrime0(sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_68])]) ).
fof(f769,plain,
( spl19_70
<=> sP5(sK15(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_70])]) ).
fof(f775,plain,
( sP4(sK15(xp))
| ~ spl19_68
| ~ spl19_70 ),
inference(subsumption_resolution,[],[f774,f754]) ).
fof(f754,plain,
( isPrime0(sK15(xp))
| ~ spl19_68 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f774,plain,
( ~ isPrime0(sK15(xp))
| sP4(sK15(xp))
| ~ spl19_70 ),
inference(resolution,[],[f770,f230]) ).
fof(f230,plain,
! [X0] :
( ~ sP5(X0)
| ~ isPrime0(X0)
| sP4(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ( ( isPrime0(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ isPrime0(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( isPrime0(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f770,plain,
( sP5(sK15(xp))
| ~ spl19_70 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f771,plain,
( spl19_70
| ~ spl19_69 ),
inference(avatar_split_clause,[],[f767,f763,f769]) ).
fof(f767,plain,
( sP5(sK15(xp))
| ~ spl19_69 ),
inference(resolution,[],[f764,f239]) ).
fof(f239,plain,
! [X0] :
( ~ aNaturalNumber0(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( sP5(X0)
| ~ aNaturalNumber0(X0) ),
inference(definition_folding,[],[f66,f127,f126]) ).
fof(f66,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( isPrime0(X0)
<=> ( ! [X1] :
( X0 = X1
| sz10 = X1
| ~ doDivides0(X1,X0)
| ~ aNaturalNumber0(X1) )
& sz10 != X0
& sz00 != X0 ) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( isPrime0(X0)
<=> ( ! [X1] :
( ( doDivides0(X1,X0)
& aNaturalNumber0(X1) )
=> ( X0 = X1
| sz10 = X1 ) )
& sz10 != X0
& sz00 != X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mDefPrime) ).
fof(f765,plain,
( spl19_69
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(avatar_split_clause,[],[f761,f446,f442,f398,f763]) ).
fof(f761,plain,
( aNaturalNumber0(sK15(xp))
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f760,f399]) ).
fof(f760,plain,
( aNaturalNumber0(sK15(xp))
| ~ aNaturalNumber0(xp)
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f757,f447]) ).
fof(f757,plain,
( aNaturalNumber0(sK15(xp))
| sQ18_eqProxy(sz00,xp)
| ~ aNaturalNumber0(xp)
| spl19_18 ),
inference(resolution,[],[f339,f443]) ).
fof(f339,plain,
! [X0] :
( sQ18_eqProxy(sz10,X0)
| aNaturalNumber0(sK15(X0))
| sQ18_eqProxy(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f240,f299,f299]) ).
fof(f240,plain,
! [X0] :
( aNaturalNumber0(sK15(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f755,plain,
( spl19_68
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(avatar_split_clause,[],[f751,f446,f442,f398,f753]) ).
fof(f751,plain,
( isPrime0(sK15(xp))
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f750,f399]) ).
fof(f750,plain,
( isPrime0(sK15(xp))
| ~ aNaturalNumber0(xp)
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f747,f447]) ).
fof(f747,plain,
( isPrime0(sK15(xp))
| sQ18_eqProxy(sz00,xp)
| ~ aNaturalNumber0(xp)
| spl19_18 ),
inference(resolution,[],[f337,f443]) ).
fof(f337,plain,
! [X0] :
( sQ18_eqProxy(sz10,X0)
| isPrime0(sK15(X0))
| sQ18_eqProxy(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f242,f299,f299]) ).
fof(f242,plain,
! [X0] :
( isPrime0(sK15(X0))
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f160]) ).
fof(f741,plain,
( spl19_67
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(avatar_split_clause,[],[f737,f446,f442,f398,f739]) ).
fof(f737,plain,
( sdtlseqdt0(sz10,xp)
| ~ spl19_7
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f736,f399]) ).
fof(f736,plain,
( sdtlseqdt0(sz10,xp)
| ~ aNaturalNumber0(xp)
| spl19_18
| spl19_19 ),
inference(subsumption_resolution,[],[f733,f447]) ).
fof(f733,plain,
( sdtlseqdt0(sz10,xp)
| sQ18_eqProxy(sz00,xp)
| ~ aNaturalNumber0(xp)
| spl19_18 ),
inference(resolution,[],[f328,f443]) ).
fof(f328,plain,
! [X0] :
( sQ18_eqProxy(sz10,X0)
| sdtlseqdt0(sz10,X0)
| sQ18_eqProxy(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(equality_proxy_replacement,[],[f227,f299,f299]) ).
fof(f227,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mLENTr) ).
fof(f725,plain,
( ~ spl19_65
| spl19_66 ),
inference(avatar_split_clause,[],[f718,f723,f720]) ).
fof(f720,plain,
( spl19_65
<=> sP1(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_65])]) ).
fof(f723,plain,
( spl19_66
<=> sQ18_eqProxy(xp,sK12(xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_66])]) ).
fof(f718,plain,
( sQ18_eqProxy(xp,sK12(xp))
| ~ sP1(xp) ),
inference(subsumption_resolution,[],[f717,f205]) ).
fof(f205,plain,
! [X0] :
( aNaturalNumber0(sK12(X0))
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( ( sK12(X0) != X0
& sz10 != sK12(X0)
& doDivides0(sK12(X0),X0)
& sP0(X0,sK12(X0))
& aNaturalNumber0(sK12(X0)) )
| ~ sP1(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f146,f147]) ).
fof(f147,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
=> ( sK12(X0) != X0
& sz10 != sK12(X0)
& doDivides0(sK12(X0),X0)
& sP0(X0,sK12(X0))
& aNaturalNumber0(sK12(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f146,plain,
! [X0] :
( ? [X1] :
( X0 != X1
& sz10 != X1
& doDivides0(X1,X0)
& sP0(X0,X1)
& aNaturalNumber0(X1) )
| ~ sP1(X0) ),
inference(rectify,[],[f145]) ).
fof(f145,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP0(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP1(X2) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X2] :
( ? [X4] :
( X2 != X4
& sz10 != X4
& doDivides0(X4,X2)
& sP0(X2,X4)
& aNaturalNumber0(X4) )
| ~ sP1(X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f717,plain,
( sQ18_eqProxy(xp,sK12(xp))
| ~ aNaturalNumber0(sK12(xp))
| ~ sP1(xp) ),
inference(subsumption_resolution,[],[f716,f316]) ).
fof(f316,plain,
! [X0] :
( ~ sQ18_eqProxy(sz10,sK12(X0))
| ~ sP1(X0) ),
inference(equality_proxy_replacement,[],[f208,f299]) ).
fof(f208,plain,
! [X0] :
( sz10 != sK12(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f716,plain,
( sQ18_eqProxy(sz10,sK12(xp))
| sQ18_eqProxy(xp,sK12(xp))
| ~ aNaturalNumber0(sK12(xp))
| ~ sP1(xp) ),
inference(resolution,[],[f307,f207]) ).
fof(f207,plain,
! [X0] :
( doDivides0(sK12(X0),X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f699,plain,
( spl19_64
| ~ spl19_24 ),
inference(avatar_split_clause,[],[f695,f466,f697]) ).
fof(f697,plain,
( spl19_64
<=> sQ18_eqProxy(sdtasdt0(xp,sK9),sdtasdt0(xr,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_64])]) ).
fof(f466,plain,
( spl19_24
<=> sQ18_eqProxy(sdtasdt0(xr,xm),sdtasdt0(xp,sK9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_24])]) ).
fof(f695,plain,
( sQ18_eqProxy(sdtasdt0(xp,sK9),sdtasdt0(xr,xm))
| ~ spl19_24 ),
inference(resolution,[],[f467,f372]) ).
fof(f467,plain,
( sQ18_eqProxy(sdtasdt0(xr,xm),sdtasdt0(xp,sK9))
| ~ spl19_24 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f694,plain,
( spl19_63
| ~ spl19_15 ),
inference(avatar_split_clause,[],[f690,f430,f692]) ).
fof(f692,plain,
( spl19_63
<=> sQ18_eqProxy(sdtasdt0(xp,sK7),sdtasdt0(xn,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_63])]) ).
fof(f430,plain,
( spl19_15
<=> sQ18_eqProxy(sdtasdt0(xn,xm),sdtasdt0(xp,sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_15])]) ).
fof(f690,plain,
( sQ18_eqProxy(sdtasdt0(xp,sK7),sdtasdt0(xn,xm))
| ~ spl19_15 ),
inference(resolution,[],[f431,f372]) ).
fof(f431,plain,
( sQ18_eqProxy(sdtasdt0(xn,xm),sdtasdt0(xp,sK7))
| ~ spl19_15 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f680,plain,
( spl19_62
| ~ spl19_4 ),
inference(avatar_split_clause,[],[f660,f386,f678]) ).
fof(f678,plain,
( spl19_62
<=> sQ18_eqProxy(sdtmndt0(xn,xp),xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_62])]) ).
fof(f386,plain,
( spl19_4
<=> sQ18_eqProxy(xr,sdtmndt0(xn,xp)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_4])]) ).
fof(f660,plain,
( sQ18_eqProxy(sdtmndt0(xn,xp),xr)
| ~ spl19_4 ),
inference(resolution,[],[f372,f387]) ).
fof(f387,plain,
( sQ18_eqProxy(xr,sdtmndt0(xn,xp))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f676,plain,
( spl19_61
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f659,f414,f674]) ).
fof(f674,plain,
( spl19_61
<=> sQ18_eqProxy(sdtpldt0(xr,sK6),xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_61])]) ).
fof(f414,plain,
( spl19_11
<=> sQ18_eqProxy(xn,sdtpldt0(xr,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_11])]) ).
fof(f659,plain,
( sQ18_eqProxy(sdtpldt0(xr,sK6),xn)
| ~ spl19_11 ),
inference(resolution,[],[f372,f415]) ).
fof(f415,plain,
( sQ18_eqProxy(xn,sdtpldt0(xr,sK6))
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f672,plain,
( spl19_60
| ~ spl19_21 ),
inference(avatar_split_clause,[],[f658,f454,f670]) ).
fof(f670,plain,
( spl19_60
<=> sQ18_eqProxy(sdtpldt0(xp,sK8),xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_60])]) ).
fof(f454,plain,
( spl19_21
<=> sQ18_eqProxy(xn,sdtpldt0(xp,sK8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_21])]) ).
fof(f658,plain,
( sQ18_eqProxy(sdtpldt0(xp,sK8),xn)
| ~ spl19_21 ),
inference(resolution,[],[f372,f455]) ).
fof(f455,plain,
( sQ18_eqProxy(xn,sdtpldt0(xp,sK8))
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f668,plain,
( spl19_59
| ~ spl19_5 ),
inference(avatar_split_clause,[],[f657,f390,f666]) ).
fof(f666,plain,
( spl19_59
<=> sQ18_eqProxy(sdtpldt0(xp,xr),xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_59])]) ).
fof(f390,plain,
( spl19_5
<=> sQ18_eqProxy(xn,sdtpldt0(xp,xr)) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_5])]) ).
fof(f657,plain,
( sQ18_eqProxy(sdtpldt0(xp,xr),xn)
| ~ spl19_5 ),
inference(resolution,[],[f372,f391]) ).
fof(f391,plain,
( sQ18_eqProxy(xn,sdtpldt0(xp,xr))
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f664,plain,
( spl19_58
| ~ spl19_1 ),
inference(avatar_split_clause,[],[f656,f375,f662]) ).
fof(f656,plain,
( sQ18_eqProxy(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ~ spl19_1 ),
inference(resolution,[],[f372,f376]) ).
fof(f654,plain,
( ~ spl19_56
| ~ spl19_40
| spl19_57 ),
inference(avatar_split_clause,[],[f652,f620,f544,f617]) ).
fof(f617,plain,
( spl19_56
<=> sP4(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_56])]) ).
fof(f544,plain,
( spl19_40
<=> sP5(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_40])]) ).
fof(f620,plain,
( spl19_57
<=> isPrime0(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_57])]) ).
fof(f652,plain,
( ~ sP4(sK9)
| ~ spl19_40
| spl19_57 ),
inference(subsumption_resolution,[],[f632,f621]) ).
fof(f621,plain,
( ~ isPrime0(sK9)
| spl19_57 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f632,plain,
( ~ sP4(sK9)
| isPrime0(sK9)
| ~ spl19_40 ),
inference(resolution,[],[f231,f545]) ).
fof(f545,plain,
( sP5(sK9)
| ~ spl19_40 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f231,plain,
! [X0] :
( ~ sP5(X0)
| ~ sP4(X0)
| isPrime0(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f651,plain,
( ~ spl19_54
| ~ spl19_39
| spl19_55 ),
inference(avatar_split_clause,[],[f649,f613,f540,f610]) ).
fof(f610,plain,
( spl19_54
<=> sP4(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_54])]) ).
fof(f540,plain,
( spl19_39
<=> sP5(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_39])]) ).
fof(f613,plain,
( spl19_55
<=> isPrime0(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_55])]) ).
fof(f649,plain,
( ~ sP4(sK8)
| ~ spl19_39
| spl19_55 ),
inference(subsumption_resolution,[],[f631,f614]) ).
fof(f614,plain,
( ~ isPrime0(sK8)
| spl19_55 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f631,plain,
( ~ sP4(sK8)
| isPrime0(sK8)
| ~ spl19_39 ),
inference(resolution,[],[f231,f541]) ).
fof(f541,plain,
( sP5(sK8)
| ~ spl19_39 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f648,plain,
( ~ spl19_52
| ~ spl19_38
| spl19_53 ),
inference(avatar_split_clause,[],[f646,f606,f536,f603]) ).
fof(f603,plain,
( spl19_52
<=> sP4(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_52])]) ).
fof(f536,plain,
( spl19_38
<=> sP5(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_38])]) ).
fof(f606,plain,
( spl19_53
<=> isPrime0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_53])]) ).
fof(f646,plain,
( ~ sP4(sK7)
| ~ spl19_38
| spl19_53 ),
inference(subsumption_resolution,[],[f630,f607]) ).
fof(f607,plain,
( ~ isPrime0(sK7)
| spl19_53 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f630,plain,
( ~ sP4(sK7)
| isPrime0(sK7)
| ~ spl19_38 ),
inference(resolution,[],[f231,f537]) ).
fof(f537,plain,
( sP5(sK7)
| ~ spl19_38 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f645,plain,
( ~ spl19_50
| ~ spl19_37
| spl19_51 ),
inference(avatar_split_clause,[],[f643,f599,f532,f596]) ).
fof(f596,plain,
( spl19_50
<=> sP4(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_50])]) ).
fof(f532,plain,
( spl19_37
<=> sP5(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_37])]) ).
fof(f599,plain,
( spl19_51
<=> isPrime0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_51])]) ).
fof(f643,plain,
( ~ sP4(sK6)
| ~ spl19_37
| spl19_51 ),
inference(subsumption_resolution,[],[f629,f600]) ).
fof(f600,plain,
( ~ isPrime0(sK6)
| spl19_51 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f629,plain,
( ~ sP4(sK6)
| isPrime0(sK6)
| ~ spl19_37 ),
inference(resolution,[],[f231,f533]) ).
fof(f533,plain,
( sP5(sK6)
| ~ spl19_37 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f642,plain,
( ~ spl19_48
| ~ spl19_36
| spl19_49 ),
inference(avatar_split_clause,[],[f640,f592,f528,f589]) ).
fof(f589,plain,
( spl19_48
<=> sP4(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_48])]) ).
fof(f528,plain,
( spl19_36
<=> sP5(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_36])]) ).
fof(f592,plain,
( spl19_49
<=> isPrime0(xr) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_49])]) ).
fof(f640,plain,
( ~ sP4(xr)
| ~ spl19_36
| spl19_49 ),
inference(subsumption_resolution,[],[f628,f593]) ).
fof(f593,plain,
( ~ isPrime0(xr)
| spl19_49 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f628,plain,
( ~ sP4(xr)
| isPrime0(xr)
| ~ spl19_36 ),
inference(resolution,[],[f231,f529]) ).
fof(f529,plain,
( sP5(xr)
| ~ spl19_36 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f639,plain,
( ~ spl19_45
| ~ spl19_34
| spl19_46 ),
inference(avatar_split_clause,[],[f637,f580,f520,f577]) ).
fof(f577,plain,
( spl19_45
<=> sP4(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_45])]) ).
fof(f520,plain,
( spl19_34
<=> sP5(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_34])]) ).
fof(f580,plain,
( spl19_46
<=> isPrime0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_46])]) ).
fof(f637,plain,
( ~ sP4(xm)
| ~ spl19_34
| spl19_46 ),
inference(subsumption_resolution,[],[f626,f581]) ).
fof(f581,plain,
( ~ isPrime0(xm)
| spl19_46 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f626,plain,
( ~ sP4(xm)
| isPrime0(xm)
| ~ spl19_34 ),
inference(resolution,[],[f231,f521]) ).
fof(f521,plain,
( sP5(xm)
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f636,plain,
( ~ spl19_43
| ~ spl19_33
| spl19_44 ),
inference(avatar_split_clause,[],[f634,f573,f516,f570]) ).
fof(f570,plain,
( spl19_43
<=> sP4(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_43])]) ).
fof(f516,plain,
( spl19_33
<=> sP5(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_33])]) ).
fof(f573,plain,
( spl19_44
<=> isPrime0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_44])]) ).
fof(f634,plain,
( ~ sP4(xn)
| ~ spl19_33
| spl19_44 ),
inference(subsumption_resolution,[],[f625,f574]) ).
fof(f574,plain,
( ~ isPrime0(xn)
| spl19_44 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f625,plain,
( ~ sP4(xn)
| isPrime0(xn)
| ~ spl19_33 ),
inference(resolution,[],[f231,f517]) ).
fof(f517,plain,
( sP5(xn)
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f622,plain,
( spl19_56
| ~ spl19_57
| ~ spl19_40 ),
inference(avatar_split_clause,[],[f557,f544,f620,f617]) ).
fof(f557,plain,
( ~ isPrime0(sK9)
| sP4(sK9)
| ~ spl19_40 ),
inference(resolution,[],[f230,f545]) ).
fof(f615,plain,
( spl19_54
| ~ spl19_55
| ~ spl19_39 ),
inference(avatar_split_clause,[],[f556,f540,f613,f610]) ).
fof(f556,plain,
( ~ isPrime0(sK8)
| sP4(sK8)
| ~ spl19_39 ),
inference(resolution,[],[f230,f541]) ).
fof(f608,plain,
( spl19_52
| ~ spl19_53
| ~ spl19_38 ),
inference(avatar_split_clause,[],[f555,f536,f606,f603]) ).
fof(f555,plain,
( ~ isPrime0(sK7)
| sP4(sK7)
| ~ spl19_38 ),
inference(resolution,[],[f230,f537]) ).
fof(f601,plain,
( spl19_50
| ~ spl19_51
| ~ spl19_37 ),
inference(avatar_split_clause,[],[f554,f532,f599,f596]) ).
fof(f554,plain,
( ~ isPrime0(sK6)
| sP4(sK6)
| ~ spl19_37 ),
inference(resolution,[],[f230,f533]) ).
fof(f594,plain,
( spl19_48
| ~ spl19_49
| ~ spl19_36 ),
inference(avatar_split_clause,[],[f553,f528,f592,f589]) ).
fof(f553,plain,
( ~ isPrime0(xr)
| sP4(xr)
| ~ spl19_36 ),
inference(resolution,[],[f230,f529]) ).
fof(f587,plain,
( spl19_47
| ~ spl19_17
| ~ spl19_35 ),
inference(avatar_split_clause,[],[f583,f524,f438,f585]) ).
fof(f585,plain,
( spl19_47
<=> sP4(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_47])]) ).
fof(f438,plain,
( spl19_17
<=> isPrime0(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_17])]) ).
fof(f524,plain,
( spl19_35
<=> sP5(xp) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_35])]) ).
fof(f583,plain,
( sP4(xp)
| ~ spl19_17
| ~ spl19_35 ),
inference(subsumption_resolution,[],[f552,f439]) ).
fof(f439,plain,
( isPrime0(xp)
| ~ spl19_17 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f552,plain,
( ~ isPrime0(xp)
| sP4(xp)
| ~ spl19_35 ),
inference(resolution,[],[f230,f525]) ).
fof(f525,plain,
( sP5(xp)
| ~ spl19_35 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f582,plain,
( spl19_45
| ~ spl19_46
| ~ spl19_34 ),
inference(avatar_split_clause,[],[f551,f520,f580,f577]) ).
fof(f551,plain,
( ~ isPrime0(xm)
| sP4(xm)
| ~ spl19_34 ),
inference(resolution,[],[f230,f521]) ).
fof(f575,plain,
( spl19_43
| ~ spl19_44
| ~ spl19_33 ),
inference(avatar_split_clause,[],[f550,f516,f573,f570]) ).
fof(f550,plain,
( ~ isPrime0(xn)
| sP4(xn)
| ~ spl19_33 ),
inference(resolution,[],[f230,f517]) ).
fof(f568,plain,
( ~ spl19_42
| spl19_29
| ~ spl19_32 ),
inference(avatar_split_clause,[],[f564,f512,f486,f566]) ).
fof(f566,plain,
( spl19_42
<=> isPrime0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_42])]) ).
fof(f486,plain,
( spl19_29
<=> sP4(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_29])]) ).
fof(f512,plain,
( spl19_32
<=> sP5(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_32])]) ).
fof(f564,plain,
( ~ isPrime0(sz10)
| spl19_29
| ~ spl19_32 ),
inference(subsumption_resolution,[],[f549,f487]) ).
fof(f487,plain,
( ~ sP4(sz10)
| spl19_29 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f549,plain,
( ~ isPrime0(sz10)
| sP4(sz10)
| ~ spl19_32 ),
inference(resolution,[],[f230,f513]) ).
fof(f513,plain,
( sP5(sz10)
| ~ spl19_32 ),
inference(avatar_component_clause,[],[f512]) ).
fof(f563,plain,
( ~ spl19_41
| spl19_30
| ~ spl19_31 ),
inference(avatar_split_clause,[],[f559,f508,f490,f561]) ).
fof(f561,plain,
( spl19_41
<=> isPrime0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_41])]) ).
fof(f490,plain,
( spl19_30
<=> sP4(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_30])]) ).
fof(f508,plain,
( spl19_31
<=> sP5(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_31])]) ).
fof(f559,plain,
( ~ isPrime0(sz00)
| spl19_30
| ~ spl19_31 ),
inference(subsumption_resolution,[],[f548,f491]) ).
fof(f491,plain,
( ~ sP4(sz00)
| spl19_30 ),
inference(avatar_component_clause,[],[f490]) ).
fof(f548,plain,
( ~ isPrime0(sz00)
| sP4(sz00)
| ~ spl19_31 ),
inference(resolution,[],[f230,f509]) ).
fof(f509,plain,
( sP5(sz00)
| ~ spl19_31 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f546,plain,
( spl19_40
| ~ spl19_25 ),
inference(avatar_split_clause,[],[f506,f470,f544]) ).
fof(f470,plain,
( spl19_25
<=> aNaturalNumber0(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_25])]) ).
fof(f506,plain,
( sP5(sK9)
| ~ spl19_25 ),
inference(resolution,[],[f239,f471]) ).
fof(f471,plain,
( aNaturalNumber0(sK9)
| ~ spl19_25 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f542,plain,
( spl19_39
| ~ spl19_22 ),
inference(avatar_split_clause,[],[f505,f458,f540]) ).
fof(f458,plain,
( spl19_22
<=> aNaturalNumber0(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_22])]) ).
fof(f505,plain,
( sP5(sK8)
| ~ spl19_22 ),
inference(resolution,[],[f239,f459]) ).
fof(f459,plain,
( aNaturalNumber0(sK8)
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f538,plain,
( spl19_38
| ~ spl19_16 ),
inference(avatar_split_clause,[],[f504,f434,f536]) ).
fof(f434,plain,
( spl19_16
<=> aNaturalNumber0(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_16])]) ).
fof(f504,plain,
( sP5(sK7)
| ~ spl19_16 ),
inference(resolution,[],[f239,f435]) ).
fof(f435,plain,
( aNaturalNumber0(sK7)
| ~ spl19_16 ),
inference(avatar_component_clause,[],[f434]) ).
fof(f534,plain,
( spl19_37
| ~ spl19_12 ),
inference(avatar_split_clause,[],[f503,f418,f532]) ).
fof(f418,plain,
( spl19_12
<=> aNaturalNumber0(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_12])]) ).
fof(f503,plain,
( sP5(sK6)
| ~ spl19_12 ),
inference(resolution,[],[f239,f419]) ).
fof(f419,plain,
( aNaturalNumber0(sK6)
| ~ spl19_12 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f530,plain,
( spl19_36
| ~ spl19_6 ),
inference(avatar_split_clause,[],[f502,f394,f528]) ).
fof(f502,plain,
( sP5(xr)
| ~ spl19_6 ),
inference(resolution,[],[f239,f395]) ).
fof(f526,plain,
( spl19_35
| ~ spl19_7 ),
inference(avatar_split_clause,[],[f501,f398,f524]) ).
fof(f501,plain,
( sP5(xp)
| ~ spl19_7 ),
inference(resolution,[],[f239,f399]) ).
fof(f522,plain,
( spl19_34
| ~ spl19_8 ),
inference(avatar_split_clause,[],[f500,f402,f520]) ).
fof(f500,plain,
( sP5(xm)
| ~ spl19_8 ),
inference(resolution,[],[f239,f403]) ).
fof(f518,plain,
( spl19_33
| ~ spl19_9 ),
inference(avatar_split_clause,[],[f499,f406,f516]) ).
fof(f499,plain,
( sP5(xn)
| ~ spl19_9 ),
inference(resolution,[],[f239,f407]) ).
fof(f514,plain,
( spl19_32
| ~ spl19_28 ),
inference(avatar_split_clause,[],[f498,f482,f512]) ).
fof(f498,plain,
( sP5(sz10)
| ~ spl19_28 ),
inference(resolution,[],[f239,f483]) ).
fof(f510,plain,
( spl19_31
| ~ spl19_26 ),
inference(avatar_split_clause,[],[f497,f474,f508]) ).
fof(f474,plain,
( spl19_26
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_26])]) ).
fof(f497,plain,
( sP5(sz00)
| ~ spl19_26 ),
inference(resolution,[],[f239,f475]) ).
fof(f475,plain,
( aNaturalNumber0(sz00)
| ~ spl19_26 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f492,plain,
~ spl19_30,
inference(avatar_split_clause,[],[f289,f490]) ).
fof(f289,plain,
~ sP4(sz00),
inference(equality_resolution,[],[f232]) ).
fof(f232,plain,
! [X0] :
( sz00 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f488,plain,
~ spl19_29,
inference(avatar_split_clause,[],[f288,f486]) ).
fof(f288,plain,
~ sP4(sz10),
inference(equality_resolution,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sz10 != X0
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f158]) ).
fof(f484,plain,
spl19_28,
inference(avatar_split_clause,[],[f217,f482]) ).
fof(f217,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mSortsC_01) ).
fof(f480,plain,
~ spl19_27,
inference(avatar_split_clause,[],[f321,f478]) ).
fof(f478,plain,
( spl19_27
<=> sQ18_eqProxy(sz00,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_27])]) ).
fof(f321,plain,
~ sQ18_eqProxy(sz00,sz10),
inference(equality_proxy_replacement,[],[f218,f299]) ).
fof(f218,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f476,plain,
spl19_26,
inference(avatar_split_clause,[],[f216,f474]) ).
fof(f216,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',mSortsC) ).
fof(f472,plain,
spl19_25,
inference(avatar_split_clause,[],[f196,f470]) ).
fof(f196,plain,
aNaturalNumber0(sK9),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( doDivides0(xp,sdtasdt0(xr,xm))
& sdtasdt0(xr,xm) = sdtasdt0(xp,sK9)
& aNaturalNumber0(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f45,f135]) ).
fof(f135,plain,
( ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xr,xm)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(xr,xm) = sdtasdt0(xp,sK9)
& aNaturalNumber0(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f45,axiom,
( doDivides0(xp,sdtasdt0(xr,xm))
& ? [X0] :
( sdtasdt0(xp,X0) = sdtasdt0(xr,xm)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1913) ).
fof(f468,plain,
spl19_24,
inference(avatar_split_clause,[],[f312,f466]) ).
fof(f312,plain,
sQ18_eqProxy(sdtasdt0(xr,xm),sdtasdt0(xp,sK9)),
inference(equality_proxy_replacement,[],[f197,f299]) ).
fof(f197,plain,
sdtasdt0(xr,xm) = sdtasdt0(xp,sK9),
inference(cnf_transformation,[],[f136]) ).
fof(f464,plain,
spl19_23,
inference(avatar_split_clause,[],[f198,f462]) ).
fof(f198,plain,
doDivides0(xp,sdtasdt0(xr,xm)),
inference(cnf_transformation,[],[f136]) ).
fof(f460,plain,
spl19_22,
inference(avatar_split_clause,[],[f193,f458]) ).
fof(f193,plain,
aNaturalNumber0(sK8),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( sdtlseqdt0(xp,xn)
& xn = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f42,f133]) ).
fof(f133,plain,
( ? [X0] :
( xn = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtpldt0(xp,sK8)
& aNaturalNumber0(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f42,axiom,
( sdtlseqdt0(xp,xn)
& ? [X0] :
( xn = sdtpldt0(xp,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1870) ).
fof(f456,plain,
spl19_21,
inference(avatar_split_clause,[],[f311,f454]) ).
fof(f311,plain,
sQ18_eqProxy(xn,sdtpldt0(xp,sK8)),
inference(equality_proxy_replacement,[],[f194,f299]) ).
fof(f194,plain,
xn = sdtpldt0(xp,sK8),
inference(cnf_transformation,[],[f134]) ).
fof(f452,plain,
spl19_20,
inference(avatar_split_clause,[],[f195,f450]) ).
fof(f195,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[],[f134]) ).
fof(f448,plain,
~ spl19_19,
inference(avatar_split_clause,[],[f310,f446]) ).
fof(f310,plain,
~ sQ18_eqProxy(sz00,xp),
inference(equality_proxy_replacement,[],[f185,f299]) ).
fof(f185,plain,
sz00 != xp,
inference(cnf_transformation,[],[f132]) ).
fof(f444,plain,
~ spl19_18,
inference(avatar_split_clause,[],[f309,f442]) ).
fof(f309,plain,
~ sQ18_eqProxy(sz10,xp),
inference(equality_proxy_replacement,[],[f186,f299]) ).
fof(f186,plain,
sz10 != xp,
inference(cnf_transformation,[],[f132]) ).
fof(f440,plain,
spl19_17,
inference(avatar_split_clause,[],[f189,f438]) ).
fof(f189,plain,
isPrime0(xp),
inference(cnf_transformation,[],[f132]) ).
fof(f436,plain,
spl19_16,
inference(avatar_split_clause,[],[f190,f434]) ).
fof(f190,plain,
aNaturalNumber0(sK7),
inference(cnf_transformation,[],[f132]) ).
fof(f432,plain,
spl19_15,
inference(avatar_split_clause,[],[f306,f430]) ).
fof(f306,plain,
sQ18_eqProxy(sdtasdt0(xn,xm),sdtasdt0(xp,sK7)),
inference(equality_proxy_replacement,[],[f191,f299]) ).
fof(f191,plain,
sdtasdt0(xn,xm) = sdtasdt0(xp,sK7),
inference(cnf_transformation,[],[f132]) ).
fof(f428,plain,
spl19_14,
inference(avatar_split_clause,[],[f192,f426]) ).
fof(f192,plain,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(cnf_transformation,[],[f132]) ).
fof(f424,plain,
~ spl19_13,
inference(avatar_split_clause,[],[f305,f422]) ).
fof(f305,plain,
~ sQ18_eqProxy(xn,xr),
inference(equality_proxy_replacement,[],[f181,f299]) ).
fof(f181,plain,
xn != xr,
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
( sdtlseqdt0(xr,xn)
& xn = sdtpldt0(xr,sK6)
& aNaturalNumber0(sK6)
& xn != xr ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f44,f129]) ).
fof(f129,plain,
( ? [X0] :
( xn = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtpldt0(xr,sK6)
& aNaturalNumber0(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f44,axiom,
( sdtlseqdt0(xr,xn)
& ? [X0] :
( xn = sdtpldt0(xr,X0)
& aNaturalNumber0(X0) )
& xn != xr ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1894) ).
fof(f420,plain,
spl19_12,
inference(avatar_split_clause,[],[f182,f418]) ).
fof(f182,plain,
aNaturalNumber0(sK6),
inference(cnf_transformation,[],[f130]) ).
fof(f416,plain,
spl19_11,
inference(avatar_split_clause,[],[f304,f414]) ).
fof(f304,plain,
sQ18_eqProxy(xn,sdtpldt0(xr,sK6)),
inference(equality_proxy_replacement,[],[f183,f299]) ).
fof(f183,plain,
xn = sdtpldt0(xr,sK6),
inference(cnf_transformation,[],[f130]) ).
fof(f412,plain,
spl19_10,
inference(avatar_split_clause,[],[f184,f410]) ).
fof(f184,plain,
sdtlseqdt0(xr,xn),
inference(cnf_transformation,[],[f130]) ).
fof(f408,plain,
spl19_9,
inference(avatar_split_clause,[],[f178,f406]) ).
fof(f178,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1837) ).
fof(f404,plain,
spl19_8,
inference(avatar_split_clause,[],[f179,f402]) ).
fof(f179,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f39]) ).
fof(f400,plain,
spl19_7,
inference(avatar_split_clause,[],[f180,f398]) ).
fof(f180,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[],[f39]) ).
fof(f396,plain,
spl19_6,
inference(avatar_split_clause,[],[f175,f394]) ).
fof(f175,plain,
aNaturalNumber0(xr),
inference(cnf_transformation,[],[f43]) ).
fof(f43,axiom,
( xr = sdtmndt0(xn,xp)
& xn = sdtpldt0(xp,xr)
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__1883) ).
fof(f392,plain,
spl19_5,
inference(avatar_split_clause,[],[f303,f390]) ).
fof(f303,plain,
sQ18_eqProxy(xn,sdtpldt0(xp,xr)),
inference(equality_proxy_replacement,[],[f176,f299]) ).
fof(f176,plain,
xn = sdtpldt0(xp,xr),
inference(cnf_transformation,[],[f43]) ).
fof(f388,plain,
spl19_4,
inference(avatar_split_clause,[],[f302,f386]) ).
fof(f302,plain,
sQ18_eqProxy(xr,sdtmndt0(xn,xp)),
inference(equality_proxy_replacement,[],[f177,f299]) ).
fof(f177,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[],[f43]) ).
fof(f384,plain,
( spl19_1
| spl19_3 ),
inference(avatar_split_clause,[],[f301,f382,f375]) ).
fof(f382,plain,
( spl19_3
<=> ! [X0] :
( ~ sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl19_3])]) ).
fof(f301,plain,
! [X0] :
( ~ sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0))
| ~ aNaturalNumber0(X0)
| sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(equality_proxy_replacement,[],[f173,f299,f299]) ).
fof(f173,plain,
! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
| ~ aNaturalNumber0(X0)
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
( ( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
& ! [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
| ~ aNaturalNumber0(X0) ) )
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,negated_conjecture,
~ ( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(negated_conjecture,[],[f46]) ).
fof(f46,conjecture,
( ( sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| ? [X0] :
( sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(sdtpldt0(xr,xm),xp),X0)
& aNaturalNumber0(X0) ) )
& sdtpldt0(sdtpldt0(xn,xm),xp) != sdtpldt0(sdtpldt0(xr,xm),xp) ),
file('/export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850',m__) ).
fof(f380,plain,
( spl19_1
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f300,f378,f375]) ).
fof(f300,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sQ18_eqProxy(sdtpldt0(sdtpldt0(xn,xm),xp),sdtpldt0(sdtpldt0(xr,xm),xp)) ),
inference(equality_proxy_replacement,[],[f174,f299]) ).
fof(f174,plain,
( ~ sdtlseqdt0(sdtpldt0(sdtpldt0(xr,xm),xp),sdtpldt0(sdtpldt0(xn,xm),xp))
| sdtpldt0(sdtpldt0(xn,xm),xp) = sdtpldt0(sdtpldt0(xr,xm),xp) ),
inference(cnf_transformation,[],[f52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM494+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Aug 25 15:35:22 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.VnCC10RGHF/Vampire---4.8_18850
% 0.15/0.37 % (18958)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.43 % (18963)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.22/0.43 % (18959)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.22/0.43 % (18964)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.22/0.43 % (18962)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.22/0.43 % (18960)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.22/0.43 % (18961)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.22/0.43 % (18965)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.22/0.52 % (18965)First to succeed.
% 0.22/0.53 % (18965)Refutation found. Thanks to Tanya!
% 0.22/0.53 % SZS status Theorem for Vampire---4
% 0.22/0.53 % SZS output start Proof for Vampire---4
% See solution above
% 0.22/0.53 % (18965)------------------------------
% 0.22/0.53 % (18965)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.22/0.53 % (18965)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.22/0.53 % (18965)Termination reason: Refutation
% 0.22/0.53
% 0.22/0.53 % (18965)Memory used [KB]: 1663
% 0.22/0.53 % (18965)Time elapsed: 0.099 s
% 0.22/0.53 % (18965)------------------------------
% 0.22/0.53 % (18965)------------------------------
% 0.22/0.53 % (18958)Success in time 0.165 s
% 0.22/0.53 % Vampire---4.8 exiting
%------------------------------------------------------------------------------