TSTP Solution File: COM125+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM125+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:48:29 EDT 2024
% Result : Theorem 0.21s 0.48s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 301
% Syntax : Number of formulae : 1075 ( 183 unt; 0 def)
% Number of atoms : 3898 (1972 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 4216 (1393 ~;1641 |; 765 &)
% ( 208 <=>; 209 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 229 ( 227 usr; 209 prp; 0-4 aty)
% Number of functors : 97 ( 97 usr; 10 con; 0-4 aty)
% Number of variables : 3852 (3282 !; 570 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2161,plain,
$false,
inference(avatar_sat_refutation,[],[f574,f579,f584,f589,f594,f598,f602,f606,f610,f614,f618,f622,f626,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f674,f678,f682,f686,f690,f694,f698,f702,f706,f710,f715,f719,f723,f727,f731,f735,f744,f748,f752,f756,f760,f764,f768,f772,f776,f784,f788,f792,f796,f800,f804,f808,f812,f816,f820,f824,f828,f840,f846,f850,f854,f858,f862,f866,f870,f874,f878,f882,f886,f890,f894,f898,f902,f906,f910,f914,f918,f922,f926,f930,f934,f955,f959,f963,f967,f971,f975,f979,f986,f990,f994,f998,f1002,f1011,f1015,f1019,f1023,f1027,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1075,f1079,f1083,f1087,f1123,f1127,f1136,f1144,f1148,f1156,f1160,f1164,f1168,f1172,f1177,f1181,f1192,f1205,f1209,f1224,f1228,f1232,f1253,f1258,f1262,f1266,f1270,f1274,f1278,f1282,f1306,f1316,f1328,f1329,f1333,f1337,f1347,f1356,f1360,f1369,f1389,f1401,f1406,f1418,f1423,f1428,f1433,f1437,f1446,f1451,f1455,f1459,f1464,f1468,f1472,f1476,f1581,f1586,f1591,f1595,f1615,f1619,f1623,f1640,f1644,f1694,f1698,f1702,f1770,f1774,f1778,f1782,f1786,f1830,f1865,f1869,f1903,f1917,f1922,f1926,f1930,f1978,f2017,f2021,f2025,f2031,f2074,f2078,f2082,f2091,f2096,f2100,f2126,f2130,f2156,f2160]) ).
fof(f2160,plain,
( ~ spl94_23
| ~ spl94_204 ),
inference(avatar_contradiction_clause,[],[f2157]) ).
fof(f2157,plain,
( $false
| ~ spl94_23
| ~ spl94_204 ),
inference(resolution,[],[f2095,f665]) ).
fof(f665,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl94_23 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f664,plain,
( spl94_23
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_23])]) ).
fof(f2095,plain,
( visFreeVar(sK14,vabs(sK14,sK18,veabs))
| ~ spl94_204 ),
inference(avatar_component_clause,[],[f2093]) ).
fof(f2093,plain,
( spl94_204
<=> visFreeVar(sK14,vabs(sK14,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_204])]) ).
fof(f2156,plain,
( spl94_208
| ~ spl94_101
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1128,f1121,f1017,f2154]) ).
fof(f2154,plain,
( spl94_208
<=> ! [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_208])]) ).
fof(f1017,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(f1121,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(f1128,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,[],[f1122,f1018]) ).
fof(f1018,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0 )
| ~ spl94_101 ),
inference(avatar_component_clause,[],[f1017]) ).
fof(f1122,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,[],[f1121]) ).
fof(f2130,plain,
( spl94_207
| ~ spl94_41
| ~ spl94_136 ),
inference(avatar_split_clause,[],[f1239,f1230,f742,f2128]) ).
fof(f2128,plain,
( spl94_207
<=> ! [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_207])]) ).
fof(f742,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(f1230,plain,
( spl94_136
<=> ! [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_136])]) ).
fof(f1239,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_136 ),
inference(resolution,[],[f1231,f743]) ).
fof(f743,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl94_41 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f1231,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_136 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f2126,plain,
( spl94_206
| ~ spl94_93
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1032,f1021,f977,f2124]) ).
fof(f2124,plain,
( spl94_206
<=> ! [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_206])]) ).
fof(f977,plain,
( spl94_93
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_93])]) ).
fof(f1021,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(f1032,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_93
| ~ spl94_102 ),
inference(superposition,[],[f1022,f978]) ).
fof(f978,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl94_93 ),
inference(avatar_component_clause,[],[f977]) ).
fof(f1022,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl94_102 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f2100,plain,
( spl94_205
| ~ spl94_118
| ~ spl94_144 ),
inference(avatar_split_clause,[],[f1297,f1280,f1125,f2098]) ).
fof(f2098,plain,
( spl94_205
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X0,X3,veabs),X4)
| visFreeVar(X0,vabs(X0,X3,veabs))
| vtcheck(vbind(X0,X5,X2),vabs(X0,X3,veabs),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_205])]) ).
fof(f1125,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(f1280,plain,
( spl94_144
<=> ! [X3,X4,X5,X2,X1] :
( vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X3,vabs(X3,X4,veabs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_144])]) ).
fof(f1297,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X0,X3,veabs),X4)
| visFreeVar(X0,vabs(X0,X3,veabs))
| vtcheck(vbind(X0,X5,X2),vabs(X0,X3,veabs),X4) )
| ~ spl94_118
| ~ spl94_144 ),
inference(resolution,[],[f1281,f1126]) ).
fof(f1126,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,[],[f1125]) ).
fof(f1281,plain,
( ! [X2,X3,X1,X4,X5] :
( vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X3,vabs(X3,X4,veabs)) )
| ~ spl94_144 ),
inference(avatar_component_clause,[],[f1280]) ).
fof(f2096,plain,
( spl94_204
| ~ spl94_171
| ~ spl94_144
| spl94_192 ),
inference(avatar_split_clause,[],[f2026,f1919,f1280,f1583,f2093]) ).
fof(f1583,plain,
( spl94_171
<=> vtcheck(sK16,vabs(sK14,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_171])]) ).
fof(f1919,plain,
( spl94_192
<=> vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_192])]) ).
fof(f2026,plain,
( ~ vtcheck(sK16,vabs(sK14,sK18,veabs),sK19)
| visFreeVar(sK14,vabs(sK14,sK18,veabs))
| ~ spl94_144
| spl94_192 ),
inference(resolution,[],[f1921,f1281]) ).
fof(f1921,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19)
| spl94_192 ),
inference(avatar_component_clause,[],[f1919]) ).
fof(f2091,plain,
( spl94_203
| ~ spl94_42
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1214,f1190,f746,f2089]) ).
fof(f2089,plain,
( spl94_203
<=> ! [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_203])]) ).
fof(f746,plain,
( spl94_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_42])]) ).
fof(f1190,plain,
( 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(f1214,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,[],[f1191,f747]) ).
fof(f747,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl94_42 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f1191,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,[],[f1190]) ).
fof(f2082,plain,
( spl94_202
| spl94_4
| ~ spl94_33
| ~ spl94_121 ),
inference(avatar_split_clause,[],[f1152,f1146,f704,f586,f2080]) ).
fof(f2080,plain,
( spl94_202
<=> ! [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_202])]) ).
fof(f586,plain,
( spl94_4
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_4])]) ).
fof(f704,plain,
( spl94_33
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_33])]) ).
fof(f1146,plain,
( spl94_121
<=> ! [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_121])]) ).
fof(f1152,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_121 ),
inference(superposition,[],[f1147,f705]) ).
fof(f705,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl94_33 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1147,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl94_121 ),
inference(avatar_component_clause,[],[f1146]) ).
fof(f2078,plain,
( spl94_201
| ~ spl94_93
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1132,f1121,f977,f2076]) ).
fof(f2076,plain,
( spl94_201
<=> ! [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_201])]) ).
fof(f1132,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_93
| ~ spl94_117 ),
inference(superposition,[],[f1122,f978]) ).
fof(f2074,plain,
( spl94_200
| ~ spl94_101
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1028,f1021,f1017,f2072]) ).
fof(f2072,plain,
( spl94_200
<=> ! [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_200])]) ).
fof(f1028,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,[],[f1022,f1018]) ).
fof(f2031,plain,
( spl94_199
| ~ spl94_113
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1140,f1125,f1073,f2029]) ).
fof(f2029,plain,
( spl94_199
<=> ! [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_199])]) ).
fof(f1073,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(f1140,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,[],[f1126,f1074]) ).
fof(f1074,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,[],[f1073]) ).
fof(f2025,plain,
( spl94_198
| ~ spl94_96
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1099,f1081,f992,f2023]) ).
fof(f2023,plain,
( spl94_198
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(veabs,X3),X5)
| ~ vtcheck(X2,veabs,varrow(X4,X5))
| visFreeVar(X0,veabs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_198])]) ).
fof(f992,plain,
( spl94_96
<=> ! [X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| visFreeVar(X0,veabs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_96])]) ).
fof(f1081,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(f1099,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(veabs,X3),X5)
| ~ vtcheck(X2,veabs,varrow(X4,X5))
| visFreeVar(X0,veabs) )
| ~ spl94_96
| ~ spl94_115 ),
inference(resolution,[],[f1082,f993]) ).
fof(f993,plain,
( ! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| visFreeVar(X0,veabs) )
| ~ spl94_96 ),
inference(avatar_component_clause,[],[f992]) ).
fof(f1082,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,[],[f1081]) ).
fof(f2021,plain,
( spl94_197
| ~ spl94_93
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1095,f1077,f977,f2019]) ).
fof(f2019,plain,
( spl94_197
<=> ! [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_197])]) ).
fof(f1077,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(f1095,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_93
| ~ spl94_114 ),
inference(superposition,[],[f1078,f978]) ).
fof(f1078,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,[],[f1077]) ).
fof(f2017,plain,
( spl94_196
| ~ spl94_97
| ~ spl94_113 ),
inference(avatar_split_clause,[],[f1092,f1073,f996,f2015]) ).
fof(f2015,plain,
( spl94_196
<=> ! [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_196])]) ).
fof(f996,plain,
( spl94_97
<=> ! [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_97])]) ).
fof(f1092,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_97
| ~ spl94_113 ),
inference(resolution,[],[f1074,f997]) ).
fof(f997,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl94_97 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1978,plain,
( spl94_195
| ~ spl94_23
| ~ spl94_136 ),
inference(avatar_split_clause,[],[f1238,f1230,f664,f1976]) ).
fof(f1976,plain,
( spl94_195
<=> ! [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_195])]) ).
fof(f1238,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_136 ),
inference(resolution,[],[f1231,f665]) ).
fof(f1930,plain,
( spl94_194
| ~ spl94_96
| ~ spl94_142 ),
inference(avatar_split_clause,[],[f1286,f1272,f992,f1928]) ).
fof(f1928,plain,
( spl94_194
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),veabs,X5)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),veabs,X5)
| visFreeVar(X2,veabs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_194])]) ).
fof(f1272,plain,
( spl94_142
<=> ! [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_142])]) ).
fof(f1286,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),veabs,X5)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),veabs,X5)
| visFreeVar(X2,veabs) )
| ~ spl94_96
| ~ spl94_142 ),
inference(resolution,[],[f1273,f993]) ).
fof(f1273,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_142 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f1926,plain,
( spl94_193
| ~ spl94_97
| ~ spl94_137 ),
inference(avatar_split_clause,[],[f1283,f1251,f996,f1924]) ).
fof(f1924,plain,
( spl94_193
<=> ! [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_193])]) ).
fof(f1251,plain,
( spl94_137
<=> ! [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_137])]) ).
fof(f1283,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_97
| ~ spl94_137 ),
inference(resolution,[],[f1252,f997]) ).
fof(f1252,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_137 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f1922,plain,
( ~ spl94_192
| spl94_5
| ~ spl94_86 ),
inference(avatar_split_clause,[],[f1363,f948,f591,f1919]) ).
fof(f591,plain,
( spl94_5
<=> vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_5])]) ).
fof(f948,plain,
( spl94_86
<=> sK14 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_86])]) ).
fof(f1363,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK14,sK18,veabs),sK19)
| spl94_5
| ~ spl94_86 ),
inference(superposition,[],[f593,f950]) ).
fof(f950,plain,
( sK14 = sK17
| ~ spl94_86 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f593,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
| spl94_5 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f1917,plain,
( spl94_191
| ~ spl94_32
| ~ spl94_136 ),
inference(avatar_split_clause,[],[f1240,f1230,f700,f1915]) ).
fof(f1915,plain,
( spl94_191
<=> ! [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_191])]) ).
fof(f700,plain,
( spl94_32
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_32])]) ).
fof(f1240,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_136 ),
inference(resolution,[],[f1231,f701]) ).
fof(f701,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl94_32 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f1903,plain,
( spl94_190
| ~ spl94_43
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1212,f1190,f750,f1901]) ).
fof(f1901,plain,
( spl94_190
<=> ! [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_190])]) ).
fof(f750,plain,
( spl94_43
<=> ! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_43])]) ).
fof(f1212,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,[],[f1191,f751]) ).
fof(f751,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK55(X0,X1,X2) = X2 )
| ~ spl94_43 ),
inference(avatar_component_clause,[],[f750]) ).
fof(f1869,plain,
( spl94_189
| spl94_4
| ~ spl94_16
| ~ spl94_120 ),
inference(avatar_split_clause,[],[f1149,f1142,f636,f586,f1867]) ).
fof(f1867,plain,
( spl94_189
<=> ! [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_189])]) ).
fof(f636,plain,
( spl94_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_16])]) ).
fof(f1142,plain,
( spl94_120
<=> ! [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_120])]) ).
fof(f1149,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_120 ),
inference(superposition,[],[f1143,f637]) ).
fof(f637,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl94_16 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f1143,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 )
| ~ spl94_120 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1865,plain,
( spl94_188
| ~ spl94_42
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1031,f1021,f746,f1863]) ).
fof(f1863,plain,
( spl94_188
<=> ! [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_188])]) ).
fof(f1031,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,[],[f1022,f747]) ).
fof(f1830,plain,
( spl94_187
| ~ spl94_11
| ~ spl94_136 ),
inference(avatar_split_clause,[],[f1242,f1230,f616,f1828]) ).
fof(f1828,plain,
( spl94_187
<=> ! [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_187])]) ).
fof(f616,plain,
( spl94_11
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_11])]) ).
fof(f1242,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_136 ),
inference(resolution,[],[f1231,f617]) ).
fof(f617,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl94_11 ),
inference(avatar_component_clause,[],[f616]) ).
fof(f1786,plain,
( spl94_186
| ~ spl94_19
| ~ spl94_145 ),
inference(avatar_split_clause,[],[f1312,f1304,f648,f1784]) ).
fof(f1784,plain,
( spl94_186
<=> ! [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_186])]) ).
fof(f648,plain,
( spl94_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_19])]) ).
fof(f1304,plain,
( spl94_145
<=> ! [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_145])]) ).
fof(f1312,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl94_19
| ~ spl94_145 ),
inference(duplicate_literal_removal,[],[f1309]) ).
fof(f1309,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_145 ),
inference(resolution,[],[f1305,f649]) ).
fof(f649,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl94_19 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f1305,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_145 ),
inference(avatar_component_clause,[],[f1304]) ).
fof(f1782,plain,
( spl94_185
| ~ spl94_42
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1131,f1121,f746,f1780]) ).
fof(f1780,plain,
( spl94_185
<=> ! [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_185])]) ).
fof(f1131,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,[],[f1122,f747]) ).
fof(f1778,plain,
( spl94_184
| ~ spl94_60
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1117,f1085,f822,f1776]) ).
fof(f1776,plain,
( spl94_184
<=> ! [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_184])]) ).
fof(f822,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(f1085,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(f1117,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,[],[f823,f1086]) ).
fof(f1086,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,[],[f1085]) ).
fof(f823,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl94_60 ),
inference(avatar_component_clause,[],[f822]) ).
fof(f1774,plain,
( spl94_183
| ~ spl94_113
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1098,f1081,f1073,f1772]) ).
fof(f1772,plain,
( spl94_183
<=> ! [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_183])]) ).
fof(f1098,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,[],[f1082,f1074]) ).
fof(f1770,plain,
( spl94_182
| ~ spl94_105
| ~ spl94_115 ),
inference(avatar_split_clause,[],[f1097,f1081,f1038,f1768]) ).
fof(f1768,plain,
( spl94_182
<=> ! [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_182])]) ).
fof(f1038,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(f1097,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,[],[f1082,f1039]) ).
fof(f1039,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,[],[f1038]) ).
fof(f1702,plain,
( spl94_181
| ~ spl94_43
| ~ spl94_117 ),
inference(avatar_split_clause,[],[f1129,f1121,f750,f1700]) ).
fof(f1700,plain,
( spl94_181
<=> ! [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_181])]) ).
fof(f1129,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,[],[f1122,f751]) ).
fof(f1698,plain,
( spl94_180
| ~ spl94_83
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1105,f1085,f924,f1696]) ).
fof(f1696,plain,
( spl94_180
<=> ! [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_180])]) ).
fof(f924,plain,
( spl94_83
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_83])]) ).
fof(f1105,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3))
| ~ spl94_83
| ~ spl94_116 ),
inference(superposition,[],[f1086,f925]) ).
fof(f925,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl94_83 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f1694,plain,
( spl94_179
| ~ spl94_83
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1102,f1085,f924,f1692]) ).
fof(f1692,plain,
( spl94_179
<=> ! [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_179])]) ).
fof(f1102,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4))
| ~ spl94_83
| ~ spl94_116 ),
inference(superposition,[],[f1086,f925]) ).
fof(f1644,plain,
( spl94_178
| ~ spl94_61
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1104,f1085,f826,f1642]) ).
fof(f1642,plain,
( spl94_178
<=> ! [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_178])]) ).
fof(f826,plain,
( spl94_61
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_61])]) ).
fof(f1104,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,[],[f1086,f827]) ).
fof(f827,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl94_61 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f1640,plain,
( spl94_177
| ~ spl94_61
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1101,f1085,f826,f1638]) ).
fof(f1638,plain,
( spl94_177
<=> ! [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_177])]) ).
fof(f1101,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,[],[f1086,f827]) ).
fof(f1623,plain,
( spl94_176
| ~ spl94_96
| ~ spl94_118 ),
inference(avatar_split_clause,[],[f1137,f1125,f992,f1621]) ).
fof(f1621,plain,
( spl94_176
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(vbind(X0,X4,X2),veabs,X3)
| visFreeVar(X0,veabs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_176])]) ).
fof(f1137,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(vbind(X0,X4,X2),veabs,X3)
| visFreeVar(X0,veabs) )
| ~ spl94_96
| ~ spl94_118 ),
inference(resolution,[],[f1126,f993]) ).
fof(f1619,plain,
( spl94_175
| ~ spl94_43
| ~ spl94_102 ),
inference(avatar_split_clause,[],[f1029,f1021,f750,f1617]) ).
fof(f1617,plain,
( spl94_175
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_175])]) ).
fof(f1029,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK55(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl94_43
| ~ spl94_102 ),
inference(resolution,[],[f1022,f751]) ).
fof(f1615,plain,
( spl94_174
| ~ spl94_59
| ~ spl94_93 ),
inference(avatar_split_clause,[],[f982,f977,f818,f1613]) ).
fof(f1613,plain,
( spl94_174
<=> ! [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_174])]) ).
fof(f818,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(f982,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl94_59
| ~ spl94_93 ),
inference(superposition,[],[f819,f978]) ).
fof(f819,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl94_59 ),
inference(avatar_component_clause,[],[f818]) ).
fof(f1595,plain,
( spl94_173
| ~ spl94_49
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1114,f1085,f774,f1593]) ).
fof(f1593,plain,
( spl94_173
<=> ! [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_173])]) ).
fof(f774,plain,
( spl94_49
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_49])]) ).
fof(f1114,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,[],[f775,f1086]) ).
fof(f775,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl94_49 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f1591,plain,
( spl94_172
| ~ spl94_47
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1111,f1085,f766,f1589]) ).
fof(f1589,plain,
( spl94_172
<=> ! [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_172])]) ).
fof(f766,plain,
( spl94_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_47])]) ).
fof(f1111,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,[],[f767,f1086]) ).
fof(f767,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl94_47 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f1586,plain,
( spl94_171
| ~ spl94_2
| ~ spl94_86 ),
inference(avatar_split_clause,[],[f1364,f948,f576,f1583]) ).
fof(f576,plain,
( spl94_2
<=> vtcheck(sK16,vabs(sK17,sK18,veabs),sK19) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_2])]) ).
fof(f1364,plain,
( vtcheck(sK16,vabs(sK14,sK18,veabs),sK19)
| ~ spl94_2
| ~ spl94_86 ),
inference(superposition,[],[f578,f950]) ).
fof(f578,plain,
( vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
| ~ spl94_2 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f1581,plain,
( spl94_170
| spl94_4
| ~ spl94_16
| ~ spl94_98 ),
inference(avatar_split_clause,[],[f1006,f1000,f636,f586,f1579]) ).
fof(f1579,plain,
( spl94_170
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_170])]) ).
fof(f1000,plain,
( spl94_98
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_98])]) ).
fof(f1006,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl94_16
| ~ spl94_98 ),
inference(superposition,[],[f1001,f637]) ).
fof(f1001,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl94_98 ),
inference(avatar_component_clause,[],[f1000]) ).
fof(f1476,plain,
( spl94_169
| ~ spl94_18
| ~ spl94_129 ),
inference(avatar_split_clause,[],[f1213,f1190,f644,f1474]) ).
fof(f1474,plain,
( spl94_169
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_169])]) ).
fof(f644,plain,
( spl94_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_18])]) ).
fof(f1213,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK61(X0,vempty,vnoType) = X0 )
| ~ spl94_18
| ~ spl94_129 ),
inference(superposition,[],[f1191,f645]) ).
fof(f645,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl94_18 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f1472,plain,
( spl94_168
| ~ spl94_40
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1110,f1085,f733,f1470]) ).
fof(f1470,plain,
( spl94_168
<=> ! [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_168])]) ).
fof(f733,plain,
( spl94_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_40])]) ).
fof(f1110,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,[],[f734,f1086]) ).
fof(f734,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl94_40 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f1468,plain,
( spl94_167
| ~ spl94_39
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1109,f1085,f729,f1466]) ).
fof(f1466,plain,
( spl94_167
<=> ! [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_167])]) ).
fof(f729,plain,
( spl94_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_39])]) ).
fof(f1109,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,[],[f730,f1086]) ).
fof(f730,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl94_39 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f1464,plain,
( spl94_166
| ~ spl94_86
| ~ spl94_130 ),
inference(avatar_split_clause,[],[f1362,f1194,f948,f1461]) ).
fof(f1461,plain,
( spl94_166
<=> sP6(sK16,sK19,vabs(sK14,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_166])]) ).
fof(f1194,plain,
( spl94_130
<=> sP6(sK16,sK19,vabs(sK17,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_130])]) ).
fof(f1362,plain,
( sP6(sK16,sK19,vabs(sK14,sK18,veabs))
| ~ spl94_86
| ~ spl94_130 ),
inference(superposition,[],[f1196,f950]) ).
fof(f1196,plain,
( sP6(sK16,sK19,vabs(sK17,sK18,veabs))
| ~ spl94_130 ),
inference(avatar_component_clause,[],[f1194]) ).
fof(f1459,plain,
( spl94_165
| ~ spl94_34
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1103,f1085,f708,f1457]) ).
fof(f1457,plain,
( spl94_165
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_165])]) ).
fof(f708,plain,
( spl94_34
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_34])]) ).
fof(f1103,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl94_34
| ~ spl94_116 ),
inference(superposition,[],[f1086,f709]) ).
fof(f709,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl94_34 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f1455,plain,
( spl94_164
| ~ spl94_34
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1100,f1085,f708,f1453]) ).
fof(f1453,plain,
( spl94_164
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_164])]) ).
fof(f1100,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl94_34
| ~ spl94_116 ),
inference(superposition,[],[f1086,f709]) ).
fof(f1451,plain,
( spl94_163
| ~ spl94_11
| ~ spl94_82 ),
inference(avatar_split_clause,[],[f942,f920,f616,f1449]) ).
fof(f1449,plain,
( spl94_163
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_163])]) ).
fof(f920,plain,
( spl94_82
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_82])]) ).
fof(f942,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl94_11
| ~ spl94_82 ),
inference(resolution,[],[f921,f617]) ).
fof(f921,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl94_82 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f1446,plain,
( spl94_162
| ~ spl94_42
| ~ spl94_59 ),
inference(avatar_split_clause,[],[f832,f818,f746,f1444]) ).
fof(f1444,plain,
( spl94_162
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_162])]) ).
fof(f832,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl94_42
| ~ spl94_59 ),
inference(superposition,[],[f819,f747]) ).
fof(f1437,plain,
( spl94_161
| ~ spl94_38
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1108,f1085,f725,f1435]) ).
fof(f1435,plain,
( spl94_161
<=> ! [X5,X4,X2,X0,X6,X3,X1] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_161])]) ).
fof(f725,plain,
( spl94_38
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_38])]) ).
fof(f1108,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl94_38
| ~ spl94_116 ),
inference(superposition,[],[f726,f1086]) ).
fof(f726,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl94_38 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f1433,plain,
( spl94_160
| ~ spl94_18
| ~ spl94_114 ),
inference(avatar_split_clause,[],[f1096,f1077,f644,f1431]) ).
fof(f1431,plain,
( spl94_160
<=> ! [X2,X0,X1,X3] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_160])]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl94_18
| ~ spl94_114 ),
inference(trivial_inequality_removal,[],[f1093]) ).
fof(f1093,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl94_18
| ~ spl94_114 ),
inference(superposition,[],[f1078,f645]) ).
fof(f1428,plain,
( ~ spl94_159
| ~ spl94_86
| spl94_132 ),
inference(avatar_split_clause,[],[f1361,f1202,f948,f1425]) ).
fof(f1425,plain,
( spl94_159
<=> sP5(sK16,sK19,vabs(sK14,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_159])]) ).
fof(f1202,plain,
( spl94_132
<=> sP5(sK16,sK19,vabs(sK17,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_132])]) ).
fof(f1361,plain,
( ~ sP5(sK16,sK19,vabs(sK14,sK18,veabs))
| ~ spl94_86
| spl94_132 ),
inference(superposition,[],[f1203,f950]) ).
fof(f1203,plain,
( ~ sP5(sK16,sK19,vabs(sK17,sK18,veabs))
| spl94_132 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1423,plain,
( spl94_158
| ~ spl94_22
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1107,f1085,f660,f1421]) ).
fof(f1421,plain,
( spl94_158
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_158])]) ).
fof(f660,plain,
( spl94_22
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_22])]) ).
fof(f1107,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl94_22
| ~ spl94_116 ),
inference(superposition,[],[f661,f1086]) ).
fof(f661,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl94_22 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f1418,plain,
( spl94_157
| spl94_1
| ~ spl94_136 ),
inference(avatar_split_clause,[],[f1247,f1230,f571,f1416]) ).
fof(f1416,plain,
( spl94_157
<=> ! [X2,X0,X1] :
( vabs(sK14,X0,vsubst(X1,vabs(sK17,sK18,veabs),X2)) = vsubst(X1,vabs(sK17,sK18,veabs),vabs(sK14,X0,X2))
| sK14 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_157])]) ).
fof(f571,plain,
( spl94_1
<=> visFreeVar(sK14,vabs(sK17,sK18,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_1])]) ).
fof(f1247,plain,
( ! [X2,X0,X1] :
( vabs(sK14,X0,vsubst(X1,vabs(sK17,sK18,veabs),X2)) = vsubst(X1,vabs(sK17,sK18,veabs),vabs(sK14,X0,X2))
| sK14 = X1 )
| spl94_1
| ~ spl94_136 ),
inference(resolution,[],[f1231,f573]) ).
fof(f573,plain,
( ~ visFreeVar(sK14,vabs(sK17,sK18,veabs))
| spl94_1 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f1406,plain,
( spl94_156
| ~ spl94_116
| ~ spl94_155 ),
inference(avatar_split_clause,[],[f1402,f1399,f1085,f1404]) ).
fof(f1404,plain,
( spl94_156
<=> ! [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_156])]) ).
fof(f1399,plain,
( spl94_155
<=> ! [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_155])]) ).
fof(f1402,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_155 ),
inference(forward_demodulation,[],[f1400,f1086]) ).
fof(f1400,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_155 ),
inference(avatar_component_clause,[],[f1399]) ).
fof(f1401,plain,
spl94_155,
inference(avatar_split_clause,[],[f484,f1399]) ).
fof(f484,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,[],[f414]) ).
fof(f414,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,[],[f297]) ).
fof(f297,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])],[f295,f296]) ).
fof(f296,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(f295,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,[],[f226]) ).
fof(f226,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,[],[f150,f225,f224,f223,f222,f221]) ).
fof(f221,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(f222,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(f223,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(f224,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(f225,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(f150,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,[],[f149]) ).
fof(f149,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,[],[f88]) ).
fof(f88,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/sandbox2/benchmark/theBenchmark.p','subst-INV') ).
fof(f1389,plain,
spl94_154,
inference(avatar_split_clause,[],[f485,f1387]) ).
fof(f1387,plain,
( spl94_154
<=> ! [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_154])]) ).
fof(f485,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,[],[f413]) ).
fof(f413,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,[],[f297]) ).
fof(f1369,plain,
spl94_153,
inference(avatar_split_clause,[],[f487,f1367]) ).
fof(f1367,plain,
( spl94_153
<=> ! [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_153])]) ).
fof(f487,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,[],[f411]) ).
fof(f411,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,[],[f297]) ).
fof(f1360,plain,
spl94_152,
inference(avatar_split_clause,[],[f486,f1358]) ).
fof(f1358,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)
| 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_152])]) ).
fof(f486,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,[],[f412]) ).
fof(f412,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,[],[f297]) ).
fof(f1356,plain,
spl94_151,
inference(avatar_split_clause,[],[f395,f1354]) ).
fof(f1354,plain,
( spl94_151
<=> ! [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_151])]) ).
fof(f395,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,[],[f282]) ).
fof(f282,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])],[f280,f281]) ).
fof(f281,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(f280,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,[],[f279]) ).
fof(f279,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,[],[f224]) ).
fof(f1347,plain,
spl94_150,
inference(avatar_split_clause,[],[f468,f1345]) ).
fof(f1345,plain,
( spl94_150
<=> ! [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_150])]) ).
fof(f468,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,[],[f345]) ).
fof(f345,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,[],[f252]) ).
fof(f252,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])],[f249,f251,f250]) ).
fof(f250,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(f251,plain,
! [X0,X1] :
( ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
=> ( vnoExp = X1
& vvar(sK44(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f249,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,[],[f214]) ).
fof(f214,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,[],[f131,f213,f212,f211,f210,f209]) ).
fof(f209,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(f210,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(f211,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(f212,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(f213,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(f131,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,[],[f130]) ).
fof(f130,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,[],[f75]) ).
fof(f75,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/sandbox2/benchmark/theBenchmark.p','reduce-INV') ).
fof(f1337,plain,
spl94_149,
inference(avatar_split_clause,[],[f568,f1335]) ).
fof(f1335,plain,
( spl94_149
<=> ! [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_149])]) ).
fof(f568,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,[],[f567]) ).
fof(f567,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,[],[f566]) ).
fof(f566,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,[],[f565]) ).
fof(f565,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,[],[f564]) ).
fof(f564,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,[],[f456]) ).
fof(f456,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,[],[f208]) ).
fof(f208,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,[],[f207]) ).
fof(f207,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,[],[f119]) ).
fof(f119,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/sandbox2/benchmark/theBenchmark.p',subst4) ).
fof(f1333,plain,
spl94_148,
inference(avatar_split_clause,[],[f388,f1331]) ).
fof(f1331,plain,
( spl94_148
<=> ! [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_148])]) ).
fof(f388,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,[],[f278]) ).
fof(f278,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])],[f276,f277]) ).
fof(f277,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(f276,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,[],[f275]) ).
fof(f275,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,[],[f225]) ).
fof(f1329,plain,
( spl94_86
| spl94_1
| ~ spl94_2
| spl94_5
| ~ spl94_146 ),
inference(avatar_split_clause,[],[f1317,f1314,f591,f576,f571,f948]) ).
fof(f1314,plain,
( spl94_146
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_146])]) ).
fof(f1317,plain,
( ~ vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
| visFreeVar(sK14,vabs(sK17,sK18,veabs))
| sK14 = sK17
| spl94_5
| ~ spl94_146 ),
inference(resolution,[],[f1315,f593]) ).
fof(f1315,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 = X3 )
| ~ spl94_146 ),
inference(avatar_component_clause,[],[f1314]) ).
fof(f1328,plain,
spl94_147,
inference(avatar_split_clause,[],[f394,f1326]) ).
fof(f1326,plain,
( spl94_147
<=> ! [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_147])]) ).
fof(f394,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,[],[f282]) ).
fof(f1316,plain,
spl94_146,
inference(avatar_split_clause,[],[f439,f1314]) ).
fof(f439,plain,
! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 = X3 ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 = X3 ),
inference(flattening,[],[f177]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 = X3 ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& X0 != X3 )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f58]) ).
fof(f58,axiom,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& ~ visFreeVar(X8,vabs(X20,X34,veabs))
& X8 != X20 )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-1') ).
fof(f1306,plain,
spl94_145,
inference(avatar_split_clause,[],[f569,f1304]) ).
fof(f569,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,[],[f465]) ).
fof(f465,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,[],[f348]) ).
fof(f348,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,[],[f252]) ).
fof(f1282,plain,
spl94_144,
inference(avatar_split_clause,[],[f517,f1280]) ).
fof(f517,plain,
! [X2,X3,X1,X4,X5] :
( vtcheck(vbind(X3,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X3,vabs(X3,X4,veabs)) ),
inference(equality_resolution,[],[f440]) ).
fof(f440,plain,
! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 != X3 ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 != X3 ),
inference(flattening,[],[f179]) ).
fof(f179,plain,
! [X0,X1,X2,X3,X4,X5] :
( vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
| ~ vtcheck(X2,vabs(X3,X4,veabs),X5)
| visFreeVar(X0,vabs(X3,X4,veabs))
| X0 != X3 ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs))
& X0 = X3 )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& ~ visFreeVar(X8,vabs(X20,X34,veabs))
& X8 = X20 )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-2') ).
fof(f1278,plain,
spl94_143,
inference(avatar_split_clause,[],[f510,f1276]) ).
fof(f1276,plain,
( spl94_143
<=> ! [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_143])]) ).
fof(f510,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,[],[f509]) ).
fof(f509,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,[],[f508]) ).
fof(f508,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,[],[f429]) ).
fof(f429,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,[],[f301]) ).
fof(f301,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])],[f170,f300]) ).
fof(f300,plain,
! [X0] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
=> vabs(sK91(X0),sK92(X0),sK93(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f170,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,[],[f169]) ).
fof(f169,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,[],[f100]) ).
fof(f100,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/sandbox2/benchmark/theBenchmark.p',reduce5) ).
fof(f1274,plain,
spl94_142,
inference(avatar_split_clause,[],[f447,f1272]) ).
fof(f447,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,[],[f190]) ).
fof(f190,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,[],[f189]) ).
fof(f189,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,[],[f110]) ).
fof(f110,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/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
fof(f1270,plain,
spl94_141,
inference(avatar_split_clause,[],[f400,f1268]) ).
fof(f1268,plain,
( spl94_141
<=> ! [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_141])]) ).
fof(f400,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,[],[f286]) ).
fof(f286,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])],[f284,f285]) ).
fof(f285,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(f284,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,[],[f283]) ).
fof(f283,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,[],[f223]) ).
fof(f1266,plain,
spl94_140,
inference(avatar_split_clause,[],[f398,f1264]) ).
fof(f1264,plain,
( spl94_140
<=> ! [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_140])]) ).
fof(f398,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,[],[f286]) ).
fof(f1262,plain,
spl94_139,
inference(avatar_split_clause,[],[f391,f1260]) ).
fof(f1260,plain,
( spl94_139
<=> ! [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_139])]) ).
fof(f391,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,[],[f282]) ).
fof(f1258,plain,
spl94_138,
inference(avatar_split_clause,[],[f385,f1256]) ).
fof(f1256,plain,
( spl94_138
<=> ! [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_138])]) ).
fof(f385,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,[],[f278]) ).
fof(f1253,plain,
spl94_137,
inference(avatar_split_clause,[],[f360,f1251]) ).
fof(f360,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,[],[f260]) ).
fof(f260,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])],[f258,f259]) ).
fof(f259,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(f258,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,[],[f257]) ).
fof(f257,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,[],[f215]) ).
fof(f215,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(f1232,plain,
spl94_136,
inference(avatar_split_clause,[],[f563,f1230]) ).
fof(f563,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,[],[f562]) ).
fof(f562,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,[],[f561]) ).
fof(f561,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,[],[f560]) ).
fof(f560,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,[],[f455]) ).
fof(f455,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,[],[f206]) ).
fof(f206,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,[],[f205]) ).
fof(f205,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,[],[f118]) ).
fof(f118,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/sandbox2/benchmark/theBenchmark.p',subst5) ).
fof(f1228,plain,
spl94_135,
inference(avatar_split_clause,[],[f362,f1226]) ).
fof(f1226,plain,
( spl94_135
<=> ! [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_135])]) ).
fof(f362,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,[],[f263]) ).
fof(f263,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])],[f261,f262]) ).
fof(f262,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(f261,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,[],[f217]) ).
fof(f217,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,[],[f140,f216,f215]) ).
fof(f216,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(f140,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,[],[f139]) ).
fof(f139,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,[],[f82]) ).
fof(f82,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/sandbox2/benchmark/theBenchmark.p','T-inv') ).
fof(f1224,plain,
spl94_134,
inference(avatar_split_clause,[],[f324,f1222]) ).
fof(f1222,plain,
( spl94_134
<=> ! [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_134])]) ).
fof(f324,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,[],[f232]) ).
fof(f232,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])],[f230,f231]) ).
fof(f231,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(f230,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,[],[f229]) ).
fof(f229,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,[],[f213]) ).
fof(f1209,plain,
spl94_133,
inference(avatar_split_clause,[],[f533,f1207]) ).
fof(f1207,plain,
( spl94_133
<=> ! [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_133])]) ).
fof(f533,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,[],[f532]) ).
fof(f532,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,[],[f531]) ).
fof(f531,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,[],[f446]) ).
fof(f446,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,[],[f188]) ).
fof(f188,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,[],[f187]) ).
fof(f187,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,[],[f109]) ).
fof(f109,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/sandbox2/benchmark/theBenchmark.p',reduce2) ).
fof(f1205,plain,
( spl94_130
| spl94_131
| spl94_132
| ~ spl94_2
| ~ spl94_126 ),
inference(avatar_split_clause,[],[f1182,f1170,f576,f1202,f1198,f1194]) ).
fof(f1198,plain,
( spl94_131
<=> vabs(sK17,sK18,veabs) = vvar(sK52(vabs(sK17,sK18,veabs),sK19,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_131])]) ).
fof(f1170,plain,
( spl94_126
<=> ! [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_126])]) ).
fof(f1182,plain,
( sP5(sK16,sK19,vabs(sK17,sK18,veabs))
| vabs(sK17,sK18,veabs) = vvar(sK52(vabs(sK17,sK18,veabs),sK19,sK16))
| sP6(sK16,sK19,vabs(sK17,sK18,veabs))
| ~ spl94_2
| ~ spl94_126 ),
inference(resolution,[],[f1171,f578]) ).
fof(f1171,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK52(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl94_126 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f1192,plain,
spl94_129,
inference(avatar_split_clause,[],[f478,f1190]) ).
fof(f478,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,[],[f371]) ).
fof(f371,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| sK61(X0,X1,X2) = X0
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,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])],[f272,f273]) ).
fof(f273,plain,
! [X0,X1,X2] :
( ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
=> ( vnoType = X2
& vempty = X1
& sK61(X0,X1,X2) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f272,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,[],[f220]) ).
fof(f220,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,[],[f142,f219,f218]) ).
fof(f218,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(f219,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(f142,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,[],[f141]) ).
fof(f141,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,[],[f83]) ).
fof(f83,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/sandbox2/benchmark/theBenchmark.p','lookup-INV') ).
fof(f1181,plain,
spl94_128,
inference(avatar_split_clause,[],[f368,f1179]) ).
fof(f1179,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(f368,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,[],[f271]) ).
fof(f271,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])],[f269,f270]) ).
fof(f270,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(f269,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,[],[f268]) ).
fof(f268,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,[],[f218]) ).
fof(f1177,plain,
spl94_127,
inference(avatar_split_clause,[],[f364,f1175]) ).
fof(f1175,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(f364,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,[],[f267]) ).
fof(f267,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])],[f265,f266]) ).
fof(f266,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(f265,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,[],[f264]) ).
fof(f264,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,[],[f219]) ).
fof(f1172,plain,
spl94_126,
inference(avatar_split_clause,[],[f361,f1170]) ).
fof(f361,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,[],[f263]) ).
fof(f1168,plain,
spl94_125,
inference(avatar_split_clause,[],[f358,f1166]) ).
fof(f1166,plain,
( spl94_125
<=> ! [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_125])]) ).
fof(f358,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,[],[f260]) ).
fof(f1164,plain,
spl94_124,
inference(avatar_split_clause,[],[f340,f1162]) ).
fof(f1162,plain,
( spl94_124
<=> ! [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_124])]) ).
fof(f340,plain,
! [X0,X1] :
( vapp(vabs(sK38(X0,X1),sK36(X0,X1),sK40(X0,X1)),sK39(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,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])],[f246,f247]) ).
fof(f247,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(f246,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,[],[f245]) ).
fof(f245,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,[],[f209]) ).
fof(f1160,plain,
spl94_123,
inference(avatar_split_clause,[],[f335,f1158]) ).
fof(f1158,plain,
( spl94_123
<=> ! [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_123])]) ).
fof(f335,plain,
! [X0,X1] :
( vapp(vabs(sK31(X0,X1),sK32(X0,X1),sK33(X0,X1)),sK35(X0,X1)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,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])],[f242,f243]) ).
fof(f243,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(f242,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,[],[f241]) ).
fof(f241,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,[],[f210]) ).
fof(f1156,plain,
spl94_122,
inference(avatar_split_clause,[],[f321,f1154]) ).
fof(f1154,plain,
( spl94_122
<=> ! [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_122])]) ).
fof(f321,plain,
! [X0,X1] :
( vapp(vabs(sK21(X0,X1),sK22(X0,X1),sK23(X0,X1)),sK20(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f1148,plain,
spl94_121,
inference(avatar_split_clause,[],[f530,f1146]) ).
fof(f530,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,[],[f529]) ).
fof(f529,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,[],[f528]) ).
fof(f528,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,[],[f445]) ).
fof(f445,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,[],[f186]) ).
fof(f186,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,[],[f185]) ).
fof(f185,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,[],[f108]) ).
fof(f108,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/sandbox2/benchmark/theBenchmark.p',reduce3) ).
fof(f1144,plain,
spl94_120,
inference(avatar_split_clause,[],[f507,f1142]) ).
fof(f507,plain,
! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 ),
inference(equality_resolution,[],[f506]) ).
fof(f506,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,[],[f505]) ).
fof(f505,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,[],[f428]) ).
fof(f428,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,[],[f299]) ).
fof(f299,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])],[f168,f298]) ).
fof(f298,plain,
! [X1] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
=> vabs(sK88(X1),sK89(X1),sK90(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f168,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,[],[f167]) ).
fof(f167,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,[],[f99]) ).
fof(f99,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/sandbox2/benchmark/theBenchmark.p',reduce6) ).
fof(f1136,plain,
( spl94_119
| ~ spl94_12
| ~ spl94_116 ),
inference(avatar_split_clause,[],[f1106,f1085,f620,f1134]) ).
fof(f1134,plain,
( spl94_119
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_119])]) ).
fof(f620,plain,
( spl94_12
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_12])]) ).
fof(f1106,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl94_12
| ~ spl94_116 ),
inference(superposition,[],[f621,f1086]) ).
fof(f621,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl94_12 ),
inference(avatar_component_clause,[],[f620]) ).
fof(f1127,plain,
spl94_118,
inference(avatar_split_clause,[],[f550,f1125]) ).
fof(f550,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,[],[f452]) ).
fof(f452,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,[],[f200]) ).
fof(f200,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,[],[f199]) ).
fof(f199,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,[],[f115]) ).
fof(f115,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/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).
fof(f1123,plain,
spl94_117,
inference(avatar_split_clause,[],[f476,f1121]) ).
fof(f476,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ),
inference(equality_resolution,[],[f373]) ).
fof(f373,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vnoType = X2
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f274]) ).
fof(f1087,plain,
spl94_116,
inference(avatar_split_clause,[],[f554,f1085]) ).
fof(f554,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f553]) ).
fof(f553,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,[],[f552]) ).
fof(f552,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,[],[f551]) ).
fof(f551,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,[],[f453]) ).
fof(f453,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,[],[f202]) ).
fof(f202,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,[],[f201]) ).
fof(f201,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,[],[f116]) ).
fof(f116,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/sandbox2/benchmark/theBenchmark.p',subst2) ).
fof(f1083,plain,
spl94_115,
inference(avatar_split_clause,[],[f430,f1081]) ).
fof(f430,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,[],[f172]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f171]) ).
fof(f171,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,[],[f101]) ).
fof(f101,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/sandbox2/benchmark/theBenchmark.p','T-app') ).
fof(f1079,plain,
spl94_114,
inference(avatar_split_clause,[],[f427,f1077]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,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/sandbox2/benchmark/theBenchmark.p','T-Weak') ).
fof(f1075,plain,
spl94_113,
inference(avatar_split_clause,[],[f422,f1073]) ).
fof(f422,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,[],[f160]) ).
fof(f160,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,[],[f95]) ).
fof(f95,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/sandbox2/benchmark/theBenchmark.p','T-abs') ).
fof(f1068,plain,
spl94_112,
inference(avatar_split_clause,[],[f409,f1066]) ).
fof(f1066,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(f409,plain,
! [X2,X3,X0,X1] :
( sK81(X0,X1,X2,X3) = sK82(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,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])],[f292,f293]) ).
fof(f293,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(f292,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,[],[f291]) ).
fof(f291,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,[],[f221]) ).
fof(f1064,plain,
spl94_111,
inference(avatar_split_clause,[],[f404,f1062]) ).
fof(f1062,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(f404,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) != sK80(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,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])],[f288,f289]) ).
fof(f289,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(f288,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,[],[f287]) ).
fof(f287,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,[],[f222]) ).
fof(f1060,plain,
spl94_110,
inference(avatar_split_clause,[],[f399,f1058]) ).
fof(f1058,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(f399,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = sK75(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f1056,plain,
spl94_109,
inference(avatar_split_clause,[],[f393,f1054]) ).
fof(f1054,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(f393,plain,
! [X2,X3,X0,X1] :
( visFreeVar(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f1052,plain,
spl94_108,
inference(avatar_split_clause,[],[f392,f1050]) ).
fof(f1050,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(f392,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) != sK70(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f1048,plain,
spl94_107,
inference(avatar_split_clause,[],[f387,f1046]) ).
fof(f1046,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(f387,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f1044,plain,
spl94_106,
inference(avatar_split_clause,[],[f386,f1042]) ).
fof(f1042,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(f386,plain,
! [X2,X3,X0,X1] :
( sK62(X0,X1,X2,X3) != sK64(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f1040,plain,
spl94_105,
inference(avatar_split_clause,[],[f356,f1038]) ).
fof(f356,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),varrow(sK47(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,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])],[f254,f255]) ).
fof(f255,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(f254,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,[],[f253]) ).
fof(f253,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,[],[f216]) ).
fof(f1036,plain,
spl94_104,
inference(avatar_split_clause,[],[f344,f1034]) ).
fof(f1034,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(f344,plain,
! [X0,X1] :
( vsomeExp(vsubst(sK38(X0,X1),sK39(X0,X1),sK40(X0,X1))) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f1027,plain,
( spl94_103
| ~ spl94_39
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f842,f794,f729,f1025]) ).
fof(f1025,plain,
( spl94_103
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_103])]) ).
fof(f794,plain,
( spl94_53
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_53])]) ).
fof(f842,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl94_39
| ~ spl94_53 ),
inference(resolution,[],[f795,f730]) ).
fof(f795,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_53 ),
inference(avatar_component_clause,[],[f794]) ).
fof(f1023,plain,
spl94_102,
inference(avatar_split_clause,[],[f477,f1021]) ).
fof(f477,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ),
inference(equality_resolution,[],[f372]) ).
fof(f372,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vempty = X1
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f274]) ).
fof(f1019,plain,
spl94_101,
inference(avatar_split_clause,[],[f366,f1017]) ).
fof(f366,plain,
! [X2,X0,X1] :
( vlookup(sK55(X0,X1,X2),sK56(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
fof(f1015,plain,
spl94_100,
inference(avatar_split_clause,[],[f359,f1013]) ).
fof(f1013,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(f359,plain,
! [X2,X0,X1] :
( varrow(sK50(X0,X1,X2),sK51(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f260]) ).
fof(f1011,plain,
spl94_99,
inference(avatar_split_clause,[],[f355,f1009]) ).
fof(f1009,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(f355,plain,
! [X2,X0,X1] :
( vapp(sK45(X0,X1,X2),sK46(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f1002,plain,
spl94_98,
inference(avatar_split_clause,[],[f527,f1000]) ).
fof(f527,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f526]) ).
fof(f526,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f525]) ).
fof(f525,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,[],[f444]) ).
fof(f444,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,[],[f184]) ).
fof(f184,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,[],[f183]) ).
fof(f183,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,[],[f107]) ).
fof(f107,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/sandbox2/benchmark/theBenchmark.p',reduce4) ).
fof(f998,plain,
spl94_97,
inference(avatar_split_clause,[],[f423,f996]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,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/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
fof(f994,plain,
spl94_96,
inference(avatar_split_clause,[],[f416,f992]) ).
fof(f416,plain,
! [X2,X3,X0,X1] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| visFreeVar(X0,veabs) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| visFreeVar(X0,veabs) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2,X3] :
( vtcheck(vbind(X0,X1,X2),veabs,X3)
| ~ vtcheck(X2,veabs,X3)
| visFreeVar(X0,veabs) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( vtcheck(X2,veabs,X3)
& ~ visFreeVar(X0,veabs) )
=> vtcheck(vbind(X0,X1,X2),veabs,X3) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X8,X9,X19,X14] :
( ( vtcheck(X19,veabs,X14)
& ~ visFreeVar(X8,veabs) )
=> vtcheck(vbind(X8,X9,X19),veabs,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs-IH') ).
fof(f990,plain,
spl94_95,
inference(avatar_split_clause,[],[f357,f988]) ).
fof(f988,plain,
( spl94_95
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_95])]) ).
fof(f357,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f986,plain,
spl94_94,
inference(avatar_split_clause,[],[f334,f984]) ).
fof(f984,plain,
( spl94_94
<=> ! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_94])]) ).
fof(f334,plain,
! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK29(X0,X1)),sK30(X0,X1))) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,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])],[f238,f239]) ).
fof(f239,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(f238,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,[],[f237]) ).
fof(f237,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,[],[f211]) ).
fof(f979,plain,
spl94_93,
inference(avatar_split_clause,[],[f545,f977]) ).
fof(f545,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f544]) ).
fof(f544,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f543]) ).
fof(f543,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,[],[f450]) ).
fof(f450,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,[],[f196]) ).
fof(f196,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,[],[f195]) ).
fof(f195,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,[],[f113]) ).
fof(f113,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/sandbox2/benchmark/theBenchmark.p',lookup2) ).
fof(f975,plain,
spl94_92,
inference(avatar_split_clause,[],[f408,f973]) ).
fof(f973,plain,
( spl94_92
<=> ! [X0,X3,X2,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_92])]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( vvar(sK82(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f971,plain,
spl94_91,
inference(avatar_split_clause,[],[f405,f969]) ).
fof(f969,plain,
( spl94_91
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_91])]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f967,plain,
spl94_90,
inference(avatar_split_clause,[],[f403,f965]) ).
fof(f965,plain,
( spl94_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_90])]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( vvar(sK80(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f963,plain,
spl94_89,
inference(avatar_split_clause,[],[f369,f961]) ).
fof(f961,plain,
( spl94_89
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_89])]) ).
fof(f369,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = sK59(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
fof(f959,plain,
spl94_88,
inference(avatar_split_clause,[],[f365,f957]) ).
fof(f957,plain,
( spl94_88
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_88])]) ).
fof(f365,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) != sK55(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
fof(f955,plain,
( spl94_86
| ~ spl94_87
| spl94_1
| ~ spl94_82 ),
inference(avatar_split_clause,[],[f941,f920,f571,f952,f948]) ).
fof(f952,plain,
( spl94_87
<=> visFreeVar(sK14,veabs) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_87])]) ).
fof(f941,plain,
( ~ visFreeVar(sK14,veabs)
| sK14 = sK17
| spl94_1
| ~ spl94_82 ),
inference(resolution,[],[f921,f573]) ).
fof(f934,plain,
( spl94_85
| ~ spl94_40
| ~ spl94_53 ),
inference(avatar_split_clause,[],[f841,f794,f733,f932]) ).
fof(f932,plain,
( spl94_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_85])]) ).
fof(f841,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl94_40
| ~ spl94_53 ),
inference(resolution,[],[f795,f734]) ).
fof(f930,plain,
( spl94_84
| ~ spl94_39
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f830,f770,f729,f928]) ).
fof(f928,plain,
( spl94_84
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_84])]) ).
fof(f770,plain,
( spl94_48
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_48])]) ).
fof(f830,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl94_39
| ~ spl94_48 ),
inference(resolution,[],[f771,f730]) ).
fof(f771,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_48 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f926,plain,
spl94_83,
inference(avatar_split_clause,[],[f559,f924]) ).
fof(f559,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f558]) ).
fof(f558,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f557]) ).
fof(f557,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,[],[f556]) ).
fof(f556,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,[],[f555]) ).
fof(f555,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,[],[f454]) ).
fof(f454,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,[],[f204]) ).
fof(f204,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,[],[f203]) ).
fof(f203,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,[],[f117]) ).
fof(f117,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/sandbox2/benchmark/theBenchmark.p',subst3) ).
fof(f922,plain,
spl94_82,
inference(avatar_split_clause,[],[f524,f920]) ).
fof(f524,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f523]) ).
fof(f523,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X1,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4
| X1 != X4 ),
inference(equality_resolution,[],[f441]) ).
fof(f441,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,[],[f182]) ).
fof(f182,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,[],[f181]) ).
fof(f181,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,[],[f106]) ).
fof(f106,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/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f918,plain,
spl94_81,
inference(avatar_split_clause,[],[f437,f916]) ).
fof(f916,plain,
( spl94_81
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_81])]) ).
fof(f437,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f176]) ).
fof(f176,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,[],[f175]) ).
fof(f175,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,[],[f103]) ).
fof(f103,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/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).
fof(f914,plain,
spl94_80,
inference(avatar_split_clause,[],[f436,f912]) ).
fof(f912,plain,
( spl94_80
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_80])]) ).
fof(f436,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f176]) ).
fof(f910,plain,
spl94_79,
inference(avatar_split_clause,[],[f435,f908]) ).
fof(f908,plain,
( spl94_79
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_79])]) ).
fof(f435,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f176]) ).
fof(f906,plain,
spl94_78,
inference(avatar_split_clause,[],[f433,f904]) ).
fof(f904,plain,
( spl94_78
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_78])]) ).
fof(f433,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f174]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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,[],[f102]) ).
fof(f102,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/sandbox2/benchmark/theBenchmark.p','EQ-bind') ).
fof(f902,plain,
spl94_77,
inference(avatar_split_clause,[],[f432,f900]) ).
fof(f900,plain,
( spl94_77
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_77])]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f174]) ).
fof(f898,plain,
spl94_76,
inference(avatar_split_clause,[],[f431,f896]) ).
fof(f896,plain,
( spl94_76
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_76])]) ).
fof(f431,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f174]) ).
fof(f894,plain,
spl94_75,
inference(avatar_split_clause,[],[f410,f892]) ).
fof(f892,plain,
( spl94_75
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_75])]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( sK83(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f890,plain,
spl94_74,
inference(avatar_split_clause,[],[f407,f888]) ).
fof(f888,plain,
( spl94_74
<=> ! [X0,X3,X2,X1] :
( sK83(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_74])]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( sK83(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f886,plain,
( spl94_73
| ~ spl94_40
| ~ spl94_48 ),
inference(avatar_split_clause,[],[f829,f770,f733,f884]) ).
fof(f884,plain,
( spl94_73
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_73])]) ).
fof(f829,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl94_40
| ~ spl94_48 ),
inference(resolution,[],[f771,f734]) ).
fof(f882,plain,
spl94_72,
inference(avatar_split_clause,[],[f406,f880]) ).
fof(f880,plain,
( spl94_72
<=> ! [X0,X3,X2,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_72])]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( sK81(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f878,plain,
spl94_71,
inference(avatar_split_clause,[],[f402,f876]) ).
fof(f876,plain,
( spl94_71
<=> ! [X0,X3,X2,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_71])]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( sK78(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f874,plain,
spl94_70,
inference(avatar_split_clause,[],[f401,f872]) ).
fof(f872,plain,
( spl94_70
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_70])]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f870,plain,
spl94_69,
inference(avatar_split_clause,[],[f397,f868]) ).
fof(f868,plain,
( spl94_69
<=> ! [X0,X3,X2,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_69])]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( sK73(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f866,plain,
spl94_68,
inference(avatar_split_clause,[],[f396,f864]) ).
fof(f864,plain,
( spl94_68
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_68])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f862,plain,
spl94_67,
inference(avatar_split_clause,[],[f390,f860]) ).
fof(f860,plain,
( spl94_67
<=> ! [X0,X3,X2,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_67])]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( sK68(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f858,plain,
spl94_66,
inference(avatar_split_clause,[],[f389,f856]) ).
fof(f856,plain,
( spl94_66
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_66])]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f854,plain,
spl94_65,
inference(avatar_split_clause,[],[f384,f852]) ).
fof(f852,plain,
( spl94_65
<=> ! [X0,X3,X2,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_65])]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( sK65(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f850,plain,
spl94_64,
inference(avatar_split_clause,[],[f383,f848]) ).
fof(f848,plain,
( spl94_64
<=> ! [X0,X3,X2,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_64])]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( sK64(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f846,plain,
spl94_63,
inference(avatar_split_clause,[],[f330,f844]) ).
fof(f844,plain,
( spl94_63
<=> ! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_63])]) ).
fof(f330,plain,
! [X0,X1] :
( vapp(sK28(X0,X1),sK30(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f840,plain,
spl94_62,
inference(avatar_split_clause,[],[f325,f838]) ).
fof(f838,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(f325,plain,
! [X0,X1] :
( vapp(sK26(X0,X1),sK25(X0,X1)) = X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,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])],[f234,f235]) ).
fof(f235,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(f234,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,[],[f233]) ).
fof(f233,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,[],[f212]) ).
fof(f828,plain,
spl94_61,
inference(avatar_split_clause,[],[f537,f826]) ).
fof(f537,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f536]) ).
fof(f536,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f535]) ).
fof(f535,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f534]) ).
fof(f534,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,[],[f448]) ).
fof(f448,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,[],[f192]) ).
fof(f192,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,[],[f191]) ).
fof(f191,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,[],[f111]) ).
fof(f111,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/sandbox2/benchmark/theBenchmark.p',subst1) ).
fof(f824,plain,
spl94_60,
inference(avatar_split_clause,[],[f500,f822]) ).
fof(f500,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f499]) ).
fof(f499,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,vapp(X2,X4))
| X0 != X3 ),
inference(equality_resolution,[],[f426]) ).
fof(f426,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,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,[],[f163]) ).
fof(f163,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,[],[f97]) ).
fof(f97,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/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f820,plain,
spl94_59,
inference(avatar_split_clause,[],[f375,f818]) ).
fof(f375,plain,
! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,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/sandbox2/benchmark/theBenchmark.p','T-var') ).
fof(f816,plain,
spl94_58,
inference(avatar_split_clause,[],[f370,f814]) ).
fof(f814,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(f370,plain,
! [X2,X0,X1] :
( vsomeType(sK60(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
fof(f812,plain,
spl94_57,
inference(avatar_split_clause,[],[f341,f810]) ).
fof(f810,plain,
( spl94_57
<=> ! [X0,X1] :
( sK37(X0,X1) = vreduce(sK39(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_57])]) ).
fof(f341,plain,
! [X0,X1] :
( sK37(X0,X1) = vreduce(sK39(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f808,plain,
spl94_56,
inference(avatar_split_clause,[],[f336,f806]) ).
fof(f806,plain,
( spl94_56
<=> ! [X0,X1] :
( sK34(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_56])]) ).
fof(f336,plain,
! [X0,X1] :
( sK34(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f804,plain,
spl94_55,
inference(avatar_split_clause,[],[f332,f802]) ).
fof(f802,plain,
( spl94_55
<=> ! [X0,X1] :
( sK29(X0,X1) = vreduce(sK28(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_55])]) ).
fof(f332,plain,
! [X0,X1] :
( sK29(X0,X1) = vreduce(sK28(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f800,plain,
spl94_54,
inference(avatar_split_clause,[],[f331,f798]) ).
fof(f798,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(f331,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK28(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f796,plain,
( spl94_53
| ~ spl94_11
| ~ spl94_40 ),
inference(avatar_split_clause,[],[f740,f733,f616,f794]) ).
fof(f740,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl94_11
| ~ spl94_40 ),
inference(resolution,[],[f734,f617]) ).
fof(f792,plain,
spl94_52,
inference(avatar_split_clause,[],[f327,f790]) ).
fof(f790,plain,
( spl94_52
<=> ! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_52])]) ).
fof(f327,plain,
! [X0,X1] :
( sK27(X0,X1) = vreduce(sK26(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f788,plain,
spl94_51,
inference(avatar_split_clause,[],[f326,f786]) ).
fof(f786,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(f326,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK26(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f784,plain,
spl94_50,
inference(avatar_split_clause,[],[f322,f782]) ).
fof(f782,plain,
( spl94_50
<=> ! [X0,X1] :
( sK24(X0,X1) = vreduce(sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_50])]) ).
fof(f322,plain,
! [X0,X1] :
( sK24(X0,X1) = vreduce(sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f776,plain,
spl94_49,
inference(avatar_split_clause,[],[f381,f774]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,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,[],[f147]) ).
fof(f147,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,[],[f87]) ).
fof(f87,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/sandbox2/benchmark/theBenchmark.p','EQ-app') ).
fof(f772,plain,
( spl94_48
| ~ spl94_11
| ~ spl94_39 ),
inference(avatar_split_clause,[],[f739,f729,f616,f770]) ).
fof(f739,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl94_11
| ~ spl94_39 ),
inference(resolution,[],[f730,f617]) ).
fof(f768,plain,
spl94_47,
inference(avatar_split_clause,[],[f380,f766]) ).
fof(f380,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f148]) ).
fof(f764,plain,
spl94_46,
inference(avatar_split_clause,[],[f378,f762]) ).
fof(f762,plain,
( spl94_46
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_46])]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,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,[],[f145]) ).
fof(f145,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,[],[f86]) ).
fof(f86,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/sandbox2/benchmark/theBenchmark.p','EQ-arrow') ).
fof(f760,plain,
spl94_45,
inference(avatar_split_clause,[],[f377,f758]) ).
fof(f758,plain,
( spl94_45
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_45])]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f146]) ).
fof(f756,plain,
spl94_44,
inference(avatar_split_clause,[],[f367,f754]) ).
fof(f754,plain,
( spl94_44
<=> ! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_44])]) ).
fof(f367,plain,
! [X2,X0,X1] :
( sK58(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f271]) ).
fof(f752,plain,
spl94_43,
inference(avatar_split_clause,[],[f363,f750]) ).
fof(f363,plain,
! [X2,X0,X1] :
( sK55(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f267]) ).
fof(f748,plain,
spl94_42,
inference(avatar_split_clause,[],[f549,f746]) ).
fof(f549,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f548]) ).
fof(f548,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f546]) ).
fof(f546,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f451]) ).
fof(f451,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,[],[f198]) ).
fof(f198,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,[],[f197]) ).
fof(f197,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,[],[f114]) ).
fof(f114,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/sandbox2/benchmark/theBenchmark.p',lookup1) ).
fof(f744,plain,
spl94_41,
inference(avatar_split_clause,[],[f519,f742]) ).
fof(f519,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f443]) ).
fof(f443,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f182]) ).
fof(f735,plain,
spl94_40,
inference(avatar_split_clause,[],[f504,f733]) ).
fof(f504,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f503]) ).
fof(f503,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f424]) ).
fof(f424,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f731,plain,
spl94_39,
inference(avatar_split_clause,[],[f502,f729]) ).
fof(f502,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f501]) ).
fof(f501,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f425]) ).
fof(f425,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f164]) ).
fof(f727,plain,
spl94_38,
inference(avatar_split_clause,[],[f420,f725]) ).
fof(f420,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f93]) ).
fof(f93,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/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f723,plain,
spl94_37,
inference(avatar_split_clause,[],[f316,f721]) ).
fof(f721,plain,
( spl94_37
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_37])]) ).
fof(f316,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,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/sandbox2/benchmark/theBenchmark.p','EQ-var') ).
fof(f719,plain,
spl94_36,
inference(avatar_split_clause,[],[f314,f717]) ).
fof(f717,plain,
( spl94_36
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_36])]) ).
fof(f314,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,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/sandbox2/benchmark/theBenchmark.p','EQ-someExp') ).
fof(f715,plain,
spl94_35,
inference(avatar_split_clause,[],[f312,f713]) ).
fof(f713,plain,
( spl94_35
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_35])]) ).
fof(f312,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,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/sandbox2/benchmark/theBenchmark.p','EQ-someType') ).
fof(f710,plain,
spl94_34,
inference(avatar_split_clause,[],[f542,f708]) ).
fof(f542,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f541]) ).
fof(f541,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f540]) ).
fof(f540,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f539]) ).
fof(f539,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f538]) ).
fof(f538,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f449]) ).
fof(f449,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,[],[f194]) ).
fof(f194,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,[],[f193]) ).
fof(f193,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,[],[f112]) ).
fof(f112,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/sandbox2/benchmark/theBenchmark.p',subst0) ).
fof(f706,plain,
spl94_33,
inference(avatar_split_clause,[],[f498,f704]) ).
fof(f498,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f497]) ).
fof(f497,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f421]) ).
fof(f421,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,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/sandbox2/benchmark/theBenchmark.p',reduce1) ).
fof(f702,plain,
spl94_32,
inference(avatar_split_clause,[],[f493,f700]) ).
fof(f493,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f492]) ).
fof(f492,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f419]) ).
fof(f419,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,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/sandbox2/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f698,plain,
spl94_31,
inference(avatar_split_clause,[],[f376,f696]) ).
fof(f696,plain,
( spl94_31
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_31])]) ).
fof(f376,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/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f694,plain,
spl94_30,
inference(avatar_split_clause,[],[f343,f692]) ).
fof(f692,plain,
( spl94_30
<=> ! [X0,X1] :
( visValue(sK39(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_30])]) ).
fof(f343,plain,
! [X0,X1] :
( visValue(sK39(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f690,plain,
spl94_29,
inference(avatar_split_clause,[],[f342,f688]) ).
fof(f688,plain,
( spl94_29
<=> ! [X0,X1] :
( ~ visSomeExp(sK37(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_29])]) ).
fof(f342,plain,
! [X0,X1] :
( ~ visSomeExp(sK37(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f686,plain,
spl94_28,
inference(avatar_split_clause,[],[f338,f684]) ).
fof(f684,plain,
( spl94_28
<=> ! [X0,X1] :
( ~ visValue(sK35(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_28])]) ).
fof(f338,plain,
! [X0,X1] :
( ~ visValue(sK35(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f682,plain,
spl94_27,
inference(avatar_split_clause,[],[f337,f680]) ).
fof(f680,plain,
( spl94_27
<=> ! [X0,X1] :
( ~ visSomeExp(sK34(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_27])]) ).
fof(f337,plain,
! [X0,X1] :
( ~ visSomeExp(sK34(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f678,plain,
spl94_26,
inference(avatar_split_clause,[],[f333,f676]) ).
fof(f676,plain,
( spl94_26
<=> ! [X0,X1] :
( visSomeExp(sK29(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_26])]) ).
fof(f333,plain,
! [X0,X1] :
( visSomeExp(sK29(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f674,plain,
spl94_25,
inference(avatar_split_clause,[],[f328,f672]) ).
fof(f672,plain,
( spl94_25
<=> ! [X0,X1] :
( ~ visSomeExp(sK27(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_25])]) ).
fof(f328,plain,
! [X0,X1] :
( ~ visSomeExp(sK27(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f670,plain,
spl94_24,
inference(avatar_split_clause,[],[f323,f668]) ).
fof(f668,plain,
( spl94_24
<=> ! [X0,X1] :
( visSomeExp(sK24(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_24])]) ).
fof(f323,plain,
! [X0,X1] :
( visSomeExp(sK24(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f666,plain,
spl94_23,
inference(avatar_split_clause,[],[f522,f664]) ).
fof(f522,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f521]) ).
fof(f521,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f520]) ).
fof(f520,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f442]) ).
fof(f442,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f182]) ).
fof(f662,plain,
spl94_22,
inference(avatar_split_clause,[],[f351,f660]) ).
fof(f351,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f78]) ).
fof(f78,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/sandbox2/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f658,plain,
spl94_21,
inference(avatar_split_clause,[],[f350,f656]) ).
fof(f656,plain,
( spl94_21
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_21])]) ).
fof(f350,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f77]) ).
fof(f77,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/sandbox2/benchmark/theBenchmark.p','DIFF-empty-bind') ).
fof(f654,plain,
spl94_20,
inference(avatar_split_clause,[],[f339,f652]) ).
fof(f652,plain,
( spl94_20
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_20])]) ).
fof(f339,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f650,plain,
spl94_19,
inference(avatar_split_clause,[],[f329,f648]) ).
fof(f329,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f646,plain,
spl94_18,
inference(avatar_split_clause,[],[f491,f644]) ).
fof(f491,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f490]) ).
fof(f490,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f489]) ).
fof(f489,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f417]) ).
fof(f417,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,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/sandbox2/benchmark/theBenchmark.p',lookup0) ).
fof(f642,plain,
spl94_17,
inference(avatar_split_clause,[],[f488,f640]) ).
fof(f640,plain,
( spl94_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_17])]) ).
fof(f488,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f415]) ).
fof(f415,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,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/sandbox2/benchmark/theBenchmark.p',isValue0) ).
fof(f638,plain,
spl94_16,
inference(avatar_split_clause,[],[f475,f636]) ).
fof(f475,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f474]) ).
fof(f474,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f354]) ).
fof(f354,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,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/sandbox2/benchmark/theBenchmark.p',reduce0) ).
fof(f634,plain,
spl94_15,
inference(avatar_split_clause,[],[f473,f632]) ).
fof(f632,plain,
( spl94_15
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_15])]) ).
fof(f473,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f472]) ).
fof(f472,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f353]) ).
fof(f353,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,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/sandbox2/benchmark/theBenchmark.p',getSomeExp0) ).
fof(f630,plain,
spl94_14,
inference(avatar_split_clause,[],[f471,f628]) ).
fof(f628,plain,
( spl94_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl94_14])]) ).
fof(f471,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f470]) ).
fof(f470,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f352]) ).
fof(f352,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,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/sandbox2/benchmark/theBenchmark.p',getSomeType0) ).
fof(f626,plain,
spl94_13,
inference(avatar_split_clause,[],[f496,f624]) ).
fof(f624,plain,
( spl94_13
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_13])]) ).
fof(f496,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f495]) ).
fof(f495,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f418]) ).
fof(f418,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f157]) ).
fof(f622,plain,
spl94_12,
inference(avatar_split_clause,[],[f479,f620]) ).
fof(f479,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f374]) ).
fof(f374,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,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/sandbox2/benchmark/theBenchmark.p',isValue2) ).
fof(f618,plain,
spl94_11,
inference(avatar_split_clause,[],[f462,f616]) ).
fof(f462,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,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/sandbox2/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f614,plain,
spl94_10,
inference(avatar_split_clause,[],[f309,f612]) ).
fof(f612,plain,
( spl94_10
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_10])]) ).
fof(f309,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3] : vnoExp != vsomeExp(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
fof(f610,plain,
spl94_9,
inference(avatar_split_clause,[],[f308,f608]) ).
fof(f608,plain,
( spl94_9
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_9])]) ).
fof(f308,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] : vnoType != vsomeType(X0),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2] : vnoType != vsomeType(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noType-someType') ).
fof(f606,plain,
spl94_8,
inference(avatar_split_clause,[],[f469,f604]) ).
fof(f604,plain,
( spl94_8
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_8])]) ).
fof(f469,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f349]) ).
fof(f349,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( vvar(X0) = X1
=> ~ visValue(X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X8,X3] :
( vvar(X8) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1) ).
fof(f602,plain,
spl94_7,
inference(avatar_split_clause,[],[f464,f600]) ).
fof(f600,plain,
( spl94_7
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_7])]) ).
fof(f464,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( vsomeExp(X0) = X1
=> visSomeExp(X1) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X10,X24] :
( vsomeExp(X10) = X24
=> visSomeExp(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).
fof(f598,plain,
spl94_6,
inference(avatar_split_clause,[],[f463,f596]) ).
fof(f596,plain,
( spl94_6
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_6])]) ).
fof(f463,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( vsomeType(X0) = X1
=> visSomeType(X1) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X10,X17] :
( vsomeType(X10) = X17
=> visSomeType(X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType1) ).
fof(f594,plain,
~ spl94_5,
inference(avatar_split_clause,[],[f304,f591]) ).
fof(f304,plain,
~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
& vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
& ~ visFreeVar(sK14,vabs(sK17,sK18,veabs)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19])],[f121,f227]) ).
fof(f227,plain,
( ? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs)) )
=> ( ~ vtcheck(vbind(sK14,sK15,sK16),vabs(sK17,sK18,veabs),sK19)
& vtcheck(sK16,vabs(sK17,sK18,veabs),sK19)
& ~ visFreeVar(sK14,vabs(sK17,sK18,veabs)) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs)) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
? [X0,X1,X2,X3,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5)
& vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,plain,
~ ! [X0,X1,X2,X3,X4,X5] :
( ( vtcheck(X2,vabs(X3,X4,veabs),X5)
& ~ visFreeVar(X0,vabs(X3,X4,veabs)) )
=> vtcheck(vbind(X0,X1,X2),vabs(X3,X4,veabs),X5) ),
inference(rectify,[],[f61]) ).
fof(f61,negated_conjecture,
~ ! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& ~ visFreeVar(X8,vabs(X20,X34,veabs)) )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
inference(negated_conjecture,[],[f60]) ).
fof(f60,conjecture,
! [X8,X9,X19,X20,X34,X14] :
( ( vtcheck(X19,vabs(X20,X34,veabs),X14)
& ~ visFreeVar(X8,vabs(X20,X34,veabs)) )
=> vtcheck(vbind(X8,X9,X19),vabs(X20,X34,veabs),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak-FreeVar-abs') ).
fof(f589,plain,
~ spl94_4,
inference(avatar_split_clause,[],[f458,f586]) ).
fof(f458,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( vnoExp = X0
=> ~ visSomeExp(X0) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X24] :
( vnoExp = X24
=> ~ visSomeExp(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp0) ).
fof(f584,plain,
~ spl94_3,
inference(avatar_split_clause,[],[f457,f581]) ).
fof(f581,plain,
( spl94_3
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl94_3])]) ).
fof(f457,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] :
( vnoType = X0
=> ~ visSomeType(X0) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X17] :
( vnoType = X17
=> ~ visSomeType(X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType0) ).
fof(f579,plain,
spl94_2,
inference(avatar_split_clause,[],[f303,f576]) ).
fof(f303,plain,
vtcheck(sK16,vabs(sK17,sK18,veabs),sK19),
inference(cnf_transformation,[],[f228]) ).
fof(f574,plain,
~ spl94_1,
inference(avatar_split_clause,[],[f302,f571]) ).
fof(f302,plain,
~ visFreeVar(sK14,vabs(sK17,sK18,veabs)),
inference(cnf_transformation,[],[f228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : COM125+1 : TPTP v8.1.2. Released v6.4.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 21:25:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (16887)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (16892)WARNING: value z3 for option sas not known
% 0.14/0.38 % (16890)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (16893)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39 % (16892)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.39 % (16891)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (16894)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.39 % (16895)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.39 % (16896)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.44 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.46 % (16894)First to succeed.
% 0.21/0.48 % (16894)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16887"
% 0.21/0.48 % (16894)Refutation found. Thanks to Tanya!
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (16894)------------------------------
% 0.21/0.49 % (16894)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.49 % (16894)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (16894)Memory used [KB]: 2243
% 0.21/0.49 % (16894)Time elapsed: 0.095 s
% 0.21/0.49 % (16894)Instructions burned: 160 (million)
% 0.21/0.49 % (16887)Success in time 0.119 s
%------------------------------------------------------------------------------