TSTP Solution File: COM135+1 by Vampire-SAT---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : COM135+1 : TPTP v8.2.0. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n029.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 : Mon Jun 24 04:59:37 EDT 2024
% Result : Theorem 2.82s 0.87s
% Output : Refutation 2.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 524
% Syntax : Number of formulae : 1871 ( 182 unt; 0 def)
% Number of atoms : 7070 (2728 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 7913 (2714 ~;3804 |; 757 &)
% ( 433 <=>; 205 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 454 ( 452 usr; 434 prp; 0-4 aty)
% Number of functors : 96 ( 96 usr; 9 con; 0-4 aty)
% Number of variables : 5644 (5074 !; 570 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9707,plain,
$false,
inference(avatar_sat_refutation,[],[f563,f568,f573,f578,f583,f587,f591,f595,f599,f603,f607,f611,f615,f619,f623,f627,f631,f635,f639,f643,f647,f651,f655,f659,f663,f667,f671,f675,f679,f683,f687,f691,f695,f699,f704,f708,f712,f716,f720,f724,f733,f737,f741,f745,f749,f753,f757,f761,f765,f773,f777,f781,f785,f789,f793,f797,f801,f805,f809,f813,f817,f828,f837,f841,f845,f849,f853,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f934,f938,f942,f946,f950,f954,f958,f962,f967,f971,f975,f979,f983,f987,f997,f1001,f1005,f1009,f1014,f1022,f1026,f1030,f1034,f1038,f1042,f1046,f1050,f1054,f1059,f1063,f1067,f1071,f1073,f1103,f1107,f1124,f1128,f1136,f1140,f1144,f1148,f1152,f1157,f1161,f1165,f1180,f1184,f1199,f1203,f1207,f1228,f1233,f1237,f1241,f1245,f1249,f1253,f1257,f1274,f1282,f1286,f1290,f1295,f1307,f1316,f1320,f1324,f1344,f1359,f1364,f1385,f1399,f1404,f1409,f1414,f1418,f1427,f1432,f1437,f1441,f1445,f1449,f1453,f1457,f1569,f1574,f1578,f1602,f1607,f1611,f1615,f1637,f1641,f1687,f1691,f1695,f1761,f1765,f1769,f1773,f1777,f1781,f1825,f1837,f1841,f1874,f1888,f1892,f1896,f1923,f1927,f1941,f1945,f1949,f1953,f1992,f1996,f2000,f2006,f2024,f2028,f2038,f2053,f2057,f2061,f2100,f2110,f2115,f2119,f2123,f2153,f2157,f2200,f2204,f2208,f2212,f2216,f2295,f2300,f2314,f2318,f2322,f2326,f2404,f2408,f2413,f2427,f2431,f2435,f2470,f2478,f2488,f2492,f2511,f2516,f2524,f2539,f2546,f2550,f2580,f2584,f2594,f2598,f2612,f2625,f2629,f2642,f2646,f2659,f2663,f2667,f2671,f2675,f2679,f2683,f2826,f2835,f2839,f2848,f2852,f2896,f2907,f2911,f2931,f2935,f2959,f2963,f3007,f3021,f3025,f3050,f3054,f3098,f3106,f3150,f3164,f3188,f3212,f3216,f3230,f3234,f3278,f3302,f3326,f3330,f3354,f3365,f3393,f3442,f3446,f3475,f3479,f3483,f3487,f3491,f3538,f3547,f3561,f3622,f3627,f3631,f3635,f3639,f3643,f3647,f3869,f3916,f3944,f3960,f3965,f3970,f3975,f3979,f3984,f4052,f4056,f4283,f4288,f4295,f4300,f4305,f4319,f4326,f4331,f4339,f4343,f4348,f4350,f4386,f4405,f4416,f4423,f4428,f4434,f4439,f4444,f4449,f4454,f4461,f4465,f4469,f4473,f4477,f4481,f4485,f4489,f4762,f4768,f4774,f4778,f4782,f4902,f4904,f4908,f4912,f4916,f5081,f5085,f5089,f5093,f5331,f5336,f5340,f5344,f5348,f5352,f5356,f5360,f5364,f5585,f5588,f5592,f5605,f5609,f5613,f5617,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f6483,f6487,f6492,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6592,f6835,f6839,f6843,f6847,f6852,f6856,f6860,f6864,f6868,f6872,f7606,f7616,f7620,f7624,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f8485,f8489,f8494,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f9691,f9701,f9705,f9706]) ).
fof(f9706,plain,
( ~ spl94_1
| spl94_3
| ~ spl94_34
| ~ spl94_63
| ~ spl94_422 ),
inference(avatar_split_clause,[],[f8801,f8491,f830,f697,f570,f560]) ).
fof(f560,plain,
( spl94_1
<=> vtcheck(sK15,sK17,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_1])]) ).
fof(f570,plain,
( spl94_3
<=> vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_3])]) ).
fof(f697,plain,
( spl94_34
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_34])]) ).
fof(f830,plain,
( spl94_63
<=> sK16 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_63])]) ).
fof(f8491,plain,
( spl94_422
<=> sK14 = sK19 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_422])]) ).
fof(f8801,plain,
( ~ vtcheck(sK15,sK17,sK14)
| spl94_3
| ~ spl94_34
| ~ spl94_63
| ~ spl94_422 ),
inference(forward_demodulation,[],[f8800,f698]) ).
fof(f698,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl94_34 ),
inference(avatar_component_clause,[],[f697]) ).
fof(f8800,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK16)),sK14)
| spl94_3
| ~ spl94_63
| ~ spl94_422 ),
inference(forward_demodulation,[],[f8778,f832]) ).
fof(f832,plain,
( sK16 = sK18
| ~ spl94_63 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f8778,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK14)
| spl94_3
| ~ spl94_422 ),
inference(superposition,[],[f572,f8493]) ).
fof(f8493,plain,
( sK14 = sK19
| ~ spl94_422 ),
inference(avatar_component_clause,[],[f8491]) ).
fof(f572,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK19)
| spl94_3 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f9705,plain,
( spl94_433
| ~ spl94_42
| ~ spl94_177 ),
inference(avatar_split_clause,[],[f1623,f1609,f735,f9703]) ).
fof(f9703,plain,
( spl94_433
<=> ! [X2,X0,X1] :
( sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vempty = vbind(X0,X1,X2)
| sK55(vsomeType(X1),vbind(X0,X1,X2),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_433])]) ).
fof(f735,plain,
( spl94_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_42])]) ).
fof(f1609,plain,
( spl94_177
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_177])]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vempty = vbind(X0,X1,X2)
| sK55(vsomeType(X1),vbind(X0,X1,X2),X0) = X0 )
| ~ spl94_42
| ~ spl94_177 ),
inference(superposition,[],[f1610,f736]) ).
fof(f736,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl94_42 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f1610,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_177 ),
inference(avatar_component_clause,[],[f1609]) ).
fof(f9701,plain,
( spl94_432
| ~ spl94_87
| ~ spl94_177 ),
inference(avatar_split_clause,[],[f1620,f1609,f940,f9699]) ).
fof(f9699,plain,
( spl94_432
<=> ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| sK59(vlookup(X1,X0),X0,X1) = sK58(vlookup(X1,X0),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_432])]) ).
fof(f940,plain,
( spl94_87
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_87])]) ).
fof(f1620,plain,
( ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| sK59(vlookup(X1,X0),X0,X1) = sK58(vlookup(X1,X0),X0,X1) )
| ~ spl94_87
| ~ spl94_177 ),
inference(resolution,[],[f1610,f941]) ).
fof(f941,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| sK58(X0,X1,X2) = sK59(X0,X1,X2) )
| ~ spl94_87 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f9691,plain,
( spl94_431
| ~ spl94_158
| ~ spl94_248 ),
inference(avatar_split_clause,[],[f3899,f2582,f1392,f9689]) ).
fof(f9689,plain,
( spl94_431
<=> ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vvar(sK16) = vapp(sK84(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0),sK87(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0))
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_431])]) ).
fof(f1392,plain,
( spl94_158
<=> vvar(sK16) = vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_158])]) ).
fof(f2582,plain,
( spl94_248
<=> ! [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_248])]) ).
fof(f3899,plain,
( ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vvar(sK16) = vapp(sK84(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0),sK87(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0))
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_158
| ~ spl94_248 ),
inference(superposition,[],[f2583,f1394]) ).
fof(f1394,plain,
( vvar(sK16) = vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| ~ spl94_158 ),
inference(avatar_component_clause,[],[f1392]) ).
fof(f2583,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_248 ),
inference(avatar_component_clause,[],[f2582]) ).
fof(f8526,plain,
( spl94_430
| ~ spl94_7
| ~ spl94_224 ),
inference(avatar_split_clause,[],[f2256,f2214,f589,f8524]) ).
fof(f8524,plain,
( spl94_430
<=> ! [X4,X0,X3,X2,X1] :
( visSomeExp(vreduce(vapp(vabs(X0,X1,X2),X3)))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK88(X3),sK89(X3),sK90(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_430])]) ).
fof(f589,plain,
( spl94_7
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_7])]) ).
fof(f2214,plain,
( spl94_224
<=> ! [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_224])]) ).
fof(f2256,plain,
( ! [X2,X3,X0,X1,X4] :
( visSomeExp(vreduce(vapp(vabs(X0,X1,X2),X3)))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK88(X3),sK89(X3),sK90(X3)) = X3 )
| ~ spl94_7
| ~ spl94_224 ),
inference(superposition,[],[f590,f2215]) ).
fof(f2215,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_224 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f590,plain,
( ! [X0] : visSomeExp(vsomeExp(X0))
| ~ spl94_7 ),
inference(avatar_component_clause,[],[f589]) ).
fof(f8522,plain,
( spl94_429
| ~ spl94_18
| ~ spl94_207 ),
inference(avatar_split_clause,[],[f2032,f2022,f633,f8520]) ).
fof(f8520,plain,
( spl94_429
<=> ! [X2,X0,X1] :
( sP8(vnoType,vbind(X1,X2,vempty),X0)
| sP7(vnoType,vbind(X1,X2,vempty),X0)
| vempty = vbind(X1,X2,vempty)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_429])]) ).
fof(f633,plain,
( spl94_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_18])]) ).
fof(f2022,plain,
( spl94_207
<=> ! [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_207])]) ).
fof(f2032,plain,
( ! [X2,X0,X1] :
( sP8(vnoType,vbind(X1,X2,vempty),X0)
| sP7(vnoType,vbind(X1,X2,vempty),X0)
| vempty = vbind(X1,X2,vempty)
| X0 = X1 )
| ~ spl94_18
| ~ spl94_207 ),
inference(superposition,[],[f2023,f634]) ).
fof(f634,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl94_18 ),
inference(avatar_component_clause,[],[f633]) ).
fof(f2023,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_207 ),
inference(avatar_component_clause,[],[f2022]) ).
fof(f8518,plain,
( spl94_428
| ~ spl94_96
| ~ spl94_196 ),
inference(avatar_split_clause,[],[f1913,f1894,f977,f8516]) ).
fof(f8516,plain,
( spl94_428
<=> ! [X2,X3,X4,X0,X6,X5,X1] :
( X0 = X1
| ~ vtcheck(vbind(X0,X2,X3),X4,X5)
| visFreeVar(X1,X4)
| vtcheck(vbind(X1,X6,X3),X4,X5)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_428])]) ).
fof(f977,plain,
( spl94_96
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_96])]) ).
fof(f1894,plain,
( spl94_196
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),X5,X6)
| visFreeVar(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_196])]) ).
fof(f1913,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( X0 = X1
| ~ vtcheck(vbind(X0,X2,X3),X4,X5)
| visFreeVar(X1,X4)
| vtcheck(vbind(X1,X6,X3),X4,X5)
| visFreeVar(X0,X4) )
| ~ spl94_96
| ~ spl94_196 ),
inference(resolution,[],[f1895,f978]) ).
fof(f978,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl94_96 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1895,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),X5,X6)
| visFreeVar(X2,X5) )
| ~ spl94_196 ),
inference(avatar_component_clause,[],[f1894]) ).
fof(f8514,plain,
( spl94_427
| ~ spl94_168
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1681,f1639,f1443,f8512]) ).
fof(f8512,plain,
( spl94_427
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vapp(X2,vvar(X3)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),vvar(X3)),X1)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_427])]) ).
fof(f1443,plain,
( spl94_168
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_168])]) ).
fof(f1639,plain,
( spl94_180
<=> ! [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_180])]) ).
fof(f1681,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vapp(X2,vvar(X3)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),vvar(X3)),X1)
| X0 = X3 )
| ~ spl94_168
| ~ spl94_180 ),
inference(superposition,[],[f1444,f1640]) ).
fof(f1640,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl94_180 ),
inference(avatar_component_clause,[],[f1639]) ).
fof(f1444,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl94_168 ),
inference(avatar_component_clause,[],[f1443]) ).
fof(f8510,plain,
( spl94_426
| ~ spl94_167
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1680,f1639,f1439,f8508]) ).
fof(f8508,plain,
( spl94_426
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X3)))) = vapp(X1,vapp(vsubst(X0,X1,X2),vvar(X3)))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_426])]) ).
fof(f1439,plain,
( spl94_167
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_167])]) ).
fof(f1680,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X3)))) = vapp(X1,vapp(vsubst(X0,X1,X2),vvar(X3)))
| X0 = X3 )
| ~ spl94_167
| ~ spl94_180 ),
inference(superposition,[],[f1440,f1640]) ).
fof(f1440,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl94_167 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f8506,plain,
( spl94_425
| ~ spl94_179
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1664,f1639,f1635,f8504]) ).
fof(f8504,plain,
( spl94_425
<=> ! [X0,X3,X2,X1] :
( vapp(vvar(X2),vsubst(X0,X1,vvar(X3))) = vapp(vsubst(X0,X1,vvar(X2)),vvar(X3))
| X0 = X3
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_425])]) ).
fof(f1635,plain,
( spl94_179
<=> ! [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_179])]) ).
fof(f1664,plain,
( ! [X2,X3,X0,X1] :
( vapp(vvar(X2),vsubst(X0,X1,vvar(X3))) = vapp(vsubst(X0,X1,vvar(X2)),vvar(X3))
| X0 = X3
| X0 = X2 )
| ~ spl94_179
| ~ spl94_180 ),
inference(superposition,[],[f1640,f1636]) ).
fof(f1636,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl94_179 ),
inference(avatar_component_clause,[],[f1635]) ).
fof(f8502,plain,
( spl94_424
| ~ spl94_168
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f1659,f1635,f1443,f8500]) ).
fof(f8500,plain,
( spl94_424
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vapp(vvar(X2),X3),vvar(X0))) = vapp(vapp(vvar(X2),vsubst(X0,X1,X3)),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_424])]) ).
fof(f1659,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vapp(vvar(X2),X3),vvar(X0))) = vapp(vapp(vvar(X2),vsubst(X0,X1,X3)),X1)
| X0 = X2 )
| ~ spl94_168
| ~ spl94_179 ),
inference(superposition,[],[f1444,f1636]) ).
fof(f8498,plain,
( spl94_423
| ~ spl94_167
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f1658,f1635,f1439,f8496]) ).
fof(f8496,plain,
( spl94_423
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X2),X3))) = vapp(X1,vapp(vvar(X2),vsubst(X0,X1,X3)))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_423])]) ).
fof(f1658,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X2),X3))) = vapp(X1,vapp(vvar(X2),vsubst(X0,X1,X3)))
| X0 = X2 )
| ~ spl94_167
| ~ spl94_179 ),
inference(superposition,[],[f1440,f1636]) ).
fof(f8494,plain,
( spl94_422
| ~ spl94_14
| ~ spl94_412 ),
inference(avatar_split_clause,[],[f7913,f7626,f617,f8491]) ).
fof(f617,plain,
( spl94_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_14])]) ).
fof(f7626,plain,
( spl94_412
<=> vsomeType(sK14) = vsomeType(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_412])]) ).
fof(f7913,plain,
( sK14 = sK19
| ~ spl94_14
| ~ spl94_412 ),
inference(forward_demodulation,[],[f7899,f618]) ).
fof(f618,plain,
( ! [X2] : vgetSomeType(vsomeType(X2)) = X2
| ~ spl94_14 ),
inference(avatar_component_clause,[],[f617]) ).
fof(f7899,plain,
( sK19 = vgetSomeType(vsomeType(sK14))
| ~ spl94_14
| ~ spl94_412 ),
inference(superposition,[],[f618,f7628]) ).
fof(f7628,plain,
( vsomeType(sK14) = vsomeType(sK19)
| ~ spl94_412 ),
inference(avatar_component_clause,[],[f7626]) ).
fof(f8489,plain,
( spl94_421
| ~ spl94_91
| ~ spl94_175 ),
inference(avatar_split_clause,[],[f1618,f1600,f956,f8487]) ).
fof(f8487,plain,
( spl94_421
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X5,X6,vbind(X1,X2,X3)),vvar(X0),X4)
| X0 = X5
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_421])]) ).
fof(f956,plain,
( spl94_91
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_91])]) ).
fof(f1600,plain,
( spl94_175
<=> ! [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_175])]) ).
fof(f1618,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X5,X6,vbind(X1,X2,X3)),vvar(X0),X4)
| X0 = X5
| X0 = X1 )
| ~ spl94_91
| ~ spl94_175 ),
inference(superposition,[],[f1601,f957]) ).
fof(f957,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl94_91 ),
inference(avatar_component_clause,[],[f956]) ).
fof(f1601,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl94_175 ),
inference(avatar_component_clause,[],[f1600]) ).
fof(f8485,plain,
( spl94_365
| spl94_339
| spl94_328
| ~ spl94_228
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3937,f3913,f2316,f4312,f4431,f5328]) ).
fof(f5328,plain,
( spl94_365
<=> vbind(sK16,sK14,sK15) = vbind(sK54(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK53(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_365])]) ).
fof(f4431,plain,
( spl94_339
<=> sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_339])]) ).
fof(f4312,plain,
( spl94_328
<=> sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_328])]) ).
fof(f2316,plain,
( spl94_228
<=> ! [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_228])]) ).
fof(f3913,plain,
( spl94_312
<=> vsomeType(sK19) = vlookup(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_312])]) ).
fof(f3937,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19))
| vbind(sK16,sK14,sK15) = vbind(sK54(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK53(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))))
| ~ spl94_228
| ~ spl94_312 ),
inference(superposition,[],[f2317,f3915]) ).
fof(f3915,plain,
( vsomeType(sK19) = vlookup(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| ~ spl94_312 ),
inference(avatar_component_clause,[],[f3913]) ).
fof(f2317,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_228 ),
inference(avatar_component_clause,[],[f2316]) ).
fof(f7661,plain,
( spl94_420
| ~ spl94_41
| ~ spl94_219 ),
inference(avatar_split_clause,[],[f2174,f2155,f731,f7659]) ).
fof(f7659,plain,
( spl94_420
<=> ! [X4,X0,X3,X2,X1] :
( ~ visFreeVar(X3,vabs(X0,X1,X2))
| visFreeVar(X3,sK90(vabs(X0,X1,X2)))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_420])]) ).
fof(f731,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(f2155,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(f2174,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ visFreeVar(X3,vabs(X0,X1,X2))
| visFreeVar(X3,sK90(vabs(X0,X1,X2)))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl94_41
| ~ spl94_219 ),
inference(superposition,[],[f732,f2156]) ).
fof(f2156,plain,
( ! [X2,X3,X0,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))) )
| ~ spl94_219 ),
inference(avatar_component_clause,[],[f2155]) ).
fof(f732,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl94_41 ),
inference(avatar_component_clause,[],[f731]) ).
fof(f7657,plain,
( spl94_419
| ~ spl94_162
| ~ spl94_201 ),
inference(avatar_split_clause,[],[f1967,f1947,f1412,f7655]) ).
fof(f7655,plain,
( spl94_419
<=> ! [X5,X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,vempty),vapp(X2,X3),X4)
| ~ vtcheck(vempty,X2,varrow(X5,X4))
| visFreeVar(X0,X2)
| ~ vtcheck(vempty,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_419])]) ).
fof(f1412,plain,
( spl94_162
<=> ! [X2,X0,X1,X3] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_162])]) ).
fof(f1947,plain,
( spl94_201
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(X5,X3),X6)
| ~ vtcheck(X2,X5,varrow(X4,X6))
| visFreeVar(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_201])]) ).
fof(f1967,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,vempty),vapp(X2,X3),X4)
| ~ vtcheck(vempty,X2,varrow(X5,X4))
| visFreeVar(X0,X2)
| ~ vtcheck(vempty,X3,X5) )
| ~ spl94_162
| ~ spl94_201 ),
inference(resolution,[],[f1948,f1413]) ).
fof(f1413,plain,
( ! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X3,vempty),X1,X2)
| ~ vtcheck(vempty,X1,X2) )
| ~ spl94_162 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f1948,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(X5,X3),X6)
| ~ vtcheck(X2,X5,varrow(X4,X6))
| visFreeVar(X0,X5) )
| ~ spl94_201 ),
inference(avatar_component_clause,[],[f1947]) ).
fof(f7653,plain,
( spl94_418
| ~ spl94_42
| ~ spl94_183 ),
inference(avatar_split_clause,[],[f1756,f1693,f735,f7651]) ).
fof(f7651,plain,
( spl94_418
<=> ! [X2,X0,X1] :
( sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1)
| sK55(vsomeType(X1),vbind(X0,X1,X2),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_418])]) ).
fof(f1693,plain,
( spl94_183
<=> ! [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_183])]) ).
fof(f1756,plain,
( ! [X2,X0,X1] :
( sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1)
| sK55(vsomeType(X1),vbind(X0,X1,X2),X0) = X0 )
| ~ spl94_42
| ~ spl94_183 ),
inference(superposition,[],[f1694,f736]) ).
fof(f1694,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_183 ),
inference(avatar_component_clause,[],[f1693]) ).
fof(f7649,plain,
( spl94_417
| ~ spl94_58
| ~ spl94_177 ),
inference(avatar_split_clause,[],[f1621,f1609,f803,f7647]) ).
fof(f7647,plain,
( spl94_417
<=> ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| vlookup(X1,X0) = vsomeType(sK60(vlookup(X1,X0),X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_417])]) ).
fof(f803,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(f1621,plain,
( ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| vlookup(X1,X0) = vsomeType(sK60(vlookup(X1,X0),X0,X1)) )
| ~ spl94_58
| ~ spl94_177 ),
inference(resolution,[],[f1610,f804]) ).
fof(f804,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| vsomeType(sK60(X0,X1,X2)) = X0 )
| ~ spl94_58 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f7645,plain,
( spl94_416
| ~ spl94_116
| ~ spl94_174 ),
inference(avatar_split_clause,[],[f1595,f1576,f1069,f7643]) ).
fof(f7643,plain,
( spl94_416
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( vsubst(X0,X1,vapp(X2,X3)) != vsubst(X4,X5,vapp(X6,X7))
| vsubst(X0,X1,X3) = vsubst(X4,X5,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_416])]) ).
fof(f1069,plain,
( spl94_116
<=> ! [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_116])]) ).
fof(f1576,plain,
( spl94_174
<=> ! [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_174])]) ).
fof(f1595,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vsubst(X4,X5,vapp(X6,X7))
| vsubst(X0,X1,X3) = vsubst(X4,X5,X7) )
| ~ spl94_116
| ~ spl94_174 ),
inference(superposition,[],[f1577,f1070]) ).
fof(f1070,plain,
( ! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7))
| ~ spl94_116 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f1577,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl94_174 ),
inference(avatar_component_clause,[],[f1576]) ).
fof(f7641,plain,
( spl94_415
| ~ spl94_116
| ~ spl94_174 ),
inference(avatar_split_clause,[],[f1589,f1576,f1069,f7639]) ).
fof(f7639,plain,
( spl94_415
<=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
( vapp(X6,X7) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| vsubst(X4,X5,vsubst(X0,X1,X3)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_415])]) ).
fof(f1589,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vapp(X6,X7) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| vsubst(X4,X5,vsubst(X0,X1,X3)) = X7 )
| ~ spl94_116
| ~ spl94_174 ),
inference(superposition,[],[f1577,f1070]) ).
fof(f7637,plain,
( spl94_414
| ~ spl94_116
| ~ spl94_173 ),
inference(avatar_split_clause,[],[f1585,f1572,f1069,f7635]) ).
fof(f7635,plain,
( spl94_414
<=> ! [X5,X4,X2,X7,X0,X6,X3,X1] :
( vsubst(X0,X1,vapp(X2,X3)) != vsubst(X4,X5,vapp(X6,X7))
| vsubst(X0,X1,X2) = vsubst(X4,X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_414])]) ).
fof(f1572,plain,
( spl94_173
<=> ! [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_173])]) ).
fof(f1585,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vsubst(X4,X5,vapp(X6,X7))
| vsubst(X0,X1,X2) = vsubst(X4,X5,X6) )
| ~ spl94_116
| ~ spl94_173 ),
inference(superposition,[],[f1573,f1070]) ).
fof(f1573,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl94_173 ),
inference(avatar_component_clause,[],[f1572]) ).
fof(f7633,plain,
( spl94_413
| ~ spl94_116
| ~ spl94_173 ),
inference(avatar_split_clause,[],[f1579,f1572,f1069,f7631]) ).
fof(f7631,plain,
( spl94_413
<=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
( vapp(X6,X7) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| vsubst(X4,X5,vsubst(X0,X1,X2)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_413])]) ).
fof(f1579,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vapp(X6,X7) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| vsubst(X4,X5,vsubst(X0,X1,X2)) = X6 )
| ~ spl94_116
| ~ spl94_173 ),
inference(superposition,[],[f1573,f1070]) ).
fof(f7629,plain,
( spl94_412
| ~ spl94_42
| ~ spl94_312
| ~ spl94_387 ),
inference(avatar_split_clause,[],[f7361,f6480,f3913,f735,f7626]) ).
fof(f6480,plain,
( spl94_387
<=> sK16 = sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_387])]) ).
fof(f7361,plain,
( vsomeType(sK14) = vsomeType(sK19)
| ~ spl94_42
| ~ spl94_312
| ~ spl94_387 ),
inference(forward_demodulation,[],[f7356,f736]) ).
fof(f7356,plain,
( vsomeType(sK19) = vlookup(sK16,vbind(sK16,sK14,sK15))
| ~ spl94_312
| ~ spl94_387 ),
inference(superposition,[],[f3915,f6482]) ).
fof(f6482,plain,
( sK16 = sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))
| ~ spl94_387 ),
inference(avatar_component_clause,[],[f6480]) ).
fof(f7624,plain,
( spl94_411
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1491,f1443,f7622]) ).
fof(f7622,plain,
( spl94_411
<=> ! [X0,X3,X2,X1] : vapp(vsubst(X1,X3,vsubst(X0,vvar(X1),X2)),X3) = vsubst(X1,X3,vsubst(X0,vvar(X1),vapp(X2,vvar(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_411])]) ).
fof(f1491,plain,
( ! [X2,X3,X0,X1] : vapp(vsubst(X1,X3,vsubst(X0,vvar(X1),X2)),X3) = vsubst(X1,X3,vsubst(X0,vvar(X1),vapp(X2,vvar(X0))))
| ~ spl94_168 ),
inference(superposition,[],[f1444,f1444]) ).
fof(f7620,plain,
( spl94_410
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1462,f1439,f7618]) ).
fof(f7618,plain,
( spl94_410
<=> ! [X0,X3,X2,X1] : vapp(X3,vsubst(X0,X3,vsubst(X1,vvar(X0),X2))) = vsubst(X0,X3,vsubst(X1,vvar(X0),vapp(vvar(X1),X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_410])]) ).
fof(f1462,plain,
( ! [X2,X3,X0,X1] : vapp(X3,vsubst(X0,X3,vsubst(X1,vvar(X0),X2))) = vsubst(X0,X3,vsubst(X1,vvar(X0),vapp(vvar(X1),X2)))
| ~ spl94_167 ),
inference(superposition,[],[f1440,f1440]) ).
fof(f7616,plain,
( spl94_409
| ~ spl94_115
| ~ spl94_162 ),
inference(avatar_split_clause,[],[f1420,f1412,f1065,f7614]) ).
fof(f7614,plain,
( spl94_409
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ vtcheck(vempty,X0,varrow(X1,X2))
| ~ vtcheck(vbind(X3,X4,vempty),X5,X1)
| vtcheck(vbind(X3,X4,vempty),vapp(X0,X5),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_409])]) ).
fof(f1065,plain,
( spl94_115
<=> ! [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_115])]) ).
fof(f1420,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ vtcheck(vempty,X0,varrow(X1,X2))
| ~ vtcheck(vbind(X3,X4,vempty),X5,X1)
| vtcheck(vbind(X3,X4,vempty),vapp(X0,X5),X2) )
| ~ spl94_115
| ~ spl94_162 ),
inference(resolution,[],[f1413,f1066]) ).
fof(f1066,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vapp(X2,X3),X4) )
| ~ spl94_115 ),
inference(avatar_component_clause,[],[f1065]) ).
fof(f7606,plain,
( spl94_408
| ~ spl94_158
| ~ spl94_236 ),
inference(avatar_split_clause,[],[f3897,f2433,f1392,f7604]) ).
fof(f7604,plain,
( spl94_408
<=> ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK85(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0)
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_408])]) ).
fof(f2433,plain,
( spl94_236
<=> ! [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_236])]) ).
fof(f3897,plain,
( ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK85(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0)
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_158
| ~ spl94_236 ),
inference(superposition,[],[f2434,f1394]) ).
fof(f2434,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_236 ),
inference(avatar_component_clause,[],[f2433]) ).
fof(f6872,plain,
( spl94_407
| ~ spl94_44
| ~ spl94_183 ),
inference(avatar_split_clause,[],[f1755,f1693,f743,f6870]) ).
fof(f6870,plain,
( spl94_407
<=> ! [X0,X1] :
( vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0
| sK58(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_407])]) ).
fof(f743,plain,
( spl94_44
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_44])]) ).
fof(f1755,plain,
( ! [X0,X1] :
( vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0
| sK58(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_44
| ~ spl94_183 ),
inference(resolution,[],[f1694,f744]) ).
fof(f744,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| sK58(X0,X1,X2) = X2 )
| ~ spl94_44 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f6868,plain,
( spl94_406
| ~ spl94_84
| ~ spl94_179
| ~ spl94_182 ),
inference(avatar_split_clause,[],[f1745,f1689,f1635,f915,f6866]) ).
fof(f6866,plain,
( spl94_406
<=> ! [X4,X0,X3,X2,X1] :
( vapp(vvar(X2),vabs(X0,X3,X4)) = vapp(vsubst(X0,X1,vvar(X2)),vabs(X0,X3,X4))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_406])]) ).
fof(f915,plain,
( spl94_84
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_84])]) ).
fof(f1689,plain,
( spl94_182
<=> ! [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_182])]) ).
fof(f1745,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(vvar(X2),vabs(X0,X3,X4)) = vapp(vsubst(X0,X1,vvar(X2)),vabs(X0,X3,X4))
| X0 = X2 )
| ~ spl94_84
| ~ spl94_179
| ~ spl94_182 ),
inference(forward_demodulation,[],[f1724,f916]) ).
fof(f916,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl94_84 ),
inference(avatar_component_clause,[],[f915]) ).
fof(f1724,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(vvar(X2),vsubst(X0,X1,vabs(X0,X3,X4))) = vapp(vsubst(X0,X1,vvar(X2)),vabs(X0,X3,X4))
| X0 = X2 )
| ~ spl94_179
| ~ spl94_182 ),
inference(superposition,[],[f1690,f1636]) ).
fof(f1690,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_182 ),
inference(avatar_component_clause,[],[f1689]) ).
fof(f6864,plain,
( spl94_405
| ~ spl94_84
| ~ spl94_180
| ~ spl94_181 ),
inference(avatar_split_clause,[],[f1717,f1685,f1639,f915,f6862]) ).
fof(f6862,plain,
( spl94_405
<=> ! [X2,X4,X0,X3,X1] :
( vapp(vabs(X0,X2,X3),vvar(X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,vvar(X4)))
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_405])]) ).
fof(f1685,plain,
( spl94_181
<=> ! [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_181])]) ).
fof(f1717,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(vabs(X0,X2,X3),vvar(X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,vvar(X4)))
| X0 = X4 )
| ~ spl94_84
| ~ spl94_180
| ~ spl94_181 ),
inference(forward_demodulation,[],[f1698,f916]) ).
fof(f1698,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(vsubst(X0,X1,vabs(X0,X2,X3)),vvar(X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,vvar(X4)))
| X0 = X4 )
| ~ spl94_180
| ~ spl94_181 ),
inference(superposition,[],[f1686,f1640]) ).
fof(f1686,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_181 ),
inference(avatar_component_clause,[],[f1685]) ).
fof(f6860,plain,
( spl94_404
| ~ spl94_174
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1671,f1639,f1576,f6858]) ).
fof(f6858,plain,
( spl94_404
<=> ! [X5,X4,X0,X3,X2,X1] :
( vapp(X4,X5) != vapp(vsubst(X0,X1,X2),vvar(X3))
| vsubst(X0,X1,vvar(X3)) = X5
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_404])]) ).
fof(f1671,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vapp(X4,X5) != vapp(vsubst(X0,X1,X2),vvar(X3))
| vsubst(X0,X1,vvar(X3)) = X5
| X0 = X3 )
| ~ spl94_174
| ~ spl94_180 ),
inference(superposition,[],[f1577,f1640]) ).
fof(f6856,plain,
( spl94_403
| ~ spl94_173
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f1649,f1635,f1572,f6854]) ).
fof(f6854,plain,
( spl94_403
<=> ! [X2,X3,X4,X0,X5,X1] :
( vapp(vvar(X2),vsubst(X0,X1,X3)) != vapp(X4,X5)
| vsubst(X0,X1,vvar(X2)) = X4
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_403])]) ).
fof(f1649,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vapp(vvar(X2),vsubst(X0,X1,X3)) != vapp(X4,X5)
| vsubst(X0,X1,vvar(X2)) = X4
| X0 = X2 )
| ~ spl94_173
| ~ spl94_179 ),
inference(superposition,[],[f1573,f1636]) ).
fof(f6852,plain,
( spl94_402
| ~ spl94_101
| ~ spl94_171 ),
inference(avatar_split_clause,[],[f1564,f1455,f1003,f6850]) ).
fof(f6850,plain,
( spl94_402
<=> ! [X0] :
( sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0
| vnoType = vlookup(sK55(vnoType,vempty,X0),sK56(vnoType,vempty,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_402])]) ).
fof(f1003,plain,
( spl94_101
<=> ! [X2,X0,X1] :
( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_101])]) ).
fof(f1455,plain,
( spl94_171
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_171])]) ).
fof(f1564,plain,
( ! [X0] :
( sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0
| vnoType = vlookup(sK55(vnoType,vempty,X0),sK56(vnoType,vempty,X0)) )
| ~ spl94_101
| ~ spl94_171 ),
inference(resolution,[],[f1456,f1004]) ).
fof(f1004,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0 )
| ~ spl94_101 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1456,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 )
| ~ spl94_171 ),
inference(avatar_component_clause,[],[f1455]) ).
fof(f6847,plain,
( spl94_401
| ~ spl94_116
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1503,f1443,f1069,f6845]) ).
fof(f6845,plain,
( spl94_401
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(X3,vapp(X2,vvar(X0)))) = vapp(vsubst(X0,X1,X3),vapp(vsubst(X0,X1,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_401])]) ).
fof(f1503,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(X3,vapp(X2,vvar(X0)))) = vapp(vsubst(X0,X1,X3),vapp(vsubst(X0,X1,X2),X1))
| ~ spl94_116
| ~ spl94_168 ),
inference(superposition,[],[f1070,f1444]) ).
fof(f6843,plain,
( spl94_400
| ~ spl94_116
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1502,f1443,f1069,f6841]) ).
fof(f6841,plain,
( spl94_400
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),X3)) = vapp(vapp(vsubst(X0,X1,X2),X1),vsubst(X0,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_400])]) ).
fof(f1502,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),X3)) = vapp(vapp(vsubst(X0,X1,X2),X1),vsubst(X0,X1,X3))
| ~ spl94_116
| ~ spl94_168 ),
inference(superposition,[],[f1070,f1444]) ).
fof(f6839,plain,
( spl94_399
| ~ spl94_116
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1471,f1439,f1069,f6837]) ).
fof(f6837,plain,
( spl94_399
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(X3,vapp(vvar(X0),X2))) = vapp(vsubst(X0,X1,X3),vapp(X1,vsubst(X0,X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_399])]) ).
fof(f1471,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(X3,vapp(vvar(X0),X2))) = vapp(vsubst(X0,X1,X3),vapp(X1,vsubst(X0,X1,X2)))
| ~ spl94_116
| ~ spl94_167 ),
inference(superposition,[],[f1070,f1440]) ).
fof(f6835,plain,
( spl94_398
| ~ spl94_116
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1470,f1439,f1069,f6833]) ).
fof(f6833,plain,
( spl94_398
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),X3)) = vapp(vapp(X1,vsubst(X0,X1,X2)),vsubst(X0,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_398])]) ).
fof(f1470,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),X3)) = vapp(vapp(X1,vsubst(X0,X1,X2)),vsubst(X0,X1,X3))
| ~ spl94_116
| ~ spl94_167 ),
inference(superposition,[],[f1070,f1440]) ).
fof(f6592,plain,
( spl94_397
| ~ spl94_43
| ~ spl94_330 ),
inference(avatar_split_clause,[],[f4334,f4323,f739,f6589]) ).
fof(f6589,plain,
( spl94_397
<=> sK16 = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_397])]) ).
fof(f739,plain,
( spl94_43
<=> ! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_43])]) ).
fof(f4323,plain,
( spl94_330
<=> sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_330])]) ).
fof(f4334,plain,
( sK16 = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16)
| ~ spl94_43
| ~ spl94_330 ),
inference(resolution,[],[f4325,f740]) ).
fof(f740,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK55(X0,X1,X2) = X2 )
| ~ spl94_43 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f4325,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16)
| ~ spl94_330 ),
inference(avatar_component_clause,[],[f4323]) ).
fof(f6526,plain,
( spl94_396
| ~ spl94_18
| ~ spl94_200 ),
inference(avatar_split_clause,[],[f1966,f1943,f633,f6524]) ).
fof(f6524,plain,
( spl94_396
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ vtcheck(vbind(X1,X2,vempty),X3,X4)
| vtcheck(vbind(X0,X5,vbind(X1,X2,vempty)),X3,X4)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_396])]) ).
fof(f1943,plain,
( spl94_200
<=> ! [X2,X6,X4,X0,X5,X3,X1] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),X4,X5)
| vtcheck(vbind(X0,X6,vbind(X1,X2,X3)),X4,X5)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_200])]) ).
fof(f1966,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ vtcheck(vbind(X1,X2,vempty),X3,X4)
| vtcheck(vbind(X0,X5,vbind(X1,X2,vempty)),X3,X4)
| X0 = X1 )
| ~ spl94_18
| ~ spl94_200 ),
inference(trivial_inequality_removal,[],[f1963]) ).
fof(f1963,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vnoType != vnoType
| ~ vtcheck(vbind(X1,X2,vempty),X3,X4)
| vtcheck(vbind(X0,X5,vbind(X1,X2,vempty)),X3,X4)
| X0 = X1 )
| ~ spl94_18
| ~ spl94_200 ),
inference(superposition,[],[f1944,f634]) ).
fof(f1944,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),X4,X5)
| vtcheck(vbind(X0,X6,vbind(X1,X2,X3)),X4,X5)
| X0 = X1 )
| ~ spl94_200 ),
inference(avatar_component_clause,[],[f1943]) ).
fof(f6522,plain,
( spl94_395
| ~ spl94_168
| ~ spl94_174 ),
inference(avatar_split_clause,[],[f1597,f1576,f1443,f6520]) ).
fof(f6520,plain,
( spl94_395
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,X1,vapp(X2,vvar(X0))) != vsubst(X3,X4,vapp(X5,X6))
| vsubst(X3,X4,X6) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_395])]) ).
fof(f1597,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,X1,vapp(X2,vvar(X0))) != vsubst(X3,X4,vapp(X5,X6))
| vsubst(X3,X4,X6) = X1 )
| ~ spl94_168
| ~ spl94_174 ),
inference(superposition,[],[f1577,f1444]) ).
fof(f6518,plain,
( spl94_394
| ~ spl94_168
| ~ spl94_174 ),
inference(avatar_split_clause,[],[f1591,f1576,f1443,f6516]) ).
fof(f6516,plain,
( spl94_394
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vapp(X5,X6) != vsubst(X3,X4,vsubst(X0,X1,vapp(X2,vvar(X0))))
| vsubst(X3,X4,X1) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_394])]) ).
fof(f1591,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vapp(X5,X6) != vsubst(X3,X4,vsubst(X0,X1,vapp(X2,vvar(X0))))
| vsubst(X3,X4,X1) = X6 )
| ~ spl94_168
| ~ spl94_174 ),
inference(superposition,[],[f1577,f1444]) ).
fof(f6514,plain,
( spl94_393
| ~ spl94_167
| ~ spl94_173 ),
inference(avatar_split_clause,[],[f1586,f1572,f1439,f6512]) ).
fof(f6512,plain,
( spl94_393
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X1,X0,vapp(vvar(X1),X2)) != vsubst(X3,X4,vapp(X5,X6))
| vsubst(X3,X4,X5) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_393])]) ).
fof(f1586,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X1,X0,vapp(vvar(X1),X2)) != vsubst(X3,X4,vapp(X5,X6))
| vsubst(X3,X4,X5) = X0 )
| ~ spl94_167
| ~ spl94_173 ),
inference(superposition,[],[f1573,f1440]) ).
fof(f6510,plain,
( spl94_392
| ~ spl94_167
| ~ spl94_173 ),
inference(avatar_split_clause,[],[f1580,f1572,f1439,f6508]) ).
fof(f6508,plain,
( spl94_392
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vapp(X5,X6) != vsubst(X3,X4,vsubst(X1,X0,vapp(vvar(X1),X2)))
| vsubst(X3,X4,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_392])]) ).
fof(f1580,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vapp(X5,X6) != vsubst(X3,X4,vsubst(X1,X0,vapp(vvar(X1),X2)))
| vsubst(X3,X4,X0) = X5 )
| ~ spl94_167
| ~ spl94_173 ),
inference(superposition,[],[f1573,f1440]) ).
fof(f6506,plain,
( spl94_391
| ~ spl94_116
| ~ spl94_170 ),
inference(avatar_split_clause,[],[f1556,f1451,f1069,f6504]) ).
fof(f6504,plain,
( spl94_391
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))))
| ~ visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_391])]) ).
fof(f1451,plain,
( spl94_170
<=> ! [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_170])]) ).
fof(f1556,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))))
| ~ visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,X2))) )
| ~ spl94_116
| ~ spl94_170 ),
inference(superposition,[],[f1452,f1070]) ).
fof(f1452,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl94_170 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f6502,plain,
( spl94_390
| ~ spl94_116
| ~ spl94_169 ),
inference(avatar_split_clause,[],[f1544,f1447,f1069,f6500]) ).
fof(f6500,plain,
( spl94_390
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))))
| ~ visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_390])]) ).
fof(f1447,plain,
( spl94_169
<=> ! [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_169])]) ).
fof(f1544,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))))
| ~ visFreeVar(X4,vsubst(X5,X6,vsubst(X0,X1,X3))) )
| ~ spl94_116
| ~ spl94_169 ),
inference(superposition,[],[f1448,f1070]) ).
fof(f1448,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl94_169 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f6492,plain,
( spl94_389
| ~ spl94_158
| ~ spl94_235 ),
inference(avatar_split_clause,[],[f3896,f2429,f1392,f6490]) ).
fof(f6490,plain,
( spl94_389
<=> ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK86(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0) = X0
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_389])]) ).
fof(f2429,plain,
( spl94_235
<=> ! [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_235])]) ).
fof(f3896,plain,
( ! [X0] :
( sP12(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP13(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP11(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK86(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16),X0) = X0
| sP10(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP9(X0,vvar(sK16),X0,sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_158
| ~ spl94_235 ),
inference(superposition,[],[f2430,f1394]) ).
fof(f2430,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_235 ),
inference(avatar_component_clause,[],[f2429]) ).
fof(f6487,plain,
( spl94_388
| ~ spl94_158
| ~ spl94_275 ),
inference(avatar_split_clause,[],[f3905,f3005,f1392,f6485]) ).
fof(f6485,plain,
( spl94_388
<=> ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| vvar(sK16) = vsubst(sK85(X1,X0,vvar(sK16),vvar(sK16)),sK86(X1,X0,vvar(sK16),vvar(sK16)),vapp(sK84(X1,X0,vvar(sK16),vvar(sK16)),sK87(X1,X0,vvar(sK16),vvar(sK16))))
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_388])]) ).
fof(f3005,plain,
( spl94_275
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK85(X0,X1,vvar(X2),vvar(X2)),sK86(X0,X1,vvar(X2),vvar(X2)),vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2))))
| sP11(vvar(X2),vvar(X2),X1,X0)
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_275])]) ).
fof(f3905,plain,
( ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| vvar(sK16) = vsubst(sK85(X1,X0,vvar(sK16),vvar(sK16)),sK86(X1,X0,vvar(sK16),vvar(sK16)),vapp(sK84(X1,X0,vvar(sK16),vvar(sK16)),sK87(X1,X0,vvar(sK16),vvar(sK16))))
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_158
| ~ spl94_275 ),
inference(superposition,[],[f3006,f1394]) ).
fof(f3006,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK85(X0,X1,vvar(X2),vvar(X2)),sK86(X0,X1,vvar(X2),vvar(X2)),vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2))))
| sP11(vvar(X2),vvar(X2),X1,X0)
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_275 ),
inference(avatar_component_clause,[],[f3005]) ).
fof(f6483,plain,
( spl94_387
| ~ spl94_32
| ~ spl94_313 ),
inference(avatar_split_clause,[],[f3945,f3941,f689,f6480]) ).
fof(f689,plain,
( spl94_32
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_32])]) ).
fof(f3941,plain,
( spl94_313
<=> visFreeVar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_313])]) ).
fof(f3945,plain,
( sK16 = sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))
| ~ spl94_32
| ~ spl94_313 ),
inference(resolution,[],[f3943,f690]) ).
fof(f690,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl94_32 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f3943,plain,
( visFreeVar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(sK16))
| ~ spl94_313 ),
inference(avatar_component_clause,[],[f3941]) ).
fof(f5645,plain,
( spl94_386
| ~ spl94_165
| ~ spl94_308 ),
inference(avatar_split_clause,[],[f3719,f3633,f1429,f5643]) ).
fof(f5643,plain,
( spl94_386
<=> ! [X4,X0,X3,X2,X1] : vvar(X0) != vsubst(X1,X2,vsubst(X3,X4,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_386])]) ).
fof(f1429,plain,
( spl94_165
<=> sK17 = vapp(sK45(sK15,sK14,sK17),sK46(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_165])]) ).
fof(f3633,plain,
( spl94_308
<=> ! [X5,X6,X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_308])]) ).
fof(f3719,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X0) != vsubst(X1,X2,vsubst(X3,X4,sK17))
| ~ spl94_165
| ~ spl94_308 ),
inference(superposition,[],[f3634,f1431]) ).
fof(f1431,plain,
( sK17 = vapp(sK45(sK15,sK14,sK17),sK46(sK15,sK14,sK17))
| ~ spl94_165 ),
inference(avatar_component_clause,[],[f1429]) ).
fof(f3634,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vvar(X4) != vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_308 ),
inference(avatar_component_clause,[],[f3633]) ).
fof(f5641,plain,
( spl94_385
| ~ spl94_23
| ~ spl94_219 ),
inference(avatar_split_clause,[],[f2170,f2155,f653,f5639]) ).
fof(f5639,plain,
( spl94_385
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK88(vabs(X0,X1,X2)),vabs(X0,X1,X2))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_385])]) ).
fof(f653,plain,
( spl94_23
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_23])]) ).
fof(f2170,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK88(vabs(X0,X1,X2)),vabs(X0,X1,X2))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3)) )
| ~ spl94_23
| ~ spl94_219 ),
inference(superposition,[],[f654,f2156]) ).
fof(f654,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl94_23 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f5637,plain,
( spl94_384
| ~ spl94_17
| ~ spl94_205 ),
inference(avatar_split_clause,[],[f2001,f1998,f629,f5635]) ).
fof(f5635,plain,
( spl94_384
<=> ! [X5,X4,X0,X3,X2,X1] : vsomeExp(vsubst(X0,vabs(X1,X2,X3),X4)) = vreduce(vapp(vabs(X0,X5,X4),vabs(X1,X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_384])]) ).
fof(f629,plain,
( spl94_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_17])]) ).
fof(f1998,plain,
( spl94_205
<=> ! [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_205])]) ).
fof(f2001,plain,
( ! [X2,X3,X0,X1,X4,X5] : vsomeExp(vsubst(X0,vabs(X1,X2,X3),X4)) = vreduce(vapp(vabs(X0,X5,X4),vabs(X1,X2,X3)))
| ~ spl94_17
| ~ spl94_205 ),
inference(resolution,[],[f1999,f630]) ).
fof(f630,plain,
( ! [X2,X0,X1] : visValue(vabs(X0,X1,X2))
| ~ spl94_17 ),
inference(avatar_component_clause,[],[f629]) ).
fof(f1999,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ visValue(vabs(X0,X1,X2))
| vsomeExp(vsubst(X3,vabs(X0,X1,X2),X4)) = vreduce(vapp(vabs(X3,X5,X4),vabs(X0,X1,X2))) )
| ~ spl94_205 ),
inference(avatar_component_clause,[],[f1998]) ).
fof(f5633,plain,
( spl94_383
| ~ spl94_169
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1668,f1639,f1447,f5631]) ).
fof(f5631,plain,
( spl94_383
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vapp(vsubst(X0,X1,X2),vvar(X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X3)))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_383])]) ).
fof(f1668,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vapp(vsubst(X0,X1,X2),vvar(X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X3)))
| X0 = X3 )
| ~ spl94_169
| ~ spl94_180 ),
inference(superposition,[],[f1448,f1640]) ).
fof(f5629,plain,
( spl94_382
| ~ spl94_170
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f1648,f1635,f1451,f5627]) ).
fof(f5627,plain,
( spl94_382
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vapp(vvar(X2),vsubst(X0,X1,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X2)))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_382])]) ).
fof(f1648,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vapp(vvar(X2),vsubst(X0,X1,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X2)))
| X0 = X2 )
| ~ spl94_170
| ~ spl94_179 ),
inference(superposition,[],[f1452,f1636]) ).
fof(f5625,plain,
( spl94_381
| ~ spl94_44
| ~ spl94_177 ),
inference(avatar_split_clause,[],[f1622,f1609,f743,f5623]) ).
fof(f5623,plain,
( spl94_381
<=> ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| sK58(vlookup(X1,X0),X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_381])]) ).
fof(f1622,plain,
( ! [X0,X1] :
( vempty = X0
| sK55(vlookup(X1,X0),X0,X1) = X1
| sK58(vlookup(X1,X0),X0,X1) = X1 )
| ~ spl94_44
| ~ spl94_177 ),
inference(resolution,[],[f1610,f744]) ).
fof(f5621,plain,
( spl94_380
| ~ spl94_42
| ~ spl94_175 ),
inference(avatar_split_clause,[],[f1617,f1600,f735,f5619]) ).
fof(f5619,plain,
( spl94_380
<=> ! [X5,X4,X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X4,X5,vbind(X0,X1,X2)),vvar(X0),X3)
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_380])]) ).
fof(f1617,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X4,X5,vbind(X0,X1,X2)),vvar(X0),X3)
| X0 = X4 )
| ~ spl94_42
| ~ spl94_175 ),
inference(superposition,[],[f1601,f736]) ).
fof(f5617,plain,
( spl94_379
| ~ spl94_167
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1508,f1443,f1439,f5615]) ).
fof(f5615,plain,
( spl94_379
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X0)))) = vapp(X1,vapp(vsubst(X0,X1,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_379])]) ).
fof(f1508,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X0)))) = vapp(X1,vapp(vsubst(X0,X1,X2),X1))
| ~ spl94_167
| ~ spl94_168 ),
inference(superposition,[],[f1440,f1444]) ).
fof(f5613,plain,
( spl94_378
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1497,f1443,f5611]) ).
fof(f5611,plain,
( spl94_378
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_378])]) ).
fof(f1497,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),X1),X1)
| ~ spl94_168 ),
inference(superposition,[],[f1444,f1444]) ).
fof(f5609,plain,
( spl94_377
| ~ spl94_167
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1496,f1443,f1439,f5607]) ).
fof(f5607,plain,
( spl94_377
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),vvar(X0))) = vapp(vapp(X1,vsubst(X0,X1,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_377])]) ).
fof(f1496,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),vvar(X0))) = vapp(vapp(X1,vsubst(X0,X1,X2)),X1)
| ~ spl94_167
| ~ spl94_168 ),
inference(superposition,[],[f1444,f1440]) ).
fof(f5605,plain,
( spl94_376
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1466,f1439,f5603]) ).
fof(f5603,plain,
( spl94_376
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X0),X2))) = vapp(X1,vapp(X1,vsubst(X0,X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_376])]) ).
fof(f1466,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X0),X2))) = vapp(X1,vapp(X1,vsubst(X0,X1,X2)))
| ~ spl94_167 ),
inference(superposition,[],[f1440,f1440]) ).
fof(f5592,plain,
( spl94_375
| ~ spl94_222
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3936,f3913,f2206,f5590]) ).
fof(f5590,plain,
( spl94_375
<=> ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(X0,X1,vbind(sK16,sK14,sK15)),vsomeType(sK19))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_375])]) ).
fof(f2206,plain,
( spl94_222
<=> ! [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_222])]) ).
fof(f3936,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(X0,X1,vbind(sK16,sK14,sK15)),vsomeType(sK19))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_222
| ~ spl94_312 ),
inference(superposition,[],[f2207,f3915]) ).
fof(f2207,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_222 ),
inference(avatar_component_clause,[],[f2206]) ).
fof(f5588,plain,
( spl94_342
| spl94_339
| spl94_328
| ~ spl94_215
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3934,f3913,f2113,f4312,f4431,f4446]) ).
fof(f4446,plain,
( spl94_342
<=> vsomeType(sK19) = vlookup(sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_342])]) ).
fof(f2113,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(f3934,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19))
| vsomeType(sK19) = vlookup(sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))))
| ~ spl94_215
| ~ spl94_312 ),
inference(superposition,[],[f2114,f3915]) ).
fof(f2114,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_215 ),
inference(avatar_component_clause,[],[f2113]) ).
fof(f5585,plain,
( spl94_374
| ~ spl94_158
| ~ spl94_256 ),
inference(avatar_split_clause,[],[f3902,f2657,f1392,f5583]) ).
fof(f5583,plain,
( spl94_374
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vabs(X3,X2,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vabs(vgensym(vapp(vapp(X0,X1),vvar(sK16))),X2,vsubst(X3,vvar(vgensym(vapp(vapp(X0,X1),vvar(sK16)))),X1)))
| vabs(X3,X4,vsubst(X5,X0,X6)) = vsubst(X5,X0,vabs(X3,X4,X6))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X3
| X3 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_374])]) ).
fof(f2657,plain,
( spl94_256
<=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
( vsubst(X0,X1,vabs(vgensym(vapp(vapp(X1,X2),vvar(X0))),X3,vsubst(X4,vvar(vgensym(vapp(vapp(X1,X2),vvar(X0)))),X2))) = vsubst(X0,X1,vabs(X4,X3,X2))
| X0 = X4
| vabs(X4,X5,vsubst(X6,X1,X7)) = vsubst(X6,X1,vabs(X4,X5,X7))
| X4 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_256])]) ).
fof(f3902,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vabs(X3,X2,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vabs(vgensym(vapp(vapp(X0,X1),vvar(sK16))),X2,vsubst(X3,vvar(vgensym(vapp(vapp(X0,X1),vvar(sK16)))),X1)))
| vabs(X3,X4,vsubst(X5,X0,X6)) = vsubst(X5,X0,vabs(X3,X4,X6))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X3
| X3 = X5 )
| ~ spl94_158
| ~ spl94_256 ),
inference(superposition,[],[f2658,f1394]) ).
fof(f2658,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,vabs(vgensym(vapp(vapp(X1,X2),vvar(X0))),X3,vsubst(X4,vvar(vgensym(vapp(vapp(X1,X2),vvar(X0)))),X2))) = vsubst(X0,X1,vabs(X4,X3,X2))
| vabs(X4,X5,vsubst(X6,X1,X7)) = vsubst(X6,X1,vabs(X4,X5,X7))
| X0 = X4
| X4 = X6 )
| ~ spl94_256 ),
inference(avatar_component_clause,[],[f2657]) ).
fof(f5364,plain,
( spl94_373
| ~ spl94_167
| ~ spl94_170 ),
inference(avatar_split_clause,[],[f1557,f1451,f1439,f5362]) ).
fof(f5362,plain,
( spl94_373
<=> ! [X3,X4,X0,X5,X2,X1] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X1,X0,vapp(vvar(X1),X2))))
| ~ visFreeVar(X3,vsubst(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_373])]) ).
fof(f1557,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X1,X0,vapp(vvar(X1),X2))))
| ~ visFreeVar(X3,vsubst(X4,X5,X0)) )
| ~ spl94_167
| ~ spl94_170 ),
inference(superposition,[],[f1452,f1440]) ).
fof(f5360,plain,
( spl94_372
| ~ spl94_168
| ~ spl94_169 ),
inference(avatar_split_clause,[],[f1546,f1447,f1443,f5358]) ).
fof(f5358,plain,
( spl94_372
<=> ! [X3,X4,X0,X5,X2,X1] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X0,X1,vapp(X2,vvar(X0)))))
| ~ visFreeVar(X3,vsubst(X4,X5,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_372])]) ).
fof(f1546,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X0,X1,vapp(X2,vvar(X0)))))
| ~ visFreeVar(X3,vsubst(X4,X5,X1)) )
| ~ spl94_168
| ~ spl94_169 ),
inference(superposition,[],[f1448,f1444]) ).
fof(f5356,plain,
( spl94_371
| ~ spl94_60
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1520,f1443,f811,f5354]) ).
fof(f5354,plain,
( spl94_371
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| visFreeVar(X3,vsubst(X0,X1,X2))
| visFreeVar(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_371])]) ).
fof(f811,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(f1520,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| visFreeVar(X3,vsubst(X0,X1,X2))
| visFreeVar(X3,X1) )
| ~ spl94_60
| ~ spl94_168 ),
inference(superposition,[],[f812,f1444]) ).
fof(f812,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl94_60 ),
inference(avatar_component_clause,[],[f811]) ).
fof(f5352,plain,
( spl94_370
| ~ spl94_60
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1487,f1439,f811,f5350]) ).
fof(f5350,plain,
( spl94_370
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| visFreeVar(X3,X0)
| visFreeVar(X3,vsubst(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_370])]) ).
fof(f1487,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| visFreeVar(X3,X0)
| visFreeVar(X3,vsubst(X1,X0,X2)) )
| ~ spl94_60
| ~ spl94_167 ),
inference(superposition,[],[f812,f1440]) ).
fof(f5348,plain,
( spl94_369
| ~ spl94_39
| ~ spl94_166 ),
inference(avatar_split_clause,[],[f1461,f1435,f718,f5346]) ).
fof(f5346,plain,
( spl94_369
<=> ! [X0,X3,X2,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_369])]) ).
fof(f718,plain,
( spl94_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_39])]) ).
fof(f1435,plain,
( spl94_166
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_166])]) ).
fof(f1461,plain,
( ! [X2,X3,X0,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X3) )
| ~ spl94_39
| ~ spl94_166 ),
inference(resolution,[],[f1436,f719]) ).
fof(f719,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl94_39 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1436,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl94_166 ),
inference(avatar_component_clause,[],[f1435]) ).
fof(f5344,plain,
( spl94_368
| ~ spl94_40
| ~ spl94_166 ),
inference(avatar_split_clause,[],[f1460,f1435,f722,f5342]) ).
fof(f5342,plain,
( spl94_368
<=> ! [X0,X3,X2,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_368])]) ).
fof(f722,plain,
( spl94_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_40])]) ).
fof(f1460,plain,
( ! [X2,X3,X0,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X2) )
| ~ spl94_40
| ~ spl94_166 ),
inference(resolution,[],[f1436,f723]) ).
fof(f723,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl94_40 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f5340,plain,
( spl94_367
| ~ spl94_48
| ~ spl94_83 ),
inference(avatar_split_clause,[],[f928,f911,f759,f5338]) ).
fof(f5338,plain,
( spl94_367
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(vgensym(vapp(X0,vabs(X1,X2,X3))),X3)
| vgensym(vapp(X0,vabs(X1,X2,X3))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_367])]) ).
fof(f759,plain,
( spl94_48
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_48])]) ).
fof(f911,plain,
( spl94_83
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_83])]) ).
fof(f928,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(vgensym(vapp(X0,vabs(X1,X2,X3))),X3)
| vgensym(vapp(X0,vabs(X1,X2,X3))) = X1 )
| ~ spl94_48
| ~ spl94_83 ),
inference(resolution,[],[f912,f760]) ).
fof(f760,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_48 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f912,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl94_83 ),
inference(avatar_component_clause,[],[f911]) ).
fof(f5336,plain,
( spl94_366
| ~ spl94_53
| ~ spl94_83 ),
inference(avatar_split_clause,[],[f927,f911,f783,f5334]) ).
fof(f5334,plain,
( spl94_366
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(vgensym(vapp(vabs(X0,X1,X2),X3)),X2)
| vgensym(vapp(vabs(X0,X1,X2),X3)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_366])]) ).
fof(f783,plain,
( spl94_53
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_53])]) ).
fof(f927,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(vgensym(vapp(vabs(X0,X1,X2),X3)),X2)
| vgensym(vapp(vabs(X0,X1,X2),X3)) = X0 )
| ~ spl94_53
| ~ spl94_83 ),
inference(resolution,[],[f912,f784]) ).
fof(f784,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_53 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f5331,plain,
( spl94_332
| spl94_365
| spl94_328
| ~ spl94_213
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3933,f3913,f2098,f4312,f5328,f4336]) ).
fof(f4336,plain,
( spl94_332
<=> vempty = vbind(sK16,sK14,sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_332])]) ).
fof(f2098,plain,
( spl94_213
<=> ! [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_213])]) ).
fof(f3933,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vbind(sK16,sK14,sK15) = vbind(sK54(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK53(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))))
| vempty = vbind(sK16,sK14,sK15)
| ~ spl94_213
| ~ spl94_312 ),
inference(superposition,[],[f2099,f3915]) ).
fof(f2099,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vbind(sK54(vlookup(X0,X1),X1,X0),sK53(vlookup(X0,X1),X1,X0),sK56(vlookup(X0,X1),X1,X0)) = X1
| vempty = X1 )
| ~ spl94_213 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f5093,plain,
( spl94_364
| ~ spl94_168
| ~ spl94_174 ),
inference(avatar_split_clause,[],[f1594,f1576,f1443,f5091]) ).
fof(f5091,plain,
( spl94_364
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vapp(vsubst(X0,X1,X2),X1)
| vsubst(X0,X1,vvar(X0)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_364])]) ).
fof(f1594,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vapp(vsubst(X0,X1,X2),X1)
| vsubst(X0,X1,vvar(X0)) = X4 )
| ~ spl94_168
| ~ spl94_174 ),
inference(superposition,[],[f1577,f1444]) ).
fof(f5089,plain,
( spl94_363
| ~ spl94_167
| ~ spl94_173 ),
inference(avatar_split_clause,[],[f1583,f1572,f1439,f5087]) ).
fof(f5087,plain,
( spl94_363
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vapp(X1,vsubst(X0,X1,X2))
| vsubst(X0,X1,vvar(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_363])]) ).
fof(f1583,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vapp(X1,vsubst(X0,X1,X2))
| vsubst(X0,X1,vvar(X0)) = X3 )
| ~ spl94_167
| ~ spl94_173 ),
inference(superposition,[],[f1573,f1440]) ).
fof(f5085,plain,
( spl94_362
| ~ spl94_84
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1495,f1443,f915,f5083]) ).
fof(f5083,plain,
( spl94_362
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),vvar(X0))) = vapp(vabs(X0,X2,X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_362])]) ).
fof(f1495,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),vvar(X0))) = vapp(vabs(X0,X2,X3),X1)
| ~ spl94_84
| ~ spl94_168 ),
inference(superposition,[],[f1444,f916]) ).
fof(f5081,plain,
( spl94_361
| ~ spl94_84
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1465,f1439,f915,f5079]) ).
fof(f5079,plain,
( spl94_361
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vvar(X0),vabs(X0,X2,X3))) = vapp(X1,vabs(X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_361])]) ).
fof(f1465,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vabs(X0,X2,X3))) = vapp(X1,vabs(X0,X2,X3))
| ~ spl94_84
| ~ spl94_167 ),
inference(superposition,[],[f1440,f916]) ).
fof(f4916,plain,
( spl94_360
| ~ spl94_43
| ~ spl94_171 ),
inference(avatar_split_clause,[],[f1565,f1455,f739,f4914]) ).
fof(f4914,plain,
( spl94_360
<=> ! [X0] :
( sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0
| sK55(vnoType,vempty,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_360])]) ).
fof(f1565,plain,
( ! [X0] :
( sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0
| sK55(vnoType,vempty,X0) = X0 )
| ~ spl94_43
| ~ spl94_171 ),
inference(resolution,[],[f1456,f740]) ).
fof(f4912,plain,
( spl94_359
| ~ spl94_61
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1494,f1443,f815,f4910]) ).
fof(f4910,plain,
( spl94_359
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),vvar(X0))) = vapp(vvar(X2),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_359])]) ).
fof(f815,plain,
( spl94_61
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_61])]) ).
fof(f1494,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),vvar(X0))) = vapp(vvar(X2),X1)
| X0 = X2 )
| ~ spl94_61
| ~ spl94_168 ),
inference(superposition,[],[f1444,f816]) ).
fof(f816,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl94_61 ),
inference(avatar_component_clause,[],[f815]) ).
fof(f4908,plain,
( spl94_358
| ~ spl94_61
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1464,f1439,f815,f4906]) ).
fof(f4906,plain,
( spl94_358
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_358])]) ).
fof(f1464,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 )
| ~ spl94_61
| ~ spl94_167 ),
inference(superposition,[],[f1440,f816]) ).
fof(f4904,plain,
( spl94_334
| spl94_339
| spl94_328
| ~ spl94_193
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3927,f3913,f1872,f4312,f4431,f4345]) ).
fof(f4345,plain,
( spl94_334
<=> sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_334])]) ).
fof(f1872,plain,
( spl94_193
<=> ! [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_193])]) ).
fof(f3927,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| ~ spl94_193
| ~ spl94_312 ),
inference(superposition,[],[f1873,f3915]) ).
fof(f1873,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK61(X0,X1,vlookup(X0,X1)) = X0
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_193 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f4902,plain,
( spl94_357
| ~ spl94_158
| ~ spl94_263 ),
inference(avatar_split_clause,[],[f3903,f2824,f1392,f4900]) ).
fof(f4900,plain,
( spl94_357
<=> ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| vvar(sK16) = vapp(sK84(X1,X0,vvar(sK16),vvar(sK16)),sK87(X1,X0,vvar(sK16),vvar(sK16)))
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_357])]) ).
fof(f2824,plain,
( spl94_263
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_263])]) ).
fof(f3903,plain,
( ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| vvar(sK16) = vapp(sK84(X1,X0,vvar(sK16),vvar(sK16)),sK87(X1,X0,vvar(sK16),vvar(sK16)))
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_158
| ~ spl94_263 ),
inference(superposition,[],[f2825,f1394]) ).
fof(f2825,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)
| vvar(X2) = vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_263 ),
inference(avatar_component_clause,[],[f2824]) ).
fof(f4782,plain,
( spl94_356
| ~ spl94_34
| ~ spl94_167
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f1682,f1639,f1439,f697,f4780]) ).
fof(f4780,plain,
( spl94_356
<=> ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_356])]) ).
fof(f1682,plain,
( ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 )
| ~ spl94_34
| ~ spl94_167
| ~ spl94_180 ),
inference(forward_demodulation,[],[f1663,f698]) ).
fof(f1663,plain,
( ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(vsubst(X0,X1,vvar(X0)),vvar(X2))
| X0 = X2 )
| ~ spl94_167
| ~ spl94_180 ),
inference(superposition,[],[f1640,f1440]) ).
fof(f4778,plain,
( spl94_355
| ~ spl94_34
| ~ spl94_168
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f1660,f1635,f1443,f697,f4776]) ).
fof(f4776,plain,
( spl94_355
<=> ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_355])]) ).
fof(f1660,plain,
( ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),X1)
| X0 = X2 )
| ~ spl94_34
| ~ spl94_168
| ~ spl94_179 ),
inference(forward_demodulation,[],[f1643,f698]) ).
fof(f1643,plain,
( ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),vsubst(X0,X1,vvar(X0)))
| X0 = X2 )
| ~ spl94_168
| ~ spl94_179 ),
inference(superposition,[],[f1636,f1444]) ).
fof(f4774,plain,
( spl94_354
| ~ spl94_165
| ~ spl94_295 ),
inference(avatar_split_clause,[],[f3459,f3391,f1429,f4772]) ).
fof(f4772,plain,
( spl94_354
<=> ! [X0] : ~ visFreeVar(vgensym(vapp(sK17,X0)),sK46(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_354])]) ).
fof(f3391,plain,
( spl94_295
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_295])]) ).
fof(f3459,plain,
( ! [X0] : ~ visFreeVar(vgensym(vapp(sK17,X0)),sK46(sK15,sK14,sK17))
| ~ spl94_165
| ~ spl94_295 ),
inference(superposition,[],[f3392,f1431]) ).
fof(f3392,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl94_295 ),
inference(avatar_component_clause,[],[f3391]) ).
fof(f4768,plain,
( spl94_353
| ~ spl94_158
| ~ spl94_234 ),
inference(avatar_split_clause,[],[f3895,f2425,f1392,f4766]) ).
fof(f4766,plain,
( spl94_353
<=> ! [X2,X0,X1] :
( vsubst(X0,vvar(sK16),vabs(vgensym(vapp(vapp(vvar(sK16),X1),vvar(X0))),X2,vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(vgensym(vapp(vapp(vvar(sK16),X1),vvar(X0)))),X1))) = vsubst(X0,vvar(sK16),vabs(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X2,X1))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_353])]) ).
fof(f2425,plain,
( spl94_234
<=> ! [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_234])]) ).
fof(f3895,plain,
( ! [X2,X0,X1] :
( vsubst(X0,vvar(sK16),vabs(vgensym(vapp(vapp(vvar(sK16),X1),vvar(X0))),X2,vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(vgensym(vapp(vapp(vvar(sK16),X1),vvar(X0)))),X1))) = vsubst(X0,vvar(sK16),vabs(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X2,X1))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_158
| ~ spl94_234 ),
inference(superposition,[],[f2426,f1394]) ).
fof(f2426,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_234 ),
inference(avatar_component_clause,[],[f2425]) ).
fof(f4762,plain,
( spl94_352
| ~ spl94_158
| ~ spl94_234 ),
inference(avatar_split_clause,[],[f3894,f2425,f1392,f4760]) ).
fof(f4760,plain,
( spl94_352
<=> ! [X2,X0,X1] :
( vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(X0),vabs(X0,X2,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(X0),vabs(vgensym(vapp(vapp(vvar(X0),X1),vvar(sK16))),X2,vsubst(X0,vvar(vgensym(vapp(vapp(vvar(X0),X1),vvar(sK16)))),X1)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_352])]) ).
fof(f3894,plain,
( ! [X2,X0,X1] :
( vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(X0),vabs(X0,X2,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(X0),vabs(vgensym(vapp(vapp(vvar(X0),X1),vvar(sK16))),X2,vsubst(X0,vvar(vgensym(vapp(vapp(vvar(X0),X1),vvar(sK16)))),X1)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_158
| ~ spl94_234 ),
inference(superposition,[],[f2426,f1394]) ).
fof(f4489,plain,
( spl94_351
| ~ spl94_48
| ~ spl94_170 ),
inference(avatar_split_clause,[],[f1553,f1451,f759,f4487]) ).
fof(f4487,plain,
( spl94_351
<=> ! [X4,X0,X3,X2,X1] : ~ visFreeVar(vgensym(vapp(X0,vsubst(X1,X2,vapp(X3,X4)))),vsubst(X1,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_351])]) ).
fof(f1553,plain,
( ! [X2,X3,X0,X1,X4] : ~ visFreeVar(vgensym(vapp(X0,vsubst(X1,X2,vapp(X3,X4)))),vsubst(X1,X2,X3))
| ~ spl94_48
| ~ spl94_170 ),
inference(resolution,[],[f1452,f760]) ).
fof(f4485,plain,
( spl94_350
| ~ spl94_98
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f3436,f1429,f985,f4483]) ).
fof(f4483,plain,
( spl94_350
<=> ! [X0] : ~ visFreeVar(vgensym(vapp(sK17,X0)),sK45(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_350])]) ).
fof(f985,plain,
( spl94_98
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_98])]) ).
fof(f3436,plain,
( ! [X0] : ~ visFreeVar(vgensym(vapp(sK17,X0)),sK45(sK15,sK14,sK17))
| ~ spl94_98
| ~ spl94_165 ),
inference(superposition,[],[f986,f1431]) ).
fof(f986,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl94_98 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f4481,plain,
( spl94_349
| ~ spl94_53
| ~ spl94_170 ),
inference(avatar_split_clause,[],[f1552,f1451,f783,f4479]) ).
fof(f4479,plain,
( spl94_349
<=> ! [X4,X0,X3,X2,X1] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(X2,X3)),X4)),vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_349])]) ).
fof(f1552,plain,
( ! [X2,X3,X0,X1,X4] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(X2,X3)),X4)),vsubst(X0,X1,X2))
| ~ spl94_53
| ~ spl94_170 ),
inference(resolution,[],[f1452,f784]) ).
fof(f4477,plain,
( spl94_348
| ~ spl94_48
| ~ spl94_169 ),
inference(avatar_split_clause,[],[f1541,f1447,f759,f4475]) ).
fof(f4475,plain,
( spl94_348
<=> ! [X4,X0,X3,X2,X1] : ~ visFreeVar(vgensym(vapp(X0,vsubst(X1,X2,vapp(X3,X4)))),vsubst(X1,X2,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_348])]) ).
fof(f1541,plain,
( ! [X2,X3,X0,X1,X4] : ~ visFreeVar(vgensym(vapp(X0,vsubst(X1,X2,vapp(X3,X4)))),vsubst(X1,X2,X4))
| ~ spl94_48
| ~ spl94_169 ),
inference(resolution,[],[f1448,f760]) ).
fof(f4473,plain,
( spl94_347
| ~ spl94_53
| ~ spl94_169 ),
inference(avatar_split_clause,[],[f1540,f1447,f783,f4471]) ).
fof(f4471,plain,
( spl94_347
<=> ! [X2,X4,X0,X3,X1] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(X2,X3)),X4)),vsubst(X0,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_347])]) ).
fof(f1540,plain,
( ! [X2,X3,X0,X1,X4] : ~ visFreeVar(vgensym(vapp(vsubst(X0,X1,vapp(X2,X3)),X4)),vsubst(X0,X1,X3))
| ~ spl94_53
| ~ spl94_169 ),
inference(resolution,[],[f1448,f784]) ).
fof(f4469,plain,
( spl94_346
| ~ spl94_49
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1517,f1443,f763,f4467]) ).
fof(f4467,plain,
( spl94_346
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vsubst(X0,X1,vapp(X2,vvar(X0)))
| X1 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_346])]) ).
fof(f763,plain,
( spl94_49
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_49])]) ).
fof(f1517,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vsubst(X0,X1,vapp(X2,vvar(X0)))
| X1 = X4 )
| ~ spl94_49
| ~ spl94_168 ),
inference(superposition,[],[f764,f1444]) ).
fof(f764,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl94_49 ),
inference(avatar_component_clause,[],[f763]) ).
fof(f4465,plain,
( spl94_345
| ~ spl94_47
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1481,f1439,f755,f4463]) ).
fof(f4463,plain,
( spl94_345
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vsubst(X1,X0,vapp(vvar(X1),X2))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_345])]) ).
fof(f755,plain,
( spl94_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_47])]) ).
fof(f1481,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vsubst(X1,X0,vapp(vvar(X1),X2))
| X0 = X3 )
| ~ spl94_47
| ~ spl94_167 ),
inference(superposition,[],[f756,f1440]) ).
fof(f756,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl94_47 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f4461,plain,
( spl94_344
| ~ spl94_116
| ~ spl94_163 ),
inference(avatar_split_clause,[],[f1423,f1416,f1069,f4459]) ).
fof(f4459,plain,
( spl94_344
<=> ! [X5,X6,X4,X0,X8,X7,X3,X2,X1] : vabs(X6,X7,X8) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_344])]) ).
fof(f1416,plain,
( spl94_163
<=> ! [X5,X4,X2,X0,X6,X3,X1] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_163])]) ).
fof(f1423,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : vabs(X6,X7,X8) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_116
| ~ spl94_163 ),
inference(superposition,[],[f1417,f1070]) ).
fof(f1417,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl94_163 ),
inference(avatar_component_clause,[],[f1416]) ).
fof(f4454,plain,
( spl94_343
| ~ spl94_207
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3931,f3913,f2022,f4452]) ).
fof(f4452,plain,
( spl94_343
<=> ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vempty = vbind(X0,X1,vbind(sK16,sK14,sK15))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_343])]) ).
fof(f3931,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vempty = vbind(X0,X1,vbind(sK16,sK14,sK15))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_207
| ~ spl94_312 ),
inference(superposition,[],[f2023,f3915]) ).
fof(f4449,plain,
( spl94_342
| spl94_332
| spl94_328
| ~ spl94_203
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3929,f3913,f1990,f4312,f4336,f4446]) ).
fof(f1990,plain,
( spl94_203
<=> ! [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_203])]) ).
fof(f3929,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vempty = vbind(sK16,sK14,sK15)
| vsomeType(sK19) = vlookup(sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),sK56(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))))
| ~ spl94_203
| ~ spl94_312 ),
inference(superposition,[],[f1991,f3915]) ).
fof(f1991,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_203 ),
inference(avatar_component_clause,[],[f1990]) ).
fof(f4444,plain,
( ~ spl94_341
| ~ spl94_32
| ~ spl94_313
| spl94_339 ),
inference(avatar_split_clause,[],[f4435,f4431,f3941,f689,f4441]) ).
fof(f4441,plain,
( spl94_341
<=> sK16 = sK61(sK16,vbind(sK16,sK14,sK15),vsomeType(sK19)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_341])]) ).
fof(f4435,plain,
( sK16 != sK61(sK16,vbind(sK16,sK14,sK15),vsomeType(sK19))
| ~ spl94_32
| ~ spl94_313
| spl94_339 ),
inference(forward_demodulation,[],[f4432,f3945]) ).
fof(f4432,plain,
( sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) != sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19))
| spl94_339 ),
inference(avatar_component_clause,[],[f4431]) ).
fof(f4439,plain,
( spl94_340
| ~ spl94_92
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f3421,f1429,f960,f4437]) ).
fof(f4437,plain,
( spl94_340
<=> ! [X0] : ~ visFreeVar(vgensym(vapp(X0,sK17)),sK46(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_340])]) ).
fof(f960,plain,
( spl94_92
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_92])]) ).
fof(f3421,plain,
( ! [X0] : ~ visFreeVar(vgensym(vapp(X0,sK17)),sK46(sK15,sK14,sK17))
| ~ spl94_92
| ~ spl94_165 ),
inference(superposition,[],[f961,f1431]) ).
fof(f961,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl94_92 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f4434,plain,
( spl94_339
| spl94_328
| spl94_329
| ~ spl94_129
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3923,f3913,f1178,f4316,f4312,f4431]) ).
fof(f4316,plain,
( spl94_329
<=> sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_329])]) ).
fof(f1178,plain,
( spl94_129
<=> ! [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_129])]) ).
fof(f3923,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK61(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15),vsomeType(sK19))
| ~ spl94_129
| ~ spl94_312 ),
inference(superposition,[],[f1179,f3915]) ).
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_129 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f4428,plain,
( spl94_338
| ~ spl94_158
| ~ spl94_250 ),
inference(avatar_split_clause,[],[f3901,f2596,f1392,f4426]) ).
fof(f4426,plain,
( spl94_338
<=> ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sK85(X1,X0,vvar(sK16),vvar(sK16)) = X1
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_338])]) ).
fof(f2596,plain,
( spl94_250
<=> ! [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_250])]) ).
fof(f3901,plain,
( ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sK85(X1,X0,vvar(sK16),vvar(sK16)) = X1
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_158
| ~ spl94_250 ),
inference(superposition,[],[f2597,f1394]) ).
fof(f2597,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_250 ),
inference(avatar_component_clause,[],[f2596]) ).
fof(f4423,plain,
( spl94_337
| ~ spl94_158
| ~ spl94_249 ),
inference(avatar_split_clause,[],[f3900,f2592,f1392,f4421]) ).
fof(f4421,plain,
( spl94_337
<=> ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sK86(X1,X0,vvar(sK16),vvar(sK16)) = X0
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_337])]) ).
fof(f2592,plain,
( spl94_249
<=> ! [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_249])]) ).
fof(f3900,plain,
( ! [X0,X1] :
( sP12(vvar(sK16),vvar(sK16),X0,X1)
| sP13(vvar(sK16),vvar(sK16),X0,X1)
| sP11(vvar(sK16),vvar(sK16),X0,X1)
| sK86(X1,X0,vvar(sK16),vvar(sK16)) = X0
| sP10(vvar(sK16),vvar(sK16),X0,X1)
| sP9(vvar(sK16),vvar(sK16),X0,X1)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_158
| ~ spl94_249 ),
inference(superposition,[],[f2593,f1394]) ).
fof(f2593,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_249 ),
inference(avatar_component_clause,[],[f2592]) ).
fof(f4416,plain,
( spl94_336
| ~ spl94_32
| ~ spl94_313
| ~ spl94_335 ),
inference(avatar_split_clause,[],[f4412,f4384,f3941,f689,f4414]) ).
fof(f4414,plain,
( spl94_336
<=> ! [X0,X1] :
( sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16)
| sK16 = X0
| sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_336])]) ).
fof(f4384,plain,
( spl94_335
<=> ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_335])]) ).
fof(f4412,plain,
( ! [X0,X1] :
( sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16)
| sK16 = X0
| sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16) )
| ~ spl94_32
| ~ spl94_313
| ~ spl94_335 ),
inference(forward_demodulation,[],[f4411,f3945]) ).
fof(f4411,plain,
( ! [X0,X1] :
( sK16 = X0
| sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16)
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_32
| ~ spl94_313
| ~ spl94_335 ),
inference(forward_demodulation,[],[f4410,f3945]) ).
fof(f4410,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK16)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_32
| ~ spl94_313
| ~ spl94_335 ),
inference(forward_demodulation,[],[f4385,f3945]) ).
fof(f4385,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))) )
| ~ spl94_335 ),
inference(avatar_component_clause,[],[f4384]) ).
fof(f4405,plain,
( ~ spl94_9
| ~ spl94_327 ),
inference(avatar_contradiction_clause,[],[f4404]) ).
fof(f4404,plain,
( $false
| ~ spl94_9
| ~ spl94_327 ),
inference(trivial_inequality_removal,[],[f4392]) ).
fof(f4392,plain,
( vnoType != vnoType
| ~ spl94_9
| ~ spl94_327 ),
inference(superposition,[],[f598,f4310]) ).
fof(f4310,plain,
( vnoType = vsomeType(sK19)
| ~ spl94_327 ),
inference(avatar_component_clause,[],[f4308]) ).
fof(f4308,plain,
( spl94_327
<=> vnoType = vsomeType(sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_327])]) ).
fof(f598,plain,
( ! [X0] : vnoType != vsomeType(X0)
| ~ spl94_9 ),
inference(avatar_component_clause,[],[f597]) ).
fof(f597,plain,
( spl94_9
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_9])]) ).
fof(f4386,plain,
( spl94_327
| spl94_335
| ~ spl94_204
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3930,f3913,f1994,f4384,f4308]) ).
fof(f1994,plain,
( spl94_204
<=> ! [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_204])]) ).
fof(f3930,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(X0,X1,vbind(sK16,sK14,sK15)),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vnoType = vsomeType(sK19)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_204
| ~ spl94_312 ),
inference(superposition,[],[f1995,f3915]) ).
fof(f1995,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_204 ),
inference(avatar_component_clause,[],[f1994]) ).
fof(f4350,plain,
( spl94_334
| spl94_332
| spl94_328
| ~ spl94_177
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3925,f3913,f1609,f4312,f4336,f4345]) ).
fof(f3925,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vempty = vbind(sK16,sK14,sK15)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| ~ spl94_177
| ~ spl94_312 ),
inference(superposition,[],[f1610,f3915]) ).
fof(f4348,plain,
( spl94_334
| spl94_327
| spl94_328
| ~ spl94_183
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3926,f3913,f1693,f4312,f4308,f4345]) ).
fof(f3926,plain,
( sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vnoType = vsomeType(sK19)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = sK55(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| ~ spl94_183
| ~ spl94_312 ),
inference(superposition,[],[f1694,f3915]) ).
fof(f4343,plain,
( spl94_333
| ~ spl94_85
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f3406,f1429,f932,f4341]) ).
fof(f4341,plain,
( spl94_333
<=> ! [X0] : ~ visFreeVar(vgensym(vapp(X0,sK17)),sK45(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_333])]) ).
fof(f932,plain,
( spl94_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_85])]) ).
fof(f3406,plain,
( ! [X0] : ~ visFreeVar(vgensym(vapp(X0,sK17)),sK45(sK15,sK14,sK17))
| ~ spl94_85
| ~ spl94_165 ),
inference(superposition,[],[f933,f1431]) ).
fof(f933,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl94_85 ),
inference(avatar_component_clause,[],[f932]) ).
fof(f4339,plain,
( spl94_332
| spl94_328
| spl94_329
| ~ spl94_102
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3920,f3913,f1007,f4316,f4312,f4336]) ).
fof(f1007,plain,
( spl94_102
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_102])]) ).
fof(f3920,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vempty = vbind(sK16,sK14,sK15)
| ~ spl94_102
| ~ spl94_312 ),
inference(superposition,[],[f1008,f3915]) ).
fof(f1008,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl94_102 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f4331,plain,
( ~ spl94_331
| ~ spl94_32
| ~ spl94_313
| spl94_328 ),
inference(avatar_split_clause,[],[f4321,f4312,f3941,f689,f4328]) ).
fof(f4328,plain,
( spl94_331
<=> sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_331])]) ).
fof(f4321,plain,
( ~ sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16)
| ~ spl94_32
| ~ spl94_313
| spl94_328 ),
inference(forward_demodulation,[],[f4313,f3945]) ).
fof(f4313,plain,
( ~ sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| spl94_328 ),
inference(avatar_component_clause,[],[f4312]) ).
fof(f4326,plain,
( spl94_330
| ~ spl94_32
| ~ spl94_313
| ~ spl94_329 ),
inference(avatar_split_clause,[],[f4320,f4316,f3941,f689,f4323]) ).
fof(f4320,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK16)
| ~ spl94_32
| ~ spl94_313
| ~ spl94_329 ),
inference(forward_demodulation,[],[f4318,f3945]) ).
fof(f4318,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| ~ spl94_329 ),
inference(avatar_component_clause,[],[f4316]) ).
fof(f4319,plain,
( spl94_327
| spl94_328
| spl94_329
| ~ spl94_117
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3922,f3913,f1101,f4316,f4312,f4308]) ).
fof(f1101,plain,
( spl94_117
<=> ! [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_117])]) ).
fof(f3922,plain,
( sP8(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP7(vsomeType(sK19),vbind(sK16,sK14,sK15),sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| vnoType = vsomeType(sK19)
| ~ spl94_117
| ~ spl94_312 ),
inference(superposition,[],[f1102,f3915]) ).
fof(f1102,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl94_117 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f4305,plain,
( spl94_326
| ~ spl94_158
| ~ spl94_194 ),
inference(avatar_split_clause,[],[f3892,f1886,f1392,f4303]) ).
fof(f4303,plain,
( spl94_326
<=> ! [X0,X3,X2,X1] :
( vabs(X0,X1,vsubst(X2,vvar(sK16),X3)) = vsubst(X2,vvar(sK16),vabs(X0,X1,X3))
| X0 = X2
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_326])]) ).
fof(f1886,plain,
( spl94_194
<=> ! [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_194])]) ).
fof(f3892,plain,
( ! [X2,X3,X0,X1] :
( vabs(X0,X1,vsubst(X2,vvar(sK16),X3)) = vsubst(X2,vvar(sK16),vabs(X0,X1,X3))
| X0 = X2
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_158
| ~ spl94_194 ),
inference(superposition,[],[f1887,f1394]) ).
fof(f1887,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_194 ),
inference(avatar_component_clause,[],[f1886]) ).
fof(f4300,plain,
( spl94_325
| ~ spl94_158
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f3888,f1443,f1392,f4298]) ).
fof(f4298,plain,
( spl94_325
<=> ! [X0,X1] : vapp(vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,X1),X0) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vapp(X1,vvar(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_325])]) ).
fof(f3888,plain,
( ! [X0,X1] : vapp(vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,X1),X0) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vapp(X1,vvar(sK16)))
| ~ spl94_158
| ~ spl94_168 ),
inference(superposition,[],[f1444,f1394]) ).
fof(f4295,plain,
( spl94_324
| ~ spl94_158
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f3887,f1439,f1392,f4293]) ).
fof(f4293,plain,
( spl94_324
<=> ! [X0,X1] : vapp(X0,vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vapp(vvar(sK16),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_324])]) ).
fof(f3887,plain,
( ! [X0,X1] : vapp(X0,vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,X1)) = vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vapp(vvar(sK16),X1))
| ~ spl94_158
| ~ spl94_167 ),
inference(superposition,[],[f1440,f1394]) ).
fof(f4288,plain,
( spl94_323
| ~ spl94_32
| ~ spl94_313
| ~ spl94_322 ),
inference(avatar_split_clause,[],[f4284,f4281,f3941,f689,f4286]) ).
fof(f4286,plain,
( spl94_323
<=> ! [X2,X0,X1] :
( sK16 = X1
| vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_323])]) ).
fof(f4281,plain,
( spl94_322
<=> ! [X2,X0,X1] :
( vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_322])]) ).
fof(f4284,plain,
( ! [X2,X0,X1] :
( sK16 = X1
| vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19) )
| ~ spl94_32
| ~ spl94_313
| ~ spl94_322 ),
inference(forward_demodulation,[],[f4282,f3945]) ).
fof(f4282,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_322 ),
inference(avatar_component_clause,[],[f4281]) ).
fof(f4283,plain,
( spl94_322
| ~ spl94_158
| ~ spl94_175
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3939,f3913,f1600,f1392,f4281]) ).
fof(f3939,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_158
| ~ spl94_175
| ~ spl94_312 ),
inference(forward_demodulation,[],[f3924,f1394]) ).
fof(f3924,plain,
( ! [X2,X0,X1] :
( vsomeType(X0) != vsomeType(sK19)
| vtcheck(vbind(X1,X2,vbind(sK16,sK14,sK15)),vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),X0)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X1 )
| ~ spl94_175
| ~ spl94_312 ),
inference(superposition,[],[f1601,f3915]) ).
fof(f4056,plain,
( spl94_321
| ~ spl94_158
| ~ spl94_180 ),
inference(avatar_split_clause,[],[f3890,f1639,f1392,f4054]) ).
fof(f4054,plain,
( spl94_321
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(X2,vvar(sK16))) = vapp(vsubst(X0,X1,X2),vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_321])]) ).
fof(f3890,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(X2,vvar(sK16))) = vapp(vsubst(X0,X1,X2),vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_158
| ~ spl94_180 ),
inference(superposition,[],[f1640,f1394]) ).
fof(f4052,plain,
( spl94_320
| ~ spl94_158
| ~ spl94_179 ),
inference(avatar_split_clause,[],[f3889,f1635,f1392,f4050]) ).
fof(f4050,plain,
( spl94_320
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(sK16),X2)) = vapp(vvar(sK16),vsubst(X0,X1,X2))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_320])]) ).
fof(f3889,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(sK16),X2)) = vapp(vvar(sK16),vsubst(X0,X1,X2))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_158
| ~ spl94_179 ),
inference(superposition,[],[f1636,f1394]) ).
fof(f3984,plain,
( spl94_319
| ~ spl94_61
| ~ spl94_158 ),
inference(avatar_split_clause,[],[f3885,f1392,f815,f3982]) ).
fof(f3982,plain,
( spl94_319
<=> ! [X0,X1] :
( vvar(sK16) = vsubst(X0,X1,vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_319])]) ).
fof(f3885,plain,
( ! [X0,X1] :
( vvar(sK16) = vsubst(X0,X1,vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_61
| ~ spl94_158 ),
inference(superposition,[],[f816,f1394]) ).
fof(f3979,plain,
( spl94_318
| ~ spl94_37
| ~ spl94_158 ),
inference(avatar_split_clause,[],[f3883,f1392,f710,f3977]) ).
fof(f3977,plain,
( spl94_318
<=> ! [X0] :
( vvar(X0) != vvar(sK16)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_318])]) ).
fof(f710,plain,
( spl94_37
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_37])]) ).
fof(f3883,plain,
( ! [X0] :
( vvar(X0) != vvar(sK16)
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_37
| ~ spl94_158 ),
inference(superposition,[],[f711,f1394]) ).
fof(f711,plain,
( ! [X0,X1] :
( vvar(X0) != vvar(X1)
| X0 = X1 )
| ~ spl94_37 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f3975,plain,
( spl94_317
| ~ spl94_165
| ~ spl94_298 ),
inference(avatar_split_clause,[],[f3497,f3473,f1429,f3973]) ).
fof(f3973,plain,
( spl94_317
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vsubst(X2,X3,sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_317])]) ).
fof(f3473,plain,
( spl94_298
<=> ! [X5,X4,X0,X3,X2,X1] : ~ visValue(vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_298])]) ).
fof(f3497,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vsubst(X2,X3,sK17)))
| ~ spl94_165
| ~ spl94_298 ),
inference(superposition,[],[f3474,f1431]) ).
fof(f3474,plain,
( ! [X2,X3,X0,X1,X4,X5] : ~ visValue(vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3))))
| ~ spl94_298 ),
inference(avatar_component_clause,[],[f3473]) ).
fof(f3970,plain,
( spl94_316
| ~ spl94_34
| ~ spl94_158 ),
inference(avatar_split_clause,[],[f3882,f1392,f697,f3968]) ).
fof(f3968,plain,
( spl94_316
<=> ! [X0] : vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_316])]) ).
fof(f3882,plain,
( ! [X0] : vsubst(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),X0,vvar(sK16)) = X0
| ~ spl94_34
| ~ spl94_158 ),
inference(superposition,[],[f698,f1394]) ).
fof(f3965,plain,
( spl94_315
| ~ spl94_32
| ~ spl94_158 ),
inference(avatar_split_clause,[],[f3881,f1392,f689,f3963]) ).
fof(f3963,plain,
( spl94_315
<=> ! [X0] :
( ~ visFreeVar(X0,vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_315])]) ).
fof(f3881,plain,
( ! [X0] :
( ~ visFreeVar(X0,vvar(sK16))
| sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)) = X0 )
| ~ spl94_32
| ~ spl94_158 ),
inference(superposition,[],[f690,f1394]) ).
fof(f3960,plain,
( spl94_314
| ~ spl94_59
| ~ spl94_158
| ~ spl94_312 ),
inference(avatar_split_clause,[],[f3938,f3913,f1392,f807,f3958]) ).
fof(f3958,plain,
( spl94_314
<=> ! [X0] :
( vtcheck(vbind(sK16,sK14,sK15),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_314])]) ).
fof(f807,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(f3938,plain,
( ! [X0] :
( vtcheck(vbind(sK16,sK14,sK15),vvar(sK16),X0)
| vsomeType(X0) != vsomeType(sK19) )
| ~ spl94_59
| ~ spl94_158
| ~ spl94_312 ),
inference(forward_demodulation,[],[f3919,f1394]) ).
fof(f3919,plain,
( ! [X0] :
( vsomeType(X0) != vsomeType(sK19)
| vtcheck(vbind(sK16,sK14,sK15),vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15))),X0) )
| ~ spl94_59
| ~ spl94_312 ),
inference(superposition,[],[f808,f3915]) ).
fof(f808,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl94_59 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f3944,plain,
( spl94_313
| ~ spl94_13
| ~ spl94_158 ),
inference(avatar_split_clause,[],[f3877,f1392,f613,f3941]) ).
fof(f613,plain,
( spl94_13
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_13])]) ).
fof(f3877,plain,
( visFreeVar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vvar(sK16))
| ~ spl94_13
| ~ spl94_158 ),
inference(superposition,[],[f614,f1394]) ).
fof(f614,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl94_13 ),
inference(avatar_component_clause,[],[f613]) ).
fof(f3916,plain,
( spl94_157
| spl94_312
| spl94_159
| ~ spl94_2
| ~ spl94_63
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1216,f1201,f830,f565,f1396,f3913,f1388]) ).
fof(f1388,plain,
( spl94_157
<=> sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_157])]) ).
fof(f1396,plain,
( spl94_159
<=> sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_159])]) ).
fof(f565,plain,
( spl94_2
<=> vtcheck(vbind(sK16,sK14,sK15),vvar(sK18),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_2])]) ).
fof(f1201,plain,
( spl94_132
<=> ! [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_132])]) ).
fof(f1216,plain,
( sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| vsomeType(sK19) = vlookup(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_132 ),
inference(forward_demodulation,[],[f1215,f832]) ).
fof(f1215,plain,
( vsomeType(sK19) = vlookup(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_132 ),
inference(forward_demodulation,[],[f1214,f832]) ).
fof(f1214,plain,
( sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| vsomeType(sK19) = vlookup(sK52(vvar(sK18),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_132 ),
inference(forward_demodulation,[],[f1209,f832]) ).
fof(f1209,plain,
( sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| vsomeType(sK19) = vlookup(sK52(vvar(sK18),sK19,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_132 ),
inference(resolution,[],[f1202,f567]) ).
fof(f567,plain,
( vtcheck(vbind(sK16,sK14,sK15),vvar(sK18),sK19)
| ~ spl94_2 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1202,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_132 ),
inference(avatar_component_clause,[],[f1201]) ).
fof(f3869,plain,
( ~ spl94_8
| ~ spl94_306 ),
inference(avatar_contradiction_clause,[],[f3866]) ).
fof(f3866,plain,
( $false
| ~ spl94_8
| ~ spl94_306 ),
inference(resolution,[],[f3626,f594]) ).
fof(f594,plain,
( ! [X0] : ~ visValue(vvar(X0))
| ~ spl94_8 ),
inference(avatar_component_clause,[],[f593]) ).
fof(f593,plain,
( spl94_8
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_8])]) ).
fof(f3626,plain,
( visValue(vvar(sK16))
| ~ spl94_306 ),
inference(avatar_component_clause,[],[f3624]) ).
fof(f3624,plain,
( spl94_306
<=> visValue(vvar(sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_306])]) ).
fof(f3647,plain,
( spl94_311
| ~ spl94_39
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1512,f1443,f718,f3645]) ).
fof(f3645,plain,
( spl94_311
<=> ! [X0,X3,X2,X1] :
( visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| ~ visFreeVar(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_311])]) ).
fof(f1512,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| ~ visFreeVar(X3,X1) )
| ~ spl94_39
| ~ spl94_168 ),
inference(superposition,[],[f719,f1444]) ).
fof(f3643,plain,
( spl94_310
| ~ spl94_40
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1480,f1439,f722,f3641]) ).
fof(f3641,plain,
( spl94_310
<=> ! [X0,X3,X2,X1] :
( visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| ~ visFreeVar(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_310])]) ).
fof(f1480,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| ~ visFreeVar(X3,X0) )
| ~ spl94_40
| ~ spl94_167 ),
inference(superposition,[],[f723,f1440]) ).
fof(f3639,plain,
( spl94_309
| ~ spl94_34
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1463,f1439,f697,f3637]) ).
fof(f3637,plain,
( spl94_309
<=> ! [X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vvar(X0))) = vapp(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_309])]) ).
fof(f1463,plain,
( ! [X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vvar(X0))) = vapp(X1,X1)
| ~ spl94_34
| ~ spl94_167 ),
inference(superposition,[],[f1440,f698]) ).
fof(f3635,plain,
( spl94_308
| ~ spl94_116
| ~ spl94_161 ),
inference(avatar_split_clause,[],[f1410,f1407,f1069,f3633]) ).
fof(f1407,plain,
( spl94_161
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_161])]) ).
fof(f1410,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vvar(X4) != vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_116
| ~ spl94_161 ),
inference(superposition,[],[f1408,f1070]) ).
fof(f1408,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl94_161 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f3631,plain,
( spl94_307
| ~ spl94_53
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1098,f1069,f783,f3629]) ).
fof(f3629,plain,
( spl94_307
<=> ! [X0,X3,X2,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_307])]) ).
fof(f1098,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X2))
| ~ spl94_53
| ~ spl94_116 ),
inference(superposition,[],[f784,f1070]) ).
fof(f3627,plain,
( spl94_306
| ~ spl94_17
| ~ spl94_304 ),
inference(avatar_split_clause,[],[f3562,f3558,f629,f3624]) ).
fof(f3558,plain,
( spl94_304
<=> vvar(sK16) = vabs(sK48(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK50(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK49(vbind(sK16,sK14,sK15),sK19,vvar(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_304])]) ).
fof(f3562,plain,
( visValue(vvar(sK16))
| ~ spl94_17
| ~ spl94_304 ),
inference(superposition,[],[f630,f3560]) ).
fof(f3560,plain,
( vvar(sK16) = vabs(sK48(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK50(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK49(vbind(sK16,sK14,sK15),sK19,vvar(sK16)))
| ~ spl94_304 ),
inference(avatar_component_clause,[],[f3558]) ).
fof(f3622,plain,
( spl94_305
| ~ spl94_48
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1095,f1069,f759,f3620]) ).
fof(f3620,plain,
( spl94_305
<=> ! [X0,X3,X2,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_305])]) ).
fof(f1095,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X3))
| ~ spl94_48
| ~ spl94_116 ),
inference(superposition,[],[f760,f1070]) ).
fof(f3561,plain,
( spl94_304
| ~ spl94_124
| ~ spl94_157 ),
inference(avatar_split_clause,[],[f3539,f1388,f1146,f3558]) ).
fof(f1146,plain,
( spl94_124
<=> ! [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_124])]) ).
fof(f3539,plain,
( vvar(sK16) = vabs(sK48(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK50(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK49(vbind(sK16,sK14,sK15),sK19,vvar(sK16)))
| ~ spl94_124
| ~ spl94_157 ),
inference(resolution,[],[f1390,f1147]) ).
fof(f1147,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vabs(sK48(X0,X1,X2),sK50(X0,X1,X2),sK49(X0,X1,X2)) = X2 )
| ~ spl94_124 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f1390,plain,
( sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| ~ spl94_157 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f3547,plain,
( spl94_303
| ~ spl94_100
| ~ spl94_157 ),
inference(avatar_split_clause,[],[f3540,f1388,f999,f3544]) ).
fof(f3544,plain,
( spl94_303
<=> sK19 = varrow(sK50(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK51(vbind(sK16,sK14,sK15),sK19,vvar(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_303])]) ).
fof(f999,plain,
( spl94_100
<=> ! [X2,X0,X1] :
( varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_100])]) ).
fof(f3540,plain,
( sK19 = varrow(sK50(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK51(vbind(sK16,sK14,sK15),sK19,vvar(sK16)))
| ~ spl94_100
| ~ spl94_157 ),
inference(resolution,[],[f1390,f1000]) ).
fof(f1000,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1 )
| ~ spl94_100 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f3538,plain,
~ spl94_297,
inference(avatar_contradiction_clause,[],[f3537]) ).
fof(f3537,plain,
( $false
| ~ spl94_297 ),
inference(equality_resolution,[],[f3445]) ).
fof(f3445,plain,
( ! [X0] : vvar(X0) != vvar(sK16)
| ~ spl94_297 ),
inference(avatar_component_clause,[],[f3444]) ).
fof(f3444,plain,
( spl94_297
<=> ! [X0] : vvar(X0) != vvar(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_297])]) ).
fof(f3491,plain,
( spl94_302
| ~ spl94_17
| ~ spl94_192 ),
inference(avatar_split_clause,[],[f1849,f1839,f629,f3489]) ).
fof(f3489,plain,
( spl94_302
<=> ! [X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vvar(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_302])]) ).
fof(f1839,plain,
( spl94_192
<=> ! [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_192])]) ).
fof(f1849,plain,
( ! [X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vvar(X0),X1)) )
| ~ spl94_17
| ~ spl94_192 ),
inference(superposition,[],[f630,f1840]) ).
fof(f1840,plain,
( ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK88(vvar(X0)),sK89(vvar(X0)),sK90(vvar(X0))) )
| ~ spl94_192 ),
inference(avatar_component_clause,[],[f1839]) ).
fof(f3487,plain,
( spl94_301
| ~ spl94_8
| ~ spl94_172 ),
inference(avatar_split_clause,[],[f1570,f1567,f593,f3485]) ).
fof(f3485,plain,
( spl94_301
<=> ! [X2,X0,X1,X3] : vnoExp = vreduce(vapp(vabs(X0,X1,X2),vvar(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_301])]) ).
fof(f1567,plain,
( spl94_172
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_172])]) ).
fof(f1570,plain,
( ! [X2,X3,X0,X1] : vnoExp = vreduce(vapp(vabs(X0,X1,X2),vvar(X3)))
| ~ spl94_8
| ~ spl94_172 ),
inference(resolution,[],[f1568,f594]) ).
fof(f1568,plain,
( ! [X2,X3,X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl94_172 ),
inference(avatar_component_clause,[],[f1567]) ).
fof(f3483,plain,
( spl94_300
| ~ spl94_48
| ~ spl94_168 ),
inference(avatar_split_clause,[],[f1516,f1443,f759,f3481]) ).
fof(f3481,plain,
( spl94_300
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,vvar(X0)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_300])]) ).
fof(f1516,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,vvar(X0)))),X1)
| ~ spl94_48
| ~ spl94_168 ),
inference(superposition,[],[f760,f1444]) ).
fof(f3479,plain,
( spl94_299
| ~ spl94_53
| ~ spl94_167 ),
inference(avatar_split_clause,[],[f1486,f1439,f783,f3477]) ).
fof(f3477,plain,
( spl94_299
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X1,X0,vapp(vvar(X1),X2))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_299])]) ).
fof(f1486,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X1,X0,vapp(vvar(X1),X2))),X0)
| ~ spl94_53
| ~ spl94_167 ),
inference(superposition,[],[f784,f1440]) ).
fof(f3475,plain,
( spl94_298
| ~ spl94_116
| ~ spl94_160 ),
inference(avatar_split_clause,[],[f1405,f1402,f1069,f3473]) ).
fof(f1402,plain,
( spl94_160
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_160])]) ).
fof(f1405,plain,
( ! [X2,X3,X0,X1,X4,X5] : ~ visValue(vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3))))
| ~ spl94_116
| ~ spl94_160 ),
inference(superposition,[],[f1403,f1070]) ).
fof(f1403,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_160 ),
inference(avatar_component_clause,[],[f1402]) ).
fof(f3446,plain,
( spl94_297
| ~ spl94_22
| ~ spl94_294 ),
inference(avatar_split_clause,[],[f3368,f3362,f649,f3444]) ).
fof(f649,plain,
( spl94_22
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_22])]) ).
fof(f3362,plain,
( spl94_294
<=> vvar(sK16) = vapp(sK45(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK46(vbind(sK16,sK14,sK15),sK19,vvar(sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_294])]) ).
fof(f3368,plain,
( ! [X0] : vvar(X0) != vvar(sK16)
| ~ spl94_22
| ~ spl94_294 ),
inference(superposition,[],[f650,f3364]) ).
fof(f3364,plain,
( vvar(sK16) = vapp(sK45(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK46(vbind(sK16,sK14,sK15),sK19,vvar(sK16)))
| ~ spl94_294 ),
inference(avatar_component_clause,[],[f3362]) ).
fof(f650,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl94_22 ),
inference(avatar_component_clause,[],[f649]) ).
fof(f3442,plain,
( spl94_296
| ~ spl94_164 ),
inference(avatar_split_clause,[],[f1433,f1425,f3440]) ).
fof(f3440,plain,
( spl94_296
<=> ! [X2,X0,X1] : vtcheck(vbind(X0,X1,X2),vvar(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_296])]) ).
fof(f1425,plain,
( spl94_164
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_164])]) ).
fof(f1433,plain,
( ! [X2,X0,X1] : vtcheck(vbind(X0,X1,X2),vvar(X0),X1)
| ~ spl94_164 ),
inference(equality_resolution,[],[f1426]) ).
fof(f1426,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl94_164 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f3393,plain,
( spl94_295
| ~ spl94_39
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f919,f783,f718,f3391]) ).
fof(f919,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl94_39
| ~ spl94_53 ),
inference(resolution,[],[f784,f719]) ).
fof(f3365,plain,
( spl94_294
| ~ spl94_99
| ~ spl94_159 ),
inference(avatar_split_clause,[],[f1400,f1396,f995,f3362]) ).
fof(f995,plain,
( spl94_99
<=> ! [X2,X0,X1] :
( vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_99])]) ).
fof(f1400,plain,
( vvar(sK16) = vapp(sK45(vbind(sK16,sK14,sK15),sK19,vvar(sK16)),sK46(vbind(sK16,sK14,sK15),sK19,vvar(sK16)))
| ~ spl94_99
| ~ spl94_159 ),
inference(resolution,[],[f1398,f996]) ).
fof(f996,plain,
( ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2 )
| ~ spl94_99 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f1398,plain,
( sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| ~ spl94_159 ),
inference(avatar_component_clause,[],[f1396]) ).
fof(f3354,plain,
( spl94_293
| ~ spl94_2
| ~ spl94_63
| ~ spl94_201 ),
inference(avatar_split_clause,[],[f1979,f1947,f830,f565,f3352]) ).
fof(f3352,plain,
( spl94_293
<=> ! [X0,X1] :
( vtcheck(vbind(sK16,sK14,sK15),vapp(X0,vvar(sK16)),X1)
| ~ vtcheck(sK15,X0,varrow(sK19,X1))
| visFreeVar(sK16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_293])]) ).
fof(f1979,plain,
( ! [X0,X1] :
( vtcheck(vbind(sK16,sK14,sK15),vapp(X0,vvar(sK16)),X1)
| ~ vtcheck(sK15,X0,varrow(sK19,X1))
| visFreeVar(sK16,X0) )
| ~ spl94_2
| ~ spl94_63
| ~ spl94_201 ),
inference(forward_demodulation,[],[f1970,f832]) ).
fof(f1970,plain,
( ! [X0,X1] :
( vtcheck(vbind(sK16,sK14,sK15),vapp(X0,vvar(sK18)),X1)
| ~ vtcheck(sK15,X0,varrow(sK19,X1))
| visFreeVar(sK16,X0) )
| ~ spl94_2
| ~ spl94_201 ),
inference(resolution,[],[f1948,f567]) ).
fof(f3330,plain,
( spl94_292
| ~ spl94_49
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1532,f1429,f763,f3328]) ).
fof(f3328,plain,
( spl94_292
<=> ! [X0,X1] :
( vapp(X0,X1) != sK17
| sK46(sK15,sK14,sK17) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_292])]) ).
fof(f1532,plain,
( ! [X0,X1] :
( vapp(X0,X1) != sK17
| sK46(sK15,sK14,sK17) = X1 )
| ~ spl94_49
| ~ spl94_165 ),
inference(superposition,[],[f764,f1431]) ).
fof(f3326,plain,
( spl94_291
| ~ spl94_148
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1365,f1362,f1314,f3324]) ).
fof(f3324,plain,
( spl94_291
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_291])]) ).
fof(f1314,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(f1362,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(f1365,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_148
| ~ spl94_153 ),
inference(resolution,[],[f1363,f1315]) ).
fof(f1315,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(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 )
| ~ spl94_148 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f1363,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| 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_153 ),
inference(avatar_component_clause,[],[f1362]) ).
fof(f3302,plain,
( spl94_290
| ~ spl94_148
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1348,f1342,f1314,f3300]) ).
fof(f3300,plain,
( spl94_290
<=> ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_290])]) ).
fof(f1342,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(f1348,plain,
( ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_148
| ~ spl94_151 ),
inference(resolution,[],[f1343,f1315]) ).
fof(f1343,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,[],[f1342]) ).
fof(f3278,plain,
( spl94_289
| ~ spl94_143
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1366,f1362,f1280,f3276]) ).
fof(f3276,plain,
( spl94_289
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_289])]) ).
fof(f1280,plain,
( spl94_143
<=> ! [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_143])]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_143
| ~ spl94_153 ),
inference(resolution,[],[f1363,f1281]) ).
fof(f1281,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK71(X0,X1,X2,X3) = vgensym(vapp(vapp(sK68(X0,X1,X2,X3),sK72(X0,X1,X2,X3)),vvar(sK67(X0,X1,X2,X3)))) )
| ~ spl94_143 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f3234,plain,
( spl94_288
| ~ spl94_148
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1333,f1322,f1314,f3232]) ).
fof(f3232,plain,
( spl94_288
<=> ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_288])]) ).
fof(f1322,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(f1333,plain,
( ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_148
| ~ spl94_150 ),
inference(resolution,[],[f1323,f1315]) ).
fof(f1323,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,[],[f1322]) ).
fof(f3230,plain,
( spl94_287
| ~ spl94_148
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1325,f1318,f1314,f3228]) ).
fof(f3228,plain,
( spl94_287
<=> ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_287])]) ).
fof(f1318,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(f1325,plain,
( ! [X2,X0,X1] :
( 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)
| vsubst(X0,X1,X2) = vsubst(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK71(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK70(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK71(vsubst(X0,X1,X2),X2,X1,X0)),sK72(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_148
| ~ spl94_149 ),
inference(resolution,[],[f1319,f1315]) ).
fof(f1319,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,[],[f1318]) ).
fof(f3216,plain,
( spl94_286
| ~ spl94_47
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1529,f1429,f755,f3214]) ).
fof(f3214,plain,
( spl94_286
<=> ! [X0,X1] :
( vapp(X0,X1) != sK17
| sK45(sK15,sK14,sK17) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_286])]) ).
fof(f1529,plain,
( ! [X0,X1] :
( vapp(X0,X1) != sK17
| sK45(sK15,sK14,sK17) = X0 )
| ~ spl94_47
| ~ spl94_165 ),
inference(superposition,[],[f756,f1431]) ).
fof(f3212,plain,
( spl94_285
| ~ spl94_84
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1372,f1362,f915,f3210]) ).
fof(f3210,plain,
( spl94_285
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vsubst(sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),vapp(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK87(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3))))
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_285])]) ).
fof(f1372,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vsubst(sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),vapp(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK87(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3))))
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl94_84
| ~ spl94_153 ),
inference(superposition,[],[f1363,f916]) ).
fof(f3188,plain,
( spl94_284
| ~ spl94_137
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1367,f1362,f1239,f3186]) ).
fof(f3186,plain,
( spl94_284
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_284])]) ).
fof(f1239,plain,
( spl94_137
<=> ! [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_137])]) ).
fof(f1367,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl94_137
| ~ spl94_153 ),
inference(resolution,[],[f1363,f1240]) ).
fof(f1240,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| vabs(sK70(X0,X1,X2,X3),sK69(X0,X1,X2,X3),sK72(X0,X1,X2,X3)) = X1 )
| ~ spl94_137 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f3164,plain,
( spl94_283
| ~ spl94_143
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1349,f1342,f1280,f3162]) ).
fof(f3162,plain,
( spl94_283
<=> ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_283])]) ).
fof(f1349,plain,
( ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_143
| ~ spl94_151 ),
inference(resolution,[],[f1343,f1281]) ).
fof(f3150,plain,
( spl94_282
| ~ spl94_84
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1355,f1342,f915,f3148]) ).
fof(f3148,plain,
( spl94_282
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vapp(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK87(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)))
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_282])]) ).
fof(f1355,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vapp(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK87(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)))
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl94_84
| ~ spl94_151 ),
inference(superposition,[],[f1343,f916]) ).
fof(f3106,plain,
( spl94_281
| ~ spl94_68
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1369,f1362,f851,f3104]) ).
fof(f3104,plain,
( spl94_281
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_281])]) ).
fof(f851,plain,
( spl94_68
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_68])]) ).
fof(f1369,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl94_68
| ~ spl94_153 ),
inference(resolution,[],[f1363,f852]) ).
fof(f852,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK67(X0,X1,X2,X3) = X3 )
| ~ spl94_68 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f3098,plain,
( spl94_280
| ~ spl94_69
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1368,f1362,f855,f3096]) ).
fof(f3096,plain,
( spl94_280
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_280])]) ).
fof(f855,plain,
( spl94_69
<=> ! [X0,X3,X2,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_69])]) ).
fof(f1368,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| 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))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl94_69
| ~ spl94_153 ),
inference(resolution,[],[f1363,f856]) ).
fof(f856,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK68(X0,X1,X2,X3) = X2 )
| ~ spl94_69 ),
inference(avatar_component_clause,[],[f855]) ).
fof(f3054,plain,
( spl94_279
| ~ spl94_143
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1334,f1322,f1280,f3052]) ).
fof(f3052,plain,
( spl94_279
<=> ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_279])]) ).
fof(f1334,plain,
( ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_143
| ~ spl94_150 ),
inference(resolution,[],[f1323,f1281]) ).
fof(f3050,plain,
( spl94_278
| ~ spl94_143
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1326,f1318,f1280,f3048]) ).
fof(f3048,plain,
( spl94_278
<=> ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_278])]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( 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)
| sK71(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK68(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK67(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl94_143
| ~ spl94_149 ),
inference(resolution,[],[f1319,f1281]) ).
fof(f3025,plain,
( spl94_277
| ~ spl94_137
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1350,f1342,f1239,f3023]) ).
fof(f3023,plain,
( spl94_277
<=> ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_277])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl94_137
| ~ spl94_151 ),
inference(resolution,[],[f1343,f1240]) ).
fof(f3021,plain,
( spl94_276
| ~ spl94_132
| ~ spl94_134 ),
inference(avatar_split_clause,[],[f1259,f1226,f1201,f3019]) ).
fof(f3019,plain,
( spl94_276
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2))
| vsomeType(sK51(X0,X1,X2)) = vlookup(sK52(sK49(X0,X1,X2),sK51(X0,X1,X2),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0)),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0))
| sP6(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_276])]) ).
fof(f1226,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(f1259,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2))
| vsomeType(sK51(X0,X1,X2)) = vlookup(sK52(sK49(X0,X1,X2),sK51(X0,X1,X2),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0)),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0))
| sP6(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2)) )
| ~ spl94_132
| ~ spl94_134 ),
inference(resolution,[],[f1227,f1202]) ).
fof(f1227,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) )
| ~ spl94_134 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f3007,plain,
( spl94_275
| ~ spl94_61
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1371,f1362,f815,f3005]) ).
fof(f1371,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK85(X0,X1,vvar(X2),vvar(X2)),sK86(X0,X1,vvar(X2),vvar(X2)),vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2))))
| sP11(vvar(X2),vvar(X2),X1,X0)
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_61
| ~ spl94_153 ),
inference(superposition,[],[f1363,f816]) ).
fof(f2963,plain,
( spl94_274
| ~ spl94_137
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1335,f1322,f1239,f2961]) ).
fof(f2961,plain,
( spl94_274
<=> ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_274])]) ).
fof(f1335,plain,
( ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl94_137
| ~ spl94_150 ),
inference(resolution,[],[f1323,f1240]) ).
fof(f2959,plain,
( spl94_273
| ~ spl94_137
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1327,f1318,f1239,f2957]) ).
fof(f2957,plain,
( spl94_273
<=> ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_273])]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( 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)
| vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK69(vsubst(X0,X1,X2),X2,X1,X0),sK72(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl94_137
| ~ spl94_149 ),
inference(resolution,[],[f1319,f1240]) ).
fof(f2935,plain,
( spl94_272
| ~ spl94_84
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1340,f1322,f915,f2933]) ).
fof(f2933,plain,
( spl94_272
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X0
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_272])]) ).
fof(f1340,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X0
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl94_84
| ~ spl94_150 ),
inference(superposition,[],[f1323,f916]) ).
fof(f2931,plain,
( spl94_271
| ~ spl94_84
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1332,f1318,f915,f2929]) ).
fof(f2929,plain,
( spl94_271
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X1
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_271])]) ).
fof(f1332,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X1
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl94_84
| ~ spl94_149 ),
inference(superposition,[],[f1319,f916]) ).
fof(f2911,plain,
( spl94_270
| ~ spl94_109
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1302,f1288,f1040,f2909]) ).
fof(f2909,plain,
( spl94_270
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,sK68(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK68(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK70(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK68(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK68(X1,X2,X3,X4),vabs(sK70(X1,X2,X3,X4),X6,X5))
| sK70(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_270])]) ).
fof(f1040,plain,
( spl94_109
<=> ! [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_109])]) ).
fof(f1288,plain,
( spl94_145
<=> ! [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_145])]) ).
fof(f1302,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,sK68(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK68(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK70(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK68(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK68(X1,X2,X3,X4),vabs(sK70(X1,X2,X3,X4),X6,X5))
| sK70(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) )
| ~ spl94_109
| ~ spl94_145 ),
inference(resolution,[],[f1289,f1041]) ).
fof(f1041,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) )
| ~ spl94_109 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1289,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_145 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f2907,plain,
( spl94_269
| ~ spl94_125
| ~ spl94_134 ),
inference(avatar_split_clause,[],[f1260,f1226,f1150,f2905]) ).
fof(f2905,plain,
( spl94_269
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2))
| sK49(X0,X1,X2) = vvar(sK52(sK49(X0,X1,X2),sK51(X0,X1,X2),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0)))
| sP6(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_269])]) ).
fof(f1150,plain,
( spl94_125
<=> ! [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_125])]) ).
fof(f1260,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2))
| sK49(X0,X1,X2) = vvar(sK52(sK49(X0,X1,X2),sK51(X0,X1,X2),vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0)))
| sP6(vbind(sK48(X0,X1,X2),sK50(X0,X1,X2),X0),sK51(X0,X1,X2),sK49(X0,X1,X2)) )
| ~ spl94_125
| ~ spl94_134 ),
inference(resolution,[],[f1227,f1151]) ).
fof(f1151,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK52(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl94_125 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f2896,plain,
( spl94_268
| ~ spl94_33
| ~ spl94_147 ),
inference(avatar_split_clause,[],[f1312,f1305,f693,f2894]) ).
fof(f2894,plain,
( spl94_268
<=> ! [X2,X0,X1] :
( sP3(vnoExp,vabs(X0,X1,X2))
| sP2(vnoExp,vabs(X0,X1,X2))
| sP1(vnoExp,vabs(X0,X1,X2))
| sP0(vnoExp,vabs(X0,X1,X2))
| sP4(vnoExp,vabs(X0,X1,X2))
| vabs(X0,X1,X2) = vabs(sK41(vabs(X0,X1,X2),vnoExp),sK42(vabs(X0,X1,X2),vnoExp),sK43(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK44(vabs(X0,X1,X2),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_268])]) ).
fof(f693,plain,
( spl94_33
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_33])]) ).
fof(f1305,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(f1312,plain,
( ! [X2,X0,X1] :
( sP3(vnoExp,vabs(X0,X1,X2))
| sP2(vnoExp,vabs(X0,X1,X2))
| sP1(vnoExp,vabs(X0,X1,X2))
| sP0(vnoExp,vabs(X0,X1,X2))
| sP4(vnoExp,vabs(X0,X1,X2))
| vabs(X0,X1,X2) = vabs(sK41(vabs(X0,X1,X2),vnoExp),sK42(vabs(X0,X1,X2),vnoExp),sK43(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK44(vabs(X0,X1,X2),vnoExp)) )
| ~ spl94_33
| ~ spl94_147 ),
inference(superposition,[],[f1306,f694]) ).
fof(f694,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl94_33 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f1306,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,[],[f1305]) ).
fof(f2852,plain,
( spl94_267
| ~ spl94_68
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1352,f1342,f851,f2850]) ).
fof(f2850,plain,
( spl94_267
<=> ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_267])]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl94_68
| ~ spl94_151 ),
inference(resolution,[],[f1343,f852]) ).
fof(f2848,plain,
( spl94_266
| ~ spl94_69
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1351,f1342,f855,f2846]) ).
fof(f2846,plain,
( spl94_266
<=> ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_266])]) ).
fof(f1351,plain,
( ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl94_69
| ~ spl94_151 ),
inference(resolution,[],[f1343,f856]) ).
fof(f2839,plain,
( spl94_265
| ~ spl94_163
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1538,f1429,f1416,f2837]) ).
fof(f2837,plain,
( spl94_265
<=> ! [X2,X4,X0,X3,X1] : vabs(X2,X3,X4) != vsubst(X0,X1,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_265])]) ).
fof(f1538,plain,
( ! [X2,X3,X0,X1,X4] : vabs(X2,X3,X4) != vsubst(X0,X1,sK17)
| ~ spl94_163
| ~ spl94_165 ),
inference(superposition,[],[f1417,f1431]) ).
fof(f2835,plain,
( spl94_264
| ~ spl94_34
| ~ spl94_153 ),
inference(avatar_split_clause,[],[f1370,f1362,f697,f2833]) ).
fof(f2833,plain,
( spl94_264
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK85(X0,X1,vvar(X0),X1),sK86(X0,X1,vvar(X0),X1),vapp(sK84(X0,X1,vvar(X0),X1),sK87(X0,X1,vvar(X0),X1))) = X1
| sP11(X1,vvar(X0),X1,X0)
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_264])]) ).
fof(f1370,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK85(X0,X1,vvar(X0),X1),sK86(X0,X1,vvar(X0),X1),vapp(sK84(X0,X1,vvar(X0),X1),sK87(X0,X1,vvar(X0),X1))) = X1
| sP11(X1,vvar(X0),X1,X0)
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl94_34
| ~ spl94_153 ),
inference(superposition,[],[f1363,f698]) ).
fof(f2826,plain,
( spl94_263
| ~ spl94_61
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1354,f1342,f815,f2824]) ).
fof(f1354,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)
| vvar(X2) = vapp(sK84(X0,X1,vvar(X2),vvar(X2)),sK87(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl94_61
| ~ spl94_151 ),
inference(superposition,[],[f1343,f816]) ).
fof(f2683,plain,
( spl94_262
| ~ spl94_68
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1337,f1322,f851,f2681]) ).
fof(f2681,plain,
( spl94_262
<=> ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_262])]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl94_68
| ~ spl94_150 ),
inference(resolution,[],[f1323,f852]) ).
fof(f2679,plain,
( spl94_261
| ~ spl94_40
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1528,f1429,f722,f2677]) ).
fof(f2677,plain,
( spl94_261
<=> ! [X0] :
( visFreeVar(X0,sK17)
| ~ visFreeVar(X0,sK45(sK15,sK14,sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_261])]) ).
fof(f1528,plain,
( ! [X0] :
( visFreeVar(X0,sK17)
| ~ visFreeVar(X0,sK45(sK15,sK14,sK17)) )
| ~ spl94_40
| ~ spl94_165 ),
inference(superposition,[],[f723,f1431]) ).
fof(f2675,plain,
( spl94_260
| ~ spl94_69
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1336,f1322,f855,f2673]) ).
fof(f2673,plain,
( spl94_260
<=> ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_260])]) ).
fof(f1336,plain,
( ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl94_69
| ~ spl94_150 ),
inference(resolution,[],[f1323,f856]) ).
fof(f2671,plain,
( spl94_259
| ~ spl94_68
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1329,f1318,f851,f2669]) ).
fof(f2669,plain,
( spl94_259
<=> ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_259])]) ).
fof(f1329,plain,
( ! [X2,X0,X1] :
( 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)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl94_68
| ~ spl94_149 ),
inference(resolution,[],[f1319,f852]) ).
fof(f2667,plain,
( spl94_258
| ~ spl94_69
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1328,f1318,f855,f2665]) ).
fof(f2665,plain,
( spl94_258
<=> ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_258])]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( 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)
| sK68(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl94_69
| ~ spl94_149 ),
inference(resolution,[],[f1319,f856]) ).
fof(f2663,plain,
( spl94_257
| ~ spl94_83
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1298,f1288,f911,f2661]) ).
fof(f2661,plain,
( spl94_257
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,vabs(X1,X2,X3),vabs(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0))),X5,vsubst(X6,vvar(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0)))),X4))) = vsubst(X0,vabs(X1,X2,X3),vabs(X6,X5,X4))
| X0 = X6
| ~ visFreeVar(X6,X3)
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_257])]) ).
fof(f1298,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,vabs(X1,X2,X3),vabs(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0))),X5,vsubst(X6,vvar(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0)))),X4))) = vsubst(X0,vabs(X1,X2,X3),vabs(X6,X5,X4))
| X0 = X6
| ~ visFreeVar(X6,X3)
| X1 = X6 )
| ~ spl94_83
| ~ spl94_145 ),
inference(resolution,[],[f1289,f912]) ).
fof(f2659,plain,
( spl94_256
| ~ spl94_133
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1296,f1288,f1205,f2657]) ).
fof(f1205,plain,
( spl94_133
<=> ! [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_133])]) ).
fof(f1296,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,vabs(vgensym(vapp(vapp(X1,X2),vvar(X0))),X3,vsubst(X4,vvar(vgensym(vapp(vapp(X1,X2),vvar(X0)))),X2))) = vsubst(X0,X1,vabs(X4,X3,X2))
| X0 = X4
| vabs(X4,X5,vsubst(X6,X1,X7)) = vsubst(X6,X1,vabs(X4,X5,X7))
| X4 = X6 )
| ~ spl94_133
| ~ spl94_145 ),
inference(resolution,[],[f1289,f1206]) ).
fof(f1206,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_133 ),
inference(avatar_component_clause,[],[f1205]) ).
fof(f2646,plain,
( spl94_255
| ~ spl94_134
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1262,f1251,f1226,f2644]) ).
fof(f2644,plain,
( spl94_255
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,vbind(sK48(vbind(X0,X1,X2),X3,X4),sK50(vbind(X0,X1,X2),X3,X4),X2)),sK49(vbind(X0,X1,X2),X3,X4),sK51(vbind(X0,X1,X2),X3,X4))
| sK48(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_255])]) ).
fof(f1251,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(f1262,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,vbind(sK48(vbind(X0,X1,X2),X3,X4),sK50(vbind(X0,X1,X2),X3,X4),X2)),sK49(vbind(X0,X1,X2),X3,X4),sK51(vbind(X0,X1,X2),X3,X4))
| sK48(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) )
| ~ spl94_134
| ~ spl94_140 ),
inference(resolution,[],[f1252,f1227]) ).
fof(f1252,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,[],[f1251]) ).
fof(f2642,plain,
( spl94_254
| ~ spl94_105
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1212,f1201,f1024,f2640]) ).
fof(f2640,plain,
( spl94_254
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| vsomeType(varrow(sK47(X0,X1,X2),X1)) = vlookup(sK52(sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_254])]) ).
fof(f1024,plain,
( spl94_105
<=> ! [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_105])]) ).
fof(f1212,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| vsomeType(varrow(sK47(X0,X1,X2),X1)) = vlookup(sK52(sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK47(X0,X1,X2),X1),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_105
| ~ spl94_132 ),
inference(resolution,[],[f1202,f1025]) ).
fof(f1025,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) )
| ~ spl94_105 ),
inference(avatar_component_clause,[],[f1024]) ).
fof(f2629,plain,
( spl94_253
| ~ spl94_39
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1527,f1429,f718,f2627]) ).
fof(f2627,plain,
( spl94_253
<=> ! [X0] :
( visFreeVar(X0,sK17)
| ~ visFreeVar(X0,sK46(sK15,sK14,sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_253])]) ).
fof(f1527,plain,
( ! [X0] :
( visFreeVar(X0,sK17)
| ~ visFreeVar(X0,sK46(sK15,sK14,sK17)) )
| ~ spl94_39
| ~ spl94_165 ),
inference(superposition,[],[f719,f1431]) ).
fof(f2625,plain,
( spl94_252
| ~ spl94_62
| ~ spl94_147 ),
inference(avatar_split_clause,[],[f1308,f1305,f826,f2623]) ).
fof(f2623,plain,
( spl94_252
<=> ! [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
| vapp(sK26(vreduce(X0),X0),sK25(vreduce(X0),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_252])]) ).
fof(f826,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(f1308,plain,
( ! [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
| vapp(sK26(vreduce(X0),X0),sK25(vreduce(X0),X0)) = X0 )
| ~ spl94_62
| ~ spl94_147 ),
inference(resolution,[],[f1306,f827]) ).
fof(f827,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vapp(sK26(X0,X1),sK25(X0,X1)) = X1 )
| ~ spl94_62 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f2612,plain,
( spl94_251
| ~ spl94_52
| ~ spl94_147 ),
inference(avatar_split_clause,[],[f1309,f1305,f779,f2610]) ).
fof(f2610,plain,
( spl94_251
<=> ! [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
| sK27(vreduce(X0),X0) = vreduce(sK26(vreduce(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_251])]) ).
fof(f779,plain,
( spl94_52
<=> ! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_52])]) ).
fof(f1309,plain,
( ! [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
| sK27(vreduce(X0),X0) = vreduce(sK26(vreduce(X0),X0)) )
| ~ spl94_52
| ~ spl94_147 ),
inference(resolution,[],[f1306,f780]) ).
fof(f780,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| sK27(X0,X1) = vreduce(sK26(X0,X1)) )
| ~ spl94_52 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f2598,plain,
( spl94_250
| ~ spl94_61
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1339,f1322,f815,f2596]) ).
fof(f1339,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,[],[f1323,f816]) ).
fof(f2594,plain,
( spl94_249
| ~ spl94_61
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1331,f1318,f815,f2592]) ).
fof(f1331,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,[],[f1319,f816]) ).
fof(f2584,plain,
( spl94_248
| ~ spl94_34
| ~ spl94_151 ),
inference(avatar_split_clause,[],[f1353,f1342,f697,f2582]) ).
fof(f1353,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,[],[f1343,f698]) ).
fof(f2580,plain,
( spl94_247
| ~ spl94_105
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1170,f1150,f1024,f2578]) ).
fof(f2578,plain,
( spl94_247
<=> ! [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_247])]) ).
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_105
| ~ spl94_125 ),
inference(resolution,[],[f1151,f1025]) ).
fof(f2550,plain,
( spl94_246
| ~ spl94_39
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1300,f1288,f718,f2548]) ).
fof(f2548,plain,
( spl94_246
<=> ! [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_246])]) ).
fof(f1300,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_145 ),
inference(resolution,[],[f1289,f719]) ).
fof(f2546,plain,
( spl94_245
| ~ spl94_40
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1299,f1288,f722,f2544]) ).
fof(f2544,plain,
( spl94_245
<=> ! [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_245])]) ).
fof(f1299,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_145 ),
inference(resolution,[],[f1289,f723]) ).
fof(f2539,plain,
( spl94_244
| ~ spl94_16
| ~ spl94_147 ),
inference(avatar_split_clause,[],[f1311,f1305,f625,f2537]) ).
fof(f2537,plain,
( spl94_244
<=> ! [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_244])]) ).
fof(f625,plain,
( spl94_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_16])]) ).
fof(f1311,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,[],[f1306,f626]) ).
fof(f626,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl94_16 ),
inference(avatar_component_clause,[],[f625]) ).
fof(f2524,plain,
( spl94_243
| ~ spl94_105
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1264,f1251,f1024,f2522]) ).
fof(f2522,plain,
( spl94_243
<=> ! [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_243])]) ).
fof(f1264,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_105
| ~ spl94_140 ),
inference(resolution,[],[f1252,f1025]) ).
fof(f2516,plain,
( spl94_242
| ~ spl94_107
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1224,f1205,f1032,f2514]) ).
fof(f2514,plain,
( spl94_242
<=> ! [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_242])]) ).
fof(f1032,plain,
( spl94_107
<=> ! [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_107])]) ).
fof(f1224,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_107
| ~ spl94_133 ),
inference(resolution,[],[f1206,f1033]) ).
fof(f1033,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) )
| ~ spl94_107 ),
inference(avatar_component_clause,[],[f1032]) ).
fof(f2511,plain,
( spl94_241
| ~ spl94_94
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1211,f1201,f969,f2509]) ).
fof(f2509,plain,
( spl94_241
<=> ! [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_241])]) ).
fof(f969,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(f1211,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_132 ),
inference(resolution,[],[f1202,f970]) ).
fof(f970,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl94_94 ),
inference(avatar_component_clause,[],[f969]) ).
fof(f2492,plain,
( spl94_240
| ~ spl94_94
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1263,f1251,f969,f2490]) ).
fof(f2490,plain,
( spl94_240
<=> ! [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_240])]) ).
fof(f1263,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,[],[f1252,f970]) ).
fof(f2488,plain,
( spl94_239
| ~ spl94_113
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1213,f1201,f1057,f2486]) ).
fof(f2486,plain,
( spl94_239
<=> ! [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_239])]) ).
fof(f1057,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(f1213,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_132 ),
inference(resolution,[],[f1202,f1058]) ).
fof(f1058,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,[],[f1057]) ).
fof(f2478,plain,
( spl94_238
| ~ spl94_113
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1171,f1150,f1057,f2476]) ).
fof(f2476,plain,
( spl94_238
<=> ! [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_238])]) ).
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_125 ),
inference(resolution,[],[f1151,f1058]) ).
fof(f2470,plain,
( spl94_237
| ~ spl94_94
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1169,f1150,f969,f2468]) ).
fof(f2468,plain,
( spl94_237
<=> ! [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_237])]) ).
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_125 ),
inference(resolution,[],[f1151,f970]) ).
fof(f2435,plain,
( spl94_236
| ~ spl94_34
| ~ spl94_150 ),
inference(avatar_split_clause,[],[f1338,f1322,f697,f2433]) ).
fof(f1338,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,[],[f1323,f698]) ).
fof(f2431,plain,
( spl94_235
| ~ spl94_34
| ~ spl94_149 ),
inference(avatar_split_clause,[],[f1330,f1318,f697,f2429]) ).
fof(f1330,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,[],[f1319,f698]) ).
fof(f2427,plain,
( spl94_234
| ~ spl94_13
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1297,f1288,f613,f2425]) ).
fof(f1297,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_145 ),
inference(resolution,[],[f1289,f614]) ).
fof(f2413,plain,
( spl94_233
| ~ spl94_105
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1119,f1105,f1024,f2411]) ).
fof(f2411,plain,
( spl94_233
<=> ! [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_233])]) ).
fof(f1105,plain,
( spl94_118
<=> ! [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_118])]) ).
fof(f1119,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_105
| ~ spl94_118 ),
inference(resolution,[],[f1106,f1025]) ).
fof(f1106,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_118 ),
inference(avatar_component_clause,[],[f1105]) ).
fof(f2408,plain,
( spl94_232
| ~ spl94_161
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1537,f1429,f1407,f2406]) ).
fof(f2406,plain,
( spl94_232
<=> ! [X2,X0,X1] : vvar(X0) != vsubst(X1,X2,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_232])]) ).
fof(f1537,plain,
( ! [X2,X0,X1] : vvar(X0) != vsubst(X1,X2,sK17)
| ~ spl94_161
| ~ spl94_165 ),
inference(superposition,[],[f1408,f1431]) ).
fof(f2404,plain,
( spl94_231
| ~ spl94_95
| ~ spl94_132 ),
inference(avatar_split_clause,[],[f1210,f1201,f973,f2402]) ).
fof(f2402,plain,
( spl94_231
<=> ! [X4,X0,X3,X2,X1] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vsomeType(X3) = vlookup(sK52(X4,X3,vbind(X0,X1,X2)),vbind(X0,X1,X2))
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_231])]) ).
fof(f973,plain,
( spl94_95
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_95])]) ).
fof(f1210,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vsomeType(X3) = vlookup(sK52(X4,X3,vbind(X0,X1,X2)),vbind(X0,X1,X2))
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) )
| ~ spl94_95
| ~ spl94_132 ),
inference(resolution,[],[f1202,f974]) ).
fof(f974,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl94_95 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f2326,plain,
( spl94_230
| ~ spl94_119
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1267,f1255,f1122,f2324]) ).
fof(f2324,plain,
( spl94_230
<=> ! [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_230])]) ).
fof(f1122,plain,
( spl94_119
<=> ! [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_119])]) ).
fof(f1255,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(f1267,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_119
| ~ spl94_141 ),
inference(resolution,[],[f1256,f1123]) ).
fof(f1123,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 )
| ~ spl94_119 ),
inference(avatar_component_clause,[],[f1122]) ).
fof(f1256,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,[],[f1255]) ).
fof(f2322,plain,
( spl94_229
| ~ spl94_120
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1266,f1255,f1126,f2320]) ).
fof(f2320,plain,
( spl94_229
<=> ! [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_229])]) ).
fof(f1126,plain,
( spl94_120
<=> ! [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_120])]) ).
fof(f1266,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_120
| ~ spl94_141 ),
inference(resolution,[],[f1256,f1127]) ).
fof(f1127,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl94_120 ),
inference(avatar_component_clause,[],[f1126]) ).
fof(f2318,plain,
( spl94_228
| ~ spl94_127
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1185,f1178,f1159,f2316]) ).
fof(f1159,plain,
( spl94_127
<=> ! [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_127])]) ).
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_127
| ~ spl94_129 ),
inference(resolution,[],[f1179,f1160]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vbind(sK54(X0,X1,X2),sK53(X0,X1,X2),sK56(X0,X1,X2)) = X1 )
| ~ spl94_127 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f2314,plain,
( spl94_227
| ~ spl94_94
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1118,f1105,f969,f2312]) ).
fof(f2312,plain,
( spl94_227
<=> ! [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_227])]) ).
fof(f1118,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_118 ),
inference(resolution,[],[f1106,f970]) ).
fof(f2300,plain,
( ~ spl94_226
| ~ spl94_53
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1534,f1429,f783,f2297]) ).
fof(f2297,plain,
( spl94_226
<=> visFreeVar(vgensym(sK17),sK45(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_226])]) ).
fof(f1534,plain,
( ~ visFreeVar(vgensym(sK17),sK45(sK15,sK14,sK17))
| ~ spl94_53
| ~ spl94_165 ),
inference(superposition,[],[f784,f1431]) ).
fof(f2295,plain,
( spl94_225
| ~ spl94_96
| ~ spl94_105 ),
inference(avatar_split_clause,[],[f1072,f1024,f977,f2293]) ).
fof(f2293,plain,
( spl94_225
<=> ! [X4,X0,X3,X2,X1] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK45(vbind(X0,X1,X2),X3,X4),varrow(sK47(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK45(vbind(X0,X1,X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_225])]) ).
fof(f1072,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK45(vbind(X0,X1,X2),X3,X4),varrow(sK47(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK45(vbind(X0,X1,X2),X3,X4)) )
| ~ spl94_96
| ~ spl94_105 ),
inference(resolution,[],[f1025,f978]) ).
fof(f2216,plain,
( spl94_224
| ~ spl94_119
| ~ spl94_130 ),
inference(avatar_split_clause,[],[f1192,f1182,f1122,f2214]) ).
fof(f1182,plain,
( spl94_130
<=> ! [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_130])]) ).
fof(f1192,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_119
| ~ spl94_130 ),
inference(resolution,[],[f1183,f1123]) ).
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_130 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f2212,plain,
( spl94_223
| ~ spl94_120
| ~ spl94_130 ),
inference(avatar_split_clause,[],[f1191,f1182,f1126,f2210]) ).
fof(f2210,plain,
( spl94_223
<=> ! [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_223])]) ).
fof(f1191,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_120
| ~ spl94_130 ),
inference(resolution,[],[f1183,f1127]) ).
fof(f2208,plain,
( spl94_222
| ~ spl94_91
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1190,f1178,f956,f2206]) ).
fof(f1190,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_91
| ~ spl94_129 ),
inference(superposition,[],[f1179,f957]) ).
fof(f2204,plain,
( spl94_221
| ~ spl94_117
| ~ spl94_127 ),
inference(avatar_split_clause,[],[f1175,f1159,f1101,f2202]) ).
fof(f2202,plain,
( spl94_221
<=> ! [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_221])]) ).
fof(f1175,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_117
| ~ spl94_127 ),
inference(resolution,[],[f1160,f1102]) ).
fof(f2200,plain,
( ~ spl94_220
| ~ spl94_48
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1531,f1429,f759,f2197]) ).
fof(f2197,plain,
( spl94_220
<=> visFreeVar(vgensym(sK17),sK46(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_220])]) ).
fof(f1531,plain,
( ~ visFreeVar(vgensym(sK17),sK46(sK15,sK14,sK17))
| ~ spl94_48
| ~ spl94_165 ),
inference(superposition,[],[f760,f1431]) ).
fof(f2157,plain,
( spl94_219
| spl94_5
| ~ spl94_33
| ~ spl94_119 ),
inference(avatar_split_clause,[],[f1130,f1122,f693,f580,f2155]) ).
fof(f580,plain,
( spl94_5
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_5])]) ).
fof(f1130,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_119 ),
inference(superposition,[],[f1123,f694]) ).
fof(f2153,plain,
( spl94_218
| ~ spl94_94
| ~ spl94_96 ),
inference(avatar_split_clause,[],[f990,f977,f969,f2151]) ).
fof(f2151,plain,
( spl94_218
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X0,sK46(vbind(X1,X2,X0),X3,X4),sK47(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK46(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_218])]) ).
fof(f990,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,sK46(vbind(X1,X2,X0),X3,X4),sK47(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK46(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) )
| ~ spl94_94
| ~ spl94_96 ),
inference(resolution,[],[f978,f970]) ).
fof(f2123,plain,
( spl94_217
| ~ spl94_97
| ~ spl94_141 ),
inference(avatar_split_clause,[],[f1268,f1255,f981,f2121]) ).
fof(f2121,plain,
( spl94_217
<=> ! [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_217])]) ).
fof(f981,plain,
( spl94_97
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_97])]) ).
fof(f1268,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_97
| ~ spl94_141 ),
inference(resolution,[],[f1256,f982]) ).
fof(f982,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl94_97 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f2119,plain,
( spl94_216
| ~ spl94_113
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1265,f1251,f1057,f2117]) ).
fof(f2117,plain,
( spl94_216
<=> ! [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_216])]) ).
fof(f1265,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,[],[f1252,f1058]) ).
fof(f2115,plain,
( spl94_215
| ~ spl94_101
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1186,f1178,f1003,f2113]) ).
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_101
| ~ spl94_129 ),
inference(resolution,[],[f1179,f1004]) ).
fof(f2110,plain,
( spl94_214
| ~ spl94_95
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1168,f1150,f973,f2108]) ).
fof(f2108,plain,
( spl94_214
<=> ! [X4,X0,X3,X2,X1] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vvar(sK52(X4,X3,vbind(X0,X1,X2))) = X4
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_214])]) ).
fof(f1168,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vvar(sK52(X4,X3,vbind(X0,X1,X2))) = X4
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) )
| ~ spl94_95
| ~ spl94_125 ),
inference(resolution,[],[f1151,f974]) ).
fof(f2100,plain,
( spl94_213
| ~ spl94_102
| ~ spl94_127 ),
inference(avatar_split_clause,[],[f1176,f1159,f1007,f2098]) ).
fof(f1176,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_102
| ~ spl94_127 ),
inference(resolution,[],[f1160,f1008]) ).
fof(f2061,plain,
( spl94_212
| ~ spl94_60
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1223,f1205,f811,f2059]) ).
fof(f2059,plain,
( spl94_212
<=> ! [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_212])]) ).
fof(f1223,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_133 ),
inference(resolution,[],[f1206,f812]) ).
fof(f2057,plain,
( spl94_211
| ~ spl94_97
| ~ spl94_130 ),
inference(avatar_split_clause,[],[f1193,f1182,f981,f2055]) ).
fof(f2055,plain,
( spl94_211
<=> ! [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_211])]) ).
fof(f1193,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_97
| ~ spl94_130 ),
inference(resolution,[],[f1183,f982]) ).
fof(f2053,plain,
( spl94_210
| ~ spl94_101
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1108,f1101,f1003,f2051]) ).
fof(f2051,plain,
( spl94_210
<=> ! [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_210])]) ).
fof(f1108,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_101
| ~ spl94_117 ),
inference(resolution,[],[f1102,f1004]) ).
fof(f2038,plain,
( spl94_209
| ~ spl94_38
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1526,f1429,f714,f2036]) ).
fof(f2036,plain,
( spl94_209
<=> ! [X2,X0,X1] : vabs(X0,X1,X2) != sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_209])]) ).
fof(f714,plain,
( spl94_38
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_38])]) ).
fof(f1526,plain,
( ! [X2,X0,X1] : vabs(X0,X1,X2) != sK17
| ~ spl94_38
| ~ spl94_165 ),
inference(superposition,[],[f715,f1431]) ).
fof(f715,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl94_38 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2028,plain,
( spl94_208
| ~ spl94_41
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1221,f1205,f731,f2026]) ).
fof(f2026,plain,
( spl94_208
<=> ! [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_208])]) ).
fof(f1221,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_133 ),
inference(resolution,[],[f1206,f732]) ).
fof(f2024,plain,
( spl94_207
| ~ spl94_91
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1018,f1007,f956,f2022]) ).
fof(f1018,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_91
| ~ spl94_102 ),
inference(superposition,[],[f1008,f957]) ).
fof(f2006,plain,
( spl94_206
| ~ spl94_42
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1189,f1178,f735,f2004]) ).
fof(f2004,plain,
( spl94_206
<=> ! [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_206])]) ).
fof(f1189,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_129 ),
inference(superposition,[],[f1179,f736]) ).
fof(f2000,plain,
( spl94_205
| spl94_5
| ~ spl94_33
| ~ spl94_120 ),
inference(avatar_split_clause,[],[f1132,f1126,f693,f580,f1998]) ).
fof(f1132,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_120 ),
inference(superposition,[],[f1127,f694]) ).
fof(f1996,plain,
( spl94_204
| ~ spl94_91
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1111,f1101,f956,f1994]) ).
fof(f1111,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_91
| ~ spl94_117 ),
inference(superposition,[],[f1102,f957]) ).
fof(f1992,plain,
( spl94_203
| ~ spl94_101
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1015,f1007,f1003,f1990]) ).
fof(f1015,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_101
| ~ spl94_102 ),
inference(resolution,[],[f1008,f1004]) ).
fof(f1953,plain,
( spl94_202
| ~ spl94_113
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1120,f1105,f1057,f1951]) ).
fof(f1951,plain,
( spl94_202
<=> ! [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_202])]) ).
fof(f1120,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_118 ),
inference(resolution,[],[f1106,f1058]) ).
fof(f1949,plain,
( spl94_201
| ~ spl94_95
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1079,f1065,f973,f1947]) ).
fof(f1079,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(X5,X3),X6)
| ~ vtcheck(X2,X5,varrow(X4,X6))
| visFreeVar(X0,X5) )
| ~ spl94_95
| ~ spl94_115 ),
inference(resolution,[],[f1066,f974]) ).
fof(f1945,plain,
( spl94_200
| ~ spl94_91
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1077,f1061,f956,f1943]) ).
fof(f1061,plain,
( spl94_114
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_114])]) ).
fof(f1077,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vnoType != vlookup(X0,X3)
| ~ vtcheck(vbind(X1,X2,X3),X4,X5)
| vtcheck(vbind(X0,X6,vbind(X1,X2,X3)),X4,X5)
| X0 = X1 )
| ~ spl94_91
| ~ spl94_114 ),
inference(superposition,[],[f1062,f957]) ).
fof(f1062,plain,
( ! [X2,X3,X0,X1,X4] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,X3,X4)
| vtcheck(vbind(X0,X1,X2),X3,X4) )
| ~ spl94_114 ),
inference(avatar_component_clause,[],[f1061]) ).
fof(f1941,plain,
( spl94_199
| ~ spl94_96
| ~ spl94_113 ),
inference(avatar_split_clause,[],[f1074,f1057,f977,f1939]) ).
fof(f1939,plain,
( spl94_199
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( ~ vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| vtcheck(X4,vabs(X0,X1,X5),varrow(X1,X6))
| visFreeVar(X2,vabs(X0,X1,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_199])]) ).
fof(f1074,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| vtcheck(X4,vabs(X0,X1,X5),varrow(X1,X6))
| visFreeVar(X2,vabs(X0,X1,X5)) )
| ~ spl94_96
| ~ spl94_113 ),
inference(resolution,[],[f1058,f978]) ).
fof(f1927,plain,
( spl94_198
| ~ spl94_160
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1536,f1429,f1402,f1925]) ).
fof(f1925,plain,
( spl94_198
<=> ! [X0,X1] : ~ visValue(vsubst(X0,X1,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_198])]) ).
fof(f1536,plain,
( ! [X0,X1] : ~ visValue(vsubst(X0,X1,sK17))
| ~ spl94_160
| ~ spl94_165 ),
inference(superposition,[],[f1403,f1431]) ).
fof(f1923,plain,
( spl94_197
| ~ spl94_23
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1220,f1205,f653,f1921]) ).
fof(f1921,plain,
( spl94_197
<=> ! [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_197])]) ).
fof(f1220,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_133 ),
inference(resolution,[],[f1206,f654]) ).
fof(f1896,plain,
( spl94_196
| ~ spl94_95
| ~ spl94_140 ),
inference(avatar_split_clause,[],[f1261,f1251,f973,f1894]) ).
fof(f1261,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),X5,X6)
| visFreeVar(X2,X5) )
| ~ spl94_95
| ~ spl94_140 ),
inference(resolution,[],[f1252,f974]) ).
fof(f1892,plain,
( spl94_195
| ~ spl94_96
| ~ spl94_134 ),
inference(avatar_split_clause,[],[f1258,f1226,f977,f1890]) ).
fof(f1890,plain,
( spl94_195
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK49(X0,X1,X2),sK51(X0,X1,X2))
| visFreeVar(sK48(X0,X1,X2),sK49(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_195])]) ).
fof(f1258,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK49(X0,X1,X2),sK51(X0,X1,X2))
| visFreeVar(sK48(X0,X1,X2),sK49(X0,X1,X2)) )
| ~ spl94_96
| ~ spl94_134 ),
inference(resolution,[],[f1227,f978]) ).
fof(f1888,plain,
( spl94_194
| ~ spl94_32
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1222,f1205,f689,f1886]) ).
fof(f1222,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_133 ),
inference(resolution,[],[f1206,f690]) ).
fof(f1874,plain,
( spl94_193
| ~ spl94_43
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1187,f1178,f739,f1872]) ).
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_129 ),
inference(resolution,[],[f1179,f740]) ).
fof(f1841,plain,
( spl94_192
| spl94_5
| ~ spl94_16
| ~ spl94_119 ),
inference(avatar_split_clause,[],[f1129,f1122,f625,f580,f1839]) ).
fof(f1129,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_119 ),
inference(superposition,[],[f1123,f626]) ).
fof(f1837,plain,
( spl94_191
| ~ spl94_42
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1017,f1007,f735,f1835]) ).
fof(f1835,plain,
( spl94_191
<=> ! [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_191])]) ).
fof(f1017,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_102 ),
inference(superposition,[],[f1008,f736]) ).
fof(f1825,plain,
( spl94_190
| ~ spl94_11
| ~ spl94_133 ),
inference(avatar_split_clause,[],[f1217,f1205,f605,f1823]) ).
fof(f1823,plain,
( spl94_190
<=> ! [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_190])]) ).
fof(f605,plain,
( spl94_11
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_11])]) ).
fof(f1217,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_133 ),
inference(resolution,[],[f1206,f606]) ).
fof(f606,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl94_11 ),
inference(avatar_component_clause,[],[f605]) ).
fof(f1781,plain,
( spl94_189
| ~ spl94_22
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1525,f1429,f649,f1779]) ).
fof(f1779,plain,
( spl94_189
<=> ! [X0] : vvar(X0) != sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_189])]) ).
fof(f1525,plain,
( ! [X0] : vvar(X0) != sK17
| ~ spl94_22
| ~ spl94_165 ),
inference(superposition,[],[f650,f1431]) ).
fof(f1777,plain,
( spl94_188
| ~ spl94_19
| ~ spl94_142 ),
inference(avatar_split_clause,[],[f1278,f1272,f637,f1775]) ).
fof(f1775,plain,
( spl94_188
<=> ! [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_188])]) ).
fof(f637,plain,
( spl94_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_19])]) ).
fof(f1272,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(f1278,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,[],[f1277]) ).
fof(f1277,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,[],[f1273,f638]) ).
fof(f638,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl94_19 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f1273,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,[],[f1272]) ).
fof(f1773,plain,
( spl94_187
| ~ spl94_42
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1110,f1101,f735,f1771]) ).
fof(f1771,plain,
( spl94_187
<=> ! [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_187])]) ).
fof(f1110,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_117 ),
inference(superposition,[],[f1102,f736]) ).
fof(f1769,plain,
( spl94_186
| ~ spl94_60
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1099,f1069,f811,f1767]) ).
fof(f1767,plain,
( spl94_186
<=> ! [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_186])]) ).
fof(f1099,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_116 ),
inference(superposition,[],[f812,f1070]) ).
fof(f1765,plain,
( spl94_185
| ~ spl94_113
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1081,f1065,f1057,f1763]) ).
fof(f1763,plain,
( spl94_185
<=> ! [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_185])]) ).
fof(f1081,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_115 ),
inference(resolution,[],[f1066,f1058]) ).
fof(f1761,plain,
( spl94_184
| ~ spl94_105
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1080,f1065,f1024,f1759]) ).
fof(f1759,plain,
( spl94_184
<=> ! [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_184])]) ).
fof(f1080,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_105
| ~ spl94_115 ),
inference(resolution,[],[f1066,f1025]) ).
fof(f1695,plain,
( spl94_183
| ~ spl94_43
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1109,f1101,f739,f1693]) ).
fof(f1109,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_117 ),
inference(resolution,[],[f1102,f740]) ).
fof(f1691,plain,
( spl94_182
| ~ spl94_84
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1087,f1069,f915,f1689]) ).
fof(f1087,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_84
| ~ spl94_116 ),
inference(superposition,[],[f1070,f916]) ).
fof(f1687,plain,
( spl94_181
| ~ spl94_84
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1084,f1069,f915,f1685]) ).
fof(f1084,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_84
| ~ spl94_116 ),
inference(superposition,[],[f1070,f916]) ).
fof(f1641,plain,
( spl94_180
| ~ spl94_61
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1086,f1069,f815,f1639]) ).
fof(f1086,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl94_61
| ~ spl94_116 ),
inference(superposition,[],[f1070,f816]) ).
fof(f1637,plain,
( spl94_179
| ~ spl94_61
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1083,f1069,f815,f1635]) ).
fof(f1083,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl94_61
| ~ spl94_116 ),
inference(superposition,[],[f1070,f816]) ).
fof(f1615,plain,
( spl94_178
| ~ spl94_95
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1117,f1105,f973,f1613]) ).
fof(f1613,plain,
( spl94_178
<=> ! [X5,X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(vbind(X0,X5,X2),X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_178])]) ).
fof(f1117,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(vbind(X0,X5,X2),X3,X4)
| visFreeVar(X0,X3) )
| ~ spl94_95
| ~ spl94_118 ),
inference(resolution,[],[f1106,f974]) ).
fof(f1611,plain,
( spl94_177
| ~ spl94_43
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1016,f1007,f739,f1609]) ).
fof(f1016,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_102 ),
inference(resolution,[],[f1008,f740]) ).
fof(f1607,plain,
( ~ spl94_176
| ~ spl94_12
| ~ spl94_165 ),
inference(avatar_split_clause,[],[f1524,f1429,f609,f1604]) ).
fof(f1604,plain,
( spl94_176
<=> visValue(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_176])]) ).
fof(f609,plain,
( spl94_12
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_12])]) ).
fof(f1524,plain,
( ~ visValue(sK17)
| ~ spl94_12
| ~ spl94_165 ),
inference(superposition,[],[f610,f1431]) ).
fof(f610,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl94_12 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f1602,plain,
( spl94_175
| ~ spl94_59
| ~ spl94_91 ),
inference(avatar_split_clause,[],[f963,f956,f807,f1600]) ).
fof(f963,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl94_59
| ~ spl94_91 ),
inference(superposition,[],[f808,f957]) ).
fof(f1578,plain,
( spl94_174
| ~ spl94_49
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1096,f1069,f763,f1576]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl94_49
| ~ spl94_116 ),
inference(superposition,[],[f764,f1070]) ).
fof(f1574,plain,
( spl94_173
| ~ spl94_47
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1093,f1069,f755,f1572]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl94_47
| ~ spl94_116 ),
inference(superposition,[],[f756,f1070]) ).
fof(f1569,plain,
( spl94_172
| spl94_5
| ~ spl94_16
| ~ spl94_97 ),
inference(avatar_split_clause,[],[f992,f981,f625,f580,f1567]) ).
fof(f992,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl94_16
| ~ spl94_97 ),
inference(superposition,[],[f982,f626]) ).
fof(f1457,plain,
( spl94_171
| ~ spl94_18
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1188,f1178,f633,f1455]) ).
fof(f1188,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 )
| ~ spl94_18
| ~ spl94_129 ),
inference(superposition,[],[f1179,f634]) ).
fof(f1453,plain,
( spl94_170
| ~ spl94_40
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1092,f1069,f722,f1451]) ).
fof(f1092,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl94_40
| ~ spl94_116 ),
inference(superposition,[],[f723,f1070]) ).
fof(f1449,plain,
( spl94_169
| ~ spl94_39
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1091,f1069,f718,f1447]) ).
fof(f1091,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl94_39
| ~ spl94_116 ),
inference(superposition,[],[f719,f1070]) ).
fof(f1445,plain,
( spl94_168
| ~ spl94_34
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1085,f1069,f697,f1443]) ).
fof(f1085,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl94_34
| ~ spl94_116 ),
inference(superposition,[],[f1070,f698]) ).
fof(f1441,plain,
( spl94_167
| ~ spl94_34
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1082,f1069,f697,f1439]) ).
fof(f1082,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl94_34
| ~ spl94_116 ),
inference(superposition,[],[f1070,f698]) ).
fof(f1437,plain,
( spl94_166
| ~ spl94_11
| ~ spl94_83 ),
inference(avatar_split_clause,[],[f926,f911,f605,f1435]) ).
fof(f926,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl94_11
| ~ spl94_83 ),
inference(resolution,[],[f912,f606]) ).
fof(f1432,plain,
( spl94_165
| ~ spl94_99
| ~ spl94_154 ),
inference(avatar_split_clause,[],[f1386,f1374,f995,f1429]) ).
fof(f1374,plain,
( spl94_154
<=> sP6(sK15,sK14,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_154])]) ).
fof(f1386,plain,
( sK17 = vapp(sK45(sK15,sK14,sK17),sK46(sK15,sK14,sK17))
| ~ spl94_99
| ~ spl94_154 ),
inference(resolution,[],[f1376,f996]) ).
fof(f1376,plain,
( sP6(sK15,sK14,sK17)
| ~ spl94_154 ),
inference(avatar_component_clause,[],[f1374]) ).
fof(f1427,plain,
( spl94_164
| ~ spl94_42
| ~ spl94_59 ),
inference(avatar_split_clause,[],[f821,f807,f735,f1425]) ).
fof(f821,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl94_42
| ~ spl94_59 ),
inference(superposition,[],[f808,f736]) ).
fof(f1418,plain,
( spl94_163
| ~ spl94_38
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1090,f1069,f714,f1416]) ).
fof(f1090,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl94_38
| ~ spl94_116 ),
inference(superposition,[],[f715,f1070]) ).
fof(f1414,plain,
( spl94_162
| ~ spl94_18
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1078,f1061,f633,f1412]) ).
fof(f1078,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl94_18
| ~ spl94_114 ),
inference(trivial_inequality_removal,[],[f1075]) ).
fof(f1075,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl94_18
| ~ spl94_114 ),
inference(superposition,[],[f1062,f634]) ).
fof(f1409,plain,
( spl94_161
| ~ spl94_22
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1089,f1069,f649,f1407]) ).
fof(f1089,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl94_22
| ~ spl94_116 ),
inference(superposition,[],[f650,f1070]) ).
fof(f1404,plain,
( spl94_160
| ~ spl94_12
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1088,f1069,f609,f1402]) ).
fof(f1088,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_12
| ~ spl94_116 ),
inference(superposition,[],[f610,f1070]) ).
fof(f1399,plain,
( spl94_157
| spl94_158
| spl94_159
| ~ spl94_2
| ~ spl94_63
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1174,f1150,f830,f565,f1396,f1392,f1388]) ).
fof(f1174,plain,
( sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| vvar(sK16) = vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_125 ),
inference(forward_demodulation,[],[f1173,f832]) ).
fof(f1173,plain,
( vvar(sK16) = vvar(sK52(vvar(sK16),sK19,vbind(sK16,sK14,sK15)))
| sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_125 ),
inference(forward_demodulation,[],[f1172,f832]) ).
fof(f1172,plain,
( sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK16))
| vvar(sK18) = vvar(sK52(vvar(sK18),sK19,vbind(sK16,sK14,sK15)))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_63
| ~ spl94_125 ),
inference(forward_demodulation,[],[f1167,f832]) ).
fof(f1167,plain,
( sP5(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| vvar(sK18) = vvar(sK52(vvar(sK18),sK19,vbind(sK16,sK14,sK15)))
| sP6(vbind(sK16,sK14,sK15),sK19,vvar(sK18))
| ~ spl94_2
| ~ spl94_125 ),
inference(resolution,[],[f1151,f567]) ).
fof(f1385,plain,
( spl94_154
| spl94_155
| spl94_156
| ~ spl94_1
| ~ spl94_125 ),
inference(avatar_split_clause,[],[f1166,f1150,f560,f1382,f1378,f1374]) ).
fof(f1378,plain,
( spl94_155
<=> sK17 = vvar(sK52(sK17,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_155])]) ).
fof(f1382,plain,
( spl94_156
<=> sP5(sK15,sK14,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_156])]) ).
fof(f1166,plain,
( sP5(sK15,sK14,sK17)
| sK17 = vvar(sK52(sK17,sK14,sK15))
| sP6(sK15,sK14,sK17)
| ~ spl94_1
| ~ spl94_125 ),
inference(resolution,[],[f1151,f562]) ).
fof(f562,plain,
( vtcheck(sK15,sK17,sK14)
| ~ spl94_1 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f1364,plain,
( spl94_153
| ~ spl94_116
| ~ spl94_152 ),
inference(avatar_split_clause,[],[f1360,f1357,f1069,f1362]) ).
fof(f1357,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(f1360,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_116
| ~ spl94_152 ),
inference(forward_demodulation,[],[f1358,f1070]) ).
fof(f1358,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,[],[f1357]) ).
fof(f1359,plain,
spl94_152,
inference(avatar_split_clause,[],[f474,f1357]) ).
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',unknown) ).
fof(f1344,plain,
spl94_151,
inference(avatar_split_clause,[],[f475,f1342]) ).
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(f1324,plain,
spl94_150,
inference(avatar_split_clause,[],[f477,f1322]) ).
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(f1320,plain,
spl94_149,
inference(avatar_split_clause,[],[f476,f1318]) ).
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(f1316,plain,
spl94_148,
inference(avatar_split_clause,[],[f387,f1314]) ).
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(f1307,plain,
spl94_147,
inference(avatar_split_clause,[],[f458,f1305]) ).
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',unknown) ).
fof(f1295,plain,
( spl94_146
| ~ spl94_2
| ~ spl94_63 ),
inference(avatar_split_clause,[],[f1115,f830,f565,f1292]) ).
fof(f1292,plain,
( spl94_146
<=> vtcheck(vbind(sK16,sK14,sK15),vvar(sK16),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_146])]) ).
fof(f1115,plain,
( vtcheck(vbind(sK16,sK14,sK15),vvar(sK16),sK19)
| ~ spl94_2
| ~ spl94_63 ),
inference(superposition,[],[f567,f832]) ).
fof(f1290,plain,
spl94_145,
inference(avatar_split_clause,[],[f557,f1288]) ).
fof(f557,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,[],[f556]) ).
fof(f556,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,[],[f555]) ).
fof(f555,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,[],[f554]) ).
fof(f554,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,[],[f553]) ).
fof(f553,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',unknown) ).
fof(f1286,plain,
spl94_144,
inference(avatar_split_clause,[],[f380,f1284]) ).
fof(f1284,plain,
( spl94_144
<=> ! [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_144])]) ).
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(f1282,plain,
spl94_143,
inference(avatar_split_clause,[],[f386,f1280]) ).
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(f1274,plain,
spl94_142,
inference(avatar_split_clause,[],[f558,f1272]) ).
fof(f558,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(f1257,plain,
spl94_141,
inference(avatar_split_clause,[],[f500,f1255]) ).
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,[],[f421]) ).
fof(f421,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])],[f166,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(f166,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,[],[f165]) ).
fof(f165,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,[],[f98]) ).
fof(f98,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',unknown) ).
fof(f1253,plain,
spl94_140,
inference(avatar_split_clause,[],[f437,f1251]) ).
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',unknown) ).
fof(f1249,plain,
spl94_139,
inference(avatar_split_clause,[],[f392,f1247]) ).
fof(f1247,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(f1245,plain,
spl94_138,
inference(avatar_split_clause,[],[f390,f1243]) ).
fof(f1243,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(f1241,plain,
spl94_137,
inference(avatar_split_clause,[],[f383,f1239]) ).
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(f1237,plain,
spl94_136,
inference(avatar_split_clause,[],[f377,f1235]) ).
fof(f1235,plain,
( spl94_136
<=> ! [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_136])]) ).
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(f1233,plain,
( ~ spl94_135
| ~ spl94_63
| spl94_64 ),
inference(avatar_split_clause,[],[f1113,f834,f830,f1230]) ).
fof(f1230,plain,
( spl94_135
<=> vtcheck(sK15,vvar(sK16),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_135])]) ).
fof(f834,plain,
( spl94_64
<=> vtcheck(sK15,vvar(sK18),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_64])]) ).
fof(f1113,plain,
( ~ vtcheck(sK15,vvar(sK16),sK19)
| ~ spl94_63
| spl94_64 ),
inference(superposition,[],[f836,f832]) ).
fof(f836,plain,
( ~ vtcheck(sK15,vvar(sK18),sK19)
| spl94_64 ),
inference(avatar_component_clause,[],[f834]) ).
fof(f1228,plain,
spl94_134,
inference(avatar_split_clause,[],[f352,f1226]) ).
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(f1207,plain,
spl94_133,
inference(avatar_split_clause,[],[f552,f1205]) ).
fof(f552,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,[],[f551]) ).
fof(f551,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,[],[f550]) ).
fof(f550,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,[],[f549]) ).
fof(f549,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',unknown) ).
fof(f1203,plain,
spl94_132,
inference(avatar_split_clause,[],[f354,f1201]) ).
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',unknown) ).
fof(f1199,plain,
spl94_131,
inference(avatar_split_clause,[],[f316,f1197]) ).
fof(f1197,plain,
( spl94_131
<=> ! [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_131])]) ).
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_130,
inference(avatar_split_clause,[],[f522,f1182]) ).
fof(f522,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,[],[f521]) ).
fof(f521,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,[],[f520]) ).
fof(f520,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',unknown) ).
fof(f1180,plain,
spl94_129,
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',unknown) ).
fof(f1165,plain,
spl94_128,
inference(avatar_split_clause,[],[f360,f1163]) ).
fof(f1163,plain,
( spl94_128
<=> ! [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_128])]) ).
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(f1161,plain,
spl94_127,
inference(avatar_split_clause,[],[f356,f1159]) ).
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(f1157,plain,
( ~ spl94_126
| spl94_3
| ~ spl94_34
| ~ spl94_63 ),
inference(avatar_split_clause,[],[f1116,f830,f697,f570,f1154]) ).
fof(f1154,plain,
( spl94_126
<=> vtcheck(sK15,sK17,sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_126])]) ).
fof(f1116,plain,
( ~ vtcheck(sK15,sK17,sK19)
| spl94_3
| ~ spl94_34
| ~ spl94_63 ),
inference(forward_demodulation,[],[f1114,f698]) ).
fof(f1114,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK16)),sK19)
| spl94_3
| ~ spl94_63 ),
inference(superposition,[],[f572,f832]) ).
fof(f1152,plain,
spl94_125,
inference(avatar_split_clause,[],[f353,f1150]) ).
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(f1148,plain,
spl94_124,
inference(avatar_split_clause,[],[f350,f1146]) ).
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(f1144,plain,
spl94_123,
inference(avatar_split_clause,[],[f332,f1142]) ).
fof(f1142,plain,
( spl94_123
<=> ! [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_123])]) ).
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(f1140,plain,
spl94_122,
inference(avatar_split_clause,[],[f327,f1138]) ).
fof(f1138,plain,
( spl94_122
<=> ! [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_122])]) ).
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(f1136,plain,
spl94_121,
inference(avatar_split_clause,[],[f313,f1134]) ).
fof(f1134,plain,
( spl94_121
<=> ! [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_121])]) ).
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(f1128,plain,
spl94_120,
inference(avatar_split_clause,[],[f519,f1126]) ).
fof(f519,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,[],[f518]) ).
fof(f518,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,[],[f517]) ).
fof(f517,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',unknown) ).
fof(f1124,plain,
spl94_119,
inference(avatar_split_clause,[],[f497,f1122]) ).
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,[],[f420]) ).
fof(f420,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])],[f164,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(f164,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,[],[f163]) ).
fof(f163,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,[],[f97]) ).
fof(f97,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',unknown) ).
fof(f1107,plain,
spl94_118,
inference(avatar_split_clause,[],[f539,f1105]) ).
fof(f539,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',unknown) ).
fof(f1103,plain,
spl94_117,
inference(avatar_split_clause,[],[f466,f1101]) ).
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(f1073,plain,
( spl94_63
| ~ spl94_32
| ~ spl94_103 ),
inference(avatar_split_clause,[],[f1055,f1011,f689,f830]) ).
fof(f1011,plain,
( spl94_103
<=> visFreeVar(sK16,vvar(sK18)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_103])]) ).
fof(f1055,plain,
( sK16 = sK18
| ~ spl94_32
| ~ spl94_103 ),
inference(resolution,[],[f1013,f690]) ).
fof(f1013,plain,
( visFreeVar(sK16,vvar(sK18))
| ~ spl94_103 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1071,plain,
spl94_116,
inference(avatar_split_clause,[],[f543,f1069]) ).
fof(f543,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f542]) ).
fof(f542,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,[],[f541]) ).
fof(f541,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,[],[f540]) ).
fof(f540,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',unknown) ).
fof(f1067,plain,
spl94_115,
inference(avatar_split_clause,[],[f422,f1065]) ).
fof(f422,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,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f167]) ).
fof(f167,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,[],[f99]) ).
fof(f99,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',unknown) ).
fof(f1063,plain,
spl94_114,
inference(avatar_split_clause,[],[f419,f1061]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,X3,X4)
& vnoType = vlookup(X0,X2) )
=> vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(X19,X10,X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f1059,plain,
spl94_113,
inference(avatar_split_clause,[],[f413,f1057]) ).
fof(f413,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,[],[f154]) ).
fof(f154,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,[],[f92]) ).
fof(f92,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',unknown) ).
fof(f1054,plain,
spl94_112,
inference(avatar_split_clause,[],[f401,f1052]) ).
fof(f1052,plain,
( spl94_112
<=> ! [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_112])]) ).
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(f1050,plain,
spl94_111,
inference(avatar_split_clause,[],[f396,f1048]) ).
fof(f1048,plain,
( spl94_111
<=> ! [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_111])]) ).
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(f1046,plain,
spl94_110,
inference(avatar_split_clause,[],[f391,f1044]) ).
fof(f1044,plain,
( spl94_110
<=> ! [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_110])]) ).
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(f1042,plain,
spl94_109,
inference(avatar_split_clause,[],[f385,f1040]) ).
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(f1038,plain,
spl94_108,
inference(avatar_split_clause,[],[f384,f1036]) ).
fof(f1036,plain,
( spl94_108
<=> ! [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_108])]) ).
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(f1034,plain,
spl94_107,
inference(avatar_split_clause,[],[f379,f1032]) ).
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(f1030,plain,
spl94_106,
inference(avatar_split_clause,[],[f378,f1028]) ).
fof(f1028,plain,
( spl94_106
<=> ! [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_106])]) ).
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(f1026,plain,
spl94_105,
inference(avatar_split_clause,[],[f348,f1024]) ).
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(f1022,plain,
spl94_104,
inference(avatar_split_clause,[],[f336,f1020]) ).
fof(f1020,plain,
( spl94_104
<=> ! [X0,X1] :
( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_104])]) ).
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(f1014,plain,
( spl94_103
| spl94_64
| ~ spl94_2
| ~ spl94_96 ),
inference(avatar_split_clause,[],[f988,f977,f565,f834,f1011]) ).
fof(f988,plain,
( vtcheck(sK15,vvar(sK18),sK19)
| visFreeVar(sK16,vvar(sK18))
| ~ spl94_2
| ~ spl94_96 ),
inference(resolution,[],[f978,f567]) ).
fof(f1009,plain,
spl94_102,
inference(avatar_split_clause,[],[f467,f1007]) ).
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(f1005,plain,
spl94_101,
inference(avatar_split_clause,[],[f358,f1003]) ).
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(f1001,plain,
spl94_100,
inference(avatar_split_clause,[],[f351,f999]) ).
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(f997,plain,
spl94_99,
inference(avatar_split_clause,[],[f347,f995]) ).
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(f987,plain,
( spl94_98
| ~ spl94_40
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f918,f783,f722,f985]) ).
fof(f918,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl94_40
| ~ spl94_53 ),
inference(resolution,[],[f784,f723]) ).
fof(f983,plain,
spl94_97,
inference(avatar_split_clause,[],[f516,f981]) ).
fof(f516,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f515]) ).
fof(f515,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f514]) ).
fof(f514,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',unknown) ).
fof(f979,plain,
spl94_96,
inference(avatar_split_clause,[],[f415,f977]) ).
fof(f415,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(vbind(X0,X1,X2),X3,X4)
& ~ visFreeVar(X0,X3) )
=> vtcheck(X2,X3,X4) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(vbind(X8,X9,X19),X10,X14)
& ~ visFreeVar(X8,X10) )
=> vtcheck(X19,X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f975,plain,
spl94_95,
inference(avatar_split_clause,[],[f414,f973]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,X3,X4)
& ~ visFreeVar(X0,X3) )
=> vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(X19,X10,X14)
& ~ visFreeVar(X8,X10) )
=> vtcheck(vbind(X8,X9,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f971,plain,
spl94_94,
inference(avatar_split_clause,[],[f349,f969]) ).
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(f967,plain,
spl94_93,
inference(avatar_split_clause,[],[f326,f965]) ).
fof(f965,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(f962,plain,
( spl94_92
| ~ spl94_39
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f819,f759,f718,f960]) ).
fof(f819,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl94_39
| ~ spl94_48 ),
inference(resolution,[],[f760,f719]) ).
fof(f958,plain,
spl94_91,
inference(avatar_split_clause,[],[f534,f956]) ).
fof(f534,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f533]) ).
fof(f533,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f532]) ).
fof(f532,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',unknown) ).
fof(f954,plain,
spl94_90,
inference(avatar_split_clause,[],[f400,f952]) ).
fof(f952,plain,
( spl94_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_90])]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f950,plain,
spl94_89,
inference(avatar_split_clause,[],[f397,f948]) ).
fof(f948,plain,
( spl94_89
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_89])]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f946,plain,
spl94_88,
inference(avatar_split_clause,[],[f395,f944]) ).
fof(f944,plain,
( spl94_88
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_88])]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f942,plain,
spl94_87,
inference(avatar_split_clause,[],[f361,f940]) ).
fof(f361,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f938,plain,
spl94_86,
inference(avatar_split_clause,[],[f357,f936]) ).
fof(f936,plain,
( spl94_86
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_86])]) ).
fof(f357,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f934,plain,
( spl94_85
| ~ spl94_40
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f818,f759,f722,f932]) ).
fof(f818,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl94_40
| ~ spl94_48 ),
inference(resolution,[],[f760,f723]) ).
fof(f917,plain,
spl94_84,
inference(avatar_split_clause,[],[f548,f915]) ).
fof(f548,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f546]) ).
fof(f546,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,[],[f545]) ).
fof(f545,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,[],[f544]) ).
fof(f544,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',unknown) ).
fof(f913,plain,
spl94_83,
inference(avatar_split_clause,[],[f513,f911]) ).
fof(f513,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f512]) ).
fof(f512,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',unknown) ).
fof(f909,plain,
spl94_82,
inference(avatar_split_clause,[],[f429,f907]) ).
fof(f907,plain,
( spl94_82
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_82])]) ).
fof(f429,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,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,[],[f171]) ).
fof(f171,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,[],[f101]) ).
fof(f101,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',unknown) ).
fof(f905,plain,
spl94_81,
inference(avatar_split_clause,[],[f428,f903]) ).
fof(f903,plain,
( spl94_81
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_81])]) ).
fof(f428,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f172]) ).
fof(f901,plain,
spl94_80,
inference(avatar_split_clause,[],[f427,f899]) ).
fof(f899,plain,
( spl94_80
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_80])]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f172]) ).
fof(f897,plain,
spl94_79,
inference(avatar_split_clause,[],[f425,f895]) ).
fof(f895,plain,
( spl94_79
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_79])]) ).
fof(f425,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,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,[],[f169]) ).
fof(f169,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,[],[f100]) ).
fof(f100,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',unknown) ).
fof(f893,plain,
spl94_78,
inference(avatar_split_clause,[],[f424,f891]) ).
fof(f891,plain,
( spl94_78
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_78])]) ).
fof(f424,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f170]) ).
fof(f889,plain,
spl94_77,
inference(avatar_split_clause,[],[f423,f887]) ).
fof(f887,plain,
( spl94_77
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_77])]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f170]) ).
fof(f885,plain,
spl94_76,
inference(avatar_split_clause,[],[f402,f883]) ).
fof(f883,plain,
( spl94_76
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_76])]) ).
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_75,
inference(avatar_split_clause,[],[f399,f879]) ).
fof(f879,plain,
( spl94_75
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_75])]) ).
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_74,
inference(avatar_split_clause,[],[f398,f875]) ).
fof(f875,plain,
( spl94_74
<=> ! [X0,X3,X2,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_74])]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f873,plain,
spl94_73,
inference(avatar_split_clause,[],[f394,f871]) ).
fof(f871,plain,
( spl94_73
<=> ! [X0,X3,X2,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_73])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f869,plain,
spl94_72,
inference(avatar_split_clause,[],[f393,f867]) ).
fof(f867,plain,
( spl94_72
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_72])]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f865,plain,
spl94_71,
inference(avatar_split_clause,[],[f389,f863]) ).
fof(f863,plain,
( spl94_71
<=> ! [X0,X3,X2,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_71])]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f861,plain,
spl94_70,
inference(avatar_split_clause,[],[f388,f859]) ).
fof(f859,plain,
( spl94_70
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_70])]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f857,plain,
spl94_69,
inference(avatar_split_clause,[],[f382,f855]) ).
fof(f382,plain,
! [X2,X3,X0,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f853,plain,
spl94_68,
inference(avatar_split_clause,[],[f381,f851]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f849,plain,
spl94_67,
inference(avatar_split_clause,[],[f376,f847]) ).
fof(f847,plain,
( spl94_67
<=> ! [X0,X3,X2,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_67])]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f845,plain,
spl94_66,
inference(avatar_split_clause,[],[f375,f843]) ).
fof(f843,plain,
( spl94_66
<=> ! [X0,X3,X2,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_66])]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f841,plain,
spl94_65,
inference(avatar_split_clause,[],[f322,f839]) ).
fof(f839,plain,
( spl94_65
<=> ! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_65])]) ).
fof(f322,plain,
! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f837,plain,
( spl94_63
| ~ spl94_64
| spl94_3
| ~ spl94_61 ),
inference(avatar_split_clause,[],[f824,f815,f570,f834,f830]) ).
fof(f824,plain,
( ~ vtcheck(sK15,vvar(sK18),sK19)
| sK16 = sK18
| spl94_3
| ~ spl94_61 ),
inference(superposition,[],[f572,f816]) ).
fof(f828,plain,
spl94_62,
inference(avatar_split_clause,[],[f317,f826]) ).
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(f817,plain,
spl94_61,
inference(avatar_split_clause,[],[f526,f815]) ).
fof(f526,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f525]) ).
fof(f525,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f524]) ).
fof(f524,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f523]) ).
fof(f523,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',unknown) ).
fof(f813,plain,
spl94_60,
inference(avatar_split_clause,[],[f490,f811]) ).
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,[],[f418]) ).
fof(f418,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f160]) ).
fof(f160,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,[],[f159]) ).
fof(f159,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,[],[f95]) ).
fof(f95,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',unknown) ).
fof(f809,plain,
spl94_59,
inference(avatar_split_clause,[],[f367,f807]) ).
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',unknown) ).
fof(f805,plain,
spl94_58,
inference(avatar_split_clause,[],[f362,f803]) ).
fof(f362,plain,
! [X2,X0,X1] :
( vsomeType(sK60(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f801,plain,
spl94_57,
inference(avatar_split_clause,[],[f333,f799]) ).
fof(f799,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(f797,plain,
spl94_56,
inference(avatar_split_clause,[],[f328,f795]) ).
fof(f795,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(f793,plain,
spl94_55,
inference(avatar_split_clause,[],[f324,f791]) ).
fof(f791,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(f789,plain,
spl94_54,
inference(avatar_split_clause,[],[f323,f787]) ).
fof(f787,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(f785,plain,
( spl94_53
| ~ spl94_11
| ~ spl94_40 ),
inference(avatar_split_clause,[],[f729,f722,f605,f783]) ).
fof(f729,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_11
| ~ spl94_40 ),
inference(resolution,[],[f723,f606]) ).
fof(f781,plain,
spl94_52,
inference(avatar_split_clause,[],[f319,f779]) ).
fof(f319,plain,
! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f777,plain,
spl94_51,
inference(avatar_split_clause,[],[f318,f775]) ).
fof(f775,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(f773,plain,
spl94_50,
inference(avatar_split_clause,[],[f314,f771]) ).
fof(f771,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(f765,plain,
spl94_49,
inference(avatar_split_clause,[],[f373,f763]) ).
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',unknown) ).
fof(f761,plain,
( spl94_48
| ~ spl94_11
| ~ spl94_39 ),
inference(avatar_split_clause,[],[f728,f718,f605,f759]) ).
fof(f728,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_11
| ~ spl94_39 ),
inference(resolution,[],[f719,f606]) ).
fof(f757,plain,
spl94_47,
inference(avatar_split_clause,[],[f372,f755]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f144]) ).
fof(f753,plain,
spl94_46,
inference(avatar_split_clause,[],[f370,f751]) ).
fof(f751,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',unknown) ).
fof(f749,plain,
spl94_45,
inference(avatar_split_clause,[],[f369,f747]) ).
fof(f747,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(f745,plain,
spl94_44,
inference(avatar_split_clause,[],[f359,f743]) ).
fof(f359,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f263]) ).
fof(f741,plain,
spl94_43,
inference(avatar_split_clause,[],[f355,f739]) ).
fof(f355,plain,
! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f737,plain,
spl94_42,
inference(avatar_split_clause,[],[f538,f735]) ).
fof(f538,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f537]) ).
fof(f537,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f536]) ).
fof(f536,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f535]) ).
fof(f535,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',unknown) ).
fof(f733,plain,
spl94_41,
inference(avatar_split_clause,[],[f508,f731]) ).
fof(f508,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f507]) ).
fof(f507,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(f724,plain,
spl94_40,
inference(avatar_split_clause,[],[f494,f722]) ).
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,[],[f416]) ).
fof(f416,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f160]) ).
fof(f720,plain,
spl94_39,
inference(avatar_split_clause,[],[f492,f718]) ).
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,[],[f417]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f160]) ).
fof(f716,plain,
spl94_38,
inference(avatar_split_clause,[],[f411,f714]) ).
fof(f411,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f90]) ).
fof(f90,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',unknown) ).
fof(f712,plain,
spl94_37,
inference(avatar_split_clause,[],[f308,f710]) ).
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',unknown) ).
fof(f708,plain,
spl94_36,
inference(avatar_split_clause,[],[f306,f706]) ).
fof(f706,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',unknown) ).
fof(f704,plain,
spl94_35,
inference(avatar_split_clause,[],[f304,f702]) ).
fof(f702,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',unknown) ).
fof(f699,plain,
spl94_34,
inference(avatar_split_clause,[],[f531,f697]) ).
fof(f531,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f530]) ).
fof(f530,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f529]) ).
fof(f529,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f528]) ).
fof(f528,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f527]) ).
fof(f527,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',unknown) ).
fof(f695,plain,
spl94_33,
inference(avatar_split_clause,[],[f488,f693]) ).
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,[],[f412]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,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',unknown) ).
fof(f691,plain,
spl94_32,
inference(avatar_split_clause,[],[f483,f689]) ).
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',unknown) ).
fof(f687,plain,
spl94_31,
inference(avatar_split_clause,[],[f368,f685]) ).
fof(f685,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',unknown) ).
fof(f683,plain,
spl94_30,
inference(avatar_split_clause,[],[f335,f681]) ).
fof(f681,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(f679,plain,
spl94_29,
inference(avatar_split_clause,[],[f334,f677]) ).
fof(f677,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(f675,plain,
spl94_28,
inference(avatar_split_clause,[],[f330,f673]) ).
fof(f673,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(f671,plain,
spl94_27,
inference(avatar_split_clause,[],[f329,f669]) ).
fof(f669,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(f667,plain,
spl94_26,
inference(avatar_split_clause,[],[f325,f665]) ).
fof(f665,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(f663,plain,
spl94_25,
inference(avatar_split_clause,[],[f320,f661]) ).
fof(f661,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(f659,plain,
spl94_24,
inference(avatar_split_clause,[],[f315,f657]) ).
fof(f657,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(f655,plain,
spl94_23,
inference(avatar_split_clause,[],[f511,f653]) ).
fof(f511,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f510]) ).
fof(f510,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f509]) ).
fof(f509,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(f651,plain,
spl94_22,
inference(avatar_split_clause,[],[f343,f649]) ).
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',unknown) ).
fof(f647,plain,
spl94_21,
inference(avatar_split_clause,[],[f342,f645]) ).
fof(f645,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',unknown) ).
fof(f643,plain,
spl94_20,
inference(avatar_split_clause,[],[f331,f641]) ).
fof(f641,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(f639,plain,
spl94_19,
inference(avatar_split_clause,[],[f321,f637]) ).
fof(f321,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f635,plain,
spl94_18,
inference(avatar_split_clause,[],[f481,f633]) ).
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',unknown) ).
fof(f631,plain,
spl94_17,
inference(avatar_split_clause,[],[f478,f629]) ).
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',unknown) ).
fof(f627,plain,
spl94_16,
inference(avatar_split_clause,[],[f465,f625]) ).
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',unknown) ).
fof(f623,plain,
spl94_15,
inference(avatar_split_clause,[],[f463,f621]) ).
fof(f621,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',unknown) ).
fof(f619,plain,
spl94_14,
inference(avatar_split_clause,[],[f461,f617]) ).
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',unknown) ).
fof(f615,plain,
spl94_13,
inference(avatar_split_clause,[],[f486,f613]) ).
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(f611,plain,
spl94_12,
inference(avatar_split_clause,[],[f469,f609]) ).
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',unknown) ).
fof(f607,plain,
spl94_11,
inference(avatar_split_clause,[],[f452,f605]) ).
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',unknown) ).
fof(f603,plain,
spl94_10,
inference(avatar_split_clause,[],[f301,f601]) ).
fof(f601,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',unknown) ).
fof(f599,plain,
spl94_9,
inference(avatar_split_clause,[],[f300,f597]) ).
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',unknown) ).
fof(f595,plain,
spl94_8,
inference(avatar_split_clause,[],[f459,f593]) ).
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',unknown) ).
fof(f591,plain,
spl94_7,
inference(avatar_split_clause,[],[f454,f589]) ).
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',unknown) ).
fof(f587,plain,
spl94_6,
inference(avatar_split_clause,[],[f453,f585]) ).
fof(f585,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',unknown) ).
fof(f583,plain,
~ spl94_5,
inference(avatar_split_clause,[],[f448,f580]) ).
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',unknown) ).
fof(f578,plain,
~ spl94_4,
inference(avatar_split_clause,[],[f447,f575]) ).
fof(f575,plain,
( spl94_4
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_4])]) ).
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',unknown) ).
fof(f573,plain,
~ spl94_3,
inference(avatar_split_clause,[],[f296,f570]) ).
fof(f296,plain,
~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK19),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK19)
& vtcheck(vbind(sK16,sK14,sK15),vvar(sK18),sK19)
& vtcheck(sK15,sK17,sK14) ),
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(X1,vsubst(X2,X3,vvar(X4)),X5)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5)
& vtcheck(X1,X3,X0) )
=> ( ~ vtcheck(sK15,vsubst(sK16,sK17,vvar(sK18)),sK19)
& vtcheck(vbind(sK16,sK14,sK15),vvar(sK18),sK19)
& vtcheck(sK15,sK17,sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5)
& vtcheck(X1,X3,X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5)
& vtcheck(vbind(X2,X0,X1),vvar(X4),X5)
& vtcheck(X1,X3,X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f60,plain,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(vbind(X2,X0,X1),vvar(X4),X5)
& vtcheck(X1,X3,X0) )
=> vtcheck(X1,vsubst(X2,X3,vvar(X4)),X5) ),
inference(rectify,[],[f59]) ).
fof(f59,negated_conjecture,
~ ! [X14,X19,X8,X10,X20,X33] :
( ( vtcheck(vbind(X8,X14,X19),vvar(X20),X33)
& vtcheck(X19,X10,X14) )
=> vtcheck(X19,vsubst(X8,X10,vvar(X20)),X33) ),
inference(negated_conjecture,[],[f58]) ).
fof(f58,conjecture,
! [X14,X19,X8,X10,X20,X33] :
( ( vtcheck(vbind(X8,X14,X19),vvar(X20),X33)
& vtcheck(X19,X10,X14) )
=> vtcheck(X19,vsubst(X8,X10,vvar(X20)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
fof(f568,plain,
spl94_2,
inference(avatar_split_clause,[],[f295,f565]) ).
fof(f295,plain,
vtcheck(vbind(sK16,sK14,sK15),vvar(sK18),sK19),
inference(cnf_transformation,[],[f220]) ).
fof(f563,plain,
spl94_1,
inference(avatar_split_clause,[],[f294,f560]) ).
fof(f294,plain,
vtcheck(sK15,sK17,sK14),
inference(cnf_transformation,[],[f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM135+1 : TPTP v8.2.0. Released v6.4.0.
% 0.03/0.12 % Command : run_vampire %s %d SAT
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 23:44:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.12/0.35 Running first-order model finding
% 0.12/0.35 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26043)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26045)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (3000ds/115Mi)
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26042)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (3000ds/152523Mi)
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26041)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26044)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (3000ds/146Mi)
% 0.19/0.41 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.41 % (26040)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:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.19/0.43 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.43 % (26039)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.19/0.43 TRYING [1]
% 0.19/0.44 TRYING [2]
% 0.19/0.46 % (26043)Instruction limit reached!
% 0.19/0.46 % (26043)------------------------------
% 0.19/0.46 % (26043)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.46 % (26043)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.46 % (26043)Termination reason: Time limit
% 0.19/0.46 % (26043)Termination phase: Saturation
% 0.19/0.46
% 0.19/0.46 % (26043)Memory used [KB]: 1918
% 0.19/0.46 % (26043)Time elapsed: 0.046 s
% 0.19/0.46 % (26043)Instructions burned: 104 (million)
% 0.19/0.46 TRYING [3]
% 0.19/0.47 % (26045)Instruction limit reached!
% 0.19/0.47 % (26045)------------------------------
% 0.19/0.47 % (26045)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.47 % (26045)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.47 % (26045)Termination reason: Time limit
% 0.19/0.47 % (26045)Termination phase: Saturation
% 0.19/0.47
% 0.19/0.47 % (26045)Memory used [KB]: 2592
% 0.19/0.47 % (26045)Time elapsed: 0.059 s
% 0.19/0.47 % (26045)Instructions burned: 115 (million)
% 0.19/0.48 Cannot represent all propositional literals internally
% 0.19/0.48 % (26042)Refutation not found, incomplete strategy% (26042)------------------------------
% 0.19/0.48 % (26042)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.48 % (26042)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.48 % (26042)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.48
% 0.19/0.48 % (26042)Memory used [KB]: 2213
% 0.19/0.48 % (26042)Time elapsed: 0.071 s
% 0.19/0.48 % (26042)Instructions burned: 149 (million)
% 0.19/0.48 % (26042)------------------------------
% 0.19/0.48 % (26042)------------------------------
% 0.19/0.49 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.49 % (26046)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2999ds/404Mi)
% 0.19/0.50 % (26044)Instruction limit reached!
% 0.19/0.50 % (26044)------------------------------
% 0.19/0.50 % (26044)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.19/0.50 % (26044)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.19/0.50 % (26044)Termination reason: Time limit
% 0.19/0.50 % (26044)Termination phase: Saturation
% 0.19/0.50
% 0.19/0.50 % (26044)Memory used [KB]: 2761
% 0.19/0.50 % (26044)Time elapsed: 0.083 s
% 0.19/0.50 % (26044)Instructions burned: 147 (million)
% 0.19/0.51 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.51 % (26047)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 0.19/0.52 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.52 % (26048)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 0.19/0.53 % (26038)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.53 % (26049)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2998ds/900Mi)
% 1.46/0.56 % (26047)Instruction limit reached!
% 1.46/0.56 % (26047)------------------------------
% 1.46/0.56 % (26047)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.46/0.56 % (26047)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.46/0.56 % (26047)Termination reason: Time limit
% 1.46/0.56 % (26047)Termination phase: Saturation
% 1.46/0.56
% 1.46/0.56 % (26047)Memory used [KB]: 3330
% 1.46/0.56 % (26047)Time elapsed: 0.057 s
% 1.46/0.56 % (26047)Instructions burned: 176 (million)
% 1.61/0.60 % (26038)Running in auto input_syntax mode. Trying TPTP
% 1.61/0.60 % (26050)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2998ds/7859Mi)
% 1.61/0.61 TRYING [1]
% 1.61/0.61 TRYING [2]
% 1.61/0.62 % (26048)Instruction limit reached!
% 1.61/0.62 % (26048)------------------------------
% 1.61/0.62 % (26048)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.61/0.62 % (26048)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.61/0.62 % (26048)Termination reason: Time limit
% 1.61/0.62 % (26048)Termination phase: Saturation
% 1.61/0.62 % (26046)Instruction limit reached!
% 1.61/0.62 % (26046)------------------------------
% 1.61/0.62 % (26046)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.61/0.62
% 1.61/0.62 % (26048)Memory used [KB]: 4148
% 1.61/0.62 % (26048)Time elapsed: 0.094 s
% 1.61/0.62 % (26048)Instructions burned: 270 (million)
% 1.61/0.62 % (26046)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.61/0.62 % (26046)Termination reason: Time limit
% 1.61/0.62 % (26046)Termination phase: Saturation
% 1.61/0.62
% 1.61/0.62 % (26046)Memory used [KB]: 4047
% 1.61/0.62 % (26046)Time elapsed: 0.127 s
% 1.61/0.62 % (26046)Instructions burned: 406 (million)
% 1.94/0.63 TRYING [3]
% 2.05/0.66 % (26038)Running in auto input_syntax mode. Trying TPTP
% 2.05/0.66 % (26051)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2997ds/2145Mi)
% 2.05/0.66 % (26038)Running in auto input_syntax mode. Trying TPTP
% 2.05/0.66 % (26052)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2997ds/1187Mi)
% 2.05/0.69 TRYING [4]
% 2.51/0.84 % (26049)Instruction limit reached!
% 2.51/0.84 % (26049)------------------------------
% 2.51/0.84 % (26049)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.51/0.84 % (26049)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.51/0.84 % (26049)Termination reason: Time limit
% 2.51/0.84 % (26049)Termination phase: Saturation
% 2.51/0.84
% 2.51/0.84 % (26049)Memory used [KB]: 9279
% 2.51/0.84 % (26049)Time elapsed: 0.305 s
% 2.51/0.84 % (26049)Instructions burned: 900 (million)
% 2.82/0.85 % (26040)First to succeed.
% 2.82/0.86 % (26040)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26038"
% 2.82/0.87 % (26038)Running in auto input_syntax mode. Trying TPTP
% 2.82/0.87 % (26040)Refutation found. Thanks to Tanya!
% 2.82/0.87 % SZS status Theorem for theBenchmark
% 2.82/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.91/0.88 % (26040)------------------------------
% 2.91/0.88 % (26040)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 2.91/0.88 % (26040)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 2.91/0.88 % (26040)Termination reason: Refutation
% 2.91/0.88
% 2.91/0.88 % (26040)Memory used [KB]: 10026
% 2.91/0.88 % (26040)Time elapsed: 0.451 s
% 2.91/0.88 % (26040)Instructions burned: 1227 (million)
% 2.91/0.88 % (26040)------------------------------
% 2.91/0.88 % (26040)------------------------------
% 2.91/0.88 % (26038)Success in time 0.507 s
%------------------------------------------------------------------------------