TSTP Solution File: COM141+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM141+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:34 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 339
% Syntax : Number of formulae : 1215 ( 181 unt; 0 def)
% Number of atoms : 4494 (2165 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 4925 (1646 ~;2065 |; 761 &)
% ( 248 <=>; 205 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 269 ( 267 usr; 249 prp; 0-4 aty)
% Number of functors : 97 ( 97 usr; 10 con; 0-4 aty)
% Number of variables : 4128 (3558 !; 570 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2640,plain,
$false,
inference(avatar_sat_refutation,[],[f564,f569,f574,f579,f584,f588,f592,f596,f600,f604,f608,f612,f616,f620,f624,f628,f632,f636,f640,f644,f648,f652,f656,f660,f664,f668,f672,f676,f680,f684,f688,f692,f696,f700,f705,f709,f713,f717,f721,f725,f734,f738,f742,f746,f750,f754,f758,f762,f766,f774,f778,f782,f786,f790,f794,f798,f802,f806,f810,f814,f818,f831,f837,f841,f845,f849,f853,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f921,f925,f940,f944,f948,f952,f956,f960,f964,f974,f978,f982,f988,f995,f999,f1003,f1013,f1017,f1021,f1034,f1038,f1042,f1046,f1050,f1054,f1058,f1062,f1066,f1070,f1074,f1109,f1113,f1126,f1130,f1138,f1142,f1146,f1150,f1154,f1158,f1162,f1167,f1180,f1184,f1200,f1204,f1208,f1226,f1236,f1240,f1244,f1249,f1253,f1257,f1261,f1265,f1279,f1288,f1298,f1308,f1312,f1316,f1326,f1335,f1339,f1343,f1363,f1378,f1383,f1395,f1402,f1409,f1418,f1424,f1442,f1448,f1453,f1467,f1472,f1476,f1484,f1490,f1494,f1498,f1502,f1506,f1510,f1587,f1620,f1625,f1629,f1649,f1663,f1667,f1688,f1692,f1742,f1747,f1751,f1755,f1824,f1828,f1832,f1836,f1840,f1849,f1892,f1906,f1911,f1915,f1949,f1965,f1980,f1996,f2001,f2011,f2014,f2018,f2036,f2040,f2044,f2051,f2055,f2080,f2084,f2109,f2113,f2119,f2163,f2176,f2180,f2184,f2188,f2222,f2264,f2268,f2272,f2276,f2354,f2366,f2370,f2374,f2378,f2383,f2460,f2470,f2474,f2478,f2513,f2517,f2527,f2531,f2547,f2551,f2556,f2560,f2571,f2578,f2582,f2610,f2614,f2624,f2628,f2639]) ).
fof(f2639,plain,
( ~ spl94_207
| ~ spl94_155
| spl94_238 ),
inference(avatar_split_clause,[],[f2583,f2544,f1400,f2048]) ).
fof(f2048,plain,
( spl94_207
<=> vtcheck(sK16,vabs(sK14,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_207])]) ).
fof(f1400,plain,
( spl94_155
<=> ! [X2,X0,X1] :
( ~ vtcheck(sK16,vabs(sK14,X0,veabs),X1)
| vtcheck(vbind(sK14,X2,sK16),vabs(sK14,X0,veabs),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_155])]) ).
fof(f2544,plain,
( spl94_238
<=> vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_238])]) ).
fof(f2583,plain,
( ~ vtcheck(sK16,vabs(sK14,sK18,veabs),sK19)
| ~ spl94_155
| spl94_238 ),
inference(resolution,[],[f2546,f1401]) ).
fof(f1401,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(sK14,X2,sK16),vabs(sK14,X0,veabs),X1)
| ~ vtcheck(sK16,vabs(sK14,X0,veabs),X1) )
| ~ spl94_155 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f2546,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19)
| spl94_238 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f2628,plain,
( spl94_248
| ~ spl94_61
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1358,f1341,f816,f2626]) ).
fof(f2626,plain,
( spl94_248
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK85(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_248])]) ).
fof(f816,plain,
( spl94_61
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_61])]) ).
fof(f1341,plain,
( spl94_150
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_150])]) ).
fof(f1358,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK85(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_61
| ~ spl94_150 ),
inference(superposition,[],[f1342,f817]) ).
fof(f817,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl94_61 ),
inference(avatar_component_clause,[],[f816]) ).
fof(f1342,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl94_150 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f2624,plain,
( spl94_247
| ~ spl94_61
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1350,f1337,f816,f2622]) ).
fof(f2622,plain,
( spl94_247
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK86(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_247])]) ).
fof(f1337,plain,
( spl94_149
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK86(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_149])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK86(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_61
| ~ spl94_149 ),
inference(superposition,[],[f1338,f817]) ).
fof(f1338,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK86(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl94_149 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f2614,plain,
( spl94_246
| ~ spl94_34
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1372,f1361,f698,f2612]) ).
fof(f2612,plain,
( spl94_246
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK84(X0,X1,vvar(X0),X1),sK87(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_246])]) ).
fof(f698,plain,
( spl94_34
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_34])]) ).
fof(f1361,plain,
( spl94_151
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_151])]) ).
fof(f1372,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK84(X0,X1,vvar(X0),X1),sK87(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl94_34
| ~ spl94_151 ),
inference(superposition,[],[f1362,f699]) ).
fof(f699,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl94_34 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f1362,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl94_151 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f2610,plain,
( spl94_245
| ~ spl94_101
| ~ spl94_124 ),
inference(avatar_split_clause,[],[f1170,f1152,f1015,f2608]) ).
fof(f2608,plain,
( spl94_245
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK52(sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_245])]) ).
fof(f1015,plain,
( spl94_101
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_101])]) ).
fof(f1152,plain,
( spl94_124
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK52(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_124])]) ).
fof(f1170,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK52(sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_101
| ~ spl94_124 ),
inference(resolution,[],[f1153,f1016]) ).
fof(f1016,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) )
| ~ spl94_101 ),
inference(avatar_component_clause,[],[f1015]) ).
fof(f1153,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK52(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl94_124 ),
inference(avatar_component_clause,[],[f1152]) ).
fof(f2582,plain,
( spl94_244
| ~ spl94_39
| ~ spl94_146 ),
inference(avatar_split_clause,[],[f1321,f1314,f719,f2580]) ).
fof(f2580,plain,
( spl94_244
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_244])]) ).
fof(f719,plain,
( spl94_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_39])]) ).
fof(f1314,plain,
( spl94_146
<=> ! [X5,X4,X9,X7,X6] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9))
| ~ visFreeVar(X7,X5)
| X4 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_146])]) ).
fof(f1321,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X2) )
| ~ spl94_39
| ~ spl94_146 ),
inference(resolution,[],[f1315,f720]) ).
fof(f720,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl94_39 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f1315,plain,
( ! [X6,X9,X7,X4,X5] :
( ~ visFreeVar(X7,X5)
| vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9))
| X4 = X7 )
| ~ spl94_146 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f2578,plain,
( spl94_243
| ~ spl94_40
| ~ spl94_146 ),
inference(avatar_split_clause,[],[f1320,f1314,f723,f2576]) ).
fof(f2576,plain,
( spl94_243
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_243])]) ).
fof(f723,plain,
( spl94_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_40])]) ).
fof(f1320,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X1) )
| ~ spl94_40
| ~ spl94_146 ),
inference(resolution,[],[f1315,f724]) ).
fof(f724,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl94_40 ),
inference(avatar_component_clause,[],[f723]) ).
fof(f2571,plain,
( spl94_242
| ~ spl94_16
| ~ spl94_147 ),
inference(avatar_split_clause,[],[f1330,f1324,f626,f2569]) ).
fof(f2569,plain,
( spl94_242
<=> ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK41(vvar(X0),vnoExp),sK42(vvar(X0),vnoExp),sK43(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK44(vvar(X0),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_242])]) ).
fof(f626,plain,
( spl94_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_16])]) ).
fof(f1324,plain,
( spl94_147
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0))) = X0
| vvar(sK44(X0,vreduce(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_147])]) ).
fof(f1330,plain,
( ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK41(vvar(X0),vnoExp),sK42(vvar(X0),vnoExp),sK43(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK44(vvar(X0),vnoExp)) )
| ~ spl94_16
| ~ spl94_147 ),
inference(superposition,[],[f1325,f627]) ).
fof(f627,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl94_16 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f1325,plain,
( ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0))) = X0
| vvar(sK44(X0,vreduce(X0))) = X0 )
| ~ spl94_147 ),
inference(avatar_component_clause,[],[f1324]) ).
fof(f2560,plain,
( spl94_241
| ~ spl94_101
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1270,f1259,f1015,f2558]) ).
fof(f2558,plain,
( spl94_241
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK45(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_241])]) ).
fof(f1259,plain,
( spl94_140
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_140])]) ).
fof(f1270,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK45(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl94_101
| ~ spl94_140 ),
inference(resolution,[],[f1260,f1016]) ).
fof(f1260,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2 )
| ~ spl94_140 ),
inference(avatar_component_clause,[],[f1259]) ).
fof(f2556,plain,
( spl94_240
| ~ spl94_106
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1222,f1206,f1036,f2554]) ).
fof(f2554,plain,
( spl94_240
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( vabs(sK62(X0,X1,X2,X3),X4,vsubst(X5,sK65(X0,X1,X2,X3),X6)) = vsubst(X5,sK65(X0,X1,X2,X3),vabs(sK62(X0,X1,X2,X3),X4,X6))
| sK62(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_240])]) ).
fof(f1036,plain,
( spl94_106
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_106])]) ).
fof(f1206,plain,
( spl94_132
<=> ! [X6,X4,X7,X5,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X6,X7,vabs(X4,X5,X8))
| visFreeVar(X4,X7)
| X4 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_132])]) ).
fof(f1222,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vabs(sK62(X0,X1,X2,X3),X4,vsubst(X5,sK65(X0,X1,X2,X3),X6)) = vsubst(X5,sK65(X0,X1,X2,X3),vabs(sK62(X0,X1,X2,X3),X4,X6))
| sK62(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) )
| ~ spl94_106
| ~ spl94_132 ),
inference(resolution,[],[f1207,f1037]) ).
fof(f1037,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) )
| ~ spl94_106 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1207,plain,
( ! [X8,X6,X7,X4,X5] :
( visFreeVar(X4,X7)
| vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X6,X7,vabs(X4,X5,X8))
| X4 = X6 )
| ~ spl94_132 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f2551,plain,
( spl94_239
| ~ spl94_94
| ~ spl94_131 ),
inference(avatar_split_clause,[],[f1210,f1202,f976,f2549]) ).
fof(f2549,plain,
( spl94_239
<=> ! [X2,X0,X1] :
( sP5(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| vsomeType(sK47(X0,X1,X2)) = vlookup(sK52(sK46(X0,X1,X2),sK47(X0,X1,X2),X0),X0)
| sP6(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_239])]) ).
fof(f976,plain,
( spl94_94
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_94])]) ).
fof(f1202,plain,
( spl94_131
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK52(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_131])]) ).
fof(f1210,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| vsomeType(sK47(X0,X1,X2)) = vlookup(sK52(sK46(X0,X1,X2),sK47(X0,X1,X2),X0),X0)
| sP6(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_94
| ~ spl94_131 ),
inference(resolution,[],[f1203,f977]) ).
fof(f977,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_94 ),
inference(avatar_component_clause,[],[f976]) ).
fof(f1203,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK52(X0,X1,X2),X2)
| sP6(X2,X1,X0) )
| ~ spl94_131 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f2547,plain,
( ~ spl94_238
| spl94_5
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f1844,f1744,f581,f2544]) ).
fof(f581,plain,
( spl94_5
<=> vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_5])]) ).
fof(f1744,plain,
( spl94_184
<=> sK14 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_184])]) ).
fof(f1844,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19)
| spl94_5
| ~ spl94_184 ),
inference(superposition,[],[f583,f1746]) ).
fof(f1746,plain,
( sK14 = sK17
| ~ spl94_184 ),
inference(avatar_component_clause,[],[f1744]) ).
fof(f583,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
| spl94_5 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f2531,plain,
( spl94_237
| ~ spl94_94
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1269,f1259,f976,f2529]) ).
fof(f2529,plain,
( spl94_237
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_237])]) ).
fof(f1269,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl94_94
| ~ spl94_140 ),
inference(resolution,[],[f1260,f977]) ).
fof(f2527,plain,
( spl94_236
| ~ spl94_113
| ~ spl94_131 ),
inference(avatar_split_clause,[],[f1212,f1202,f1064,f2525]) ).
fof(f2525,plain,
( spl94_236
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK52(vabs(X3,X1,X4),varrow(X1,X2),X0),X0)
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_236])]) ).
fof(f1064,plain,
( spl94_113
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_113])]) ).
fof(f1212,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK52(vabs(X3,X1,X4),varrow(X1,X2),X0),X0)
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl94_113
| ~ spl94_131 ),
inference(resolution,[],[f1203,f1065]) ).
fof(f1065,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) )
| ~ spl94_113 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f2517,plain,
( spl94_235
| ~ spl94_113
| ~ spl94_124 ),
inference(avatar_split_clause,[],[f1171,f1152,f1064,f2515]) ).
fof(f2515,plain,
( spl94_235
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK52(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_235])]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK52(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl94_113
| ~ spl94_124 ),
inference(resolution,[],[f1153,f1065]) ).
fof(f2513,plain,
( spl94_234
| ~ spl94_94
| ~ spl94_124 ),
inference(avatar_split_clause,[],[f1169,f1152,f976,f2511]) ).
fof(f2511,plain,
( spl94_234
<=> ! [X2,X0,X1] :
( sP5(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| sK46(X0,X1,X2) = vvar(sK52(sK46(X0,X1,X2),sK47(X0,X1,X2),X0))
| sP6(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_234])]) ).
fof(f1169,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| sK46(X0,X1,X2) = vvar(sK52(sK46(X0,X1,X2),sK47(X0,X1,X2),X0))
| sP6(X0,sK47(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_94
| ~ spl94_124 ),
inference(resolution,[],[f1153,f977]) ).
fof(f2478,plain,
( spl94_233
| ~ spl94_34
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1357,f1341,f698,f2476]) ).
fof(f2476,plain,
( spl94_233
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK85(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_233])]) ).
fof(f1357,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK85(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl94_34
| ~ spl94_150 ),
inference(superposition,[],[f1342,f699]) ).
fof(f2474,plain,
( spl94_232
| ~ spl94_34
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1349,f1337,f698,f2472]) ).
fof(f2472,plain,
( spl94_232
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK86(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_232])]) ).
fof(f1349,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK86(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl94_34
| ~ spl94_149 ),
inference(superposition,[],[f1338,f699]) ).
fof(f2470,plain,
( spl94_231
| ~ spl94_13
| ~ spl94_146 ),
inference(avatar_split_clause,[],[f1318,f1314,f614,f2468]) ).
fof(f2468,plain,
( spl94_231
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,vvar(X1),vabs(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0))),X3,vsubst(X1,vvar(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0)))),X2))) = vsubst(X0,vvar(X1),vabs(X1,X3,X2))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_231])]) ).
fof(f614,plain,
( spl94_13
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_13])]) ).
fof(f1318,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,vvar(X1),vabs(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0))),X3,vsubst(X1,vvar(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0)))),X2))) = vsubst(X0,vvar(X1),vabs(X1,X3,X2))
| X0 = X1 )
| ~ spl94_13
| ~ spl94_146 ),
inference(resolution,[],[f1315,f615]) ).
fof(f615,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl94_13 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f2460,plain,
( spl94_230
| ~ spl94_101
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1121,f1111,f1015,f2458]) ).
fof(f2458,plain,
( spl94_230
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK45(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_230])]) ).
fof(f1111,plain,
( spl94_117
<=> ! [X5,X4,X2,X6,X3,X1] :
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_117])]) ).
fof(f1121,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK45(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl94_101
| ~ spl94_117 ),
inference(resolution,[],[f1112,f1016]) ).
fof(f1112,plain,
( ! [X2,X3,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6)
| vtcheck(vbind(X2,X3,X4),X5,X6) )
| ~ spl94_117 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f2383,plain,
( ~ spl94_105
| ~ spl94_229
| ~ spl94_87
| ~ spl94_157 ),
inference(avatar_split_clause,[],[f1485,f1415,f942,f2380,f1031]) ).
fof(f1031,plain,
( spl94_105
<=> sP8(vnoType,sK16,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_105])]) ).
fof(f2380,plain,
( spl94_229
<=> sK14 = sK54(vnoType,sK16,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_229])]) ).
fof(f942,plain,
( spl94_87
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_87])]) ).
fof(f1415,plain,
( spl94_157
<=> sK14 = sK55(vnoType,sK16,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_157])]) ).
fof(f1485,plain,
( sK14 != sK54(vnoType,sK16,sK14)
| ~ sP8(vnoType,sK16,sK14)
| ~ spl94_87
| ~ spl94_157 ),
inference(superposition,[],[f943,f1417]) ).
fof(f1417,plain,
( sK14 = sK55(vnoType,sK16,sK14)
| ~ spl94_157 ),
inference(avatar_component_clause,[],[f1415]) ).
fof(f943,plain,
( ! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) )
| ~ spl94_87 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f2378,plain,
( spl94_228
| ~ spl94_118
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1281,f1263,f1124,f2376]) ).
fof(f2376,plain,
( spl94_228
<=> ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK88(X0),sK89(X0),sK90(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_228])]) ).
fof(f1124,plain,
( spl94_118
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_118])]) ).
fof(f1263,plain,
( spl94_141
<=> ! [X4,X0] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_141])]) ).
fof(f1281,plain,
( ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK88(X0),sK89(X0),sK90(X0)) = X0 )
| ~ spl94_118
| ~ spl94_141 ),
inference(resolution,[],[f1264,f1125]) ).
fof(f1125,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 )
| ~ spl94_118 ),
inference(avatar_component_clause,[],[f1124]) ).
fof(f1264,plain,
( ! [X0,X4] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0 )
| ~ spl94_141 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f2374,plain,
( spl94_227
| ~ spl94_119
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1280,f1263,f1128,f2372]) ).
fof(f2372,plain,
( spl94_227
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_227])]) ).
fof(f1128,plain,
( spl94_119
<=> ! [X5,X4,X0,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5))
| ~ visValue(X5)
| visSomeExp(vreduce(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_119])]) ).
fof(f1280,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) )
| ~ spl94_119
| ~ spl94_141 ),
inference(resolution,[],[f1264,f1129]) ).
fof(f1129,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl94_119 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f2370,plain,
( spl94_226
| ~ spl94_125
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1185,f1178,f1156,f2368]) ).
fof(f2368,plain,
( spl94_226
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_226])]) ).
fof(f1156,plain,
( spl94_125
<=> ! [X2,X0,X1] :
( vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_125])]) ).
fof(f1178,plain,
( spl94_128
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_128])]) ).
fof(f1185,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1 )
| ~ spl94_125
| ~ spl94_128 ),
inference(resolution,[],[f1179,f1157]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1 )
| ~ spl94_125 ),
inference(avatar_component_clause,[],[f1156]) ).
fof(f1179,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0 )
| ~ spl94_128 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f2366,plain,
( spl94_225
| ~ spl94_94
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1120,f1111,f976,f2364]) ).
fof(f2364,plain,
( spl94_225
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_225])]) ).
fof(f1120,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl94_94
| ~ spl94_117 ),
inference(resolution,[],[f1112,f977]) ).
fof(f2354,plain,
( spl94_224
| ~ spl94_92
| ~ spl94_143 ),
inference(avatar_split_clause,[],[f1302,f1296,f962,f2352]) ).
fof(f2352,plain,
( spl94_224
<=> ! [X5,X4,X2,X0,X7,X6,X3,X1] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),vabs(X4,X5,veabs),X6)
| vtcheck(vbind(X0,X7,vbind(X1,X2,X3)),vabs(X4,X5,veabs),X6)
| X0 = X4
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_224])]) ).
fof(f962,plain,
( spl94_92
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_92])]) ).
fof(f1296,plain,
( spl94_143
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_143])]) ).
fof(f1302,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),vabs(X4,X5,veabs),X6)
| vtcheck(vbind(X0,X7,vbind(X1,X2,X3)),vabs(X4,X5,veabs),X6)
| X0 = X4
| X0 = X1 )
| ~ spl94_92
| ~ spl94_143 ),
inference(superposition,[],[f1297,f963]) ).
fof(f963,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl94_92 ),
inference(avatar_component_clause,[],[f962]) ).
fof(f1297,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| X0 = X3 )
| ~ spl94_143 ),
inference(avatar_component_clause,[],[f1296]) ).
fof(f2276,plain,
( spl94_223
| ~ spl94_118
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1193,f1182,f1124,f2274]) ).
fof(f2274,plain,
( spl94_223
<=> ! [X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK88(X3),sK89(X3),sK90(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_223])]) ).
fof(f1182,plain,
( spl94_129
<=> ! [X4,X0,X5,X3] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0))
| ~ visSomeExp(vreduce(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_129])]) ).
fof(f1193,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK88(X3),sK89(X3),sK90(X3)) = X3 )
| ~ spl94_118
| ~ spl94_129 ),
inference(resolution,[],[f1183,f1125]) ).
fof(f1183,plain,
( ! [X3,X0,X4,X5] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0)) )
| ~ spl94_129 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f2272,plain,
( spl94_222
| ~ spl94_119
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1192,f1182,f1128,f2270]) ).
fof(f2270,plain,
( spl94_222
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| ~ visValue(X3)
| vsomeExp(vsubst(X4,X3,X5)) = vreduce(vapp(vabs(X4,X6,X5),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_222])]) ).
fof(f1192,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| ~ visValue(X3)
| vsomeExp(vsubst(X4,X3,X5)) = vreduce(vapp(vabs(X4,X6,X5),X3)) )
| ~ spl94_119
| ~ spl94_129 ),
inference(resolution,[],[f1183,f1129]) ).
fof(f2268,plain,
( spl94_221
| ~ spl94_92
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1191,f1178,f962,f2266]) ).
fof(f2266,plain,
( spl94_221
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK61(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_221])]) ).
fof(f1191,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK61(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 )
| ~ spl94_92
| ~ spl94_128 ),
inference(superposition,[],[f1179,f963]) ).
fof(f2264,plain,
( spl94_220
| ~ spl94_116
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1172,f1156,f1107,f2262]) ).
fof(f2262,plain,
( spl94_220
<=> ! [X0,X1] :
( vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_220])]) ).
fof(f1107,plain,
( spl94_116
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_116])]) ).
fof(f1172,plain,
( ! [X0,X1] :
( vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl94_116
| ~ spl94_125 ),
inference(resolution,[],[f1157,f1108]) ).
fof(f1108,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl94_116 ),
inference(avatar_component_clause,[],[f1107]) ).
fof(f2222,plain,
( spl94_219
| spl94_4
| ~ spl94_33
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1132,f1124,f694,f576,f2220]) ).
fof(f2220,plain,
( spl94_219
<=> ! [X0,X3,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK88(vabs(X0,X1,X2)),sK89(vabs(X0,X1,X2)),sK90(vabs(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_219])]) ).
fof(f576,plain,
( spl94_4
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_4])]) ).
fof(f694,plain,
( spl94_33
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_33])]) ).
fof(f1132,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK88(vabs(X0,X1,X2)),sK89(vabs(X0,X1,X2)),sK90(vabs(X0,X1,X2))) )
| ~ spl94_33
| ~ spl94_118 ),
inference(superposition,[],[f1125,f695]) ).
fof(f695,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl94_33 ),
inference(avatar_component_clause,[],[f694]) ).
fof(f2188,plain,
( spl94_218
| ~ spl94_95
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1282,f1263,f980,f2186]) ).
fof(f2186,plain,
( spl94_218
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_218])]) ).
fof(f980,plain,
( spl94_95
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_95])]) ).
fof(f1282,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) )
| ~ spl94_95
| ~ spl94_141 ),
inference(resolution,[],[f1264,f981]) ).
fof(f981,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl94_95 ),
inference(avatar_component_clause,[],[f980]) ).
fof(f2184,plain,
( spl94_217
| ~ spl94_113
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1271,f1259,f1064,f2182]) ).
fof(f2182,plain,
( spl94_217
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),vabs(X5,X6,X7),varrow(X6,X8))
| X0 = X2
| ~ vtcheck(vbind(X5,X6,vbind(X2,X3,vbind(X0,X1,X4))),X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_217])]) ).
fof(f1271,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),vabs(X5,X6,X7),varrow(X6,X8))
| X0 = X2
| ~ vtcheck(vbind(X5,X6,vbind(X2,X3,vbind(X0,X1,X4))),X7,X8) )
| ~ spl94_113
| ~ spl94_140 ),
inference(resolution,[],[f1260,f1065]) ).
fof(f2180,plain,
( spl94_216
| ~ spl94_92
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1230,f1224,f962,f2178]) ).
fof(f2178,plain,
( spl94_216
<=> ! [X2,X6,X4,X0,X5,X3,X1] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),vabs(X0,X4,veabs),X5)
| vtcheck(vbind(X0,X6,vbind(X1,X2,X3)),vabs(X0,X4,veabs),X5)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_216])]) ).
fof(f1224,plain,
( spl94_133
<=> ! [X3,X4,X5,X2,X1] :
( vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_133])]) ).
fof(f1230,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),vabs(X0,X4,veabs),X5)
| vtcheck(vbind(X0,X6,vbind(X1,X2,X3)),vabs(X0,X4,veabs),X5)
| X0 = X1 )
| ~ spl94_92
| ~ spl94_133 ),
inference(superposition,[],[f1225,f963]) ).
fof(f1225,plain,
( ! [X2,X3,X1,X4,X5] :
( vnoType != vlookup(X3,X2)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5) )
| ~ spl94_133 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f2176,plain,
( spl94_215
| ~ spl94_98
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1186,f1178,f997,f2174]) ).
fof(f2174,plain,
( spl94_215
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_215])]) ).
fof(f997,plain,
( spl94_98
<=> ! [X2,X0,X1] :
( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_98])]) ).
fof(f1186,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) )
| ~ spl94_98
| ~ spl94_128 ),
inference(resolution,[],[f1179,f998]) ).
fof(f998,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0 )
| ~ spl94_98 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f2163,plain,
( spl94_214
| ~ spl94_99
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1173,f1156,f1001,f2161]) ).
fof(f2161,plain,
( spl94_214
<=> ! [X0,X1] :
( vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_214])]) ).
fof(f1001,plain,
( spl94_99
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_99])]) ).
fof(f1173,plain,
( ! [X0,X1] :
( vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl94_99
| ~ spl94_125 ),
inference(resolution,[],[f1157,f1002]) ).
fof(f1002,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl94_99 ),
inference(avatar_component_clause,[],[f1001]) ).
fof(f2119,plain,
( spl94_213
| ~ spl94_60
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1221,f1206,f812,f2117]) ).
fof(f2117,plain,
( spl94_213
<=> ! [X2,X3,X4,X0,X5,X1] :
( vabs(X0,X1,vsubst(X2,vapp(X3,X4),X5)) = vsubst(X2,vapp(X3,X4),vabs(X0,X1,X5))
| X0 = X2
| visFreeVar(X0,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_213])]) ).
fof(f812,plain,
( spl94_60
<=> ! [X4,X2,X3] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_60])]) ).
fof(f1221,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,vsubst(X2,vapp(X3,X4),X5)) = vsubst(X2,vapp(X3,X4),vabs(X0,X1,X5))
| X0 = X2
| visFreeVar(X0,X3)
| visFreeVar(X0,X4) )
| ~ spl94_60
| ~ spl94_132 ),
inference(resolution,[],[f1207,f813]) ).
fof(f813,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl94_60 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f2113,plain,
( spl94_212
| ~ spl94_95
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1194,f1182,f980,f2111]) ).
fof(f2111,plain,
( spl94_212
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| visValue(X3)
| vnoExp = vreduce(vapp(vabs(X4,X5,X6),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_212])]) ).
fof(f1194,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| visValue(X3)
| vnoExp = vreduce(vapp(vabs(X4,X5,X6),X3)) )
| ~ spl94_95
| ~ spl94_129 ),
inference(resolution,[],[f1183,f981]) ).
fof(f2109,plain,
( spl94_211
| ~ spl94_98
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1114,f1107,f997,f2107]) ).
fof(f2107,plain,
( spl94_211
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_211])]) ).
fof(f1114,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) )
| ~ spl94_98
| ~ spl94_116 ),
inference(resolution,[],[f1108,f998]) ).
fof(f2084,plain,
( spl94_210
| ~ spl94_41
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1219,f1206,f732,f2082]) ).
fof(f2082,plain,
( spl94_210
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vabs(X0,X1,vsubst(X2,vabs(X3,X4,X5),X6)) = vsubst(X2,vabs(X3,X4,X5),vabs(X0,X1,X6))
| X0 = X2
| visFreeVar(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_210])]) ).
fof(f732,plain,
( spl94_41
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_41])]) ).
fof(f1219,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vabs(X0,X1,vsubst(X2,vabs(X3,X4,X5),X6)) = vsubst(X2,vabs(X3,X4,X5),vabs(X0,X1,X6))
| X0 = X2
| visFreeVar(X0,X5) )
| ~ spl94_41
| ~ spl94_132 ),
inference(resolution,[],[f1207,f733]) ).
fof(f733,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl94_41 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f2080,plain,
( spl94_209
| ~ spl94_92
| ~ spl94_99 ),
inference(avatar_split_clause,[],[f1009,f1001,f962,f2078]) ).
fof(f2078,plain,
( spl94_209
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| vempty = vbind(X1,X2,X3)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_209])]) ).
fof(f1009,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| vempty = vbind(X1,X2,X3)
| X0 = X1 )
| ~ spl94_92
| ~ spl94_99 ),
inference(superposition,[],[f1002,f963]) ).
fof(f2055,plain,
( spl94_208
| ~ spl94_42
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1190,f1178,f736,f2053]) ).
fof(f2053,plain,
( spl94_208
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK61(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_208])]) ).
fof(f736,plain,
( spl94_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_42])]) ).
fof(f1190,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK61(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 )
| ~ spl94_42
| ~ spl94_128 ),
inference(superposition,[],[f1179,f737]) ).
fof(f737,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl94_42 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f2051,plain,
( spl94_207
| ~ spl94_2
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f1845,f1744,f566,f2048]) ).
fof(f566,plain,
( spl94_2
<=> vtcheck(sK16,vabs(sK17,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_2])]) ).
fof(f1845,plain,
( vtcheck(sK16,vabs(sK14,sK18,veabs),sK19)
| ~ spl94_2
| ~ spl94_184 ),
inference(superposition,[],[f568,f1746]) ).
fof(f568,plain,
( vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
| ~ spl94_2 ),
inference(avatar_component_clause,[],[f566]) ).
fof(f2044,plain,
( spl94_206
| spl94_4
| ~ spl94_33
| ~ spl94_119 ),
inference(avatar_split_clause,[],[f1134,f1128,f694,f576,f2042]) ).
fof(f2042,plain,
( spl94_206
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ visValue(vabs(X0,X1,X2))
| vsomeExp(vsubst(X3,vabs(X0,X1,X2),X4)) = vreduce(vapp(vabs(X3,X5,X4),vabs(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_206])]) ).
fof(f1134,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visSomeExp(vnoExp)
| ~ visValue(vabs(X0,X1,X2))
| vsomeExp(vsubst(X3,vabs(X0,X1,X2),X4)) = vreduce(vapp(vabs(X3,X5,X4),vabs(X0,X1,X2))) )
| ~ spl94_33
| ~ spl94_119 ),
inference(superposition,[],[f1129,f695]) ).
fof(f2040,plain,
( spl94_205
| ~ spl94_92
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1119,f1107,f962,f2038]) ).
fof(f2038,plain,
( spl94_205
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| vnoType = vlookup(X0,X3)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_205])]) ).
fof(f1119,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| vnoType = vlookup(X0,X3)
| X0 = X1 )
| ~ spl94_92
| ~ spl94_116 ),
inference(superposition,[],[f1108,f963]) ).
fof(f2036,plain,
( spl94_204
| ~ spl94_98
| ~ spl94_99 ),
inference(avatar_split_clause,[],[f1004,f1001,f997,f2034]) ).
fof(f2034,plain,
( spl94_204
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_204])]) ).
fof(f1004,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK55(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) )
| ~ spl94_98
| ~ spl94_99 ),
inference(resolution,[],[f1002,f998]) ).
fof(f2018,plain,
( spl94_203
| ~ spl94_113
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1122,f1111,f1064,f2016]) ).
fof(f2016,plain,
( spl94_203
<=> ! [X5,X4,X2,X0,X7,X6,X3,X1] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,X5),varrow(X4,X6))
| ~ vtcheck(vbind(X3,X4,vbind(X0,X1,vbind(X0,X7,X2))),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_203])]) ).
fof(f1122,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,X5),varrow(X4,X6))
| ~ vtcheck(vbind(X3,X4,vbind(X0,X1,vbind(X0,X7,X2))),X5,X6) )
| ~ spl94_113
| ~ spl94_117 ),
inference(resolution,[],[f1112,f1065]) ).
fof(f2014,plain,
( spl94_195
| ~ spl94_161
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f2012,f1744,f1439,f1908]) ).
fof(f1908,plain,
( spl94_195
<=> sP5(sK16,sK19,vabs(sK14,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_195])]) ).
fof(f1439,plain,
( spl94_161
<=> sP5(sK16,sK19,vabs(sK17,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_161])]) ).
fof(f2012,plain,
( sP5(sK16,sK19,vabs(sK14,sK18,veabs))
| ~ spl94_161
| ~ spl94_184 ),
inference(forward_demodulation,[],[f1441,f1746]) ).
fof(f1441,plain,
( sP5(sK16,sK19,vabs(sK17,sK18,veabs))
| ~ spl94_161 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f2011,plain,
( spl94_202
| ~ spl94_160
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f2005,f1744,f1435,f2008]) ).
fof(f2008,plain,
( spl94_202
<=> vsomeType(sK19) = vlookup(sK52(vabs(sK14,sK18,veabs),sK19,sK16),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_202])]) ).
fof(f1435,plain,
( spl94_160
<=> vsomeType(sK19) = vlookup(sK52(vabs(sK17,sK18,veabs),sK19,sK16),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_160])]) ).
fof(f2005,plain,
( vsomeType(sK19) = vlookup(sK52(vabs(sK14,sK18,veabs),sK19,sK16),sK16)
| ~ spl94_160
| ~ spl94_184 ),
inference(forward_demodulation,[],[f1437,f1746]) ).
fof(f1437,plain,
( vsomeType(sK19) = vlookup(sK52(vabs(sK17,sK18,veabs),sK19,sK16),sK16)
| ~ spl94_160 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f2001,plain,
( spl94_201
| ~ spl94_159
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f1843,f1744,f1431,f1998]) ).
fof(f1998,plain,
( spl94_201
<=> sP6(sK16,sK19,vabs(sK14,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_201])]) ).
fof(f1431,plain,
( spl94_159
<=> sP6(sK16,sK19,vabs(sK17,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_159])]) ).
fof(f1843,plain,
( sP6(sK16,sK19,vabs(sK14,sK18,veabs))
| ~ spl94_159
| ~ spl94_184 ),
inference(superposition,[],[f1433,f1746]) ).
fof(f1433,plain,
( sP6(sK16,sK19,vabs(sK17,sK18,veabs))
| ~ spl94_159 ),
inference(avatar_component_clause,[],[f1431]) ).
fof(f1996,plain,
( spl94_200
| ~ spl94_92
| ~ spl94_112 ),
inference(avatar_split_clause,[],[f1078,f1060,f962,f1994]) ).
fof(f1994,plain,
( spl94_200
<=> ! [X5,X4,X0,X3,X2,X1] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),veabs,X4)
| vtcheck(vbind(X0,X5,vbind(X1,X2,X3)),veabs,X4)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_200])]) ).
fof(f1060,plain,
( spl94_112
<=> ! [X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| vnoType != vlookup(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_112])]) ).
fof(f1078,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),veabs,X4)
| vtcheck(vbind(X0,X5,vbind(X1,X2,X3)),veabs,X4)
| X0 = X1 )
| ~ spl94_92
| ~ spl94_112 ),
inference(superposition,[],[f1061,f963]) ).
fof(f1061,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,veabs,X3)
| vtcheck(vbind(X0,X1,X2),veabs,X3) )
| ~ spl94_112 ),
inference(avatar_component_clause,[],[f1060]) ).
fof(f1980,plain,
( spl94_199
| ~ spl94_23
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1218,f1206,f654,f1978]) ).
fof(f1978,plain,
( spl94_199
<=> ! [X2,X3,X4,X0,X5,X1] :
( vabs(X0,X1,vsubst(X2,vabs(X0,X3,X4),X5)) = vsubst(X2,vabs(X0,X3,X4),vabs(X0,X1,X5))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_199])]) ).
fof(f654,plain,
( spl94_23
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_23])]) ).
fof(f1218,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,vsubst(X2,vabs(X0,X3,X4),X5)) = vsubst(X2,vabs(X0,X3,X4),vabs(X0,X1,X5))
| X0 = X2 )
| ~ spl94_23
| ~ spl94_132 ),
inference(resolution,[],[f1207,f655]) ).
fof(f655,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl94_23 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f1965,plain,
( spl94_198
| ~ spl94_32
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1220,f1206,f690,f1963]) ).
fof(f1963,plain,
( spl94_198
<=> ! [X2,X4,X0,X3,X1] :
( vabs(X0,X1,vsubst(X2,vvar(X3),X4)) = vsubst(X2,vvar(X3),vabs(X0,X1,X4))
| X0 = X2
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_198])]) ).
fof(f690,plain,
( spl94_32
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_32])]) ).
fof(f1220,plain,
( ! [X2,X3,X0,X1,X4] :
( vabs(X0,X1,vsubst(X2,vvar(X3),X4)) = vsubst(X2,vvar(X3),vabs(X0,X1,X4))
| X0 = X2
| X0 = X3 )
| ~ spl94_32
| ~ spl94_132 ),
inference(resolution,[],[f1207,f691]) ).
fof(f691,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl94_32 ),
inference(avatar_component_clause,[],[f690]) ).
fof(f1949,plain,
( spl94_197
| ~ spl94_43
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1187,f1178,f740,f1947]) ).
fof(f1947,plain,
( spl94_197
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| sK55(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_197])]) ).
fof(f740,plain,
( spl94_43
<=> ! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_43])]) ).
fof(f1187,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_128 ),
inference(resolution,[],[f1179,f741]) ).
fof(f741,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK55(X0,X1,X2) = X2 )
| ~ spl94_43 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f1915,plain,
( spl94_196
| spl94_4
| ~ spl94_16
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1131,f1124,f626,f576,f1913]) ).
fof(f1913,plain,
( spl94_196
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK88(vvar(X0)),sK89(vvar(X0)),sK90(vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_196])]) ).
fof(f1131,plain,
( ! [X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK88(vvar(X0)),sK89(vvar(X0)),sK90(vvar(X0))) )
| ~ spl94_16
| ~ spl94_118 ),
inference(superposition,[],[f1125,f627]) ).
fof(f1911,plain,
( ~ spl94_195
| spl94_161
| ~ spl94_184 ),
inference(avatar_split_clause,[],[f1842,f1744,f1439,f1908]) ).
fof(f1842,plain,
( ~ sP5(sK16,sK19,vabs(sK14,sK18,veabs))
| spl94_161
| ~ spl94_184 ),
inference(superposition,[],[f1440,f1746]) ).
fof(f1440,plain,
( ~ sP5(sK16,sK19,vabs(sK17,sK18,veabs))
| spl94_161 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1906,plain,
( spl94_194
| ~ spl94_42
| ~ spl94_99 ),
inference(avatar_split_clause,[],[f1008,f1001,f736,f1904]) ).
fof(f1904,plain,
( spl94_194
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vempty = vbind(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_194])]) ).
fof(f1008,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vempty = vbind(X0,X1,X2) )
| ~ spl94_42
| ~ spl94_99 ),
inference(superposition,[],[f1002,f737]) ).
fof(f1892,plain,
( spl94_193
| ~ spl94_11
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1213,f1206,f606,f1890]) ).
fof(f1890,plain,
( spl94_193
<=> ! [X0,X3,X2,X1] :
( vabs(vgensym(X0),X1,vsubst(X2,X0,X3)) = vsubst(X2,X0,vabs(vgensym(X0),X1,X3))
| vgensym(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_193])]) ).
fof(f606,plain,
( spl94_11
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_11])]) ).
fof(f1213,plain,
( ! [X2,X3,X0,X1] :
( vabs(vgensym(X0),X1,vsubst(X2,X0,X3)) = vsubst(X2,X0,vabs(vgensym(X0),X1,X3))
| vgensym(X0) = X2 )
| ~ spl94_11
| ~ spl94_132 ),
inference(resolution,[],[f1207,f607]) ).
fof(f607,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl94_11 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f1849,plain,
( spl94_192
| ~ spl94_18
| ~ spl94_143 ),
inference(avatar_split_clause,[],[f1303,f1296,f634,f1847]) ).
fof(f1847,plain,
( spl94_192
<=> ! [X4,X0,X3,X2,X1] :
( ~ vtcheck(vempty,vabs(X1,X2,veabs),X3)
| vtcheck(vbind(X0,X4,vempty),vabs(X1,X2,veabs),X3)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_192])]) ).
fof(f634,plain,
( spl94_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_18])]) ).
fof(f1303,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vempty,vabs(X1,X2,veabs),X3)
| vtcheck(vbind(X0,X4,vempty),vabs(X1,X2,veabs),X3)
| X0 = X1 )
| ~ spl94_18
| ~ spl94_143 ),
inference(trivial_inequality_removal,[],[f1300]) ).
fof(f1300,plain,
( ! [X2,X3,X0,X1,X4] :
( vnoType != vnoType
| ~ vtcheck(vempty,vabs(X1,X2,veabs),X3)
| vtcheck(vbind(X0,X4,vempty),vabs(X1,X2,veabs),X3)
| X0 = X1 )
| ~ spl94_18
| ~ spl94_143 ),
inference(superposition,[],[f1297,f635]) ).
fof(f635,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl94_18 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f1840,plain,
( spl94_191
| ~ spl94_19
| ~ spl94_142 ),
inference(avatar_split_clause,[],[f1294,f1286,f638,f1838]) ).
fof(f1838,plain,
( spl94_191
<=> ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_191])]) ).
fof(f638,plain,
( spl94_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_19])]) ).
fof(f1286,plain,
( spl94_142
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_142])]) ).
fof(f1294,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl94_19
| ~ spl94_142 ),
inference(duplicate_literal_removal,[],[f1291]) ).
fof(f1291,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0)
| vnoExp = vreduce(X0) )
| ~ spl94_19
| ~ spl94_142 ),
inference(resolution,[],[f1287,f639]) ).
fof(f639,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl94_19 ),
inference(avatar_component_clause,[],[f638]) ).
fof(f1287,plain,
( ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl94_142 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f1836,plain,
( spl94_190
| ~ spl94_42
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1118,f1107,f736,f1834]) ).
fof(f1834,plain,
( spl94_190
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_190])]) ).
fof(f1118,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1) )
| ~ spl94_42
| ~ spl94_116 ),
inference(superposition,[],[f1108,f737]) ).
fof(f1832,plain,
( spl94_189
| ~ spl94_60
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1103,f1072,f812,f1830]) ).
fof(f1830,plain,
( spl94_189
<=> ! [X4,X0,X3,X2,X1] :
( ~ visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| visFreeVar(X4,vsubst(X0,X1,X2))
| visFreeVar(X4,vsubst(X0,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_189])]) ).
fof(f1072,plain,
( spl94_115
<=> ! [X5,X4,X7,X6] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_115])]) ).
fof(f1103,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| visFreeVar(X4,vsubst(X0,X1,X2))
| visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl94_60
| ~ spl94_115 ),
inference(superposition,[],[f813,f1073]) ).
fof(f1073,plain,
( ! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7))
| ~ spl94_115 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1828,plain,
( spl94_188
| ~ spl94_113
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1085,f1068,f1064,f1826]) ).
fof(f1826,plain,
( spl94_188
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ vtcheck(X0,X1,X2)
| vtcheck(X0,vapp(vabs(X3,X2,X4),X1),X5)
| ~ vtcheck(vbind(X3,X2,X0),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_188])]) ).
fof(f1068,plain,
( spl94_114
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_114])]) ).
fof(f1085,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ vtcheck(X0,X1,X2)
| vtcheck(X0,vapp(vabs(X3,X2,X4),X1),X5)
| ~ vtcheck(vbind(X3,X2,X0),X4,X5) )
| ~ spl94_113
| ~ spl94_114 ),
inference(resolution,[],[f1069,f1065]) ).
fof(f1069,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vapp(X2,X3),X4) )
| ~ spl94_114 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f1824,plain,
( spl94_187
| ~ spl94_101
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1084,f1068,f1015,f1822]) ).
fof(f1822,plain,
( spl94_187
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(X0,X1,sK47(X0,X2,X3))
| vtcheck(X0,vapp(sK45(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_187])]) ).
fof(f1084,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(X0,X1,sK47(X0,X2,X3))
| vtcheck(X0,vapp(sK45(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) )
| ~ spl94_101
| ~ spl94_114 ),
inference(resolution,[],[f1069,f1016]) ).
fof(f1755,plain,
( spl94_186
| ~ spl94_43
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1115,f1107,f740,f1753]) ).
fof(f1753,plain,
( spl94_186
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_186])]) ).
fof(f1115,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_116 ),
inference(resolution,[],[f1108,f741]) ).
fof(f1751,plain,
( spl94_185
| ~ spl94_83
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1091,f1072,f915,f1749]) ).
fof(f1749,plain,
( spl94_185
<=> ! [X4,X0,X3,X2,X1] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_185])]) ).
fof(f915,plain,
( spl94_83
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_83])]) ).
fof(f1091,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3))
| ~ spl94_83
| ~ spl94_115 ),
inference(superposition,[],[f1073,f916]) ).
fof(f916,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl94_83 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f1747,plain,
( spl94_184
| ~ spl94_2
| spl94_5
| ~ spl94_156 ),
inference(avatar_split_clause,[],[f1410,f1407,f581,f566,f1744]) ).
fof(f1407,plain,
( spl94_156
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(sK16,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(sK14,X3,sK16),vabs(X0,X1,veabs),X2)
| sK14 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_156])]) ).
fof(f1410,plain,
( ~ vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
| sK14 = sK17
| spl94_5
| ~ spl94_156 ),
inference(resolution,[],[f1408,f583]) ).
fof(f1408,plain,
( ! [X2,X3,X0,X1] :
( vtcheck(vbind(sK14,X3,sK16),vabs(X0,X1,veabs),X2)
| ~ vtcheck(sK16,vabs(X0,X1,veabs),X2)
| sK14 = X0 )
| ~ spl94_156 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f1742,plain,
( spl94_183
| ~ spl94_83
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1088,f1072,f915,f1740]) ).
fof(f1740,plain,
( spl94_183
<=> ! [X2,X4,X0,X3,X1] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_183])]) ).
fof(f1088,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4))
| ~ spl94_83
| ~ spl94_115 ),
inference(superposition,[],[f1073,f916]) ).
fof(f1692,plain,
( spl94_182
| ~ spl94_61
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1090,f1072,f816,f1690]) ).
fof(f1690,plain,
( spl94_182
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_182])]) ).
fof(f1090,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl94_61
| ~ spl94_115 ),
inference(superposition,[],[f1073,f817]) ).
fof(f1688,plain,
( spl94_181
| ~ spl94_61
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1087,f1072,f816,f1686]) ).
fof(f1686,plain,
( spl94_181
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_181])]) ).
fof(f1087,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl94_61
| ~ spl94_115 ),
inference(superposition,[],[f1073,f817]) ).
fof(f1667,plain,
( spl94_180
| ~ spl94_18
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1231,f1224,f634,f1665]) ).
fof(f1665,plain,
( spl94_180
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(vempty,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(X0,X3,vempty),vabs(X0,X1,veabs),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_180])]) ).
fof(f1231,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(X0,X3,vempty),vabs(X0,X1,veabs),X2) )
| ~ spl94_18
| ~ spl94_133 ),
inference(trivial_inequality_removal,[],[f1228]) ).
fof(f1228,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(X0,X3,vempty),vabs(X0,X1,veabs),X2) )
| ~ spl94_18
| ~ spl94_133 ),
inference(superposition,[],[f1225,f635]) ).
fof(f1663,plain,
( spl94_179
| ~ spl94_43
| ~ spl94_99 ),
inference(avatar_split_clause,[],[f1005,f1001,f740,f1661]) ).
fof(f1661,plain,
( spl94_179
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_179])]) ).
fof(f1005,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_99 ),
inference(resolution,[],[f1002,f741]) ).
fof(f1649,plain,
( spl94_178
| ~ spl94_59
| ~ spl94_92 ),
inference(avatar_split_clause,[],[f970,f962,f808,f1647]) ).
fof(f1647,plain,
( spl94_178
<=> ! [X4,X0,X3,X2,X1] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_178])]) ).
fof(f808,plain,
( spl94_59
<=> ! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_59])]) ).
fof(f970,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl94_59
| ~ spl94_92 ),
inference(superposition,[],[f809,f963]) ).
fof(f809,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl94_59 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f1629,plain,
( spl94_177
| ~ spl94_49
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1100,f1072,f764,f1627]) ).
fof(f1627,plain,
( spl94_177
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_177])]) ).
fof(f764,plain,
( spl94_49
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_49])]) ).
fof(f1100,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl94_49
| ~ spl94_115 ),
inference(superposition,[],[f765,f1073]) ).
fof(f765,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl94_49 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f1625,plain,
( spl94_176
| ~ spl94_47
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1097,f1072,f756,f1623]) ).
fof(f1623,plain,
( spl94_176
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_176])]) ).
fof(f756,plain,
( spl94_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_47])]) ).
fof(f1097,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl94_47
| ~ spl94_115 ),
inference(superposition,[],[f757,f1073]) ).
fof(f757,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl94_47 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f1620,plain,
( spl94_175
| spl94_4
| ~ spl94_16
| ~ spl94_95 ),
inference(avatar_split_clause,[],[f983,f980,f626,f576,f1618]) ).
fof(f1618,plain,
( spl94_175
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_175])]) ).
fof(f983,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl94_16
| ~ spl94_95 ),
inference(superposition,[],[f981,f627]) ).
fof(f1587,plain,
( spl94_174
| ~ spl94_98
| ~ spl94_105
| ~ spl94_157 ),
inference(avatar_split_clause,[],[f1425,f1415,f1031,f997,f1584]) ).
fof(f1584,plain,
( spl94_174
<=> vnoType = vlookup(sK14,sK56(vnoType,sK16,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_174])]) ).
fof(f1425,plain,
( vnoType = vlookup(sK14,sK56(vnoType,sK16,sK14))
| ~ spl94_98
| ~ spl94_105
| ~ spl94_157 ),
inference(forward_demodulation,[],[f1365,f1417]) ).
fof(f1365,plain,
( vnoType = vlookup(sK55(vnoType,sK16,sK14),sK56(vnoType,sK16,sK14))
| ~ spl94_98
| ~ spl94_105 ),
inference(resolution,[],[f1033,f998]) ).
fof(f1033,plain,
( sP8(vnoType,sK16,sK14)
| ~ spl94_105 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1510,plain,
( spl94_173
| ~ spl94_18
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1189,f1178,f634,f1508]) ).
fof(f1508,plain,
( spl94_173
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_173])]) ).
fof(f1189,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 )
| ~ spl94_18
| ~ spl94_128 ),
inference(superposition,[],[f1179,f635]) ).
fof(f1506,plain,
( spl94_172
| ~ spl94_40
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1096,f1072,f723,f1504]) ).
fof(f1504,plain,
( spl94_172
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_172])]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl94_40
| ~ spl94_115 ),
inference(superposition,[],[f724,f1073]) ).
fof(f1502,plain,
( spl94_171
| ~ spl94_39
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1095,f1072,f719,f1500]) ).
fof(f1500,plain,
( spl94_171
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_171])]) ).
fof(f1095,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl94_39
| ~ spl94_115 ),
inference(superposition,[],[f720,f1073]) ).
fof(f1498,plain,
( spl94_170
| ~ spl94_34
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1089,f1072,f698,f1496]) ).
fof(f1496,plain,
( spl94_170
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_170])]) ).
fof(f1089,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl94_34
| ~ spl94_115 ),
inference(superposition,[],[f1073,f699]) ).
fof(f1494,plain,
( spl94_169
| ~ spl94_34
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1086,f1072,f698,f1492]) ).
fof(f1492,plain,
( spl94_169
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_169])]) ).
fof(f1086,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl94_34
| ~ spl94_115 ),
inference(superposition,[],[f1073,f699]) ).
fof(f1490,plain,
( spl94_168
| ~ spl94_11
| ~ spl94_82 ),
inference(avatar_split_clause,[],[f932,f911,f606,f1488]) ).
fof(f1488,plain,
( spl94_168
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_168])]) ).
fof(f911,plain,
( spl94_82
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_82])]) ).
fof(f932,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl94_11
| ~ spl94_82 ),
inference(resolution,[],[f912,f607]) ).
fof(f912,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl94_82 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f1484,plain,
( spl94_167
| ~ spl94_42
| ~ spl94_59 ),
inference(avatar_split_clause,[],[f823,f808,f736,f1482]) ).
fof(f1482,plain,
( spl94_167
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_167])]) ).
fof(f823,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl94_42
| ~ spl94_59 ),
inference(superposition,[],[f809,f737]) ).
fof(f1476,plain,
( spl94_166
| ~ spl94_38
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1094,f1072,f715,f1474]) ).
fof(f1474,plain,
( spl94_166
<=> ! [X5,X4,X2,X0,X6,X3,X1] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_166])]) ).
fof(f715,plain,
( spl94_38
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_38])]) ).
fof(f1094,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl94_38
| ~ spl94_115 ),
inference(superposition,[],[f716,f1073]) ).
fof(f716,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl94_38 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f1472,plain,
( spl94_165
| ~ spl94_18
| ~ spl94_112 ),
inference(avatar_split_clause,[],[f1079,f1060,f634,f1470]) ).
fof(f1470,plain,
( spl94_165
<=> ! [X2,X0,X1] :
( ~ vtcheck(vempty,veabs,X1)
| vtcheck(vbind(X0,X2,vempty),veabs,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_165])]) ).
fof(f1079,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(vempty,veabs,X1)
| vtcheck(vbind(X0,X2,vempty),veabs,X1) )
| ~ spl94_18
| ~ spl94_112 ),
inference(trivial_inequality_removal,[],[f1076]) ).
fof(f1076,plain,
( ! [X2,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,veabs,X1)
| vtcheck(vbind(X0,X2,vempty),veabs,X1) )
| ~ spl94_18
| ~ spl94_112 ),
inference(superposition,[],[f1061,f635]) ).
fof(f1467,plain,
( spl94_164
| ~ spl94_22
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1093,f1072,f650,f1465]) ).
fof(f1465,plain,
( spl94_164
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_164])]) ).
fof(f650,plain,
( spl94_22
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_22])]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl94_22
| ~ spl94_115 ),
inference(superposition,[],[f651,f1073]) ).
fof(f651,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl94_22 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f1453,plain,
( spl94_163
| ~ spl94_18
| ~ spl94_103 ),
inference(avatar_split_clause,[],[f1419,f1023,f634,f1451]) ).
fof(f1451,plain,
( spl94_163
<=> ! [X0] : vnoType = vlookup(X0,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_163])]) ).
fof(f1023,plain,
( spl94_103
<=> vempty = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_103])]) ).
fof(f1419,plain,
( ! [X0] : vnoType = vlookup(X0,sK16)
| ~ spl94_18
| ~ spl94_103 ),
inference(superposition,[],[f635,f1025]) ).
fof(f1025,plain,
( vempty = sK16
| ~ spl94_103 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1448,plain,
( spl94_162
| ~ spl94_12
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1092,f1072,f610,f1446]) ).
fof(f1446,plain,
( spl94_162
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_162])]) ).
fof(f610,plain,
( spl94_12
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_12])]) ).
fof(f1092,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_12
| ~ spl94_115 ),
inference(superposition,[],[f611,f1073]) ).
fof(f611,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl94_12 ),
inference(avatar_component_clause,[],[f610]) ).
fof(f1442,plain,
( spl94_159
| spl94_160
| spl94_161
| ~ spl94_2
| ~ spl94_131 ),
inference(avatar_split_clause,[],[f1209,f1202,f566,f1439,f1435,f1431]) ).
fof(f1209,plain,
( sP5(sK16,sK19,vabs(sK17,sK18,veabs))
| vsomeType(sK19) = vlookup(sK52(vabs(sK17,sK18,veabs),sK19,sK16),sK16)
| sP6(sK16,sK19,vabs(sK17,sK18,veabs))
| ~ spl94_2
| ~ spl94_131 ),
inference(resolution,[],[f1203,f568]) ).
fof(f1424,plain,
( spl94_158
| spl94_104
| spl94_105
| ~ spl94_1
| ~ spl94_128 ),
inference(avatar_split_clause,[],[f1188,f1178,f561,f1031,f1027,f1421]) ).
fof(f1421,plain,
( spl94_158
<=> sK14 = sK61(sK14,sK16,vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_158])]) ).
fof(f1027,plain,
( spl94_104
<=> sP7(vnoType,sK16,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_104])]) ).
fof(f561,plain,
( spl94_1
<=> vnoType = vlookup(sK14,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_1])]) ).
fof(f1188,plain,
( sP8(vnoType,sK16,sK14)
| sP7(vnoType,sK16,sK14)
| sK14 = sK61(sK14,sK16,vnoType)
| ~ spl94_1
| ~ spl94_128 ),
inference(superposition,[],[f1179,f563]) ).
fof(f563,plain,
( vnoType = vlookup(sK14,sK16)
| ~ spl94_1 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f1418,plain,
( spl94_157
| ~ spl94_43
| ~ spl94_105 ),
inference(avatar_split_clause,[],[f1366,f1031,f740,f1415]) ).
fof(f1366,plain,
( sK14 = sK55(vnoType,sK16,sK14)
| ~ spl94_43
| ~ spl94_105 ),
inference(resolution,[],[f1033,f741]) ).
fof(f1409,plain,
( spl94_156
| ~ spl94_1
| ~ spl94_143 ),
inference(avatar_split_clause,[],[f1304,f1296,f561,f1407]) ).
fof(f1304,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(sK16,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(sK14,X3,sK16),vabs(X0,X1,veabs),X2)
| sK14 = X0 )
| ~ spl94_1
| ~ spl94_143 ),
inference(trivial_inequality_removal,[],[f1299]) ).
fof(f1299,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(sK16,vabs(X0,X1,veabs),X2)
| vtcheck(vbind(sK14,X3,sK16),vabs(X0,X1,veabs),X2)
| sK14 = X0 )
| ~ spl94_1
| ~ spl94_143 ),
inference(superposition,[],[f1297,f563]) ).
fof(f1402,plain,
( spl94_155
| ~ spl94_1
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1232,f1224,f561,f1400]) ).
fof(f1232,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(sK16,vabs(sK14,X0,veabs),X1)
| vtcheck(vbind(sK14,X2,sK16),vabs(sK14,X0,veabs),X1) )
| ~ spl94_1
| ~ spl94_133 ),
inference(trivial_inequality_removal,[],[f1227]) ).
fof(f1227,plain,
( ! [X2,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(sK16,vabs(sK14,X0,veabs),X1)
| vtcheck(vbind(sK14,X2,sK16),vabs(sK14,X0,veabs),X1) )
| ~ spl94_1
| ~ spl94_133 ),
inference(superposition,[],[f1225,f563]) ).
fof(f1395,plain,
( spl94_154
| ~ spl94_1
| ~ spl94_112 ),
inference(avatar_split_clause,[],[f1080,f1060,f561,f1393]) ).
fof(f1393,plain,
( spl94_154
<=> ! [X0,X1] :
( ~ vtcheck(sK16,veabs,X0)
| vtcheck(vbind(sK14,X1,sK16),veabs,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_154])]) ).
fof(f1080,plain,
( ! [X0,X1] :
( ~ vtcheck(sK16,veabs,X0)
| vtcheck(vbind(sK14,X1,sK16),veabs,X0) )
| ~ spl94_1
| ~ spl94_112 ),
inference(trivial_inequality_removal,[],[f1075]) ).
fof(f1075,plain,
( ! [X0,X1] :
( vnoType != vnoType
| ~ vtcheck(sK16,veabs,X0)
| vtcheck(vbind(sK14,X1,sK16),veabs,X0) )
| ~ spl94_1
| ~ spl94_112 ),
inference(superposition,[],[f1061,f563]) ).
fof(f1383,plain,
( spl94_153
| ~ spl94_115
| ~ spl94_152 ),
inference(avatar_split_clause,[],[f1379,f1376,f1072,f1381]) ).
fof(f1381,plain,
( spl94_153
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))))
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_153])]) ).
fof(f1376,plain,
( spl94_152
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vapp(vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK84(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_152])]) ).
fof(f1379,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))))
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl94_115
| ~ spl94_152 ),
inference(forward_demodulation,[],[f1377,f1073]) ).
fof(f1377,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vapp(vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK84(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl94_152 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f1378,plain,
spl94_152,
inference(avatar_split_clause,[],[f474,f1376]) ).
fof(f474,plain,
! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vapp(vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK84(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f406]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK84(X0,X1,X2,X3)),vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3))) = X3
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ( vapp(vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK84(X0,X1,X2,X3)),vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3))) = X3
& vapp(sK84(X0,X1,X2,X3),sK87(X0,X1,X2,X3)) = X2
& sK86(X0,X1,X2,X3) = X1
& sK85(X0,X1,X2,X3) = X0 )
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84,sK85,sK86,sK87])],[f287,f288]) ).
fof(f288,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3
& vapp(X4,X7) = X2
& X1 = X6
& X0 = X5 )
=> ( vapp(vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK84(X0,X1,X2,X3)),vsubst(sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3))) = X3
& vapp(sK84(X0,X1,X2,X3),sK87(X0,X1,X2,X3)) = X2
& sK86(X0,X1,X2,X3) = X1
& sK85(X0,X1,X2,X3) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f287,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ? [X4,X5,X6,X7] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3
& vapp(X4,X7) = X2
& X1 = X6
& X0 = X5 )
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(rectify,[],[f218]) ).
fof(f218,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(definition_folding,[],[f146,f217,f216,f215,f214,f213]) ).
fof(f213,plain,
! [X3,X2,X1,X0] :
( ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 )
| ~ sP9(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f214,plain,
! [X3,X2,X1,X0] :
( ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ~ sP10(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f215,plain,
! [X3,X2,X1,X0] :
( ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ~ sP11(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f216,plain,
! [X3,X2,X1,X0] :
( ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ~ sP12(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f217,plain,
! [X3,X2,X1,X0] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ~ sP13(X3,X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 )
| vsubst(X0,X1,X2) != X3 ),
inference(flattening,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 )
| vsubst(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( vsubst(X0,X1,X2) = X3
=> ( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X3,X5,X18] :
( vsubst(X0,X3,X5) = X18
=> ( ? [X20,X14,X8,X10,X11] :
( vabs(X20,X14,vsubst(X8,X10,X11)) = X18
& ~ visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X10,X14,X20,X23,X11] :
( vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18
& vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20,X14,X11] :
( vabs(X20,X14,X11) = X18
& X8 = X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X11,X8,X10,X12] :
( vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18
& vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20] :
( vvar(X20) = X18
& X8 != X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X20,X10] :
( X10 = X18
& X8 = X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','subst-INV') ).
fof(f1363,plain,
spl94_151,
inference(avatar_split_clause,[],[f475,f1361]) ).
fof(f475,plain,
! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f405]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(sK84(X0,X1,X2,X3),sK87(X0,X1,X2,X3)) = X2
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f289]) ).
fof(f1343,plain,
spl94_150,
inference(avatar_split_clause,[],[f477,f1341]) ).
fof(f477,plain,
! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f403]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK85(X0,X1,X2,X3) = X0
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f289]) ).
fof(f1339,plain,
spl94_149,
inference(avatar_split_clause,[],[f476,f1337]) ).
fof(f476,plain,
! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK86(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f404]) ).
fof(f404,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK86(X0,X1,X2,X3) = X1
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f289]) ).
fof(f1335,plain,
spl94_148,
inference(avatar_split_clause,[],[f387,f1333]) ).
fof(f1333,plain,
( spl94_148
<=> ! [X0,X3,X2,X1] :
( vsubst(sK67(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vabs(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vsubst(sK70(X0,X1,X2,X3),vvar(sK71(X0,X1,X2,X3)),sK72(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_148])]) ).
fof(f387,plain,
! [X2,X3,X0,X1] :
( vsubst(sK67(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vabs(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vsubst(sK70(X0,X1,X2,X3),vvar(sK71(X0,X1,X2,X3)),sK72(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1,X2,X3] :
( ( vsubst(sK67(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vabs(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vsubst(sK70(X0,X1,X2,X3),vvar(sK71(X0,X1,X2,X3)),sK72(X0,X1,X2,X3)))) = X0
& sK71(X0,X1,X2,X3) = vgensym(vapp(vapp(sK68(X0,X1,X2,X3),sK72(X0,X1,X2,X3)),vvar(sK67(X0,X1,X2,X3))))
& visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
& sK67(X0,X1,X2,X3) != sK70(X0,X1,X2,X3)
& vabs(sK70(X0,X1,X2,X3),sK69(X0,X1,X2,X3),sK72(X0,X1,X2,X3)) = X1
& sK68(X0,X1,X2,X3) = X2
& sK67(X0,X1,X2,X3) = X3 )
| ~ sP12(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68,sK69,sK70,sK71,sK72])],[f272,f273]) ).
fof(f273,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8,X9] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X0
& vgensym(vapp(vapp(X5,X9),vvar(X4))) = X8
& visFreeVar(X7,X5)
& X4 != X7
& vabs(X7,X6,X9) = X1
& X2 = X5
& X3 = X4 )
=> ( vsubst(sK67(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vabs(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vsubst(sK70(X0,X1,X2,X3),vvar(sK71(X0,X1,X2,X3)),sK72(X0,X1,X2,X3)))) = X0
& sK71(X0,X1,X2,X3) = vgensym(vapp(vapp(sK68(X0,X1,X2,X3),sK72(X0,X1,X2,X3)),vvar(sK67(X0,X1,X2,X3))))
& visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
& sK67(X0,X1,X2,X3) != sK70(X0,X1,X2,X3)
& vabs(sK70(X0,X1,X2,X3),sK69(X0,X1,X2,X3),sK72(X0,X1,X2,X3)) = X1
& sK68(X0,X1,X2,X3) = X2
& sK67(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8,X9] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X0
& vgensym(vapp(vapp(X5,X9),vvar(X4))) = X8
& visFreeVar(X7,X5)
& X4 != X7
& vabs(X7,X6,X9) = X1
& X2 = X5
& X3 = X4 )
| ~ sP12(X0,X1,X2,X3) ),
inference(rectify,[],[f271]) ).
fof(f271,plain,
! [X3,X2,X1,X0] :
( ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ~ sP12(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f216]) ).
fof(f1326,plain,
spl94_147,
inference(avatar_split_clause,[],[f458,f1324]) ).
fof(f458,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0))) = X0
| vvar(sK44(X0,vreduce(X0))) = X0 ),
inference(equality_resolution,[],[f337]) ).
fof(f337,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| vabs(sK41(X0,X1),sK42(X0,X1),sK43(X0,X1)) = X0
| vvar(sK44(X0,X1)) = X0
| vreduce(X0) != X1 ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ( vnoExp = X1
& vabs(sK41(X0,X1),sK42(X0,X1),sK43(X0,X1)) = X0 )
| ( vnoExp = X1
& vvar(sK44(X0,X1)) = X0 )
| vreduce(X0) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43,sK44])],[f241,f243,f242]) ).
fof(f242,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& vabs(X2,X3,X4) = X0 )
=> ( vnoExp = X1
& vabs(sK41(X0,X1),sK42(X0,X1),sK43(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f243,plain,
! [X0,X1] :
( ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
=> ( vnoExp = X1
& vvar(sK44(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f241,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ? [X2,X3,X4] :
( vnoExp = X1
& vabs(X2,X3,X4) = X0 )
| ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
| vreduce(X0) != X1 ),
inference(rectify,[],[f206]) ).
fof(f206,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 )
| vreduce(X0) != X1 ),
inference(definition_folding,[],[f127,f205,f204,f203,f202,f201]) ).
fof(f201,plain,
! [X1,X0] :
( ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f202,plain,
! [X1,X0] :
( ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f203,plain,
! [X1,X0] :
( ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f204,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ~ sP3(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f205,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f127,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 )
| vreduce(X0) != X1 ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 )
| vreduce(X0) != X1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( vreduce(X0) = X1
=> ( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X3,X18] :
( vreduce(X3) = X18
=> ( ? [X12,X11,X26] :
( vnoExp = X18
& ~ visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X11,X26,X12] :
( vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18
& visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X8,X9,X11,X25,X12] :
( vnoExp = X18
& ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X9,X25,X8,X12,X11] :
( vsomeExp(vsubst(X8,X12,X11)) = X18
& visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X12,X8,X9,X11,X25] :
( vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18
& visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X8,X9,X10] :
( vnoExp = X18
& vabs(X8,X9,X10) = X3 )
| ? [X8] :
( vnoExp = X18
& vvar(X8) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-INV') ).
fof(f1316,plain,
spl94_146,
inference(avatar_split_clause,[],[f558,f1314]) ).
fof(f558,plain,
! [X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9))
| ~ visFreeVar(X7,X5)
| X4 = X7 ),
inference(equality_resolution,[],[f557]) ).
fof(f557,plain,
! [X0,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X0,X5,vabs(X7,X6,X9))
| ~ visFreeVar(X7,X5)
| X4 = X7
| X0 != X4 ),
inference(equality_resolution,[],[f556]) ).
fof(f556,plain,
! [X0,X1,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X0,X1,vabs(X7,X6,X9))
| ~ visFreeVar(X7,X5)
| X4 = X7
| X1 != X5
| X0 != X4 ),
inference(equality_resolution,[],[f555]) ).
fof(f555,plain,
! [X2,X0,X1,X6,X9,X7,X4,X5] :
( vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9)))
| ~ visFreeVar(X7,X5)
| X4 = X7
| vabs(X7,X6,X9) != X2
| X1 != X5
| X0 != X4 ),
inference(equality_resolution,[],[f554]) ).
fof(f554,plain,
! [X2,X0,X1,X8,X6,X9,X7,X4,X5] :
( vsubst(X0,X1,X2) = vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9)))
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| ~ visFreeVar(X7,X5)
| X4 = X7
| vabs(X7,X6,X9) != X2
| X1 != X5
| X0 != X4 ),
inference(equality_resolution,[],[f446]) ).
fof(f446,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3
| vsubst(X0,X1,X2) != X3
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| ~ visFreeVar(X7,X5)
| X4 = X7
| vabs(X7,X6,X9) != X2
| X1 != X5
| X0 != X4 ),
inference(cnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3
| vsubst(X0,X1,X2) != X3
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| ~ visFreeVar(X7,X5)
| X4 = X7
| vabs(X7,X6,X9) != X2
| X1 != X5
| X0 != X4 ),
inference(flattening,[],[f199]) ).
fof(f199,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3
| vsubst(X0,X1,X2) != X3
| vgensym(vapp(vapp(X5,X9),vvar(X4))) != X8
| ~ visFreeVar(X7,X5)
| X4 = X7
| vabs(X7,X6,X9) != X2
| X1 != X5
| X0 != X4 ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( vabs(X7,X6,X9) = X2
& X1 = X5
& X0 = X4 )
=> ( ( vgensym(vapp(vapp(X5,X9),vvar(X4))) = X8
& visFreeVar(X7,X5)
& X4 != X7 )
=> ( vsubst(X0,X1,X2) = X3
=> vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3 ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X3,X5,X18,X8,X10,X14,X20,X23,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst4) ).
fof(f1312,plain,
spl94_145,
inference(avatar_split_clause,[],[f380,f1310]) ).
fof(f1310,plain,
( spl94_145
<=> ! [X0,X3,X2,X1] :
( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),vsubst(sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_145])]) ).
fof(f380,plain,
! [X2,X3,X0,X1] :
( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),vsubst(sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),vsubst(sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
& sK62(X0,X1,X2,X3) != sK64(X0,X1,X2,X3)
& vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3)) = X1
& sK65(X0,X1,X2,X3) = X2
& sK64(X0,X1,X2,X3) = X3 )
| ~ sP13(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63,sK64,sK65,sK66])],[f268,f269]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X0
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X1
& X2 = X7
& X3 = X6 )
=> ( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),vsubst(sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
& sK62(X0,X1,X2,X3) != sK64(X0,X1,X2,X3)
& vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3)) = X1
& sK65(X0,X1,X2,X3) = X2
& sK64(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f268,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X0
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X1
& X2 = X7
& X3 = X6 )
| ~ sP13(X0,X1,X2,X3) ),
inference(rectify,[],[f267]) ).
fof(f267,plain,
! [X3,X2,X1,X0] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ~ sP13(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f217]) ).
fof(f1308,plain,
spl94_144,
inference(avatar_split_clause,[],[f386,f1306]) ).
fof(f1306,plain,
( spl94_144
<=> ! [X0,X3,X2,X1] :
( sK71(X0,X1,X2,X3) = vgensym(vapp(vapp(sK68(X0,X1,X2,X3),sK72(X0,X1,X2,X3)),vvar(sK67(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_144])]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( sK71(X0,X1,X2,X3) = vgensym(vapp(vapp(sK68(X0,X1,X2,X3),sK72(X0,X1,X2,X3)),vvar(sK67(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1298,plain,
spl94_143,
inference(avatar_split_clause,[],[f429,f1296]) ).
fof(f429,plain,
! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 = X3 ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 = X3 ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 = X3 ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2)
& X0 != X3 )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& vnoType = vlookup(X8,X19)
& X8 != X20 )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs-1') ).
fof(f1288,plain,
spl94_142,
inference(avatar_split_clause,[],[f559,f1286]) ).
fof(f559,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) ),
inference(duplicate_literal_removal,[],[f455]) ).
fof(f455,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0)
| vnoExp = vreduce(X0) ),
inference(equality_resolution,[],[f340]) ).
fof(f340,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| vnoExp = X1
| vnoExp = X1
| vreduce(X0) != X1 ),
inference(cnf_transformation,[],[f244]) ).
fof(f1279,plain,
( ~ spl94_9
| ~ spl94_137 ),
inference(avatar_contradiction_clause,[],[f1278]) ).
fof(f1278,plain,
( $false
| ~ spl94_9
| ~ spl94_137 ),
inference(trivial_inequality_removal,[],[f1276]) ).
fof(f1276,plain,
( vnoType != vnoType
| ~ spl94_9
| ~ spl94_137 ),
inference(superposition,[],[f599,f1248]) ).
fof(f1248,plain,
( vnoType = vsomeType(sK60(vnoType,sK16,sK14))
| ~ spl94_137 ),
inference(avatar_component_clause,[],[f1246]) ).
fof(f1246,plain,
( spl94_137
<=> vnoType = vsomeType(sK60(vnoType,sK16,sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_137])]) ).
fof(f599,plain,
( ! [X0] : vnoType != vsomeType(X0)
| ~ spl94_9 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f598,plain,
( spl94_9
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_9])]) ).
fof(f1265,plain,
spl94_141,
inference(avatar_split_clause,[],[f500,f1263]) ).
fof(f500,plain,
! [X0,X4] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0 ),
inference(equality_resolution,[],[f499]) ).
fof(f499,plain,
! [X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f498]) ).
fof(f498,plain,
! [X3,X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(X3),X4))
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f419]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK91(X0),sK92(X0),sK93(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92,sK93])],[f162,f292]) ).
fof(f292,plain,
! [X0] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
=> vabs(sK91(X0),sK92(X0),sK93(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
| vapp(X0,X4) != X1 ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
| vapp(X0,X4) != X1 ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X0
& vapp(X0,X4) = X1 )
=> ( ( visSomeExp(X3)
& vreduce(X0) = X3 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2 ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X11,X3,X18,X26,X12] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce5) ).
fof(f1261,plain,
spl94_140,
inference(avatar_split_clause,[],[f437,f1259]) ).
fof(f437,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2 ),
inference(flattening,[],[f181]) ).
fof(f181,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2 ),
inference(ennf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 != X2 )
=> vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 != X20 )
=> vtcheck(vbind(X20,X21,vbind(X8,X22,X19)),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
fof(f1257,plain,
spl94_139,
inference(avatar_split_clause,[],[f392,f1255]) ).
fof(f1255,plain,
( spl94_139
<=> ! [X0,X3,X2,X1] :
( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_139])]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X0
& sK74(X0,X1,X2,X3) = sK75(X0,X1,X2,X3)
& vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X1
& sK73(X0,X1,X2,X3) = X2
& sK74(X0,X1,X2,X3) = X3 )
| ~ sP11(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74,sK75,sK76,sK77])],[f276,f277]) ).
fof(f277,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) = X0
& X5 = X6
& vabs(X6,X7,X8) = X1
& X2 = X4
& X3 = X5 )
=> ( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X0
& sK74(X0,X1,X2,X3) = sK75(X0,X1,X2,X3)
& vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X1
& sK73(X0,X1,X2,X3) = X2
& sK74(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f276,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) = X0
& X5 = X6
& vabs(X6,X7,X8) = X1
& X2 = X4
& X3 = X5 )
| ~ sP11(X0,X1,X2,X3) ),
inference(rectify,[],[f275]) ).
fof(f275,plain,
! [X3,X2,X1,X0] :
( ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ~ sP11(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f215]) ).
fof(f1253,plain,
spl94_138,
inference(avatar_split_clause,[],[f390,f1251]) ).
fof(f1251,plain,
( spl94_138
<=> ! [X0,X3,X2,X1] :
( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_138])]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( vabs(sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f1249,plain,
( spl94_137
| ~ spl94_58
| ~ spl94_104 ),
inference(avatar_split_clause,[],[f1082,f1027,f804,f1246]) ).
fof(f804,plain,
( spl94_58
<=> ! [X2,X0,X1] :
( vsomeType(sK60(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_58])]) ).
fof(f1082,plain,
( vnoType = vsomeType(sK60(vnoType,sK16,sK14))
| ~ spl94_58
| ~ spl94_104 ),
inference(resolution,[],[f1029,f805]) ).
fof(f805,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| vsomeType(sK60(X0,X1,X2)) = X0 )
| ~ spl94_58 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f1029,plain,
( sP7(vnoType,sK16,sK14)
| ~ spl94_104 ),
inference(avatar_component_clause,[],[f1027]) ).
fof(f1244,plain,
spl94_136,
inference(avatar_split_clause,[],[f383,f1242]) ).
fof(f1242,plain,
( spl94_136
<=> ! [X0,X3,X2,X1] :
( vabs(sK70(X0,X1,X2,X3),sK69(X0,X1,X2,X3),sK72(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_136])]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( vabs(sK70(X0,X1,X2,X3),sK69(X0,X1,X2,X3),sK72(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1240,plain,
spl94_135,
inference(avatar_split_clause,[],[f377,f1238]) ).
fof(f1238,plain,
( spl94_135
<=> ! [X0,X3,X2,X1] :
( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_135])]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( vabs(sK62(X0,X1,X2,X3),sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1236,plain,
spl94_134,
inference(avatar_split_clause,[],[f352,f1234]) ).
fof(f1234,plain,
( spl94_134
<=> ! [X2,X0,X1] :
( vtcheck(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK49(X0,X1,X2),sK51(X0,X1,X2))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_134])]) ).
fof(f352,plain,
! [X2,X0,X1] :
( vtcheck(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK49(X0,X1,X2),sK51(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0,X1,X2] :
( ( vtcheck(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK49(X0,X1,X2),sK51(X0,X1,X2))
& varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
& vabs(sK48(X0,X1,X2),sK50(X0,X1,X2),sK49(X0,X1,X2)) = X2 )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49,sK50,sK51])],[f250,f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vtcheck(vbind(X3,X5,X0),X4,X6)
& varrow(X5,X6) = X1
& vabs(X3,X5,X4) = X2 )
=> ( vtcheck(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK49(X0,X1,X2),sK51(X0,X1,X2))
& varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
& vabs(sK48(X0,X1,X2),sK50(X0,X1,X2),sK49(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vtcheck(vbind(X3,X5,X0),X4,X6)
& varrow(X5,X6) = X1
& vabs(X3,X5,X4) = X2 )
| ~ sP5(X0,X1,X2) ),
inference(rectify,[],[f249]) ).
fof(f249,plain,
! [X2,X1,X0] :
( ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ~ sP5(X2,X1,X0) ),
inference(nnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X2,X1,X0] :
( ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ~ sP5(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1226,plain,
spl94_133,
inference(avatar_split_clause,[],[f507,f1224]) ).
fof(f507,plain,
! [X2,X3,X1,X4,X5] :
( vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X3,X2) ),
inference(equality_resolution,[],[f430]) ).
fof(f430,plain,
! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 != X3 ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 != X3 ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| vnoType != vlookup(X0,X2)
| X0 != X3 ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2)
& X0 = X3 )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& vnoType = vlookup(X8,X19)
& X8 = X20 )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs-2') ).
fof(f1208,plain,
spl94_132,
inference(avatar_split_clause,[],[f553,f1206]) ).
fof(f553,plain,
! [X8,X6,X7,X4,X5] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X6,X7,vabs(X4,X5,X8))
| visFreeVar(X4,X7)
| X4 = X6 ),
inference(equality_resolution,[],[f552]) ).
fof(f552,plain,
! [X0,X8,X6,X7,X4,X5] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X0,X7,vabs(X4,X5,X8))
| visFreeVar(X4,X7)
| X4 = X6
| X0 != X6 ),
inference(equality_resolution,[],[f551]) ).
fof(f551,plain,
! [X0,X1,X8,X6,X7,X4,X5] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X0,X1,vabs(X4,X5,X8))
| visFreeVar(X4,X7)
| X4 = X6
| X1 != X7
| X0 != X6 ),
inference(equality_resolution,[],[f550]) ).
fof(f550,plain,
! [X2,X0,X1,X8,X6,X7,X4,X5] :
( vsubst(X0,X1,X2) = vabs(X4,X5,vsubst(X6,X7,X8))
| visFreeVar(X4,X7)
| X4 = X6
| vabs(X4,X5,X8) != X2
| X1 != X7
| X0 != X6 ),
inference(equality_resolution,[],[f445]) ).
fof(f445,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
| vsubst(X0,X1,X2) != X3
| visFreeVar(X4,X7)
| X4 = X6
| vabs(X4,X5,X8) != X2
| X1 != X7
| X0 != X6 ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
| vsubst(X0,X1,X2) != X3
| visFreeVar(X4,X7)
| X4 = X6
| vabs(X4,X5,X8) != X2
| X1 != X7
| X0 != X6 ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
| vsubst(X0,X1,X2) != X3
| visFreeVar(X4,X7)
| X4 = X6
| vabs(X4,X5,X8) != X2
| X1 != X7
| X0 != X6 ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
=> ( ( ~ visFreeVar(X4,X7)
& X4 != X6 )
=> ( vsubst(X0,X1,X2) = X3
=> vabs(X4,X5,vsubst(X6,X7,X8)) = X3 ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X3,X5,X18,X20,X14,X8,X10,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( ~ visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,vsubst(X8,X10,X11)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst5) ).
fof(f1204,plain,
spl94_131,
inference(avatar_split_clause,[],[f354,f1202]) ).
fof(f354,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK52(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ( vsomeType(X1) = vlookup(sK52(X0,X1,X2),X2)
& vvar(sK52(X0,X1,X2)) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ? [X3] :
( vsomeType(X1) = vlookup(X3,X2)
& vvar(X3) = X0 )
=> ( vsomeType(X1) = vlookup(sK52(X0,X1,X2),X2)
& vvar(sK52(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ? [X3] :
( vsomeType(X1) = vlookup(X3,X2)
& vvar(X3) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(rectify,[],[f209]) ).
fof(f209,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(definition_folding,[],[f136,f208,f207]) ).
fof(f208,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ~ sP6(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f136,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X10,X14,X19] :
( vtcheck(X19,X10,X14)
=> ( ? [X11,X12,X9] :
( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14))
& vapp(X11,X12) = X10 )
| ? [X8,X12,X32,X33] :
( vtcheck(vbind(X8,X32,X19),X12,X33)
& varrow(X32,X33) = X14
& vabs(X8,X32,X12) = X10 )
| ? [X8] :
( vlookup(X8,X19) = vsomeType(X14)
& vvar(X8) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-inv') ).
fof(f1200,plain,
spl94_130,
inference(avatar_split_clause,[],[f316,f1198]) ).
fof(f1198,plain,
( spl94_130
<=> ! [X0,X1] :
( vsomeExp(vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),vgetSomeExp(sK24(X0,X1)))) = X0
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_130])]) ).
fof(f316,plain,
! [X0,X1] :
( vsomeExp(vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),vgetSomeExp(sK24(X0,X1)))) = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),vgetSomeExp(sK24(X0,X1)))) = X0
& visSomeExp(sK24(X0,X1))
& sK24(X0,X1) = vreduce(sK20(X0,X1))
& vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),sK20(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f222,f223]) ).
fof(f223,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X0
& visSomeExp(X6)
& vreduce(X2) = X6
& vapp(vabs(X3,X4,X5),X2) = X1 )
=> ( vsomeExp(vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),vgetSomeExp(sK24(X0,X1)))) = X0
& visSomeExp(sK24(X0,X1))
& sK24(X0,X1) = vreduce(sK20(X0,X1))
& vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),sK20(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f222,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X0
& visSomeExp(X6)
& vreduce(X2) = X6
& vapp(vabs(X3,X4,X5),X2) = X1 )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f221]) ).
fof(f221,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f205]) ).
fof(f1184,plain,
spl94_129,
inference(avatar_split_clause,[],[f523,f1182]) ).
fof(f523,plain,
! [X3,X0,X4,X5] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0))
| ~ visSomeExp(vreduce(X0)) ),
inference(equality_resolution,[],[f522]) ).
fof(f522,plain,
! [X3,X0,X1,X4,X5] :
( vreduce(X1) = vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0))))
| ~ visSomeExp(vreduce(X0))
| vapp(vabs(X3,X4,X5),X0) != X1 ),
inference(equality_resolution,[],[f521]) ).
fof(f521,plain,
! [X3,X0,X1,X6,X4,X5] :
( vreduce(X1) = vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6)))
| ~ visSomeExp(X6)
| vreduce(X0) != X6
| vapp(vabs(X3,X4,X5),X0) != X1 ),
inference(equality_resolution,[],[f436]) ).
fof(f436,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X6)
| vreduce(X0) != X6
| vapp(vabs(X3,X4,X5),X0) != X1 ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X6)
| vreduce(X0) != X6
| vapp(vabs(X3,X4,X5),X0) != X1 ),
inference(flattening,[],[f179]) ).
fof(f179,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X6)
| vreduce(X0) != X6
| vapp(vabs(X3,X4,X5),X0) != X1 ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X3,X4,X5),X0) = X1
=> ( ( visSomeExp(X6)
& vreduce(X0) = X6 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2 ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X12,X3,X18,X8,X9,X11,X25] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce2) ).
fof(f1180,plain,
spl94_128,
inference(avatar_split_clause,[],[f468,f1178]) ).
fof(f468,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0 ),
inference(equality_resolution,[],[f363]) ).
fof(f363,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| sK61(X0,X1,X2) = X0
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ( vnoType = X2
& vempty = X1
& sK61(X0,X1,X2) = X0 )
| vlookup(X0,X1) != X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f264,f265]) ).
fof(f265,plain,
! [X0,X1,X2] :
( ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
=> ( vnoType = X2
& vempty = X1
& sK61(X0,X1,X2) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f264,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
| vlookup(X0,X1) != X2 ),
inference(rectify,[],[f212]) ).
fof(f212,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 )
| vlookup(X0,X1) != X2 ),
inference(definition_folding,[],[f138,f211,f210]) ).
fof(f210,plain,
! [X2,X1,X0] :
( ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ~ sP7(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f211,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ~ sP8(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f138,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 )
| vlookup(X0,X1) != X2 ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 )
| vlookup(X0,X1) != X2 ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( vlookup(X0,X1) = X2
=> ( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X15,X18] :
( vlookup(X0,X15) = X18
=> ( ? [X21,X20,X8,X19] :
( vlookup(X8,X19) = X18
& X8 != X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X19,X8,X20,X21] :
( vsomeType(X21) = X18
& X8 = X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X8] :
( vnoType = X18
& vempty = X15
& X0 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookup-INV') ).
fof(f1167,plain,
( spl94_127
| ~ spl94_44
| ~ spl94_104 ),
inference(avatar_split_clause,[],[f1083,f1027,f744,f1164]) ).
fof(f1164,plain,
( spl94_127
<=> sK14 = sK58(vnoType,sK16,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_127])]) ).
fof(f744,plain,
( spl94_44
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_44])]) ).
fof(f1083,plain,
( sK14 = sK58(vnoType,sK16,sK14)
| ~ spl94_44
| ~ spl94_104 ),
inference(resolution,[],[f1029,f745]) ).
fof(f745,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| sK58(X0,X1,X2) = X2 )
| ~ spl94_44 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f1162,plain,
spl94_126,
inference(avatar_split_clause,[],[f360,f1160]) ).
fof(f1160,plain,
( spl94_126
<=> ! [X2,X0,X1] :
( vbind(sK59(X0,X1,X2),sK60(X0,X1,X2),sK57(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_126])]) ).
fof(f360,plain,
! [X2,X0,X1] :
( vbind(sK59(X0,X1,X2),sK60(X0,X1,X2),sK57(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ( vsomeType(sK60(X0,X1,X2)) = X0
& sK58(X0,X1,X2) = sK59(X0,X1,X2)
& vbind(sK59(X0,X1,X2),sK60(X0,X1,X2),sK57(X0,X1,X2)) = X1
& sK58(X0,X1,X2) = X2 )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60])],[f261,f262]) ).
fof(f262,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
=> ( vsomeType(sK60(X0,X1,X2)) = X0
& sK58(X0,X1,X2) = sK59(X0,X1,X2)
& vbind(sK59(X0,X1,X2),sK60(X0,X1,X2),sK57(X0,X1,X2)) = X1
& sK58(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
| ~ sP7(X0,X1,X2) ),
inference(rectify,[],[f260]) ).
fof(f260,plain,
! [X2,X1,X0] :
( ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ~ sP7(X2,X1,X0) ),
inference(nnf_transformation,[],[f210]) ).
fof(f1158,plain,
spl94_125,
inference(avatar_split_clause,[],[f356,f1156]) ).
fof(f356,plain,
! [X2,X0,X1] :
( vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
& sK54(X0,X1,X2) != sK55(X0,X1,X2)
& vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1
& sK55(X0,X1,X2) = X2 )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f257,f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
=> ( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
& sK54(X0,X1,X2) != sK55(X0,X1,X2)
& vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1
& sK55(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
| ~ sP8(X0,X1,X2) ),
inference(rectify,[],[f256]) ).
fof(f256,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ~ sP8(X2,X1,X0) ),
inference(nnf_transformation,[],[f211]) ).
fof(f1154,plain,
spl94_124,
inference(avatar_split_clause,[],[f353,f1152]) ).
fof(f353,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK52(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1150,plain,
spl94_123,
inference(avatar_split_clause,[],[f350,f1148]) ).
fof(f1148,plain,
( spl94_123
<=> ! [X2,X0,X1] :
( vabs(sK48(X0,X1,X2),sK50(X0,X1,X2),sK49(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_123])]) ).
fof(f350,plain,
! [X2,X0,X1] :
( vabs(sK48(X0,X1,X2),sK50(X0,X1,X2),sK49(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f252]) ).
fof(f1146,plain,
spl94_122,
inference(avatar_split_clause,[],[f332,f1144]) ).
fof(f1144,plain,
( spl94_122
<=> ! [X0,X1] :
( vapp(vabs(sK38(X0,X1),sK36(X0,X1),sK40(X0,X1)),sK39(X0,X1)) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_122])]) ).
fof(f332,plain,
! [X0,X1] :
( vapp(vabs(sK38(X0,X1),sK36(X0,X1),sK40(X0,X1)),sK39(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( ( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
& visValue(sK39(X0,X1))
& ~ visSomeExp(sK37(X0,X1))
& sK37(X0,X1) = vreduce(sK39(X0,X1))
& vapp(vabs(sK38(X0,X1),sK36(X0,X1),sK40(X0,X1)),sK39(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37,sK38,sK39,sK40])],[f238,f239]) ).
fof(f239,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X0
& visValue(X5)
& ~ visSomeExp(X3)
& vreduce(X5) = X3
& vapp(vabs(X4,X2,X6),X5) = X1 )
=> ( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
& visValue(sK39(X0,X1))
& ~ visSomeExp(sK37(X0,X1))
& sK37(X0,X1) = vreduce(sK39(X0,X1))
& vapp(vabs(sK38(X0,X1),sK36(X0,X1),sK40(X0,X1)),sK39(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f238,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X0
& visValue(X5)
& ~ visSomeExp(X3)
& vreduce(X5) = X3
& vapp(vabs(X4,X2,X6),X5) = X1 )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f237]) ).
fof(f237,plain,
! [X1,X0] :
( ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f1142,plain,
spl94_121,
inference(avatar_split_clause,[],[f327,f1140]) ).
fof(f1140,plain,
( spl94_121
<=> ! [X0,X1] :
( vapp(vabs(sK31(X0,X1),sK32(X0,X1),sK33(X0,X1)),sK35(X0,X1)) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_121])]) ).
fof(f327,plain,
! [X0,X1] :
( vapp(vabs(sK31(X0,X1),sK32(X0,X1),sK33(X0,X1)),sK35(X0,X1)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visValue(sK35(X0,X1))
& ~ visSomeExp(sK34(X0,X1))
& sK34(X0,X1) = vreduce(sK35(X0,X1))
& vapp(vabs(sK31(X0,X1),sK32(X0,X1),sK33(X0,X1)),sK35(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34,sK35])],[f234,f235]) ).
fof(f235,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vnoExp = X0
& ~ visValue(X6)
& ~ visSomeExp(X5)
& vreduce(X6) = X5
& vapp(vabs(X2,X3,X4),X6) = X1 )
=> ( vnoExp = X0
& ~ visValue(sK35(X0,X1))
& ~ visSomeExp(sK34(X0,X1))
& sK34(X0,X1) = vreduce(sK35(X0,X1))
& vapp(vabs(sK31(X0,X1),sK32(X0,X1),sK33(X0,X1)),sK35(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f234,plain,
! [X0,X1] :
( ? [X2,X3,X4,X5,X6] :
( vnoExp = X0
& ~ visValue(X6)
& ~ visSomeExp(X5)
& vreduce(X6) = X5
& vapp(vabs(X2,X3,X4),X6) = X1 )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f233]) ).
fof(f233,plain,
! [X1,X0] :
( ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f1138,plain,
spl94_120,
inference(avatar_split_clause,[],[f313,f1136]) ).
fof(f1136,plain,
( spl94_120
<=> ! [X0,X1] :
( vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),sK20(X0,X1)) = X1
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_120])]) ).
fof(f313,plain,
! [X0,X1] :
( vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),sK20(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f1130,plain,
spl94_119,
inference(avatar_split_clause,[],[f520,f1128]) ).
fof(f520,plain,
! [X0,X6,X4,X5] :
( vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5))
| ~ visValue(X5)
| visSomeExp(vreduce(X5)) ),
inference(equality_resolution,[],[f519]) ).
fof(f519,plain,
! [X2,X0,X6,X4,X5] :
( vreduce(X2) = vsomeExp(vsubst(X4,X5,X6))
| ~ visValue(X5)
| visSomeExp(vreduce(X5))
| vapp(vabs(X4,X0,X6),X5) != X2 ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
! [X2,X0,X1,X6,X4,X5] :
( vreduce(X2) = vsomeExp(vsubst(X4,X5,X6))
| ~ visValue(X5)
| visSomeExp(X1)
| vreduce(X5) != X1
| vapp(vabs(X4,X0,X6),X5) != X2 ),
inference(equality_resolution,[],[f435]) ).
fof(f435,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeExp(vsubst(X4,X5,X6)) = X3
| vreduce(X2) != X3
| ~ visValue(X5)
| visSomeExp(X1)
| vreduce(X5) != X1
| vapp(vabs(X4,X0,X6),X5) != X2 ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X3
| vreduce(X2) != X3
| ~ visValue(X5)
| visSomeExp(X1)
| vreduce(X5) != X1
| vapp(vabs(X4,X0,X6),X5) != X2 ),
inference(flattening,[],[f177]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeExp(vsubst(X4,X5,X6)) = X3
| vreduce(X2) != X3
| ~ visValue(X5)
| visSomeExp(X1)
| vreduce(X5) != X1
| vapp(vabs(X4,X0,X6),X5) != X2 ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X4,X0,X6),X5) = X2
=> ( ( visValue(X5)
& ~ visSomeExp(X1)
& vreduce(X5) = X1 )
=> ( vreduce(X2) = X3
=> vsomeExp(vsubst(X4,X5,X6)) = X3 ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X9,X25,X3,X18,X8,X12,X11] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vsubst(X8,X12,X11)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce3) ).
fof(f1126,plain,
spl94_118,
inference(avatar_split_clause,[],[f497,f1124]) ).
fof(f497,plain,
! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 ),
inference(equality_resolution,[],[f496]) ).
fof(f496,plain,
! [X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(vreduce(X1))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f495]) ).
fof(f495,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f418]) ).
fof(f418,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK88,sK89,sK90])],[f160,f290]) ).
fof(f290,plain,
! [X1] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
=> vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
| vapp(X1,X0) != X3 ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
| vapp(X1,X0) != X3 ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X1
& vapp(X1,X0) = X3 )
=> ( ( ~ visSomeExp(X2)
& vreduce(X1) = X2 )
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X12,X11,X26,X3,X18] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( ~ visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce6) ).
fof(f1113,plain,
spl94_117,
inference(avatar_split_clause,[],[f540,f1111]) ).
fof(f540,plain,
! [X2,X3,X1,X6,X4,X5] :
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6) ),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 != X2 ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 != X2 ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(vbind(X2,X3,X4),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 != X2 ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 = X2 )
=> vtcheck(vbind(X2,X3,X4),X5,X6) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 = X20 )
=> vtcheck(vbind(X8,X22,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Duplicate') ).
fof(f1109,plain,
spl94_116,
inference(avatar_split_clause,[],[f466,f1107]) ).
fof(f466,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ),
inference(equality_resolution,[],[f365]) ).
fof(f365,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vnoType = X2
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f266]) ).
fof(f1074,plain,
spl94_115,
inference(avatar_split_clause,[],[f544,f1072]) ).
fof(f544,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f543]) ).
fof(f543,plain,
! [X0,X6,X7,X4,X5] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X0,X6,vapp(X4,X7))
| X0 != X5 ),
inference(equality_resolution,[],[f542]) ).
fof(f542,plain,
! [X0,X1,X6,X7,X4,X5] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X0,X1,vapp(X4,X7))
| X1 != X6
| X0 != X5 ),
inference(equality_resolution,[],[f541]) ).
fof(f541,plain,
! [X2,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,X2) = vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7))
| vapp(X4,X7) != X2
| X1 != X6
| X0 != X5 ),
inference(equality_resolution,[],[f443]) ).
fof(f443,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3
| vsubst(X0,X1,X2) != X3
| vapp(X4,X7) != X2
| X1 != X6
| X0 != X5 ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3
| vsubst(X0,X1,X2) != X3
| vapp(X4,X7) != X2
| X1 != X6
| X0 != X5 ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3
| vsubst(X0,X1,X2) != X3
| vapp(X4,X7) != X2
| X1 != X6
| X0 != X5 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vapp(X4,X7) = X2
& X1 = X6
& X0 = X5 )
=> ( vsubst(X0,X1,X2) = X3
=> vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3 ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X3,X5,X18,X11,X8,X10,X12] :
( ( vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
=> ( vsubst(X0,X3,X5) = X18
=> vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst2) ).
fof(f1070,plain,
spl94_114,
inference(avatar_split_clause,[],[f420,f1068]) ).
fof(f420,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X3,X0)
& vtcheck(X1,X2,varrow(X0,X4)) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X9,X19,X11,X12,X14] :
( ( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14)) )
=> vtcheck(X19,vapp(X11,X12),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
fof(f1066,plain,
spl94_113,
inference(avatar_split_clause,[],[f414,f1064]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X1,X3,X0),X2,X4)
=> vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4)) ),
inference(rectify,[],[f52]) ).
fof(f52,axiom,
! [X19,X8,X10,X9,X14] :
( vtcheck(vbind(X8,X9,X19),X10,X14)
=> vtcheck(X19,vabs(X8,X9,X10),varrow(X9,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-abs') ).
fof(f1062,plain,
spl94_112,
inference(avatar_split_clause,[],[f411,f1060]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( vtcheck(X2,veabs,X3)
& vnoType = vlookup(X0,X2) )
=> vtcheck(vbind(X0,X1,X2),veabs,X3) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X8,X9,X19,X14] :
( ( vtcheck(X19,veabs,X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),veabs,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs-IH') ).
fof(f1058,plain,
spl94_111,
inference(avatar_split_clause,[],[f401,f1056]) ).
fof(f1056,plain,
( spl94_111
<=> ! [X0,X3,X2,X1] :
( sK81(X0,X1,X2,X3) = sK82(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_111])]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( sK81(X0,X1,X2,X3) = sK82(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1,X2,X3] :
( ( sK83(X0,X1,X2,X3) = X0
& sK81(X0,X1,X2,X3) = sK82(X0,X1,X2,X3)
& vvar(sK82(X0,X1,X2,X3)) = X1
& sK83(X0,X1,X2,X3) = X2
& sK81(X0,X1,X2,X3) = X3 )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82,sK83])],[f284,f285]) ).
fof(f285,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( X0 = X6
& X4 = X5
& vvar(X5) = X1
& X2 = X6
& X3 = X4 )
=> ( sK83(X0,X1,X2,X3) = X0
& sK81(X0,X1,X2,X3) = sK82(X0,X1,X2,X3)
& vvar(sK82(X0,X1,X2,X3)) = X1
& sK83(X0,X1,X2,X3) = X2
& sK81(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( X0 = X6
& X4 = X5
& vvar(X5) = X1
& X2 = X6
& X3 = X4 )
| ~ sP9(X0,X1,X2,X3) ),
inference(rectify,[],[f283]) ).
fof(f283,plain,
! [X3,X2,X1,X0] :
( ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 )
| ~ sP9(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f213]) ).
fof(f1054,plain,
spl94_110,
inference(avatar_split_clause,[],[f396,f1052]) ).
fof(f1052,plain,
( spl94_110
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) != sK80(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_110])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) != sK80(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1,X2,X3] :
( ( vvar(sK80(X0,X1,X2,X3)) = X0
& sK79(X0,X1,X2,X3) != sK80(X0,X1,X2,X3)
& vvar(sK80(X0,X1,X2,X3)) = X1
& sK78(X0,X1,X2,X3) = X2
& sK79(X0,X1,X2,X3) = X3 )
| ~ sP10(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78,sK79,sK80])],[f280,f281]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( vvar(X6) = X0
& X5 != X6
& vvar(X6) = X1
& X2 = X4
& X3 = X5 )
=> ( vvar(sK80(X0,X1,X2,X3)) = X0
& sK79(X0,X1,X2,X3) != sK80(X0,X1,X2,X3)
& vvar(sK80(X0,X1,X2,X3)) = X1
& sK78(X0,X1,X2,X3) = X2
& sK79(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f280,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( vvar(X6) = X0
& X5 != X6
& vvar(X6) = X1
& X2 = X4
& X3 = X5 )
| ~ sP10(X0,X1,X2,X3) ),
inference(rectify,[],[f279]) ).
fof(f279,plain,
! [X3,X2,X1,X0] :
( ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ~ sP10(X3,X2,X1,X0) ),
inference(nnf_transformation,[],[f214]) ).
fof(f1050,plain,
spl94_109,
inference(avatar_split_clause,[],[f391,f1048]) ).
fof(f1048,plain,
( spl94_109
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = sK75(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_109])]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = sK75(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f1046,plain,
spl94_108,
inference(avatar_split_clause,[],[f385,f1044]) ).
fof(f1044,plain,
( spl94_108
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_108])]) ).
fof(f385,plain,
! [X2,X3,X0,X1] :
( visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1042,plain,
spl94_107,
inference(avatar_split_clause,[],[f384,f1040]) ).
fof(f1040,plain,
( spl94_107
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) != sK70(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_107])]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) != sK70(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1038,plain,
spl94_106,
inference(avatar_split_clause,[],[f379,f1036]) ).
fof(f379,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1034,plain,
( spl94_103
| spl94_104
| spl94_105
| ~ spl94_1
| ~ spl94_99 ),
inference(avatar_split_clause,[],[f1006,f1001,f561,f1031,f1027,f1023]) ).
fof(f1006,plain,
( sP8(vnoType,sK16,sK14)
| sP7(vnoType,sK16,sK14)
| vempty = sK16
| ~ spl94_1
| ~ spl94_99 ),
inference(superposition,[],[f1002,f563]) ).
fof(f1021,plain,
spl94_102,
inference(avatar_split_clause,[],[f378,f1019]) ).
fof(f1019,plain,
( spl94_102
<=> ! [X0,X3,X2,X1] :
( sK62(X0,X1,X2,X3) != sK64(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_102])]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( sK62(X0,X1,X2,X3) != sK64(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1017,plain,
spl94_101,
inference(avatar_split_clause,[],[f348,f1015]) ).
fof(f348,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
& vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
& vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2 )
| ~ sP6(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47])],[f246,f247]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X0,X4,X5)
& vtcheck(X0,X3,varrow(X5,X1))
& vapp(X3,X4) = X2 )
=> ( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
& vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
& vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X0,X4,X5)
& vtcheck(X0,X3,varrow(X5,X1))
& vapp(X3,X4) = X2 )
| ~ sP6(X0,X1,X2) ),
inference(rectify,[],[f245]) ).
fof(f245,plain,
! [X2,X1,X0] :
( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ~ sP6(X2,X1,X0) ),
inference(nnf_transformation,[],[f208]) ).
fof(f1013,plain,
spl94_100,
inference(avatar_split_clause,[],[f336,f1011]) ).
fof(f1011,plain,
( spl94_100
<=> ! [X0,X1] :
( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_100])]) ).
fof(f336,plain,
! [X0,X1] :
( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f1003,plain,
spl94_99,
inference(avatar_split_clause,[],[f467,f1001]) ).
fof(f467,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ),
inference(equality_resolution,[],[f364]) ).
fof(f364,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vempty = X1
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f266]) ).
fof(f999,plain,
spl94_98,
inference(avatar_split_clause,[],[f358,f997]) ).
fof(f358,plain,
! [X2,X0,X1] :
( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f995,plain,
spl94_97,
inference(avatar_split_clause,[],[f351,f993]) ).
fof(f993,plain,
( spl94_97
<=> ! [X2,X0,X1] :
( varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_97])]) ).
fof(f351,plain,
! [X2,X0,X1] :
( varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f252]) ).
fof(f988,plain,
spl94_96,
inference(avatar_split_clause,[],[f347,f986]) ).
fof(f986,plain,
( spl94_96
<=> ! [X2,X0,X1] :
( vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_96])]) ).
fof(f347,plain,
! [X2,X0,X1] :
( vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f982,plain,
spl94_95,
inference(avatar_split_clause,[],[f517,f980]) ).
fof(f517,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f516]) ).
fof(f516,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f515]) ).
fof(f515,plain,
! [X2,X3,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(X3)
| vreduce(X4) != X3
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f434]) ).
fof(f434,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vnoExp = X6
| vreduce(X5) != X6
| visValue(X4)
| visSomeExp(X3)
| vreduce(X4) != X3
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vnoExp = X6
| vreduce(X5) != X6
| visValue(X4)
| visSomeExp(X3)
| vreduce(X4) != X3
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(flattening,[],[f175]) ).
fof(f175,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vnoExp = X6
| vreduce(X5) != X6
| visValue(X4)
| visSomeExp(X3)
| vreduce(X4) != X3
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X0,X1,X2),X4) = X5
=> ( ( ~ visValue(X4)
& ~ visSomeExp(X3)
& vreduce(X4) = X3 )
=> ( vreduce(X5) = X6
=> vnoExp = X6 ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X8,X9,X11,X25,X12,X3,X18] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce4) ).
fof(f978,plain,
spl94_94,
inference(avatar_split_clause,[],[f349,f976]) ).
fof(f349,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f974,plain,
spl94_93,
inference(avatar_split_clause,[],[f326,f972]) ).
fof(f972,plain,
( spl94_93
<=> ! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_93])]) ).
fof(f326,plain,
! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
& visSomeExp(sK29(X0,X1))
& sK29(X0,X1) = vreduce(sK28(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK28(X0,X1)
& vapp(sK28(X0,X1),sK30(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29,sK30])],[f230,f231]) ).
fof(f231,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X0
& visSomeExp(X3)
& vreduce(X2) = X3
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X2
& vapp(X2,X4) = X1 )
=> ( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
& visSomeExp(sK29(X0,X1))
& sK29(X0,X1) = vreduce(sK28(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK28(X0,X1)
& vapp(sK28(X0,X1),sK30(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f230,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X0
& visSomeExp(X3)
& vreduce(X2) = X3
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X2
& vapp(X2,X4) = X1 )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f229]) ).
fof(f229,plain,
! [X1,X0] :
( ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f964,plain,
spl94_92,
inference(avatar_split_clause,[],[f535,f962]) ).
fof(f535,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f534]) ).
fof(f534,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f533]) ).
fof(f533,plain,
! [X2,X3,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,X3)
| X1 = X5
| vbind(X1,X0,X6) != X3
| X2 != X5 ),
inference(equality_resolution,[],[f440]) ).
fof(f440,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vlookup(X5,X6) = X4
| vlookup(X2,X3) != X4
| X1 = X5
| vbind(X1,X0,X6) != X3
| X2 != X5 ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vlookup(X5,X6) = X4
| vlookup(X2,X3) != X4
| X1 = X5
| vbind(X1,X0,X6) != X3
| X2 != X5 ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vlookup(X5,X6) = X4
| vlookup(X2,X3) != X4
| X1 = X5
| vbind(X1,X0,X6) != X3
| X2 != X5 ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X1,X0,X6) = X3
& X2 = X5 )
=> ( X1 != X5
=> ( vlookup(X2,X3) = X4
=> vlookup(X5,X6) = X4 ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X21,X20,X0,X15,X18,X8,X19] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 != X20
=> ( vlookup(X0,X15) = X18
=> vlookup(X8,X19) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup2) ).
fof(f960,plain,
spl94_91,
inference(avatar_split_clause,[],[f400,f958]) ).
fof(f958,plain,
( spl94_91
<=> ! [X0,X3,X2,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_91])]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f956,plain,
spl94_90,
inference(avatar_split_clause,[],[f397,f954]) ).
fof(f954,plain,
( spl94_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_90])]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f952,plain,
spl94_89,
inference(avatar_split_clause,[],[f395,f950]) ).
fof(f950,plain,
( spl94_89
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_89])]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f948,plain,
spl94_88,
inference(avatar_split_clause,[],[f361,f946]) ).
fof(f946,plain,
( spl94_88
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_88])]) ).
fof(f361,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f944,plain,
spl94_87,
inference(avatar_split_clause,[],[f357,f942]) ).
fof(f357,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f940,plain,
( spl94_86
| ~ spl94_39
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f833,f784,f719,f938]) ).
fof(f938,plain,
( spl94_86
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_86])]) ).
fof(f784,plain,
( spl94_53
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_53])]) ).
fof(f833,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl94_39
| ~ spl94_53 ),
inference(resolution,[],[f785,f720]) ).
fof(f785,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_53 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f925,plain,
( spl94_85
| ~ spl94_40
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f832,f784,f723,f923]) ).
fof(f923,plain,
( spl94_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_85])]) ).
fof(f832,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl94_40
| ~ spl94_53 ),
inference(resolution,[],[f785,f724]) ).
fof(f921,plain,
( spl94_84
| ~ spl94_39
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f820,f760,f719,f919]) ).
fof(f919,plain,
( spl94_84
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_84])]) ).
fof(f760,plain,
( spl94_48
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_48])]) ).
fof(f820,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl94_39
| ~ spl94_48 ),
inference(resolution,[],[f761,f720]) ).
fof(f761,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_48 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f917,plain,
spl94_83,
inference(avatar_split_clause,[],[f549,f915]) ).
fof(f549,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f548]) ).
fof(f548,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X2,X3,X0,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X0 != X3
| X2 != X6 ),
inference(equality_resolution,[],[f546]) ).
fof(f546,plain,
! [X2,X3,X0,X8,X6,X7,X4] :
( vsubst(X2,X3,X4) = vabs(X6,X7,X8)
| vabs(X6,X7,X8) != X4
| X0 != X3
| X2 != X6 ),
inference(equality_resolution,[],[f545]) ).
fof(f545,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4] :
( vsubst(X2,X3,X4) = vabs(X6,X7,X8)
| X1 != X6
| vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f444]) ).
fof(f444,plain,
! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vabs(X6,X7,X8) = X5
| vsubst(X2,X3,X4) != X5
| X1 != X6
| vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) = X5
| vsubst(X2,X3,X4) != X5
| X1 != X6
| vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2 ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( vabs(X6,X7,X8) = X5
| vsubst(X2,X3,X4) != X5
| X1 != X6
| vabs(X6,X7,X8) != X4
| X0 != X3
| X1 != X2 ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X6,X7,X8) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 = X6
=> ( vsubst(X2,X3,X4) = X5
=> vabs(X6,X7,X8) = X5 ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X10,X8,X0,X3,X5,X18,X20,X14,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,X11) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst3) ).
fof(f913,plain,
spl94_82,
inference(avatar_split_clause,[],[f514,f911]) ).
fof(f514,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f513]) ).
fof(f513,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X1,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4
| X1 != X4 ),
inference(equality_resolution,[],[f431]) ).
fof(f431,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( ( visFreeVar(X4,X5)
& X3 != X4 )
| ~ visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4 ) )
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(flattening,[],[f173]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( ( visFreeVar(X4,X5)
& X3 != X4 )
| ~ visFreeVar(X1,X2) )
& ( visFreeVar(X1,X2)
| ~ visFreeVar(X4,X5)
| X3 = X4 ) )
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(ennf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X3,X0,X5) = X2
& X1 = X4 )
=> ( ( visFreeVar(X1,X2)
=> ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ( visFreeVar(X4,X5)
& X3 != X4 )
=> visFreeVar(X1,X2) ) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X14,X0,X3,X8,X13,X10] :
( ( vabs(X8,X14,X10) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X10)
& X8 != X13 ) )
& ( ( visFreeVar(X13,X10)
& X8 != X13 )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f909,plain,
spl94_81,
inference(avatar_split_clause,[],[f427,f907]) ).
fof(f907,plain,
( spl94_81
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_81])]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vabs(X0,X1,X2) = vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2,X3,X1,X4,X5] :
( ( ( X3 = X5
& X2 = X4
& X0 = X1 )
=> vabs(X0,X2,X3) = vabs(X1,X4,X5) )
& ( vabs(X0,X2,X3) = vabs(X1,X4,X5)
=> ( X3 = X5
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
fof(f905,plain,
spl94_80,
inference(avatar_split_clause,[],[f426,f903]) ).
fof(f903,plain,
( spl94_80
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_80])]) ).
fof(f426,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f901,plain,
spl94_79,
inference(avatar_split_clause,[],[f425,f899]) ).
fof(f899,plain,
( spl94_79
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_79])]) ).
fof(f425,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f897,plain,
spl94_78,
inference(avatar_split_clause,[],[f423,f895]) ).
fof(f895,plain,
( spl94_78
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_78])]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vbind(X0,X1,X2) = vbind(X3,X4,X5) )
& ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X15,X1,X4,X16] :
( ( ( X15 = X16
& X2 = X4
& X0 = X1 )
=> vbind(X0,X2,X15) = vbind(X1,X4,X16) )
& ( vbind(X0,X2,X15) = vbind(X1,X4,X16)
=> ( X15 = X16
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
fof(f893,plain,
spl94_77,
inference(avatar_split_clause,[],[f422,f891]) ).
fof(f891,plain,
( spl94_77
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_77])]) ).
fof(f422,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f889,plain,
spl94_76,
inference(avatar_split_clause,[],[f421,f887]) ).
fof(f887,plain,
( spl94_76
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_76])]) ).
fof(f421,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f885,plain,
spl94_75,
inference(avatar_split_clause,[],[f402,f883]) ).
fof(f883,plain,
( spl94_75
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_75])]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( sK83(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f881,plain,
spl94_74,
inference(avatar_split_clause,[],[f399,f879]) ).
fof(f879,plain,
( spl94_74
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_74])]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( sK83(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f877,plain,
( spl94_73
| ~ spl94_40
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f819,f760,f723,f875]) ).
fof(f875,plain,
( spl94_73
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_73])]) ).
fof(f819,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl94_40
| ~ spl94_48 ),
inference(resolution,[],[f761,f724]) ).
fof(f873,plain,
spl94_72,
inference(avatar_split_clause,[],[f398,f871]) ).
fof(f871,plain,
( spl94_72
<=> ! [X0,X3,X2,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_72])]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f869,plain,
spl94_71,
inference(avatar_split_clause,[],[f394,f867]) ).
fof(f867,plain,
( spl94_71
<=> ! [X0,X3,X2,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_71])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f865,plain,
spl94_70,
inference(avatar_split_clause,[],[f393,f863]) ).
fof(f863,plain,
( spl94_70
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_70])]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f861,plain,
spl94_69,
inference(avatar_split_clause,[],[f389,f859]) ).
fof(f859,plain,
( spl94_69
<=> ! [X0,X3,X2,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_69])]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f857,plain,
spl94_68,
inference(avatar_split_clause,[],[f388,f855]) ).
fof(f855,plain,
( spl94_68
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_68])]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f853,plain,
spl94_67,
inference(avatar_split_clause,[],[f382,f851]) ).
fof(f851,plain,
( spl94_67
<=> ! [X0,X3,X2,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_67])]) ).
fof(f382,plain,
! [X2,X3,X0,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f849,plain,
spl94_66,
inference(avatar_split_clause,[],[f381,f847]) ).
fof(f847,plain,
( spl94_66
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_66])]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f845,plain,
spl94_65,
inference(avatar_split_clause,[],[f376,f843]) ).
fof(f843,plain,
( spl94_65
<=> ! [X0,X3,X2,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_65])]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f841,plain,
spl94_64,
inference(avatar_split_clause,[],[f375,f839]) ).
fof(f839,plain,
( spl94_64
<=> ! [X0,X3,X2,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_64])]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f837,plain,
spl94_63,
inference(avatar_split_clause,[],[f322,f835]) ).
fof(f835,plain,
( spl94_63
<=> ! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_63])]) ).
fof(f322,plain,
! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f831,plain,
spl94_62,
inference(avatar_split_clause,[],[f317,f829]) ).
fof(f829,plain,
( spl94_62
<=> ! [X0,X1] :
( vapp(sK26(X0,X1),sK25(X0,X1)) = X1
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_62])]) ).
fof(f317,plain,
! [X0,X1] :
( vapp(sK26(X0,X1),sK25(X0,X1)) = X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visSomeExp(sK27(X0,X1))
& sK27(X0,X1) = vreduce(sK26(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK26(X0,X1)
& vapp(sK26(X0,X1),sK25(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f226,f227]) ).
fof(f227,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X0
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X1 )
=> ( vnoExp = X0
& ~ visSomeExp(sK27(X0,X1))
& sK27(X0,X1) = vreduce(sK26(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK26(X0,X1)
& vapp(sK26(X0,X1),sK25(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f226,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X0
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X1 )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f225]) ).
fof(f225,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ~ sP3(X1,X0) ),
inference(nnf_transformation,[],[f204]) ).
fof(f818,plain,
spl94_61,
inference(avatar_split_clause,[],[f527,f816]) ).
fof(f527,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f526]) ).
fof(f526,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f525]) ).
fof(f525,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f524]) ).
fof(f524,plain,
! [X2,X3,X0,X1,X6,X4] :
( vvar(X6) = vsubst(X2,X3,X4)
| X1 = X6
| vvar(X6) != X4
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f438]) ).
fof(f438,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vvar(X6) = X5
| vsubst(X2,X3,X4) != X5
| X1 = X6
| vvar(X6) != X4
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vvar(X6) = X5
| vsubst(X2,X3,X4) != X5
| X1 = X6
| vvar(X6) != X4
| X0 != X3
| X1 != X2 ),
inference(flattening,[],[f183]) ).
fof(f183,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vvar(X6) = X5
| vsubst(X2,X3,X4) != X5
| X1 = X6
| vvar(X6) != X4
| X0 != X3
| X1 != X2 ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X6) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 != X6
=> ( vsubst(X2,X3,X4) = X5
=> vvar(X6) = X5 ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X10,X8,X0,X3,X5,X18,X20] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 != X20
=> ( vsubst(X0,X3,X5) = X18
=> vvar(X20) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst1) ).
fof(f814,plain,
spl94_60,
inference(avatar_split_clause,[],[f490,f812]) ).
fof(f490,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f489]) ).
fof(f489,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,vapp(X2,X4))
| X0 != X3 ),
inference(equality_resolution,[],[f417]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X4)
& ~ visFreeVar(X3,X2) ) ) )
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| ( ~ visFreeVar(X3,X4)
& ~ visFreeVar(X3,X2) ) ) )
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( vapp(X2,X4) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) ) )
& ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) )
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X3,X11,X13,X12] :
( ( vapp(X11,X12) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) ) )
& ( ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f810,plain,
spl94_59,
inference(avatar_split_clause,[],[f367,f808]) ).
fof(f367,plain,
! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0,X1,X2] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( vsomeType(X2) = vlookup(X1,X0)
=> vtcheck(X0,vvar(X1),X2) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X19,X8,X14] :
( vlookup(X8,X19) = vsomeType(X14)
=> vtcheck(X19,vvar(X8),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-var') ).
fof(f806,plain,
spl94_58,
inference(avatar_split_clause,[],[f362,f804]) ).
fof(f362,plain,
! [X2,X0,X1] :
( vsomeType(sK60(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f802,plain,
spl94_57,
inference(avatar_split_clause,[],[f333,f800]) ).
fof(f800,plain,
( spl94_57
<=> ! [X0,X1] :
( sK37(X0,X1) = vreduce(sK39(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_57])]) ).
fof(f333,plain,
! [X0,X1] :
( sK37(X0,X1) = vreduce(sK39(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f798,plain,
spl94_56,
inference(avatar_split_clause,[],[f328,f796]) ).
fof(f796,plain,
( spl94_56
<=> ! [X0,X1] :
( sK34(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_56])]) ).
fof(f328,plain,
! [X0,X1] :
( sK34(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f794,plain,
spl94_55,
inference(avatar_split_clause,[],[f324,f792]) ).
fof(f792,plain,
( spl94_55
<=> ! [X0,X1] :
( sK29(X0,X1) = vreduce(sK28(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_55])]) ).
fof(f324,plain,
! [X0,X1] :
( sK29(X0,X1) = vreduce(sK28(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f790,plain,
spl94_54,
inference(avatar_split_clause,[],[f323,f788]) ).
fof(f788,plain,
( spl94_54
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK28(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_54])]) ).
fof(f323,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK28(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f786,plain,
( spl94_53
| ~ spl94_11
| ~ spl94_40 ),
inference(avatar_split_clause,[],[f730,f723,f606,f784]) ).
fof(f730,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_11
| ~ spl94_40 ),
inference(resolution,[],[f724,f607]) ).
fof(f782,plain,
spl94_52,
inference(avatar_split_clause,[],[f319,f780]) ).
fof(f780,plain,
( spl94_52
<=> ! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_52])]) ).
fof(f319,plain,
! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f778,plain,
spl94_51,
inference(avatar_split_clause,[],[f318,f776]) ).
fof(f776,plain,
( spl94_51
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK26(X0,X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_51])]) ).
fof(f318,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK26(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f774,plain,
spl94_50,
inference(avatar_split_clause,[],[f314,f772]) ).
fof(f772,plain,
( spl94_50
<=> ! [X0,X1] :
( sK24(X0,X1) = vreduce(sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_50])]) ).
fof(f314,plain,
! [X0,X1] :
( sK24(X0,X1) = vreduce(sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f766,plain,
spl94_49,
inference(avatar_split_clause,[],[f373,f764]) ).
fof(f373,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| vapp(X0,X1) != vapp(X2,X3) ) ),
inference(flattening,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( ( vapp(X0,X1) = vapp(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| vapp(X0,X1) != vapp(X2,X3) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X5,X6,X7] :
( ( ( X5 = X7
& X3 = X6 )
=> vapp(X3,X5) = vapp(X6,X7) )
& ( vapp(X3,X5) = vapp(X6,X7)
=> ( X5 = X7
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-app') ).
fof(f762,plain,
( spl94_48
| ~ spl94_11
| ~ spl94_39 ),
inference(avatar_split_clause,[],[f729,f719,f606,f760]) ).
fof(f729,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_11
| ~ spl94_39 ),
inference(resolution,[],[f720,f607]) ).
fof(f758,plain,
spl94_47,
inference(avatar_split_clause,[],[f372,f756]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f754,plain,
spl94_46,
inference(avatar_split_clause,[],[f370,f752]) ).
fof(f752,plain,
( spl94_46
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_46])]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2,X3] :
( ( varrow(X0,X1) = varrow(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| varrow(X0,X1) != varrow(X2,X3) ) ),
inference(flattening,[],[f141]) ).
fof(f141,plain,
! [X0,X1,X2,X3] :
( ( varrow(X0,X1) = varrow(X2,X3)
| X1 != X3
| X0 != X2 )
& ( ( X1 = X3
& X0 = X2 )
| varrow(X0,X1) != varrow(X2,X3) ) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> varrow(X0,X1) = varrow(X2,X3) )
& ( varrow(X0,X1) = varrow(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X2,X4,X30,X31] :
( ( ( X4 = X31
& X2 = X30 )
=> varrow(X2,X4) = varrow(X30,X31) )
& ( varrow(X2,X4) = varrow(X30,X31)
=> ( X4 = X31
& X2 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-arrow') ).
fof(f750,plain,
spl94_45,
inference(avatar_split_clause,[],[f369,f748]) ).
fof(f748,plain,
( spl94_45
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_45])]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f746,plain,
spl94_44,
inference(avatar_split_clause,[],[f359,f744]) ).
fof(f359,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f742,plain,
spl94_43,
inference(avatar_split_clause,[],[f355,f740]) ).
fof(f355,plain,
! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f738,plain,
spl94_42,
inference(avatar_split_clause,[],[f539,f736]) ).
fof(f539,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f538]) ).
fof(f538,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f537]) ).
fof(f537,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f536]) ).
fof(f536,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f441]) ).
fof(f441,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vsomeType(X6) = X5
| vlookup(X3,X4) != X5
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X2,X6,X0) = X4
& X1 = X3 )
=> ( X1 = X2
=> ( vlookup(X3,X4) = X5
=> vsomeType(X6) = X5 ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X19,X8,X20,X0,X15,X18,X21] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 = X20
=> ( vlookup(X0,X15) = X18
=> vsomeType(X21) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup1) ).
fof(f734,plain,
spl94_41,
inference(avatar_split_clause,[],[f509,f732]) ).
fof(f509,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f508]) ).
fof(f508,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f433]) ).
fof(f433,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f725,plain,
spl94_40,
inference(avatar_split_clause,[],[f494,f723]) ).
fof(f494,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f493]) ).
fof(f493,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f415]) ).
fof(f415,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f158]) ).
fof(f721,plain,
spl94_39,
inference(avatar_split_clause,[],[f492,f719]) ).
fof(f492,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f491]) ).
fof(f491,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f416]) ).
fof(f416,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f158]) ).
fof(f717,plain,
spl94_38,
inference(avatar_split_clause,[],[f412,f715]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X3,X5,X6] : vabs(X0,X2,X3) != vapp(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f713,plain,
spl94_37,
inference(avatar_split_clause,[],[f308,f711]) ).
fof(f711,plain,
( spl94_37
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_37])]) ).
fof(f308,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ( vvar(X0) = vvar(X1)
| X0 != X1 )
& ( X0 = X1
| vvar(X0) != vvar(X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( X0 = X1
=> vvar(X0) = vvar(X1) )
& ( vvar(X0) = vvar(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-var') ).
fof(f709,plain,
spl94_36,
inference(avatar_split_clause,[],[f306,f707]) ).
fof(f707,plain,
( spl94_36
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_36])]) ).
fof(f306,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeExp(X0) = vsomeExp(X1) )
& ( vsomeExp(X0) = vsomeExp(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X3,X5] :
( ( X3 = X5
=> vsomeExp(X3) = vsomeExp(X5) )
& ( vsomeExp(X3) = vsomeExp(X5)
=> X3 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
fof(f705,plain,
spl94_35,
inference(avatar_split_clause,[],[f304,f703]) ).
fof(f703,plain,
( spl94_35
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_35])]) ).
fof(f304,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeType(X0) = vsomeType(X1) )
& ( vsomeType(X0) = vsomeType(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X2,X4] :
( ( X2 = X4
=> vsomeType(X2) = vsomeType(X4) )
& ( vsomeType(X2) = vsomeType(X4)
=> X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someType') ).
fof(f700,plain,
spl94_34,
inference(avatar_split_clause,[],[f532,f698]) ).
fof(f532,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f531]) ).
fof(f531,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f530]) ).
fof(f530,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f529]) ).
fof(f529,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f528]) ).
fof(f528,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f439]) ).
fof(f439,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(flattening,[],[f185]) ).
fof(f185,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( X5 = X6
| vsubst(X2,X3,X4) != X5
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X1) = X4
& X3 = X6
& X0 = X2 )
=> ( X0 = X1
=> ( vsubst(X2,X3,X4) = X5
=> X5 = X6 ) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X8,X20,X0,X3,X5,X18,X10] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> X10 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
fof(f696,plain,
spl94_33,
inference(avatar_split_clause,[],[f488,f694]) ).
fof(f488,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f487]) ).
fof(f487,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f413]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4] :
( vabs(X0,X1,X2) = X3
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X8,X9,X10,X3,X18] :
( vabs(X8,X9,X10) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
fof(f692,plain,
spl94_32,
inference(avatar_split_clause,[],[f483,f690]) ).
fof(f483,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f482]) ).
fof(f482,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f410]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ( vvar(X2) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> X2 = X3 )
& ( X2 = X3
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3,X8,X13] :
( ( vvar(X8) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> X8 = X13 )
& ( X8 = X13
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f688,plain,
spl94_31,
inference(avatar_split_clause,[],[f368,f686]) ).
fof(f686,plain,
( spl94_31
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_31])]) ).
fof(f368,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f684,plain,
spl94_30,
inference(avatar_split_clause,[],[f335,f682]) ).
fof(f682,plain,
( spl94_30
<=> ! [X0,X1] :
( visValue(sK39(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_30])]) ).
fof(f335,plain,
! [X0,X1] :
( visValue(sK39(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f680,plain,
spl94_29,
inference(avatar_split_clause,[],[f334,f678]) ).
fof(f678,plain,
( spl94_29
<=> ! [X0,X1] :
( ~ visSomeExp(sK37(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_29])]) ).
fof(f334,plain,
! [X0,X1] :
( ~ visSomeExp(sK37(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f676,plain,
spl94_28,
inference(avatar_split_clause,[],[f330,f674]) ).
fof(f674,plain,
( spl94_28
<=> ! [X0,X1] :
( ~ visValue(sK35(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_28])]) ).
fof(f330,plain,
! [X0,X1] :
( ~ visValue(sK35(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f672,plain,
spl94_27,
inference(avatar_split_clause,[],[f329,f670]) ).
fof(f670,plain,
( spl94_27
<=> ! [X0,X1] :
( ~ visSomeExp(sK34(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_27])]) ).
fof(f329,plain,
! [X0,X1] :
( ~ visSomeExp(sK34(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f668,plain,
spl94_26,
inference(avatar_split_clause,[],[f325,f666]) ).
fof(f666,plain,
( spl94_26
<=> ! [X0,X1] :
( visSomeExp(sK29(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_26])]) ).
fof(f325,plain,
! [X0,X1] :
( visSomeExp(sK29(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f664,plain,
spl94_25,
inference(avatar_split_clause,[],[f320,f662]) ).
fof(f662,plain,
( spl94_25
<=> ! [X0,X1] :
( ~ visSomeExp(sK27(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_25])]) ).
fof(f320,plain,
! [X0,X1] :
( ~ visSomeExp(sK27(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f660,plain,
spl94_24,
inference(avatar_split_clause,[],[f315,f658]) ).
fof(f658,plain,
( spl94_24
<=> ! [X0,X1] :
( visSomeExp(sK24(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_24])]) ).
fof(f315,plain,
! [X0,X1] :
( visSomeExp(sK24(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f656,plain,
spl94_23,
inference(avatar_split_clause,[],[f512,f654]) ).
fof(f512,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f511]) ).
fof(f511,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f510]) ).
fof(f510,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f174]) ).
fof(f652,plain,
spl94_22,
inference(avatar_split_clause,[],[f343,f650]) ).
fof(f343,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3,X5] : vvar(X0) != vapp(X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f648,plain,
spl94_21,
inference(avatar_split_clause,[],[f342,f646]) ).
fof(f646,plain,
( spl94_21
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_21])]) ).
fof(f342,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] : vempty != vbind(X0,X1,X2),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X15] : vempty != vbind(X0,X2,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
fof(f644,plain,
spl94_20,
inference(avatar_split_clause,[],[f331,f642]) ).
fof(f642,plain,
( spl94_20
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_20])]) ).
fof(f331,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f640,plain,
spl94_19,
inference(avatar_split_clause,[],[f321,f638]) ).
fof(f321,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f636,plain,
spl94_18,
inference(avatar_split_clause,[],[f481,f634]) ).
fof(f481,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f480]) ).
fof(f480,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f408]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ( vempty = X2
& X0 = X1 )
=> ( vlookup(X1,X2) = X3
=> vnoType = X3 ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X8,X0,X15,X18] :
( ( vempty = X15
& X0 = X8 )
=> ( vlookup(X0,X15) = X18
=> vnoType = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup0) ).
fof(f632,plain,
spl94_17,
inference(avatar_split_clause,[],[f478,f630]) ).
fof(f630,plain,
( spl94_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_17])]) ).
fof(f478,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f407]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) = X3
=> visValue(X3) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X10,X3] :
( vabs(X8,X9,X10) = X3
=> visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue0) ).
fof(f628,plain,
spl94_16,
inference(avatar_split_clause,[],[f465,f626]) ).
fof(f465,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f464]) ).
fof(f464,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f346]) ).
fof(f346,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( vvar(X0) = X1
=> ( vreduce(X1) = X2
=> vnoExp = X2 ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X3,X18] :
( vvar(X8) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce0) ).
fof(f624,plain,
spl94_15,
inference(avatar_split_clause,[],[f463,f622]) ).
fof(f622,plain,
( spl94_15
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_15])]) ).
fof(f463,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f462]) ).
fof(f462,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f345]) ).
fof(f345,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( vsomeExp(X2) = X0
=> ( vgetSomeExp(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X24,X18,X10] :
( vsomeExp(X10) = X24
=> ( vgetSomeExp(X24) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeExp0) ).
fof(f620,plain,
spl94_14,
inference(avatar_split_clause,[],[f461,f618]) ).
fof(f618,plain,
( spl94_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_14])]) ).
fof(f461,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f460]) ).
fof(f460,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f344]) ).
fof(f344,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( vsomeType(X2) = X0
=> ( vgetSomeType(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X17,X18,X10] :
( vsomeType(X10) = X17
=> ( vgetSomeType(X17) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeType0) ).
fof(f616,plain,
spl94_13,
inference(avatar_split_clause,[],[f486,f614]) ).
fof(f486,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f485]) ).
fof(f485,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f484]) ).
fof(f484,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f409]) ).
fof(f409,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f151]) ).
fof(f612,plain,
spl94_12,
inference(avatar_split_clause,[],[f469,f610]) ).
fof(f469,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f366]) ).
fof(f366,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( vapp(X0,X1) = X2
=> ~ visValue(X2) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X11,X12,X3] :
( vapp(X11,X12) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
fof(f608,plain,
spl94_11,
inference(avatar_split_clause,[],[f452,f606]) ).
fof(f452,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( vgensym(X1) = X0
=> ~ visFreeVar(X0,X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X13,X10] :
( vgensym(X10) = X13
=> ~ visFreeVar(X13,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f604,plain,
spl94_10,
inference(avatar_split_clause,[],[f301,f602]) ).
fof(f602,plain,
( spl94_10
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_10])]) ).
fof(f301,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3] : vnoExp != vsomeExp(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
fof(f600,plain,
spl94_9,
inference(avatar_split_clause,[],[f300,f598]) ).
fof(f300,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] : vnoType != vsomeType(X0),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2] : vnoType != vsomeType(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noType-someType') ).
fof(f596,plain,
spl94_8,
inference(avatar_split_clause,[],[f459,f594]) ).
fof(f594,plain,
( spl94_8
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_8])]) ).
fof(f459,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f341]) ).
fof(f341,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( vvar(X0) = X1
=> ~ visValue(X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X8,X3] :
( vvar(X8) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
fof(f592,plain,
spl94_7,
inference(avatar_split_clause,[],[f454,f590]) ).
fof(f590,plain,
( spl94_7
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_7])]) ).
fof(f454,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f312]) ).
fof(f312,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( vsomeExp(X0) = X1
=> visSomeExp(X1) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X10,X24] :
( vsomeExp(X10) = X24
=> visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp1) ).
fof(f588,plain,
spl94_6,
inference(avatar_split_clause,[],[f453,f586]) ).
fof(f586,plain,
( spl94_6
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_6])]) ).
fof(f453,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f311]) ).
fof(f311,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( vsomeType(X0) = X1
=> visSomeType(X1) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X10,X17] :
( vsomeType(X10) = X17
=> visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType1) ).
fof(f584,plain,
~ spl94_5,
inference(avatar_split_clause,[],[f296,f581]) ).
fof(f296,plain,
~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
& vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
& vnoType = vlookup(sK14,sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19])],[f117,f219]) ).
fof(f219,plain,
( ? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2) )
=> ( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
& vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
& vnoType = vlookup(sK14,sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& vnoType = vlookup(X0,X2) )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f59]) ).
fof(f59,negated_conjecture,
~ ! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
inference(negated_conjecture,[],[f58]) ).
fof(f58,conjecture,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs') ).
fof(f579,plain,
~ spl94_4,
inference(avatar_split_clause,[],[f448,f576]) ).
fof(f448,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f303]) ).
fof(f303,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( vnoExp = X0
=> ~ visSomeExp(X0) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X24] :
( vnoExp = X24
=> ~ visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp0) ).
fof(f574,plain,
~ spl94_3,
inference(avatar_split_clause,[],[f447,f571]) ).
fof(f571,plain,
( spl94_3
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_3])]) ).
fof(f447,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( vnoType = X0
=> ~ visSomeType(X0) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X17] :
( vnoType = X17
=> ~ visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType0) ).
fof(f569,plain,
spl94_2,
inference(avatar_split_clause,[],[f295,f566]) ).
fof(f295,plain,
vtcheck(sK16,vabs(sK17,sK18,veabs),sK19),
inference(cnf_transformation,[],[f220]) ).
fof(f564,plain,
spl94_1,
inference(avatar_split_clause,[],[f294,f561]) ).
fof(f294,plain,
vnoType = vlookup(sK14,sK16),
inference(cnf_transformation,[],[f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : COM141+1 : TPTP v8.1.2. Released v6.4.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n004.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 21:24:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (9680)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (9685)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (9683)WARNING: value z3 for option sas not known
% 0.14/0.38 % (9681)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (9682)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (9684)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (9683)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (9686)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (9687)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.43 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.44 % (9685)First to succeed.
% 0.21/0.46 % (9685)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-9680"
% 0.21/0.46 % (9685)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.47 % (9685)------------------------------
% 0.21/0.47 % (9685)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.47 % (9685)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (9685)Memory used [KB]: 2656
% 0.21/0.47 % (9685)Time elapsed: 0.085 s
% 0.21/0.47 % (9685)Instructions burned: 236 (million)
% 0.21/0.47 % (9680)Success in time 0.104 s
%------------------------------------------------------------------------------