TSTP Solution File: COM133+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM133+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 : n002.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 : Tue Apr 30 10:47:55 EDT 2024
% Result : Theorem 0.21s 0.52s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 362
% Syntax : Number of formulae : 1294 ( 185 unt; 0 def)
% Number of atoms : 4813 (2128 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 5304 (1785 ~;2264 |; 775 &)
% ( 267 <=>; 213 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 288 ( 286 usr; 268 prp; 0-4 aty)
% Number of functors : 98 ( 98 usr; 11 con; 0-4 aty)
% Number of variables : 4437 (3864 !; 573 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2940,plain,
$false,
inference(avatar_sat_refutation,[],[f584,f589,f594,f599,f604,f608,f612,f616,f620,f624,f628,f632,f636,f640,f644,f648,f652,f656,f660,f664,f668,f672,f676,f680,f684,f688,f692,f696,f700,f704,f708,f712,f716,f720,f725,f729,f733,f737,f741,f745,f754,f758,f762,f766,f770,f774,f778,f782,f786,f794,f798,f802,f806,f810,f814,f818,f822,f826,f830,f834,f838,f850,f856,f860,f864,f868,f872,f876,f880,f884,f888,f892,f896,f900,f904,f908,f912,f916,f920,f924,f928,f932,f936,f940,f944,f959,f963,f967,f971,f975,f979,f983,f993,f997,f1001,f1005,f1009,f1022,f1026,f1030,f1034,f1043,f1052,f1056,f1060,f1064,f1068,f1072,f1076,f1080,f1084,f1089,f1093,f1097,f1101,f1111,f1143,f1147,f1160,f1164,f1168,f1177,f1181,f1185,f1189,f1193,f1197,f1201,f1214,f1218,f1233,f1237,f1241,f1261,f1277,f1281,f1285,f1289,f1293,f1297,f1301,f1319,f1324,f1330,f1340,f1344,f1348,f1358,f1362,f1372,f1381,f1385,f1389,f1409,f1422,f1426,f1431,f1454,f1460,f1468,f1472,f1476,f1490,f1497,f1502,f1510,f1515,f1519,f1532,f1537,f1541,f1545,f1549,f1553,f1557,f1662,f1669,f1674,f1678,f1698,f1702,f1706,f1728,f1732,f1736,f1789,f1823,f1826,f1833,f1838,f1842,f1846,f1922,f1926,f1930,f1934,f1938,f1986,f2000,f2004,f2045,f2053,f2064,f2068,f2072,f2076,f2122,f2140,f2144,f2148,f2152,f2190,f2195,f2199,f2203,f2209,f2229,f2233,f2241,f2265,f2269,f2273,f2332,f2343,f2348,f2360,f2364,f2368,f2403,f2407,f2450,f2454,f2458,f2462,f2466,f2470,f2560,f2564,f2579,f2587,f2591,f2614,f2629,f2633,f2637,f2641,f2731,f2738,f2753,f2757,f2761,f2783,f2797,f2801,f2811,f2815,f2836,f2841,f2845,f2861,f2868,f2872,f2910,f2914,f2924,f2928,f2939]) ).
fof(f2939,plain,
( ~ spl95_229
| spl95_5
| ~ spl95_83
| ~ spl95_117 ),
inference(avatar_split_clause,[],[f2580,f1104,f934,f601,f2345]) ).
fof(f2345,plain,
( spl95_229
<=> vtcheck(sK15,vabs(sK16,sK19,veabs),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_229])]) ).
fof(f601,plain,
( spl95_5
<=> vtcheck(sK15,vsubst(sK16,sK17,vabs(sK18,sK19,veabs)),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_5])]) ).
fof(f934,plain,
( spl95_83
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_83])]) ).
fof(f1104,plain,
( spl95_117
<=> sK16 = sK18 ),
introduced(avatar_definition,[new_symbols(naming,[spl95_117])]) ).
fof(f2580,plain,
( ~ vtcheck(sK15,vabs(sK16,sK19,veabs),sK20)
| spl95_5
| ~ spl95_83
| ~ spl95_117 ),
inference(forward_demodulation,[],[f1848,f935]) ).
fof(f935,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl95_83 ),
inference(avatar_component_clause,[],[f934]) ).
fof(f1848,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vabs(sK16,sK19,veabs)),sK20)
| spl95_5
| ~ spl95_117 ),
inference(superposition,[],[f603,f1106]) ).
fof(f1106,plain,
( sK16 = sK18
| ~ spl95_117 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f603,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vabs(sK18,sK19,veabs)),sK20)
| spl95_5 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f2928,plain,
( spl95_267
| ~ spl95_61
| ~ spl95_157 ),
inference(avatar_split_clause,[],[f1404,f1387,f836,f2926]) ).
fof(f2926,plain,
( spl95_267
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK86(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_267])]) ).
fof(f836,plain,
( spl95_61
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_61])]) ).
fof(f1387,plain,
( spl95_157
<=> ! [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)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_157])]) ).
fof(f1404,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK86(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl95_61
| ~ spl95_157 ),
inference(superposition,[],[f1388,f837]) ).
fof(f837,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl95_61 ),
inference(avatar_component_clause,[],[f836]) ).
fof(f1388,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK86(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl95_157 ),
inference(avatar_component_clause,[],[f1387]) ).
fof(f2924,plain,
( spl95_266
| ~ spl95_61
| ~ spl95_156 ),
inference(avatar_split_clause,[],[f1396,f1383,f836,f2922]) ).
fof(f2922,plain,
( spl95_266
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK87(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_266])]) ).
fof(f1383,plain,
( spl95_156
<=> ! [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)
| sK87(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,[spl95_156])]) ).
fof(f1396,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK87(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl95_61
| ~ spl95_156 ),
inference(superposition,[],[f1384,f837]) ).
fof(f1384,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK87(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl95_156 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f2914,plain,
( spl95_265
| ~ spl95_34
| ~ spl95_158 ),
inference(avatar_split_clause,[],[f1415,f1407,f718,f2912]) ).
fof(f2912,plain,
( spl95_265
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK85(X0,X1,vvar(X0),X1),sK88(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_265])]) ).
fof(f718,plain,
( spl95_34
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl95_34])]) ).
fof(f1407,plain,
( spl95_158
<=> ! [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(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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,[spl95_158])]) ).
fof(f1415,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK85(X0,X1,vvar(X0),X1),sK88(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl95_34
| ~ spl95_158 ),
inference(superposition,[],[f1408,f719]) ).
fof(f719,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl95_34 ),
inference(avatar_component_clause,[],[f718]) ).
fof(f1408,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK88(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl95_158 ),
inference(avatar_component_clause,[],[f1407]) ).
fof(f2910,plain,
( spl95_264
| ~ spl95_105
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1206,f1191,f1054,f2908]) ).
fof(f2908,plain,
( spl95_264
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK48(X0,X1,X2),X1),sK46(X0,X1,X2))
| sK46(X0,X1,X2) = vvar(sK53(sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK48(X0,X1,X2),X1),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_264])]) ).
fof(f1054,plain,
( spl95_105
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_105])]) ).
fof(f1191,plain,
( spl95_128
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK53(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_128])]) ).
fof(f1206,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK48(X0,X1,X2),X1),sK46(X0,X1,X2))
| sK46(X0,X1,X2) = vvar(sK53(sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK48(X0,X1,X2),X1),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl95_105
| ~ spl95_128 ),
inference(resolution,[],[f1192,f1055]) ).
fof(f1055,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) )
| ~ spl95_105 ),
inference(avatar_component_clause,[],[f1054]) ).
fof(f1192,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK53(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl95_128 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f2872,plain,
( spl95_263
| ~ spl95_39
| ~ spl95_153 ),
inference(avatar_split_clause,[],[f1367,f1360,f739,f2870]) ).
fof(f2870,plain,
( spl95_263
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_263])]) ).
fof(f739,plain,
( spl95_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_39])]) ).
fof(f1360,plain,
( spl95_153
<=> ! [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,[spl95_153])]) ).
fof(f1367,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X2) )
| ~ spl95_39
| ~ spl95_153 ),
inference(resolution,[],[f1361,f740]) ).
fof(f740,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl95_39 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f1361,plain,
( ! [X6,X9,X7,X4,X5] :
( ~ visFreeVar(X7,X5)
| vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9))
| X4 = X7 )
| ~ spl95_153 ),
inference(avatar_component_clause,[],[f1360]) ).
fof(f2868,plain,
( spl95_262
| ~ spl95_40
| ~ spl95_153 ),
inference(avatar_split_clause,[],[f1366,f1360,f743,f2866]) ).
fof(f2866,plain,
( spl95_262
<=> ! [X3,X4,X0,X5,X2,X1] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_262])]) ).
fof(f743,plain,
( spl95_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_40])]) ).
fof(f1366,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,vapp(X1,X2),vabs(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0))),X4,vsubst(X5,vvar(vgensym(vapp(vapp(vapp(X1,X2),X3),vvar(X0)))),X3))) = vsubst(X0,vapp(X1,X2),vabs(X5,X4,X3))
| X0 = X5
| ~ visFreeVar(X5,X1) )
| ~ spl95_40
| ~ spl95_153 ),
inference(resolution,[],[f1361,f744]) ).
fof(f744,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl95_40 ),
inference(avatar_component_clause,[],[f743]) ).
fof(f2861,plain,
( spl95_261
| ~ spl95_16
| ~ spl95_154 ),
inference(avatar_split_clause,[],[f1376,f1370,f646,f2859]) ).
fof(f2859,plain,
( spl95_261
<=> ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK42(vvar(X0),vnoExp),sK43(vvar(X0),vnoExp),sK44(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK45(vvar(X0),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_261])]) ).
fof(f646,plain,
( spl95_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_16])]) ).
fof(f1370,plain,
( spl95_154
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0)),sK44(X0,vreduce(X0))) = X0
| vvar(sK45(X0,vreduce(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_154])]) ).
fof(f1376,plain,
( ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK42(vvar(X0),vnoExp),sK43(vvar(X0),vnoExp),sK44(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK45(vvar(X0),vnoExp)) )
| ~ spl95_16
| ~ spl95_154 ),
inference(superposition,[],[f1371,f647]) ).
fof(f647,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl95_16 ),
inference(avatar_component_clause,[],[f646]) ).
fof(f1371,plain,
( ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0)),sK44(X0,vreduce(X0))) = X0
| vvar(sK45(X0,vreduce(X0))) = X0 )
| ~ spl95_154 ),
inference(avatar_component_clause,[],[f1370]) ).
fof(f2845,plain,
( spl95_260
| ~ spl95_105
| ~ spl95_144 ),
inference(avatar_split_clause,[],[f1309,f1295,f1054,f2843]) ).
fof(f2843,plain,
( spl95_260
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK48(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_260])]) ).
fof(f1295,plain,
( spl95_144
<=> ! [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,[spl95_144])]) ).
fof(f1309,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK48(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl95_105
| ~ spl95_144 ),
inference(resolution,[],[f1296,f1055]) ).
fof(f1296,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 )
| ~ spl95_144 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f2841,plain,
( spl95_259
| ~ spl95_107
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1273,f1239,f1062,f2839]) ).
fof(f2839,plain,
( spl95_259
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( vabs(sK63(X0,X1,X2,X3),X4,vsubst(X5,sK66(X0,X1,X2,X3),X6)) = vsubst(X5,sK66(X0,X1,X2,X3),vabs(sK63(X0,X1,X2,X3),X4,X6))
| sK63(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_259])]) ).
fof(f1062,plain,
( spl95_107
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_107])]) ).
fof(f1239,plain,
( spl95_135
<=> ! [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,[spl95_135])]) ).
fof(f1273,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vabs(sK63(X0,X1,X2,X3),X4,vsubst(X5,sK66(X0,X1,X2,X3),X6)) = vsubst(X5,sK66(X0,X1,X2,X3),vabs(sK63(X0,X1,X2,X3),X4,X6))
| sK63(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) )
| ~ spl95_107
| ~ spl95_135 ),
inference(resolution,[],[f1240,f1063]) ).
fof(f1063,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) )
| ~ spl95_107 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f1240,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 )
| ~ spl95_135 ),
inference(avatar_component_clause,[],[f1239]) ).
fof(f2836,plain,
( spl95_258
| ~ spl95_94
| ~ spl95_134 ),
inference(avatar_split_clause,[],[f1246,f1235,f995,f2834]) ).
fof(f2834,plain,
( spl95_258
<=> ! [X2,X0,X1] :
( sP5(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| vsomeType(sK48(X0,X1,X2)) = vlookup(sK53(sK47(X0,X1,X2),sK48(X0,X1,X2),X0),X0)
| sP6(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_258])]) ).
fof(f995,plain,
( spl95_94
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK47(X0,X1,X2),sK48(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_94])]) ).
fof(f1235,plain,
( spl95_134
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK53(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_134])]) ).
fof(f1246,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| vsomeType(sK48(X0,X1,X2)) = vlookup(sK53(sK47(X0,X1,X2),sK48(X0,X1,X2),X0),X0)
| sP6(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl95_94
| ~ spl95_134 ),
inference(resolution,[],[f1236,f996]) ).
fof(f996,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK47(X0,X1,X2),sK48(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl95_94 ),
inference(avatar_component_clause,[],[f995]) ).
fof(f1236,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK53(X0,X1,X2),X2)
| sP6(X2,X1,X0) )
| ~ spl95_134 ),
inference(avatar_component_clause,[],[f1235]) ).
fof(f2815,plain,
( spl95_257
| ~ spl95_94
| ~ spl95_144 ),
inference(avatar_split_clause,[],[f1308,f1295,f995,f2813]) ).
fof(f2813,plain,
( spl95_257
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK48(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_257])]) ).
fof(f1308,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK47(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK48(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl95_94
| ~ spl95_144 ),
inference(resolution,[],[f1296,f996]) ).
fof(f2811,plain,
( spl95_256
| ~ spl95_113
| ~ spl95_134 ),
inference(avatar_split_clause,[],[f1248,f1235,f1087,f2809]) ).
fof(f2809,plain,
( spl95_256
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK53(vabs(X3,X1,X4),varrow(X1,X2),X0),X0)
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_256])]) ).
fof(f1087,plain,
( spl95_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,[spl95_113])]) ).
fof(f1248,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK53(vabs(X3,X1,X4),varrow(X1,X2),X0),X0)
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl95_113
| ~ spl95_134 ),
inference(resolution,[],[f1236,f1088]) ).
fof(f1088,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) )
| ~ spl95_113 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f2801,plain,
( spl95_255
| ~ spl95_113
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1207,f1191,f1087,f2799]) ).
fof(f2799,plain,
( spl95_255
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK53(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_255])]) ).
fof(f1207,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK53(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl95_113
| ~ spl95_128 ),
inference(resolution,[],[f1192,f1088]) ).
fof(f2797,plain,
( spl95_254
| ~ spl95_94
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1205,f1191,f995,f2795]) ).
fof(f2795,plain,
( spl95_254
<=> ! [X2,X0,X1] :
( sP5(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| sK47(X0,X1,X2) = vvar(sK53(sK47(X0,X1,X2),sK48(X0,X1,X2),X0))
| sP6(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_254])]) ).
fof(f1205,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| sK47(X0,X1,X2) = vvar(sK53(sK47(X0,X1,X2),sK48(X0,X1,X2),X0))
| sP6(X0,sK48(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl95_94
| ~ spl95_128 ),
inference(resolution,[],[f1192,f996]) ).
fof(f2783,plain,
( spl95_207
| ~ spl95_117
| ~ spl95_192 ),
inference(avatar_split_clause,[],[f2664,f1786,f1104,f2050]) ).
fof(f2050,plain,
( spl95_207
<=> visFreeVar(sK16,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_207])]) ).
fof(f1786,plain,
( spl95_192
<=> visFreeVar(sK18,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_192])]) ).
fof(f2664,plain,
( visFreeVar(sK16,sK17)
| ~ spl95_117
| ~ spl95_192 ),
inference(superposition,[],[f1788,f1106]) ).
fof(f1788,plain,
( visFreeVar(sK18,sK17)
| ~ spl95_192 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f2761,plain,
( spl95_253
| ~ spl95_34
| ~ spl95_157 ),
inference(avatar_split_clause,[],[f1403,f1387,f718,f2759]) ).
fof(f2759,plain,
( spl95_253
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK86(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_253])]) ).
fof(f1403,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK86(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl95_34
| ~ spl95_157 ),
inference(superposition,[],[f1388,f719]) ).
fof(f2757,plain,
( spl95_252
| ~ spl95_34
| ~ spl95_156 ),
inference(avatar_split_clause,[],[f1395,f1383,f718,f2755]) ).
fof(f2755,plain,
( spl95_252
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK87(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_252])]) ).
fof(f1395,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK87(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl95_34
| ~ spl95_156 ),
inference(superposition,[],[f1384,f719]) ).
fof(f2753,plain,
( spl95_251
| ~ spl95_13
| ~ spl95_153 ),
inference(avatar_split_clause,[],[f1364,f1360,f634,f2751]) ).
fof(f2751,plain,
( spl95_251
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,vvar(X1),vabs(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0))),X3,vsubst(X1,vvar(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0)))),X2))) = vsubst(X0,vvar(X1),vabs(X1,X3,X2))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_251])]) ).
fof(f634,plain,
( spl95_13
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_13])]) ).
fof(f1364,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,vvar(X1),vabs(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0))),X3,vsubst(X1,vvar(vgensym(vapp(vapp(vvar(X1),X2),vvar(X0)))),X2))) = vsubst(X0,vvar(X1),vabs(X1,X3,X2))
| X0 = X1 )
| ~ spl95_13
| ~ spl95_153 ),
inference(resolution,[],[f1361,f635]) ).
fof(f635,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl95_13 ),
inference(avatar_component_clause,[],[f634]) ).
fof(f2738,plain,
( spl95_250
| ~ spl95_105
| ~ spl95_120 ),
inference(avatar_split_clause,[],[f1155,f1145,f1054,f2736]) ).
fof(f2736,plain,
( spl95_250
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK48(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_250])]) ).
fof(f1145,plain,
( spl95_120
<=> ! [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,[spl95_120])]) ).
fof(f1155,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK48(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl95_105
| ~ spl95_120 ),
inference(resolution,[],[f1146,f1055]) ).
fof(f1146,plain,
( ! [X2,X3,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6)
| vtcheck(vbind(X2,X3,X4),X5,X6) )
| ~ spl95_120 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f2731,plain,
( spl95_249
| ~ spl95_95
| ~ spl95_134 ),
inference(avatar_split_clause,[],[f1245,f1235,f999,f2729]) ).
fof(f2729,plain,
( spl95_249
<=> ! [X4,X0,X3,X2,X1] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vsomeType(X3) = vlookup(sK53(X4,X3,vbind(X0,X1,X2)),vbind(X0,X1,X2))
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_249])]) ).
fof(f999,plain,
( spl95_95
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_95])]) ).
fof(f1245,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vsomeType(X3) = vlookup(sK53(X4,X3,vbind(X0,X1,X2)),vbind(X0,X1,X2))
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) )
| ~ spl95_95
| ~ spl95_134 ),
inference(resolution,[],[f1236,f1000]) ).
fof(f1000,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl95_95 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f2641,plain,
( spl95_248
| ~ spl95_122
| ~ spl95_145 ),
inference(avatar_split_clause,[],[f1312,f1299,f1162,f2639]) ).
fof(f2639,plain,
( spl95_248
<=> ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK89(X0),sK90(X0),sK91(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_248])]) ).
fof(f1162,plain,
( spl95_122
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_122])]) ).
fof(f1299,plain,
( spl95_145
<=> ! [X4,X0] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_145])]) ).
fof(f1312,plain,
( ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK89(X0),sK90(X0),sK91(X0)) = X0 )
| ~ spl95_122
| ~ spl95_145 ),
inference(resolution,[],[f1300,f1163]) ).
fof(f1163,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1 )
| ~ spl95_122 ),
inference(avatar_component_clause,[],[f1162]) ).
fof(f1300,plain,
( ! [X0,X4] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0 )
| ~ spl95_145 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f2637,plain,
( spl95_247
| ~ spl95_123
| ~ spl95_145 ),
inference(avatar_split_clause,[],[f1311,f1299,f1166,f2635]) ).
fof(f2635,plain,
( spl95_247
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_247])]) ).
fof(f1166,plain,
( spl95_123
<=> ! [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,[spl95_123])]) ).
fof(f1311,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) )
| ~ spl95_123
| ~ spl95_145 ),
inference(resolution,[],[f1300,f1167]) ).
fof(f1167,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl95_123 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f2633,plain,
( spl95_246
| ~ spl95_129
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1219,f1212,f1195,f2631]) ).
fof(f2631,plain,
( spl95_246
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_246])]) ).
fof(f1195,plain,
( spl95_129
<=> ! [X2,X0,X1] :
( vbind(sK55(X0,X1,X2),sK54(X0,X1,X2),sK57(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_129])]) ).
fof(f1212,plain,
( spl95_131
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_131])]) ).
fof(f1219,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1 )
| ~ spl95_129
| ~ spl95_131 ),
inference(resolution,[],[f1213,f1196]) ).
fof(f1196,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vbind(sK55(X0,X1,X2),sK54(X0,X1,X2),sK57(X0,X1,X2)) = X1 )
| ~ spl95_129 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f1213,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0 )
| ~ spl95_131 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f2629,plain,
( spl95_245
| ~ spl95_94
| ~ spl95_120 ),
inference(avatar_split_clause,[],[f1154,f1145,f995,f2627]) ).
fof(f2627,plain,
( spl95_245
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK48(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_245])]) ).
fof(f1154,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK47(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK48(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl95_94
| ~ spl95_120 ),
inference(resolution,[],[f1146,f996]) ).
fof(f2614,plain,
( spl95_244
| ~ spl95_96
| ~ spl95_105 ),
inference(avatar_split_clause,[],[f1102,f1054,f1003,f2612]) ).
fof(f2612,plain,
( spl95_244
<=> ! [X4,X0,X3,X2,X1] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK46(vbind(X0,X1,X2),X3,X4),varrow(sK48(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK46(vbind(X0,X1,X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_244])]) ).
fof(f1003,plain,
( spl95_96
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_96])]) ).
fof(f1102,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK46(vbind(X0,X1,X2),X3,X4),varrow(sK48(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK46(vbind(X0,X1,X2),X3,X4)) )
| ~ spl95_96
| ~ spl95_105 ),
inference(resolution,[],[f1055,f1004]) ).
fof(f1004,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl95_96 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f2591,plain,
( ~ spl95_23
| ~ spl95_243 ),
inference(avatar_contradiction_clause,[],[f2588]) ).
fof(f2588,plain,
( $false
| ~ spl95_23
| ~ spl95_243 ),
inference(resolution,[],[f2586,f675]) ).
fof(f675,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl95_23 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f674,plain,
( spl95_23
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_23])]) ).
fof(f2586,plain,
( visFreeVar(sK16,vabs(sK16,sK19,veabs))
| ~ spl95_243 ),
inference(avatar_component_clause,[],[f2584]) ).
fof(f2584,plain,
( spl95_243
<=> visFreeVar(sK16,vabs(sK16,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_243])]) ).
fof(f2587,plain,
( spl95_243
| ~ spl95_102
| ~ spl95_117 ),
inference(avatar_split_clause,[],[f2582,f1104,f1036,f2584]) ).
fof(f1036,plain,
( spl95_102
<=> visFreeVar(sK16,vabs(sK18,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_102])]) ).
fof(f2582,plain,
( visFreeVar(sK16,vabs(sK16,sK19,veabs))
| ~ spl95_102
| ~ spl95_117 ),
inference(forward_demodulation,[],[f1038,f1106]) ).
fof(f1038,plain,
( visFreeVar(sK16,vabs(sK18,sK19,veabs))
| ~ spl95_102 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f2579,plain,
( ~ spl95_1
| ~ spl95_192
| spl95_5
| ~ spl95_165 ),
inference(avatar_split_clause,[],[f1504,f1470,f601,f1786,f581]) ).
fof(f581,plain,
( spl95_1
<=> vtcheck(sK15,sK17,sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_1])]) ).
fof(f1470,plain,
( spl95_165
<=> ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| ~ visFreeVar(sK18,X0)
| ~ vtcheck(sK15,X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_165])]) ).
fof(f1504,plain,
( ~ visFreeVar(sK18,sK17)
| ~ vtcheck(sK15,sK17,sK14)
| spl95_5
| ~ spl95_165 ),
inference(resolution,[],[f1471,f603]) ).
fof(f1471,plain,
( ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| ~ visFreeVar(sK18,X0)
| ~ vtcheck(sK15,X0,sK14) )
| ~ spl95_165 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f2564,plain,
( spl95_242
| ~ spl95_95
| ~ spl95_151 ),
inference(avatar_split_clause,[],[f1353,f1346,f999,f2562]) ).
fof(f2562,plain,
( spl95_242
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),X5)
| ~ vtcheck(X0,X2,X6)
| ~ visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(X0,vabs(X3,X4,veabs),X5)
| visFreeVar(X1,vabs(X3,X4,veabs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_242])]) ).
fof(f1346,plain,
( spl95_151
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| ~ visFreeVar(X4,X3)
| X2 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_151])]) ).
fof(f1353,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),X5)
| ~ vtcheck(X0,X2,X6)
| ~ visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(X0,vabs(X3,X4,veabs),X5)
| visFreeVar(X1,vabs(X3,X4,veabs)) )
| ~ spl95_95
| ~ spl95_151 ),
inference(resolution,[],[f1347,f1000]) ).
fof(f1347,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(X1,X3,X0)
| ~ visFreeVar(X4,X3)
| X2 = X4 )
| ~ spl95_151 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f2560,plain,
( spl95_241
| ~ spl95_95
| ~ spl95_150 ),
inference(avatar_split_clause,[],[f1350,f1342,f999,f2558]) ).
fof(f2558,plain,
( spl95_241
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),X5)
| ~ vtcheck(X0,X2,X6)
| visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(X0,vabs(X3,X4,veabs),X5)
| visFreeVar(X1,vabs(X3,X4,veabs)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_241])]) ).
fof(f1342,plain,
( spl95_150
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| visFreeVar(X4,X3)
| X2 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_150])]) ).
fof(f1350,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),X5)
| ~ vtcheck(X0,X2,X6)
| visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(X0,vabs(X3,X4,veabs),X5)
| visFreeVar(X1,vabs(X3,X4,veabs)) )
| ~ spl95_95
| ~ spl95_150 ),
inference(resolution,[],[f1343,f1000]) ).
fof(f1343,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(X1,X3,X0)
| visFreeVar(X4,X3)
| X2 = X4 )
| ~ spl95_150 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f2470,plain,
( spl95_240
| ~ spl95_113
| ~ spl95_151 ),
inference(avatar_split_clause,[],[f1354,f1346,f1087,f2468]) ).
fof(f2468,plain,
( spl95_240
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),varrow(X4,X5))
| ~ vtcheck(X0,X2,X6)
| ~ visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(vbind(X3,X4,vbind(X1,X6,X0)),veabs,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_240])]) ).
fof(f1354,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),varrow(X4,X5))
| ~ vtcheck(X0,X2,X6)
| ~ visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(vbind(X3,X4,vbind(X1,X6,X0)),veabs,X5) )
| ~ spl95_113
| ~ spl95_151 ),
inference(resolution,[],[f1347,f1088]) ).
fof(f2466,plain,
( spl95_239
| ~ spl95_113
| ~ spl95_150 ),
inference(avatar_split_clause,[],[f1351,f1342,f1087,f2464]) ).
fof(f2464,plain,
( spl95_239
<=> ! [X3,X4,X0,X6,X5,X2,X1] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),varrow(X4,X5))
| ~ vtcheck(X0,X2,X6)
| visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(vbind(X3,X4,vbind(X1,X6,X0)),veabs,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_239])]) ).
fof(f1351,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X0,vsubst(X1,X2,vabs(X3,X4,veabs)),varrow(X4,X5))
| ~ vtcheck(X0,X2,X6)
| visFreeVar(X3,X2)
| X1 = X3
| ~ vtcheck(vbind(X3,X4,vbind(X1,X6,X0)),veabs,X5) )
| ~ spl95_113
| ~ spl95_150 ),
inference(resolution,[],[f1343,f1088]) ).
fof(f2462,plain,
( spl95_238
| ~ spl95_122
| ~ spl95_132 ),
inference(avatar_split_clause,[],[f1226,f1216,f1162,f2460]) ).
fof(f2460,plain,
( spl95_238
<=> ! [X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK89(X3),sK90(X3),sK91(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_238])]) ).
fof(f1216,plain,
( spl95_132
<=> ! [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,[spl95_132])]) ).
fof(f1226,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| vnoExp = vreduce(vapp(X3,X4))
| vabs(sK89(X3),sK90(X3),sK91(X3)) = X3 )
| ~ spl95_122
| ~ spl95_132 ),
inference(resolution,[],[f1217,f1163]) ).
fof(f1217,plain,
( ! [X3,X0,X4,X5] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0)) )
| ~ spl95_132 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f2458,plain,
( spl95_237
| ~ spl95_123
| ~ spl95_132 ),
inference(avatar_split_clause,[],[f1225,f1216,f1166,f2456]) ).
fof(f2456,plain,
( spl95_237
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| ~ visValue(X3)
| vsomeExp(vsubst(X4,X3,X5)) = vreduce(vapp(vabs(X4,X6,X5),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_237])]) ).
fof(f1225,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| ~ visValue(X3)
| vsomeExp(vsubst(X4,X3,X5)) = vreduce(vapp(vabs(X4,X6,X5),X3)) )
| ~ spl95_123
| ~ spl95_132 ),
inference(resolution,[],[f1217,f1167]) ).
fof(f2454,plain,
( spl95_236
| ~ spl95_92
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1224,f1212,f981,f2452]) ).
fof(f2452,plain,
( spl95_236
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK62(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_236])]) ).
fof(f981,plain,
( spl95_92
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_92])]) ).
fof(f1224,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK62(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 )
| ~ spl95_92
| ~ spl95_131 ),
inference(superposition,[],[f1213,f982]) ).
fof(f982,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl95_92 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f2450,plain,
( spl95_235
| ~ spl95_119
| ~ spl95_129 ),
inference(avatar_split_clause,[],[f1208,f1195,f1141,f2448]) ).
fof(f2448,plain,
( spl95_235
<=> ! [X0,X1] :
( vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_235])]) ).
fof(f1141,plain,
( spl95_119
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_119])]) ).
fof(f1208,plain,
( ! [X0,X1] :
( vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl95_119
| ~ spl95_129 ),
inference(resolution,[],[f1196,f1142]) ).
fof(f1142,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl95_119 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f2407,plain,
( spl95_234
| spl95_3
| ~ spl95_33
| ~ spl95_122 ),
inference(avatar_split_clause,[],[f1171,f1162,f714,f591,f2405]) ).
fof(f2405,plain,
( spl95_234
<=> ! [X0,X3,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK89(vabs(X0,X1,X2)),sK90(vabs(X0,X1,X2)),sK91(vabs(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_234])]) ).
fof(f591,plain,
( spl95_3
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_3])]) ).
fof(f714,plain,
( spl95_33
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_33])]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK89(vabs(X0,X1,X2)),sK90(vabs(X0,X1,X2)),sK91(vabs(X0,X1,X2))) )
| ~ spl95_33
| ~ spl95_122 ),
inference(superposition,[],[f1163,f715]) ).
fof(f715,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl95_33 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f2403,plain,
( spl95_233
| ~ spl95_94
| ~ spl95_96 ),
inference(avatar_split_clause,[],[f1015,f1003,f995,f2401]) ).
fof(f2401,plain,
( spl95_233
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X0,sK47(vbind(X1,X2,X0),X3,X4),sK48(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK47(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_233])]) ).
fof(f1015,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,sK47(vbind(X1,X2,X0),X3,X4),sK48(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK47(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) )
| ~ spl95_94
| ~ spl95_96 ),
inference(resolution,[],[f1004,f996]) ).
fof(f2368,plain,
( spl95_232
| ~ spl95_97
| ~ spl95_145 ),
inference(avatar_split_clause,[],[f1313,f1299,f1007,f2366]) ).
fof(f2366,plain,
( spl95_232
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_232])]) ).
fof(f1007,plain,
( spl95_97
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_97])]) ).
fof(f1313,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) )
| ~ spl95_97
| ~ spl95_145 ),
inference(resolution,[],[f1300,f1008]) ).
fof(f1008,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl95_97 ),
inference(avatar_component_clause,[],[f1007]) ).
fof(f2364,plain,
( spl95_231
| ~ spl95_113
| ~ spl95_144 ),
inference(avatar_split_clause,[],[f1310,f1295,f1087,f2362]) ).
fof(f2362,plain,
( spl95_231
<=> ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),vabs(X5,X6,X7),varrow(X6,X8))
| X0 = X2
| ~ vtcheck(vbind(X5,X6,vbind(X2,X3,vbind(X0,X1,X4))),X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_231])]) ).
fof(f1310,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),vabs(X5,X6,X7),varrow(X6,X8))
| X0 = X2
| ~ vtcheck(vbind(X5,X6,vbind(X2,X3,vbind(X0,X1,X4))),X7,X8) )
| ~ spl95_113
| ~ spl95_144 ),
inference(resolution,[],[f1296,f1088]) ).
fof(f2360,plain,
( spl95_230
| ~ spl95_100
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1220,f1212,f1028,f2358]) ).
fof(f2358,plain,
( spl95_230
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_230])]) ).
fof(f1028,plain,
( spl95_100
<=> ! [X2,X0,X1] :
( vlookup(sK56(X0,X1,X2),sK57(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_100])]) ).
fof(f1220,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) )
| ~ spl95_100
| ~ spl95_131 ),
inference(resolution,[],[f1213,f1029]) ).
fof(f1029,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK56(X0,X1,X2),sK57(X0,X1,X2)) = X0 )
| ~ spl95_100 ),
inference(avatar_component_clause,[],[f1028]) ).
fof(f2348,plain,
( spl95_229
| ~ spl95_103
| ~ spl95_117 ),
inference(avatar_split_clause,[],[f1850,f1104,f1040,f2345]) ).
fof(f1040,plain,
( spl95_103
<=> vtcheck(sK15,vabs(sK18,sK19,veabs),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_103])]) ).
fof(f1850,plain,
( vtcheck(sK15,vabs(sK16,sK19,veabs),sK20)
| ~ spl95_103
| ~ spl95_117 ),
inference(superposition,[],[f1042,f1106]) ).
fof(f1042,plain,
( vtcheck(sK15,vabs(sK18,sK19,veabs),sK20)
| ~ spl95_103 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f2343,plain,
( spl95_228
| ~ spl95_95
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1204,f1191,f999,f2341]) ).
fof(f2341,plain,
( spl95_228
<=> ! [X4,X0,X3,X2,X1] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vvar(sK53(X4,X3,vbind(X0,X1,X2))) = X4
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_228])]) ).
fof(f1204,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(vbind(X0,X1,X2),X3,X4)
| vvar(sK53(X4,X3,vbind(X0,X1,X2))) = X4
| sP6(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X4,X3)
| visFreeVar(X0,X4) )
| ~ spl95_95
| ~ spl95_128 ),
inference(resolution,[],[f1192,f1000]) ).
fof(f2332,plain,
( spl95_227
| ~ spl95_101
| ~ spl95_129 ),
inference(avatar_split_clause,[],[f1209,f1195,f1032,f2330]) ).
fof(f2330,plain,
( spl95_227
<=> ! [X0,X1] :
( vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_227])]) ).
fof(f1032,plain,
( spl95_101
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_101])]) ).
fof(f1209,plain,
( ! [X0,X1] :
( vbind(sK55(vlookup(X0,X1),X1,X0),sK54(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl95_101
| ~ spl95_129 ),
inference(resolution,[],[f1196,f1033]) ).
fof(f1033,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl95_101 ),
inference(avatar_component_clause,[],[f1032]) ).
fof(f2273,plain,
( spl95_226
| ~ spl95_60
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1265,f1239,f832,f2271]) ).
fof(f2271,plain,
( spl95_226
<=> ! [X2,X3,X4,X0,X5,X1] :
( vabs(X0,X1,vsubst(X2,vapp(X3,X4),X5)) = vsubst(X2,vapp(X3,X4),vabs(X0,X1,X5))
| X0 = X2
| visFreeVar(X0,X3)
| visFreeVar(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_226])]) ).
fof(f832,plain,
( spl95_60
<=> ! [X4,X2,X3] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_60])]) ).
fof(f1265,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vabs(X0,X1,vsubst(X2,vapp(X3,X4),X5)) = vsubst(X2,vapp(X3,X4),vabs(X0,X1,X5))
| X0 = X2
| visFreeVar(X0,X3)
| visFreeVar(X0,X4) )
| ~ spl95_60
| ~ spl95_135 ),
inference(resolution,[],[f1240,f833]) ).
fof(f833,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl95_60 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f2269,plain,
( spl95_225
| ~ spl95_97
| ~ spl95_132 ),
inference(avatar_split_clause,[],[f1227,f1216,f1007,f2267]) ).
fof(f2267,plain,
( spl95_225
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| visValue(X3)
| vnoExp = vreduce(vapp(vabs(X4,X5,X6),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_225])]) ).
fof(f1227,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| visValue(X3)
| vnoExp = vreduce(vapp(vabs(X4,X5,X6),X3)) )
| ~ spl95_97
| ~ spl95_132 ),
inference(resolution,[],[f1217,f1008]) ).
fof(f2265,plain,
( spl95_224
| ~ spl95_100
| ~ spl95_119 ),
inference(avatar_split_clause,[],[f1148,f1141,f1028,f2263]) ).
fof(f2263,plain,
( spl95_224
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_224])]) ).
fof(f1148,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) )
| ~ spl95_100
| ~ spl95_119 ),
inference(resolution,[],[f1142,f1029]) ).
fof(f2241,plain,
( ~ spl95_17
| spl95_218 ),
inference(avatar_contradiction_clause,[],[f2240]) ).
fof(f2240,plain,
( $false
| ~ spl95_17
| spl95_218 ),
inference(resolution,[],[f2194,f651]) ).
fof(f651,plain,
( ! [X2,X0,X1] : visValue(vabs(X0,X1,X2))
| ~ spl95_17 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f650,plain,
( spl95_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_17])]) ).
fof(f2194,plain,
( ~ visValue(vabs(sK16,sK19,veabs))
| spl95_218 ),
inference(avatar_component_clause,[],[f2192]) ).
fof(f2192,plain,
( spl95_218
<=> visValue(vabs(sK16,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_218])]) ).
fof(f2233,plain,
( spl95_223
| ~ spl95_41
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1263,f1239,f752,f2231]) ).
fof(f2231,plain,
( spl95_223
<=> ! [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,[spl95_223])]) ).
fof(f752,plain,
( spl95_41
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_41])]) ).
fof(f1263,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) )
| ~ spl95_41
| ~ spl95_135 ),
inference(resolution,[],[f1240,f753]) ).
fof(f753,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl95_41 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f2229,plain,
( spl95_222
| ~ spl95_92
| ~ spl95_101 ),
inference(avatar_split_clause,[],[f1048,f1032,f981,f2227]) ).
fof(f2227,plain,
( spl95_222
<=> ! [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,[spl95_222])]) ).
fof(f1048,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 )
| ~ spl95_92
| ~ spl95_101 ),
inference(superposition,[],[f1033,f982]) ).
fof(f2209,plain,
( spl95_221
| ~ spl95_42
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1223,f1212,f756,f2207]) ).
fof(f2207,plain,
( spl95_221
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK62(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_221])]) ).
fof(f756,plain,
( spl95_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_42])]) ).
fof(f1223,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK62(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 )
| ~ spl95_42
| ~ spl95_131 ),
inference(superposition,[],[f1213,f757]) ).
fof(f757,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl95_42 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f2203,plain,
( spl95_220
| spl95_3
| ~ spl95_33
| ~ spl95_123 ),
inference(avatar_split_clause,[],[f1173,f1166,f714,f591,f2201]) ).
fof(f2201,plain,
( spl95_220
<=> ! [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,[spl95_220])]) ).
fof(f1173,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))) )
| ~ spl95_33
| ~ spl95_123 ),
inference(superposition,[],[f1167,f715]) ).
fof(f2199,plain,
( spl95_219
| ~ spl95_92
| ~ spl95_119 ),
inference(avatar_split_clause,[],[f1152,f1141,f981,f2197]) ).
fof(f2197,plain,
( spl95_219
<=> ! [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,[spl95_219])]) ).
fof(f1152,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 )
| ~ spl95_92
| ~ spl95_119 ),
inference(superposition,[],[f1142,f982]) ).
fof(f2195,plain,
( ~ spl95_218
| ~ spl95_8
| ~ spl95_117
| ~ spl95_168 ),
inference(avatar_split_clause,[],[f1805,f1483,f1104,f614,f2192]) ).
fof(f614,plain,
( spl95_8
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_8])]) ).
fof(f1483,plain,
( spl95_168
<=> vabs(sK18,sK19,veabs) = vvar(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_168])]) ).
fof(f1805,plain,
( ~ visValue(vabs(sK16,sK19,veabs))
| ~ spl95_8
| ~ spl95_117
| ~ spl95_168 ),
inference(forward_demodulation,[],[f1790,f1106]) ).
fof(f1790,plain,
( ~ visValue(vabs(sK18,sK19,veabs))
| ~ spl95_8
| ~ spl95_168 ),
inference(superposition,[],[f615,f1485]) ).
fof(f1485,plain,
( vabs(sK18,sK19,veabs) = vvar(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15)))
| ~ spl95_168 ),
inference(avatar_component_clause,[],[f1483]) ).
fof(f615,plain,
( ! [X0] : ~ visValue(vvar(X0))
| ~ spl95_8 ),
inference(avatar_component_clause,[],[f614]) ).
fof(f2190,plain,
( spl95_217
| ~ spl95_100
| ~ spl95_101 ),
inference(avatar_split_clause,[],[f1044,f1032,f1028,f2188]) ).
fof(f2188,plain,
( spl95_217
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_217])]) ).
fof(f1044,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK56(vlookup(X0,X1),X1,X0),sK57(vlookup(X0,X1),X1,X0)) )
| ~ spl95_100
| ~ spl95_101 ),
inference(resolution,[],[f1033,f1029]) ).
fof(f2152,plain,
( spl95_216
| ~ spl95_113
| ~ spl95_120 ),
inference(avatar_split_clause,[],[f1156,f1145,f1087,f2150]) ).
fof(f2150,plain,
( spl95_216
<=> ! [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,[spl95_216])]) ).
fof(f1156,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) )
| ~ spl95_113
| ~ spl95_120 ),
inference(resolution,[],[f1146,f1088]) ).
fof(f2148,plain,
( spl95_215
| ~ spl95_95
| ~ spl95_115 ),
inference(avatar_split_clause,[],[f1117,f1095,f999,f2146]) ).
fof(f2146,plain,
( spl95_215
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(X5,X3),X6)
| ~ vtcheck(X2,X5,varrow(X4,X6))
| visFreeVar(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_215])]) ).
fof(f1095,plain,
( spl95_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,[spl95_115])]) ).
fof(f1117,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(vbind(X0,X1,X2),vapp(X5,X3),X6)
| ~ vtcheck(X2,X5,varrow(X4,X6))
| visFreeVar(X0,X5) )
| ~ spl95_95
| ~ spl95_115 ),
inference(resolution,[],[f1096,f1000]) ).
fof(f1096,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vapp(X2,X3),X4) )
| ~ spl95_115 ),
inference(avatar_component_clause,[],[f1095]) ).
fof(f2144,plain,
( spl95_214
| ~ spl95_92
| ~ spl95_114 ),
inference(avatar_split_clause,[],[f1115,f1091,f981,f2142]) ).
fof(f2142,plain,
( spl95_214
<=> ! [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,[spl95_214])]) ).
fof(f1091,plain,
( spl95_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,[spl95_114])]) ).
fof(f1115,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 )
| ~ spl95_92
| ~ spl95_114 ),
inference(superposition,[],[f1092,f982]) ).
fof(f1092,plain,
( ! [X2,X3,X0,X1,X4] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,X3,X4)
| vtcheck(vbind(X0,X1,X2),X3,X4) )
| ~ spl95_114 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f2140,plain,
( spl95_213
| ~ spl95_96
| ~ spl95_113 ),
inference(avatar_split_clause,[],[f1112,f1087,f1003,f2138]) ).
fof(f2138,plain,
( spl95_213
<=> ! [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,[spl95_213])]) ).
fof(f1112,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)) )
| ~ spl95_96
| ~ spl95_113 ),
inference(resolution,[],[f1088,f1004]) ).
fof(f2122,plain,
( spl95_212
| ~ spl95_23
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1262,f1239,f674,f2120]) ).
fof(f2120,plain,
( spl95_212
<=> ! [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,[spl95_212])]) ).
fof(f1262,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 )
| ~ spl95_23
| ~ spl95_135 ),
inference(resolution,[],[f1240,f675]) ).
fof(f2076,plain,
( spl95_211
| ~ spl95_113
| ~ spl95_147 ),
inference(avatar_split_clause,[],[f1326,f1322,f1087,f2074]) ).
fof(f2074,plain,
( spl95_211
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vtcheck(X0,vabs(X1,X2,X3),varrow(X2,X4))
| ~ vtcheck(X0,X5,X6)
| ~ vtcheck(vbind(X1,X2,vbind(X1,X6,X0)),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_211])]) ).
fof(f1322,plain,
( spl95_147
<=> ! [X5,X3,X4,X7,X0,X6,X1] :
( vtcheck(X1,vabs(X4,X5,X6),X7)
| ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_147])]) ).
fof(f1326,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X0,vabs(X1,X2,X3),varrow(X2,X4))
| ~ vtcheck(X0,X5,X6)
| ~ vtcheck(vbind(X1,X2,vbind(X1,X6,X0)),X3,X4) )
| ~ spl95_113
| ~ spl95_147 ),
inference(resolution,[],[f1323,f1088]) ).
fof(f1323,plain,
( ! [X3,X0,X1,X6,X7,X4,X5] :
( ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| vtcheck(X1,vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) )
| ~ spl95_147 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f2072,plain,
( spl95_210
| ~ spl95_95
| ~ spl95_144 ),
inference(avatar_split_clause,[],[f1306,f1295,f999,f2070]) ).
fof(f2070,plain,
( spl95_210
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),X5,X6)
| visFreeVar(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_210])]) ).
fof(f1306,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| X0 = X2
| ~ vtcheck(vbind(X0,X1,X4),X5,X6)
| visFreeVar(X2,X5) )
| ~ spl95_95
| ~ spl95_144 ),
inference(resolution,[],[f1296,f1000]) ).
fof(f2068,plain,
( spl95_209
| ~ spl95_96
| ~ spl95_139 ),
inference(avatar_split_clause,[],[f1302,f1275,f1003,f2066]) ).
fof(f2066,plain,
( spl95_209
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK50(X0,X1,X2),sK52(X0,X1,X2))
| visFreeVar(sK49(X0,X1,X2),sK50(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_209])]) ).
fof(f1275,plain,
( spl95_139
<=> ! [X2,X0,X1] :
( vtcheck(vbind(sK49(X0,X1,X2),sK51(X0,X1,X2),X0),sK50(X0,X1,X2),sK52(X0,X1,X2))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_139])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK50(X0,X1,X2),sK52(X0,X1,X2))
| visFreeVar(sK49(X0,X1,X2),sK50(X0,X1,X2)) )
| ~ spl95_96
| ~ spl95_139 ),
inference(resolution,[],[f1276,f1004]) ).
fof(f1276,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(sK49(X0,X1,X2),sK51(X0,X1,X2),X0),sK50(X0,X1,X2),sK52(X0,X1,X2))
| ~ sP5(X0,X1,X2) )
| ~ spl95_139 ),
inference(avatar_component_clause,[],[f1275]) ).
fof(f2064,plain,
( spl95_208
| ~ spl95_32
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1264,f1239,f710,f2062]) ).
fof(f2062,plain,
( spl95_208
<=> ! [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,[spl95_208])]) ).
fof(f710,plain,
( spl95_32
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_32])]) ).
fof(f1264,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 )
| ~ spl95_32
| ~ spl95_135 ),
inference(resolution,[],[f1240,f711]) ).
fof(f711,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl95_32 ),
inference(avatar_component_clause,[],[f710]) ).
fof(f2053,plain,
( ~ spl95_207
| ~ spl95_117
| spl95_192 ),
inference(avatar_split_clause,[],[f1956,f1786,f1104,f2050]) ).
fof(f1956,plain,
( ~ visFreeVar(sK16,sK17)
| ~ spl95_117
| spl95_192 ),
inference(superposition,[],[f1787,f1106]) ).
fof(f1787,plain,
( ~ visFreeVar(sK18,sK17)
| spl95_192 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f2045,plain,
( spl95_206
| ~ spl95_43
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1221,f1212,f760,f2043]) ).
fof(f2043,plain,
( spl95_206
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| sK56(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_206])]) ).
fof(f760,plain,
( spl95_43
<=> ! [X2,X0,X1] :
( sK56(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_43])]) ).
fof(f1221,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0
| sK56(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl95_43
| ~ spl95_131 ),
inference(resolution,[],[f1213,f761]) ).
fof(f761,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK56(X0,X1,X2) = X2 )
| ~ spl95_43 ),
inference(avatar_component_clause,[],[f760]) ).
fof(f2004,plain,
( spl95_205
| spl95_3
| ~ spl95_16
| ~ spl95_122 ),
inference(avatar_split_clause,[],[f1170,f1162,f646,f591,f2002]) ).
fof(f2002,plain,
( spl95_205
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK89(vvar(X0)),sK90(vvar(X0)),sK91(vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_205])]) ).
fof(f1170,plain,
( ! [X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK89(vvar(X0)),sK90(vvar(X0)),sK91(vvar(X0))) )
| ~ spl95_16
| ~ spl95_122 ),
inference(superposition,[],[f1163,f647]) ).
fof(f2000,plain,
( spl95_204
| ~ spl95_42
| ~ spl95_101 ),
inference(avatar_split_clause,[],[f1047,f1032,f756,f1998]) ).
fof(f1998,plain,
( spl95_204
<=> ! [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,[spl95_204])]) ).
fof(f1047,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) )
| ~ spl95_42
| ~ spl95_101 ),
inference(superposition,[],[f1033,f757]) ).
fof(f1986,plain,
( spl95_203
| ~ spl95_11
| ~ spl95_135 ),
inference(avatar_split_clause,[],[f1266,f1239,f626,f1984]) ).
fof(f1984,plain,
( spl95_203
<=> ! [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,[spl95_203])]) ).
fof(f626,plain,
( spl95_11
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_11])]) ).
fof(f1266,plain,
( ! [X2,X3,X0,X1] :
( vabs(vgensym(X0),X1,vsubst(X2,X0,X3)) = vsubst(X2,X0,vabs(vgensym(X0),X1,X3))
| vgensym(X0) = X2 )
| ~ spl95_11
| ~ spl95_135 ),
inference(resolution,[],[f1240,f627]) ).
fof(f627,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl95_11 ),
inference(avatar_component_clause,[],[f626]) ).
fof(f1938,plain,
( spl95_202
| ~ spl95_19
| ~ spl95_148 ),
inference(avatar_split_clause,[],[f1336,f1328,f658,f1936]) ).
fof(f1936,plain,
( spl95_202
<=> ! [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,[spl95_202])]) ).
fof(f658,plain,
( spl95_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_19])]) ).
fof(f1328,plain,
( spl95_148
<=> ! [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,[spl95_148])]) ).
fof(f1336,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl95_19
| ~ spl95_148 ),
inference(duplicate_literal_removal,[],[f1333]) ).
fof(f1333,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0)
| vnoExp = vreduce(X0) )
| ~ spl95_19
| ~ spl95_148 ),
inference(resolution,[],[f1329,f659]) ).
fof(f659,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl95_19 ),
inference(avatar_component_clause,[],[f658]) ).
fof(f1329,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) )
| ~ spl95_148 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1934,plain,
( spl95_201
| ~ spl95_42
| ~ spl95_119 ),
inference(avatar_split_clause,[],[f1151,f1141,f756,f1932]) ).
fof(f1932,plain,
( spl95_201
<=> ! [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,[spl95_201])]) ).
fof(f1151,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1) )
| ~ spl95_42
| ~ spl95_119 ),
inference(superposition,[],[f1142,f757]) ).
fof(f1930,plain,
( spl95_200
| ~ spl95_60
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1137,f1099,f832,f1928]) ).
fof(f1928,plain,
( spl95_200
<=> ! [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,[spl95_200])]) ).
fof(f1099,plain,
( spl95_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,[spl95_116])]) ).
fof(f1137,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)) )
| ~ spl95_60
| ~ spl95_116 ),
inference(superposition,[],[f833,f1100]) ).
fof(f1100,plain,
( ! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7))
| ~ spl95_116 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1926,plain,
( spl95_199
| ~ spl95_113
| ~ spl95_115 ),
inference(avatar_split_clause,[],[f1119,f1095,f1087,f1924]) ).
fof(f1924,plain,
( spl95_199
<=> ! [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,[spl95_199])]) ).
fof(f1119,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) )
| ~ spl95_113
| ~ spl95_115 ),
inference(resolution,[],[f1096,f1088]) ).
fof(f1922,plain,
( spl95_198
| ~ spl95_105
| ~ spl95_115 ),
inference(avatar_split_clause,[],[f1118,f1095,f1054,f1920]) ).
fof(f1920,plain,
( spl95_198
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(X0,X1,sK48(X0,X2,X3))
| vtcheck(X0,vapp(sK46(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_198])]) ).
fof(f1118,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(X0,X1,sK48(X0,X2,X3))
| vtcheck(X0,vapp(sK46(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) )
| ~ spl95_105
| ~ spl95_115 ),
inference(resolution,[],[f1096,f1055]) ).
fof(f1846,plain,
( spl95_197
| ~ spl95_43
| ~ spl95_119 ),
inference(avatar_split_clause,[],[f1149,f1141,f760,f1844]) ).
fof(f1844,plain,
( spl95_197
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK56(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_197])]) ).
fof(f1149,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK56(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl95_43
| ~ spl95_119 ),
inference(resolution,[],[f1142,f761]) ).
fof(f1842,plain,
( spl95_196
| ~ spl95_83
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1125,f1099,f934,f1840]) ).
fof(f1840,plain,
( spl95_196
<=> ! [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,[spl95_196])]) ).
fof(f1125,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3))
| ~ spl95_83
| ~ spl95_116 ),
inference(superposition,[],[f1100,f935]) ).
fof(f1838,plain,
( spl95_195
| ~ spl95_83
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1122,f1099,f934,f1836]) ).
fof(f1836,plain,
( spl95_195
<=> ! [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,[spl95_195])]) ).
fof(f1122,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4))
| ~ spl95_83
| ~ spl95_116 ),
inference(superposition,[],[f1100,f935]) ).
fof(f1833,plain,
( ~ spl95_194
| ~ spl95_117
| spl95_193 ),
inference(avatar_split_clause,[],[f1824,f1820,f1104,f1830]) ).
fof(f1830,plain,
( spl95_194
<=> vsomeType(sK20) = vlookup(sK53(vabs(sK16,sK19,veabs),sK20,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_194])]) ).
fof(f1820,plain,
( spl95_193
<=> vsomeType(sK20) = vlookup(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_193])]) ).
fof(f1824,plain,
( vsomeType(sK20) != vlookup(sK53(vabs(sK16,sK19,veabs),sK20,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| ~ spl95_117
| spl95_193 ),
inference(forward_demodulation,[],[f1821,f1106]) ).
fof(f1821,plain,
( vsomeType(sK20) != vlookup(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| spl95_193 ),
inference(avatar_component_clause,[],[f1820]) ).
fof(f1826,plain,
( spl95_170
| ~ spl95_117
| ~ spl95_169 ),
inference(avatar_split_clause,[],[f1825,f1487,f1104,f1494]) ).
fof(f1494,plain,
( spl95_170
<=> sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK16,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_170])]) ).
fof(f1487,plain,
( spl95_169
<=> sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_169])]) ).
fof(f1825,plain,
( sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK16,sK19,veabs))
| ~ spl95_117
| ~ spl95_169 ),
inference(forward_demodulation,[],[f1489,f1106]) ).
fof(f1489,plain,
( sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| ~ spl95_169 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f1823,plain,
( spl95_167
| spl95_193
| spl95_169
| ~ spl95_4
| ~ spl95_134 ),
inference(avatar_split_clause,[],[f1244,f1235,f596,f1487,f1820,f1479]) ).
fof(f1479,plain,
( spl95_167
<=> sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_167])]) ).
fof(f596,plain,
( spl95_4
<=> vtcheck(vbind(sK16,sK14,sK15),vabs(sK18,sK19,veabs),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_4])]) ).
fof(f1244,plain,
( sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| vsomeType(sK20) = vlookup(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15)),vbind(sK16,sK14,sK15))
| sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| ~ spl95_4
| ~ spl95_134 ),
inference(resolution,[],[f1236,f598]) ).
fof(f598,plain,
( vtcheck(vbind(sK16,sK14,sK15),vabs(sK18,sK19,veabs),sK20)
| ~ spl95_4 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f1789,plain,
( ~ spl95_1
| spl95_192
| spl95_5
| ~ spl95_163 ),
inference(avatar_split_clause,[],[f1461,f1458,f601,f1786,f581]) ).
fof(f1458,plain,
( spl95_163
<=> ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| visFreeVar(sK18,X0)
| ~ vtcheck(sK15,X0,sK14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_163])]) ).
fof(f1461,plain,
( visFreeVar(sK18,sK17)
| ~ vtcheck(sK15,sK17,sK14)
| spl95_5
| ~ spl95_163 ),
inference(resolution,[],[f1459,f603]) ).
fof(f1459,plain,
( ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| visFreeVar(sK18,X0)
| ~ vtcheck(sK15,X0,sK14) )
| ~ spl95_163 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f1736,plain,
( spl95_191
| ~ spl95_95
| ~ spl95_121 ),
inference(avatar_split_clause,[],[f1169,f1158,f999,f1734]) ).
fof(f1734,plain,
( spl95_191
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X0,vsubst(X1,X2,veabs),X3)
| ~ vtcheck(X0,X2,X4)
| ~ vtcheck(X0,veabs,X3)
| visFreeVar(X1,veabs) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_191])]) ).
fof(f1158,plain,
( spl95_121
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X1,vsubst(X2,X3,veabs),X4)
| ~ vtcheck(vbind(X2,X0,X1),veabs,X4)
| ~ vtcheck(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_121])]) ).
fof(f1169,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vsubst(X1,X2,veabs),X3)
| ~ vtcheck(X0,X2,X4)
| ~ vtcheck(X0,veabs,X3)
| visFreeVar(X1,veabs) )
| ~ spl95_95
| ~ spl95_121 ),
inference(resolution,[],[f1159,f1000]) ).
fof(f1159,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X2,X0,X1),veabs,X4)
| vtcheck(X1,vsubst(X2,X3,veabs),X4)
| ~ vtcheck(X1,X3,X0) )
| ~ spl95_121 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f1732,plain,
( spl95_190
| ~ spl95_61
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1124,f1099,f836,f1730]) ).
fof(f1730,plain,
( spl95_190
<=> ! [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,[spl95_190])]) ).
fof(f1124,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl95_61
| ~ spl95_116 ),
inference(superposition,[],[f1100,f837]) ).
fof(f1728,plain,
( spl95_189
| ~ spl95_61
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1121,f1099,f836,f1726]) ).
fof(f1726,plain,
( spl95_189
<=> ! [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,[spl95_189])]) ).
fof(f1121,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl95_61
| ~ spl95_116 ),
inference(superposition,[],[f1100,f837]) ).
fof(f1706,plain,
( spl95_188
| ~ spl95_95
| ~ spl95_120 ),
inference(avatar_split_clause,[],[f1153,f1145,f999,f1704]) ).
fof(f1704,plain,
( spl95_188
<=> ! [X5,X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(vbind(X0,X5,X2),X3,X4)
| visFreeVar(X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_188])]) ).
fof(f1153,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(vbind(X0,X5,X2),X3,X4)
| visFreeVar(X0,X3) )
| ~ spl95_95
| ~ spl95_120 ),
inference(resolution,[],[f1146,f1000]) ).
fof(f1702,plain,
( spl95_187
| ~ spl95_43
| ~ spl95_101 ),
inference(avatar_split_clause,[],[f1045,f1032,f760,f1700]) ).
fof(f1700,plain,
( spl95_187
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK56(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_187])]) ).
fof(f1045,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK56(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl95_43
| ~ spl95_101 ),
inference(resolution,[],[f1033,f761]) ).
fof(f1698,plain,
( spl95_186
| ~ spl95_59
| ~ spl95_92 ),
inference(avatar_split_clause,[],[f989,f981,f828,f1696]) ).
fof(f1696,plain,
( spl95_186
<=> ! [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,[spl95_186])]) ).
fof(f828,plain,
( spl95_59
<=> ! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_59])]) ).
fof(f989,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl95_59
| ~ spl95_92 ),
inference(superposition,[],[f829,f982]) ).
fof(f829,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl95_59 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f1678,plain,
( spl95_185
| ~ spl95_49
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1134,f1099,f784,f1676]) ).
fof(f1676,plain,
( spl95_185
<=> ! [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,[spl95_185])]) ).
fof(f784,plain,
( spl95_49
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_49])]) ).
fof(f1134,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl95_49
| ~ spl95_116 ),
inference(superposition,[],[f785,f1100]) ).
fof(f785,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl95_49 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1674,plain,
( spl95_184
| ~ spl95_47
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1131,f1099,f776,f1672]) ).
fof(f1672,plain,
( spl95_184
<=> ! [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,[spl95_184])]) ).
fof(f776,plain,
( spl95_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_47])]) ).
fof(f1131,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl95_47
| ~ spl95_116 ),
inference(superposition,[],[f777,f1100]) ).
fof(f777,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl95_47 ),
inference(avatar_component_clause,[],[f776]) ).
fof(f1669,plain,
( spl95_183
| spl95_3
| ~ spl95_16
| ~ spl95_97 ),
inference(avatar_split_clause,[],[f1017,f1007,f646,f591,f1667]) ).
fof(f1667,plain,
( spl95_183
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_183])]) ).
fof(f1017,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl95_16
| ~ spl95_97 ),
inference(superposition,[],[f1008,f647]) ).
fof(f1662,plain,
( spl95_182
| ~ spl95_16
| ~ spl95_137 ),
inference(avatar_split_clause,[],[f1442,f1254,f646,f1659]) ).
fof(f1659,plain,
( spl95_182
<=> vnoExp = vreduce(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_182])]) ).
fof(f1254,plain,
( spl95_137
<=> sK17 = vvar(sK53(sK17,sK14,sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_137])]) ).
fof(f1442,plain,
( vnoExp = vreduce(sK17)
| ~ spl95_16
| ~ spl95_137 ),
inference(superposition,[],[f647,f1256]) ).
fof(f1256,plain,
( sK17 = vvar(sK53(sK17,sK14,sK15))
| ~ spl95_137 ),
inference(avatar_component_clause,[],[f1254]) ).
fof(f1557,plain,
( spl95_181
| ~ spl95_18
| ~ spl95_131 ),
inference(avatar_split_clause,[],[f1222,f1212,f654,f1555]) ).
fof(f1555,plain,
( spl95_181
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK62(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_181])]) ).
fof(f654,plain,
( spl95_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_18])]) ).
fof(f1222,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK62(X0,vempty,vnoType) = X0 )
| ~ spl95_18
| ~ spl95_131 ),
inference(superposition,[],[f1213,f655]) ).
fof(f655,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl95_18 ),
inference(avatar_component_clause,[],[f654]) ).
fof(f1553,plain,
( spl95_180
| ~ spl95_40
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1130,f1099,f743,f1551]) ).
fof(f1551,plain,
( spl95_180
<=> ! [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,[spl95_180])]) ).
fof(f1130,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl95_40
| ~ spl95_116 ),
inference(superposition,[],[f744,f1100]) ).
fof(f1549,plain,
( spl95_179
| ~ spl95_39
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1129,f1099,f739,f1547]) ).
fof(f1547,plain,
( spl95_179
<=> ! [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,[spl95_179])]) ).
fof(f1129,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl95_39
| ~ spl95_116 ),
inference(superposition,[],[f740,f1100]) ).
fof(f1545,plain,
( spl95_178
| ~ spl95_34
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1123,f1099,f718,f1543]) ).
fof(f1543,plain,
( spl95_178
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_178])]) ).
fof(f1123,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl95_34
| ~ spl95_116 ),
inference(superposition,[],[f1100,f719]) ).
fof(f1541,plain,
( spl95_177
| ~ spl95_34
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1120,f1099,f718,f1539]) ).
fof(f1539,plain,
( spl95_177
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_177])]) ).
fof(f1120,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl95_34
| ~ spl95_116 ),
inference(superposition,[],[f1100,f719]) ).
fof(f1537,plain,
( spl95_176
| ~ spl95_11
| ~ spl95_82 ),
inference(avatar_split_clause,[],[f951,f930,f626,f1535]) ).
fof(f1535,plain,
( spl95_176
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_176])]) ).
fof(f930,plain,
( spl95_82
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_82])]) ).
fof(f951,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl95_11
| ~ spl95_82 ),
inference(resolution,[],[f931,f627]) ).
fof(f931,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl95_82 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f1532,plain,
( spl95_175
| ~ spl95_42
| ~ spl95_59 ),
inference(avatar_split_clause,[],[f842,f828,f756,f1530]) ).
fof(f1530,plain,
( spl95_175
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_175])]) ).
fof(f842,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl95_42
| ~ spl95_59 ),
inference(superposition,[],[f829,f757]) ).
fof(f1519,plain,
( spl95_174
| ~ spl95_38
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1128,f1099,f735,f1517]) ).
fof(f1517,plain,
( spl95_174
<=> ! [X5,X6,X4,X0,X3,X2,X1] : vabs(X4,X5,X6) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_174])]) ).
fof(f735,plain,
( spl95_38
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_38])]) ).
fof(f1128,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vabs(X4,X5,X6) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl95_38
| ~ spl95_116 ),
inference(superposition,[],[f736,f1100]) ).
fof(f736,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl95_38 ),
inference(avatar_component_clause,[],[f735]) ).
fof(f1515,plain,
( spl95_173
| ~ spl95_18
| ~ spl95_114 ),
inference(avatar_split_clause,[],[f1116,f1091,f654,f1513]) ).
fof(f1513,plain,
( spl95_173
<=> ! [X2,X0,X1,X3] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_173])]) ).
fof(f1116,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl95_18
| ~ spl95_114 ),
inference(trivial_inequality_removal,[],[f1113]) ).
fof(f1113,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl95_18
| ~ spl95_114 ),
inference(superposition,[],[f1092,f655]) ).
fof(f1510,plain,
( spl95_172
| ~ spl95_22
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1127,f1099,f670,f1508]) ).
fof(f1508,plain,
( spl95_172
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_172])]) ).
fof(f670,plain,
( spl95_22
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_22])]) ).
fof(f1127,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl95_22
| ~ spl95_116 ),
inference(superposition,[],[f671,f1100]) ).
fof(f671,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl95_22 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f1502,plain,
( spl95_171
| ~ spl95_117
| ~ spl95_167 ),
inference(avatar_split_clause,[],[f1492,f1479,f1104,f1499]) ).
fof(f1499,plain,
( spl95_171
<=> sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK16,sK19,veabs)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_171])]) ).
fof(f1492,plain,
( sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK16,sK19,veabs))
| ~ spl95_117
| ~ spl95_167 ),
inference(forward_demodulation,[],[f1481,f1106]) ).
fof(f1481,plain,
( sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| ~ spl95_167 ),
inference(avatar_component_clause,[],[f1479]) ).
fof(f1497,plain,
( ~ spl95_170
| ~ spl95_117
| spl95_169 ),
inference(avatar_split_clause,[],[f1491,f1487,f1104,f1494]) ).
fof(f1491,plain,
( ~ sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK16,sK19,veabs))
| ~ spl95_117
| spl95_169 ),
inference(forward_demodulation,[],[f1488,f1106]) ).
fof(f1488,plain,
( ~ sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| spl95_169 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f1490,plain,
( spl95_167
| spl95_168
| spl95_169
| ~ spl95_4
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1203,f1191,f596,f1487,f1483,f1479]) ).
fof(f1203,plain,
( sP5(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| vabs(sK18,sK19,veabs) = vvar(sK53(vabs(sK18,sK19,veabs),sK20,vbind(sK16,sK14,sK15)))
| sP6(vbind(sK16,sK14,sK15),sK20,vabs(sK18,sK19,veabs))
| ~ spl95_4
| ~ spl95_128 ),
inference(resolution,[],[f1192,f598]) ).
fof(f1476,plain,
( spl95_166
| ~ spl95_12
| ~ spl95_116 ),
inference(avatar_split_clause,[],[f1126,f1099,f630,f1474]) ).
fof(f1474,plain,
( spl95_166
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_166])]) ).
fof(f630,plain,
( spl95_12
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_12])]) ).
fof(f1126,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl95_12
| ~ spl95_116 ),
inference(superposition,[],[f631,f1100]) ).
fof(f631,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl95_12 ),
inference(avatar_component_clause,[],[f630]) ).
fof(f1472,plain,
( spl95_117
| spl95_165
| ~ spl95_4
| ~ spl95_151 ),
inference(avatar_split_clause,[],[f1352,f1346,f596,f1470,f1104]) ).
fof(f1352,plain,
( ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| ~ vtcheck(sK15,X0,sK14)
| ~ visFreeVar(sK18,X0)
| sK16 = sK18 )
| ~ spl95_4
| ~ spl95_151 ),
inference(resolution,[],[f1347,f598]) ).
fof(f1468,plain,
( ~ spl95_164
| ~ spl95_8
| ~ spl95_137 ),
inference(avatar_split_clause,[],[f1440,f1254,f614,f1465]) ).
fof(f1465,plain,
( spl95_164
<=> visValue(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_164])]) ).
fof(f1440,plain,
( ~ visValue(sK17)
| ~ spl95_8
| ~ spl95_137 ),
inference(superposition,[],[f615,f1256]) ).
fof(f1460,plain,
( spl95_117
| spl95_163
| ~ spl95_4
| ~ spl95_150 ),
inference(avatar_split_clause,[],[f1349,f1342,f596,f1458,f1104]) ).
fof(f1349,plain,
( ! [X0] :
( vtcheck(sK15,vsubst(sK16,X0,vabs(sK18,sK19,veabs)),sK20)
| ~ vtcheck(sK15,X0,sK14)
| visFreeVar(sK18,X0)
| sK16 = sK18 )
| ~ spl95_4
| ~ spl95_150 ),
inference(resolution,[],[f1343,f598]) ).
fof(f1454,plain,
( spl95_136
| spl95_162
| spl95_138
| ~ spl95_1
| ~ spl95_134 ),
inference(avatar_split_clause,[],[f1242,f1235,f581,f1258,f1451,f1250]) ).
fof(f1250,plain,
( spl95_136
<=> sP6(sK15,sK14,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_136])]) ).
fof(f1451,plain,
( spl95_162
<=> vsomeType(sK14) = vlookup(sK53(sK17,sK14,sK15),sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_162])]) ).
fof(f1258,plain,
( spl95_138
<=> sP5(sK15,sK14,sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_138])]) ).
fof(f1242,plain,
( sP5(sK15,sK14,sK17)
| vsomeType(sK14) = vlookup(sK53(sK17,sK14,sK15),sK15)
| sP6(sK15,sK14,sK17)
| ~ spl95_1
| ~ spl95_134 ),
inference(resolution,[],[f1236,f583]) ).
fof(f583,plain,
( vtcheck(sK15,sK17,sK14)
| ~ spl95_1 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f1431,plain,
( spl95_161
| ~ spl95_116
| ~ spl95_160 ),
inference(avatar_split_clause,[],[f1427,f1424,f1099,f1429]) ).
fof(f1429,plain,
( spl95_161
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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,[spl95_161])]) ).
fof(f1424,plain,
( spl95_160
<=> ! [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(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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,[spl95_160])]) ).
fof(f1427,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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) )
| ~ spl95_116
| ~ spl95_160 ),
inference(forward_demodulation,[],[f1425,f1100]) ).
fof(f1425,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(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK88(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl95_160 ),
inference(avatar_component_clause,[],[f1424]) ).
fof(f1426,plain,
spl95_160,
inference(avatar_split_clause,[],[f494,f1424]) ).
fof(f494,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(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK86(X0,X1,X2,vsubst(X0,X1,X2)),sK87(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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,[],[f422]) ).
fof(f422,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(vsubst(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK85(X0,X1,X2,X3)),vsubst(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK88(X0,X1,X2,X3))) = X3
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ( vapp(vsubst(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK85(X0,X1,X2,X3)),vsubst(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK88(X0,X1,X2,X3))) = X3
& vapp(sK85(X0,X1,X2,X3),sK88(X0,X1,X2,X3)) = X2
& sK87(X0,X1,X2,X3) = X1
& sK86(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,[sK85,sK86,sK87,sK88])],[f303,f304]) ).
fof(f304,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(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK85(X0,X1,X2,X3)),vsubst(sK86(X0,X1,X2,X3),sK87(X0,X1,X2,X3),sK88(X0,X1,X2,X3))) = X3
& vapp(sK85(X0,X1,X2,X3),sK88(X0,X1,X2,X3)) = X2
& sK87(X0,X1,X2,X3) = X1
& sK86(X0,X1,X2,X3) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f303,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,[],[f234]) ).
fof(f234,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,[],[f154,f233,f232,f231,f230,f229]) ).
fof(f229,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(f230,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(f231,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(f232,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(f233,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(f154,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,[],[f153]) ).
fof(f153,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,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( vsubst(X0,X1,X2) = X3
=> ( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X3,X5,X18] :
( vsubst(X0,X3,X5) = X18
=> ( ? [X20,X14,X8,X10,X11] :
( vabs(X20,X14,vsubst(X8,X10,X11)) = X18
& ~ visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X10,X14,X20,X23,X11] :
( vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18
& vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20,X14,X11] :
( vabs(X20,X14,X11) = X18
& X8 = X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X11,X8,X10,X12] :
( vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18
& vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20] :
( vvar(X20) = X18
& X8 != X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X20,X10] :
( X10 = X18
& X8 = X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','subst-INV') ).
fof(f1422,plain,
( spl95_159
| ~ spl95_98
| ~ spl95_136 ),
inference(avatar_split_clause,[],[f1305,f1250,f1020,f1419]) ).
fof(f1419,plain,
( spl95_159
<=> sK17 = vapp(sK46(sK15,sK14,sK17),sK47(sK15,sK14,sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_159])]) ).
fof(f1020,plain,
( spl95_98
<=> ! [X2,X0,X1] :
( vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_98])]) ).
fof(f1305,plain,
( sK17 = vapp(sK46(sK15,sK14,sK17),sK47(sK15,sK14,sK17))
| ~ spl95_98
| ~ spl95_136 ),
inference(resolution,[],[f1252,f1021]) ).
fof(f1021,plain,
( ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X2 )
| ~ spl95_98 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1252,plain,
( sP6(sK15,sK14,sK17)
| ~ spl95_136 ),
inference(avatar_component_clause,[],[f1250]) ).
fof(f1409,plain,
spl95_158,
inference(avatar_split_clause,[],[f495,f1407]) ).
fof(f495,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(sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK88(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,[],[f421]) ).
fof(f421,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(sK85(X0,X1,X2,X3),sK88(X0,X1,X2,X3)) = X2
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f305]) ).
fof(f1389,plain,
spl95_157,
inference(avatar_split_clause,[],[f497,f1387]) ).
fof(f497,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)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f419]) ).
fof(f419,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) = X0
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f305]) ).
fof(f1385,plain,
spl95_156,
inference(avatar_split_clause,[],[f496,f1383]) ).
fof(f496,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)
| sK87(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,[],[f420]) ).
fof(f420,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK87(X0,X1,X2,X3) = X1
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f305]) ).
fof(f1381,plain,
spl95_155,
inference(avatar_split_clause,[],[f403,f1379]) ).
fof(f1379,plain,
( spl95_155
<=> ! [X0,X3,X2,X1] :
( vsubst(sK68(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vabs(sK72(X0,X1,X2,X3),sK70(X0,X1,X2,X3),vsubst(sK71(X0,X1,X2,X3),vvar(sK72(X0,X1,X2,X3)),sK73(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_155])]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( vsubst(sK68(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vabs(sK72(X0,X1,X2,X3),sK70(X0,X1,X2,X3),vsubst(sK71(X0,X1,X2,X3),vvar(sK72(X0,X1,X2,X3)),sK73(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0,X1,X2,X3] :
( ( vsubst(sK68(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vabs(sK72(X0,X1,X2,X3),sK70(X0,X1,X2,X3),vsubst(sK71(X0,X1,X2,X3),vvar(sK72(X0,X1,X2,X3)),sK73(X0,X1,X2,X3)))) = X0
& sK72(X0,X1,X2,X3) = vgensym(vapp(vapp(sK69(X0,X1,X2,X3),sK73(X0,X1,X2,X3)),vvar(sK68(X0,X1,X2,X3))))
& visFreeVar(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3))
& sK68(X0,X1,X2,X3) != sK71(X0,X1,X2,X3)
& vabs(sK71(X0,X1,X2,X3),sK70(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
& sK69(X0,X1,X2,X3) = X2
& sK68(X0,X1,X2,X3) = X3 )
| ~ sP12(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70,sK71,sK72,sK73])],[f288,f289]) ).
fof(f289,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(sK68(X0,X1,X2,X3),sK69(X0,X1,X2,X3),vabs(sK72(X0,X1,X2,X3),sK70(X0,X1,X2,X3),vsubst(sK71(X0,X1,X2,X3),vvar(sK72(X0,X1,X2,X3)),sK73(X0,X1,X2,X3)))) = X0
& sK72(X0,X1,X2,X3) = vgensym(vapp(vapp(sK69(X0,X1,X2,X3),sK73(X0,X1,X2,X3)),vvar(sK68(X0,X1,X2,X3))))
& visFreeVar(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3))
& sK68(X0,X1,X2,X3) != sK71(X0,X1,X2,X3)
& vabs(sK71(X0,X1,X2,X3),sK70(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
& sK69(X0,X1,X2,X3) = X2
& sK68(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f288,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,[],[f287]) ).
fof(f287,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,[],[f232]) ).
fof(f1372,plain,
spl95_154,
inference(avatar_split_clause,[],[f478,f1370]) ).
fof(f478,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK42(X0,vreduce(X0)),sK43(X0,vreduce(X0)),sK44(X0,vreduce(X0))) = X0
| vvar(sK45(X0,vreduce(X0))) = X0 ),
inference(equality_resolution,[],[f353]) ).
fof(f353,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| vabs(sK42(X0,X1),sK43(X0,X1),sK44(X0,X1)) = X0
| vvar(sK45(X0,X1)) = X0
| vreduce(X0) != X1 ),
inference(cnf_transformation,[],[f260]) ).
fof(f260,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ( vnoExp = X1
& vabs(sK42(X0,X1),sK43(X0,X1),sK44(X0,X1)) = X0 )
| ( vnoExp = X1
& vvar(sK45(X0,X1)) = X0 )
| vreduce(X0) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44,sK45])],[f257,f259,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& vabs(X2,X3,X4) = X0 )
=> ( vnoExp = X1
& vabs(sK42(X0,X1),sK43(X0,X1),sK44(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
! [X0,X1] :
( ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
=> ( vnoExp = X1
& vvar(sK45(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f257,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,[],[f222]) ).
fof(f222,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,[],[f135,f221,f220,f219,f218,f217]) ).
fof(f217,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(f218,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(f219,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(f220,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(f221,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f135,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,[],[f134]) ).
fof(f134,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,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( vreduce(X0) = X1
=> ( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X3,X18] :
( vreduce(X3) = X18
=> ( ? [X12,X11,X26] :
( vnoExp = X18
& ~ visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X11,X26,X12] :
( vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18
& visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X8,X9,X11,X25,X12] :
( vnoExp = X18
& ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X9,X25,X8,X12,X11] :
( vsomeExp(vsubst(X8,X12,X11)) = X18
& visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X12,X8,X9,X11,X25] :
( vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18
& visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X8,X9,X10] :
( vnoExp = X18
& vabs(X8,X9,X10) = X3 )
| ? [X8] :
( vnoExp = X18
& vvar(X8) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-INV') ).
fof(f1362,plain,
spl95_153,
inference(avatar_split_clause,[],[f578,f1360]) ).
fof(f578,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,[],[f577]) ).
fof(f577,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,[],[f576]) ).
fof(f576,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,[],[f575]) ).
fof(f575,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,[],[f574]) ).
fof(f574,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,[],[f466]) ).
fof(f466,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,[],[f216]) ).
fof(f216,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,[],[f215]) ).
fof(f215,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,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( vabs(X7,X6,X9) = X2
& X1 = X5
& X0 = X4 )
=> ( ( vgensym(vapp(vapp(X5,X9),vvar(X4))) = X8
& visFreeVar(X7,X5)
& X4 != X7 )
=> ( vsubst(X0,X1,X2) = X3
=> vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3 ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X3,X5,X18,X8,X10,X14,X20,X23,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst4) ).
fof(f1358,plain,
spl95_152,
inference(avatar_split_clause,[],[f396,f1356]) ).
fof(f1356,plain,
( spl95_152
<=> ! [X0,X3,X2,X1] :
( vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vsubst(sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_152])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vsubst(sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vsubst(sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3))
& sK63(X0,X1,X2,X3) != sK65(X0,X1,X2,X3)
& vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK67(X0,X1,X2,X3)) = X1
& sK66(X0,X1,X2,X3) = X2
& sK65(X0,X1,X2,X3) = X3 )
| ~ sP13(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64,sK65,sK66,sK67])],[f284,f285]) ).
fof(f285,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(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vsubst(sK65(X0,X1,X2,X3),sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3))
& sK63(X0,X1,X2,X3) != sK65(X0,X1,X2,X3)
& vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK67(X0,X1,X2,X3)) = X1
& sK66(X0,X1,X2,X3) = X2
& sK65(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f284,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,[],[f283]) ).
fof(f283,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,[],[f233]) ).
fof(f1348,plain,
spl95_151,
inference(avatar_split_clause,[],[f455,f1346]) ).
fof(f455,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| ~ visFreeVar(X4,X3)
| X2 = X4 ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| ~ visFreeVar(X4,X3)
| X2 = X4 ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| ~ visFreeVar(X4,X3)
| X2 = X4 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0)
& visFreeVar(X4,X3)
& X2 != X4 )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X14,X19,X8,X10,X20,X9,X33] :
( ( vtcheck(vbind(X8,X14,X19),vabs(X20,X9,veabs),X33)
& vtcheck(X19,X10,X14)
& visFreeVar(X20,X10)
& X8 != X20 )
=> vtcheck(X19,vsubst(X8,X10,vabs(X20,X9,veabs)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-3') ).
fof(f1344,plain,
spl95_150,
inference(avatar_split_clause,[],[f454,f1342]) ).
fof(f454,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| visFreeVar(X4,X3)
| X2 = X4 ),
inference(cnf_transformation,[],[f192]) ).
fof(f192,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| visFreeVar(X4,X3)
| X2 = X4 ),
inference(flattening,[],[f191]) ).
fof(f191,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
| ~ vtcheck(X1,X3,X0)
| visFreeVar(X4,X3)
| X2 = X4 ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0)
& ~ visFreeVar(X4,X3)
& X2 != X4 )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X14,X19,X8,X10,X20,X9,X33] :
( ( vtcheck(vbind(X8,X14,X19),vabs(X20,X9,veabs),X33)
& vtcheck(X19,X10,X14)
& ~ visFreeVar(X20,X10)
& X8 != X20 )
=> vtcheck(X19,vsubst(X8,X10,vabs(X20,X9,veabs)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-2') ).
fof(f1340,plain,
spl95_149,
inference(avatar_split_clause,[],[f402,f1338]) ).
fof(f1338,plain,
( spl95_149
<=> ! [X0,X3,X2,X1] :
( sK72(X0,X1,X2,X3) = vgensym(vapp(vapp(sK69(X0,X1,X2,X3),sK73(X0,X1,X2,X3)),vvar(sK68(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_149])]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( sK72(X0,X1,X2,X3) = vgensym(vapp(vapp(sK69(X0,X1,X2,X3),sK73(X0,X1,X2,X3)),vvar(sK68(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f1330,plain,
spl95_148,
inference(avatar_split_clause,[],[f579,f1328]) ).
fof(f579,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,[],[f475]) ).
fof(f475,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,[],[f356]) ).
fof(f356,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,[],[f260]) ).
fof(f1324,plain,
( spl95_147
| ~ spl95_83
| ~ spl95_146 ),
inference(avatar_split_clause,[],[f1320,f1317,f934,f1322]) ).
fof(f1317,plain,
( spl95_146
<=> ! [X5,X4,X7,X0,X6,X3,X1] :
( vtcheck(X1,vsubst(X4,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_146])]) ).
fof(f1320,plain,
( ! [X3,X0,X1,X6,X7,X4,X5] :
( vtcheck(X1,vabs(X4,X5,X6),X7)
| ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) )
| ~ spl95_83
| ~ spl95_146 ),
inference(forward_demodulation,[],[f1318,f935]) ).
fof(f1318,plain,
( ! [X3,X0,X1,X6,X7,X4,X5] :
( vtcheck(X1,vsubst(X4,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) )
| ~ spl95_146 ),
inference(avatar_component_clause,[],[f1317]) ).
fof(f1319,plain,
spl95_146,
inference(avatar_split_clause,[],[f564,f1317]) ).
fof(f564,plain,
! [X3,X0,X1,X6,X7,X4,X5] :
( vtcheck(X1,vsubst(X4,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X4,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0) ),
inference(equality_resolution,[],[f463]) ).
fof(f463,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0)
| X2 != X4 ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0)
| X2 != X4 ),
inference(flattening,[],[f209]) ).
fof(f209,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7)
| ~ vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
| ~ vtcheck(X1,X3,X0)
| X2 != X4 ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,X6),X7)
& vtcheck(X1,X3,X0)
& X2 = X4 )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,X6)),X7) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X14,X19,X8,X10,X20,X9,X11,X33] :
( ( vtcheck(vbind(X8,X14,X19),vabs(X20,X9,X11),X33)
& vtcheck(X19,X10,X14)
& X8 = X20 )
=> vtcheck(X19,vsubst(X8,X10,vabs(X20,X9,X11)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs-1') ).
fof(f1301,plain,
spl95_145,
inference(avatar_split_clause,[],[f520,f1299]) ).
fof(f520,plain,
! [X0,X4] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0 ),
inference(equality_resolution,[],[f519]) ).
fof(f519,plain,
! [X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
! [X3,X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(X3),X4))
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f438]) ).
fof(f438,plain,
! [X2,X3,X0,X1,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK92(X0),sK93(X0),sK94(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK92,sK93,sK94])],[f176,f308]) ).
fof(f308,plain,
! [X0] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
=> vabs(sK92(X0),sK93(X0),sK94(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f176,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,[],[f175]) ).
fof(f175,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,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X0
& vapp(X0,X4) = X1 )
=> ( ( visSomeExp(X3)
& vreduce(X0) = X3 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2 ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X11,X3,X18,X26,X12] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce5) ).
fof(f1297,plain,
spl95_144,
inference(avatar_split_clause,[],[f456,f1295]) ).
fof(f456,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,[],[f196]) ).
fof(f196,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,[],[f195]) ).
fof(f195,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,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 != X2 )
=> vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 != X20 )
=> vtcheck(vbind(X20,X21,vbind(X8,X22,X19)),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Swap') ).
fof(f1293,plain,
spl95_143,
inference(avatar_split_clause,[],[f408,f1291]) ).
fof(f1291,plain,
( spl95_143
<=> ! [X0,X3,X2,X1] :
( vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_143])]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X0
& sK75(X0,X1,X2,X3) = sK76(X0,X1,X2,X3)
& vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X1
& sK74(X0,X1,X2,X3) = X2
& sK75(X0,X1,X2,X3) = X3 )
| ~ sP11(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76,sK77,sK78])],[f292,f293]) ).
fof(f293,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(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X0
& sK75(X0,X1,X2,X3) = sK76(X0,X1,X2,X3)
& vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X1
& sK74(X0,X1,X2,X3) = X2
& sK75(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f292,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,[],[f291]) ).
fof(f291,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,[],[f231]) ).
fof(f1289,plain,
spl95_142,
inference(avatar_split_clause,[],[f406,f1287]) ).
fof(f1287,plain,
( spl95_142
<=> ! [X0,X3,X2,X1] :
( vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_142])]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( vabs(sK76(X0,X1,X2,X3),sK77(X0,X1,X2,X3),sK78(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f1285,plain,
spl95_141,
inference(avatar_split_clause,[],[f399,f1283]) ).
fof(f1283,plain,
( spl95_141
<=> ! [X0,X3,X2,X1] :
( vabs(sK71(X0,X1,X2,X3),sK70(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_141])]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( vabs(sK71(X0,X1,X2,X3),sK70(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f1281,plain,
spl95_140,
inference(avatar_split_clause,[],[f393,f1279]) ).
fof(f1279,plain,
( spl95_140
<=> ! [X0,X3,X2,X1] :
( vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK67(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_140])]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( vabs(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK67(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f1277,plain,
spl95_139,
inference(avatar_split_clause,[],[f368,f1275]) ).
fof(f368,plain,
! [X2,X0,X1] :
( vtcheck(vbind(sK49(X0,X1,X2),sK51(X0,X1,X2),X0),sK50(X0,X1,X2),sK52(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0,X1,X2] :
( ( vtcheck(vbind(sK49(X0,X1,X2),sK51(X0,X1,X2),X0),sK50(X0,X1,X2),sK52(X0,X1,X2))
& varrow(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X1
& vabs(sK49(X0,X1,X2),sK51(X0,X1,X2),sK50(X0,X1,X2)) = X2 )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52])],[f266,f267]) ).
fof(f267,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(sK49(X0,X1,X2),sK51(X0,X1,X2),X0),sK50(X0,X1,X2),sK52(X0,X1,X2))
& varrow(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X1
& vabs(sK49(X0,X1,X2),sK51(X0,X1,X2),sK50(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f266,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,[],[f265]) ).
fof(f265,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,[],[f223]) ).
fof(f223,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(f1261,plain,
( spl95_136
| spl95_137
| spl95_138
| ~ spl95_1
| ~ spl95_128 ),
inference(avatar_split_clause,[],[f1202,f1191,f581,f1258,f1254,f1250]) ).
fof(f1202,plain,
( sP5(sK15,sK14,sK17)
| sK17 = vvar(sK53(sK17,sK14,sK15))
| sP6(sK15,sK14,sK17)
| ~ spl95_1
| ~ spl95_128 ),
inference(resolution,[],[f1192,f583]) ).
fof(f1241,plain,
spl95_135,
inference(avatar_split_clause,[],[f573,f1239]) ).
fof(f573,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,[],[f572]) ).
fof(f572,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,[],[f571]) ).
fof(f571,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,[],[f570]) ).
fof(f570,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,[],[f465]) ).
fof(f465,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,[],[f214]) ).
fof(f214,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,[],[f213]) ).
fof(f213,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,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
=> ( ( ~ visFreeVar(X4,X7)
& X4 != X6 )
=> ( vsubst(X0,X1,X2) = X3
=> vabs(X4,X5,vsubst(X6,X7,X8)) = X3 ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X3,X5,X18,X20,X14,X8,X10,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( ~ visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,vsubst(X8,X10,X11)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst5) ).
fof(f1237,plain,
spl95_134,
inference(avatar_split_clause,[],[f370,f1235]) ).
fof(f370,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK53(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ( vsomeType(X1) = vlookup(sK53(X0,X1,X2),X2)
& vvar(sK53(X0,X1,X2)) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f269,f270]) ).
fof(f270,plain,
! [X0,X1,X2] :
( ? [X3] :
( vsomeType(X1) = vlookup(X3,X2)
& vvar(X3) = X0 )
=> ( vsomeType(X1) = vlookup(sK53(X0,X1,X2),X2)
& vvar(sK53(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f269,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,[],[f225]) ).
fof(f225,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,[],[f144,f224,f223]) ).
fof(f224,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(f144,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,[],[f143]) ).
fof(f143,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,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X10,X14,X19] :
( vtcheck(X19,X10,X14)
=> ( ? [X11,X12,X9] :
( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14))
& vapp(X11,X12) = X10 )
| ? [X8,X12,X32,X33] :
( vtcheck(vbind(X8,X32,X19),X12,X33)
& varrow(X32,X33) = X14
& vabs(X8,X32,X12) = X10 )
| ? [X8] :
( vlookup(X8,X19) = vsomeType(X14)
& vvar(X8) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-inv') ).
fof(f1233,plain,
spl95_133,
inference(avatar_split_clause,[],[f332,f1231]) ).
fof(f1231,plain,
( spl95_133
<=> ! [X0,X1] :
( vsomeExp(vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),vgetSomeExp(sK25(X0,X1)))) = X0
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_133])]) ).
fof(f332,plain,
! [X0,X1] :
( vsomeExp(vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),vgetSomeExp(sK25(X0,X1)))) = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),vgetSomeExp(sK25(X0,X1)))) = X0
& visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK21(X0,X1))
& vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),sK21(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23,sK24,sK25])],[f238,f239]) ).
fof(f239,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(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),vgetSomeExp(sK25(X0,X1)))) = X0
& visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK21(X0,X1))
& vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),sK21(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f238,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,[],[f237]) ).
fof(f237,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,[],[f221]) ).
fof(f1218,plain,
spl95_132,
inference(avatar_split_clause,[],[f542,f1216]) ).
fof(f542,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,[],[f541]) ).
fof(f541,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,[],[f540]) ).
fof(f540,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,[],[f453]) ).
fof(f453,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,[],[f190]) ).
fof(f190,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,[],[f189]) ).
fof(f189,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,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X3,X4,X5),X0) = X1
=> ( ( visSomeExp(X6)
& vreduce(X0) = X6 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2 ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X12,X3,X18,X8,X9,X11,X25] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce2) ).
fof(f1214,plain,
spl95_131,
inference(avatar_split_clause,[],[f488,f1212]) ).
fof(f488,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK62(X0,X1,vlookup(X0,X1)) = X0 ),
inference(equality_resolution,[],[f379]) ).
fof(f379,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| sK62(X0,X1,X2) = X0
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ( vnoType = X2
& vempty = X1
& sK62(X0,X1,X2) = X0 )
| vlookup(X0,X1) != X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f280,f281]) ).
fof(f281,plain,
! [X0,X1,X2] :
( ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
=> ( vnoType = X2
& vempty = X1
& sK62(X0,X1,X2) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f280,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,[],[f228]) ).
fof(f228,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,[],[f146,f227,f226]) ).
fof(f226,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(f227,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(f146,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,[],[f145]) ).
fof(f145,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,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( vlookup(X0,X1) = X2
=> ( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X15,X18] :
( vlookup(X0,X15) = X18
=> ( ? [X21,X20,X8,X19] :
( vlookup(X8,X19) = X18
& X8 != X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X19,X8,X20,X21] :
( vsomeType(X21) = X18
& X8 = X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X8] :
( vnoType = X18
& vempty = X15
& X0 = X8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lookup-INV') ).
fof(f1201,plain,
spl95_130,
inference(avatar_split_clause,[],[f376,f1199]) ).
fof(f1199,plain,
( spl95_130
<=> ! [X2,X0,X1] :
( vbind(sK60(X0,X1,X2),sK61(X0,X1,X2),sK58(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_130])]) ).
fof(f376,plain,
! [X2,X0,X1] :
( vbind(sK60(X0,X1,X2),sK61(X0,X1,X2),sK58(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1,X2] :
( ( vsomeType(sK61(X0,X1,X2)) = X0
& sK59(X0,X1,X2) = sK60(X0,X1,X2)
& vbind(sK60(X0,X1,X2),sK61(X0,X1,X2),sK58(X0,X1,X2)) = X1
& sK59(X0,X1,X2) = X2 )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61])],[f277,f278]) ).
fof(f278,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
=> ( vsomeType(sK61(X0,X1,X2)) = X0
& sK59(X0,X1,X2) = sK60(X0,X1,X2)
& vbind(sK60(X0,X1,X2),sK61(X0,X1,X2),sK58(X0,X1,X2)) = X1
& sK59(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f277,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,[],[f276]) ).
fof(f276,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,[],[f226]) ).
fof(f1197,plain,
spl95_129,
inference(avatar_split_clause,[],[f372,f1195]) ).
fof(f372,plain,
! [X2,X0,X1] :
( vbind(sK55(X0,X1,X2),sK54(X0,X1,X2),sK57(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1,X2] :
( ( vlookup(sK56(X0,X1,X2),sK57(X0,X1,X2)) = X0
& sK55(X0,X1,X2) != sK56(X0,X1,X2)
& vbind(sK55(X0,X1,X2),sK54(X0,X1,X2),sK57(X0,X1,X2)) = X1
& sK56(X0,X1,X2) = X2 )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57])],[f273,f274]) ).
fof(f274,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
=> ( vlookup(sK56(X0,X1,X2),sK57(X0,X1,X2)) = X0
& sK55(X0,X1,X2) != sK56(X0,X1,X2)
& vbind(sK55(X0,X1,X2),sK54(X0,X1,X2),sK57(X0,X1,X2)) = X1
& sK56(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f273,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,[],[f272]) ).
fof(f272,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,[],[f227]) ).
fof(f1193,plain,
spl95_128,
inference(avatar_split_clause,[],[f369,f1191]) ).
fof(f369,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK53(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f1189,plain,
spl95_127,
inference(avatar_split_clause,[],[f366,f1187]) ).
fof(f1187,plain,
( spl95_127
<=> ! [X2,X0,X1] :
( vabs(sK49(X0,X1,X2),sK51(X0,X1,X2),sK50(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_127])]) ).
fof(f366,plain,
! [X2,X0,X1] :
( vabs(sK49(X0,X1,X2),sK51(X0,X1,X2),sK50(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f1185,plain,
spl95_126,
inference(avatar_split_clause,[],[f348,f1183]) ).
fof(f1183,plain,
( spl95_126
<=> ! [X0,X1] :
( vapp(vabs(sK39(X0,X1),sK37(X0,X1),sK41(X0,X1)),sK40(X0,X1)) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_126])]) ).
fof(f348,plain,
! [X0,X1] :
( vapp(vabs(sK39(X0,X1),sK37(X0,X1),sK41(X0,X1)),sK40(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1] :
( ( vsomeExp(vsubst(sK39(X0,X1),sK40(X0,X1),sK41(X0,X1))) = X0
& visValue(sK40(X0,X1))
& ~ visSomeExp(sK38(X0,X1))
& sK38(X0,X1) = vreduce(sK40(X0,X1))
& vapp(vabs(sK39(X0,X1),sK37(X0,X1),sK41(X0,X1)),sK40(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41])],[f254,f255]) ).
fof(f255,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(sK39(X0,X1),sK40(X0,X1),sK41(X0,X1))) = X0
& visValue(sK40(X0,X1))
& ~ visSomeExp(sK38(X0,X1))
& sK38(X0,X1) = vreduce(sK40(X0,X1))
& vapp(vabs(sK39(X0,X1),sK37(X0,X1),sK41(X0,X1)),sK40(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f254,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,[],[f253]) ).
fof(f253,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,[],[f217]) ).
fof(f1181,plain,
spl95_125,
inference(avatar_split_clause,[],[f343,f1179]) ).
fof(f1179,plain,
( spl95_125
<=> ! [X0,X1] :
( vapp(vabs(sK32(X0,X1),sK33(X0,X1),sK34(X0,X1)),sK36(X0,X1)) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_125])]) ).
fof(f343,plain,
! [X0,X1] :
( vapp(vabs(sK32(X0,X1),sK33(X0,X1),sK34(X0,X1)),sK36(X0,X1)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visValue(sK36(X0,X1))
& ~ visSomeExp(sK35(X0,X1))
& sK35(X0,X1) = vreduce(sK36(X0,X1))
& vapp(vabs(sK32(X0,X1),sK33(X0,X1),sK34(X0,X1)),sK36(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35,sK36])],[f250,f251]) ).
fof(f251,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(sK36(X0,X1))
& ~ visSomeExp(sK35(X0,X1))
& sK35(X0,X1) = vreduce(sK36(X0,X1))
& vapp(vabs(sK32(X0,X1),sK33(X0,X1),sK34(X0,X1)),sK36(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f250,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,[],[f249]) ).
fof(f249,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,[],[f218]) ).
fof(f1177,plain,
spl95_124,
inference(avatar_split_clause,[],[f329,f1175]) ).
fof(f1175,plain,
( spl95_124
<=> ! [X0,X1] :
( vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),sK21(X0,X1)) = X1
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_124])]) ).
fof(f329,plain,
! [X0,X1] :
( vapp(vabs(sK22(X0,X1),sK23(X0,X1),sK24(X0,X1)),sK21(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f1168,plain,
spl95_123,
inference(avatar_split_clause,[],[f539,f1166]) ).
fof(f539,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,[],[f538]) ).
fof(f538,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,[],[f537]) ).
fof(f537,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,[],[f452]) ).
fof(f452,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,[],[f188]) ).
fof(f188,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,[],[f187]) ).
fof(f187,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,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X4,X0,X6),X5) = X2
=> ( ( visValue(X5)
& ~ visSomeExp(X1)
& vreduce(X5) = X1 )
=> ( vreduce(X2) = X3
=> vsomeExp(vsubst(X4,X5,X6)) = X3 ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X9,X25,X3,X18,X8,X12,X11] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vsubst(X8,X12,X11)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce3) ).
fof(f1164,plain,
spl95_122,
inference(avatar_split_clause,[],[f517,f1162]) ).
fof(f517,plain,
! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1 ),
inference(equality_resolution,[],[f516]) ).
fof(f516,plain,
! [X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(vreduce(X1))
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f515]) ).
fof(f515,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f437]) ).
fof(f437,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK89(X1),sK90(X1),sK91(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89,sK90,sK91])],[f174,f306]) ).
fof(f306,plain,
! [X1] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
=> vabs(sK89(X1),sK90(X1),sK91(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X1
& vapp(X1,X0) = X3 )
=> ( ( ~ visSomeExp(X2)
& vreduce(X1) = X2 )
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X12,X11,X26,X3,X18] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( ~ visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce6) ).
fof(f1160,plain,
spl95_121,
inference(avatar_split_clause,[],[f435,f1158]) ).
fof(f435,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X1,vsubst(X2,X3,veabs),X4)
| ~ vtcheck(vbind(X2,X0,X1),veabs,X4)
| ~ vtcheck(X1,X3,X0) ),
inference(cnf_transformation,[],[f170]) ).
fof(f170,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vsubst(X2,X3,veabs),X4)
| ~ vtcheck(vbind(X2,X0,X1),veabs,X4)
| ~ vtcheck(X1,X3,X0) ),
inference(flattening,[],[f169]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vsubst(X2,X3,veabs),X4)
| ~ vtcheck(vbind(X2,X0,X1),veabs,X4)
| ~ vtcheck(X1,X3,X0) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(vbind(X2,X0,X1),veabs,X4)
& vtcheck(X1,X3,X0) )
=> vtcheck(X1,vsubst(X2,X3,veabs),X4) ),
inference(rectify,[],[f58]) ).
fof(f58,axiom,
! [X14,X19,X8,X10,X33] :
( ( vtcheck(vbind(X8,X14,X19),veabs,X33)
& vtcheck(X19,X10,X14) )
=> vtcheck(X19,vsubst(X8,X10,veabs),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-IH-abs') ).
fof(f1147,plain,
spl95_120,
inference(avatar_split_clause,[],[f559,f1145]) ).
fof(f559,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,[],[f461]) ).
fof(f461,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,[],[f206]) ).
fof(f206,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,[],[f205]) ).
fof(f205,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,[],[f118]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 = X2 )
=> vtcheck(vbind(X2,X3,X4),X5,X6) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 = X20 )
=> vtcheck(vbind(X8,X22,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Context-Duplicate') ).
fof(f1143,plain,
spl95_119,
inference(avatar_split_clause,[],[f486,f1141]) ).
fof(f486,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ),
inference(equality_resolution,[],[f381]) ).
fof(f381,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vnoType = X2
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f282]) ).
fof(f1111,plain,
( spl95_117
| ~ spl95_118
| ~ spl95_82
| spl95_102 ),
inference(avatar_split_clause,[],[f1085,f1036,f930,f1108,f1104]) ).
fof(f1108,plain,
( spl95_118
<=> visFreeVar(sK16,veabs) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_118])]) ).
fof(f1085,plain,
( ~ visFreeVar(sK16,veabs)
| sK16 = sK18
| ~ spl95_82
| spl95_102 ),
inference(resolution,[],[f1037,f931]) ).
fof(f1037,plain,
( ~ visFreeVar(sK16,vabs(sK18,sK19,veabs))
| spl95_102 ),
inference(avatar_component_clause,[],[f1036]) ).
fof(f1101,plain,
spl95_116,
inference(avatar_split_clause,[],[f563,f1099]) ).
fof(f563,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f562]) ).
fof(f562,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,[],[f561]) ).
fof(f561,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,[],[f560]) ).
fof(f560,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,[],[f462]) ).
fof(f462,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,[],[f208]) ).
fof(f208,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,[],[f207]) ).
fof(f207,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,[],[f119]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vapp(X4,X7) = X2
& X1 = X6
& X0 = X5 )
=> ( vsubst(X0,X1,X2) = X3
=> vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3 ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X3,X5,X18,X11,X8,X10,X12] :
( ( vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
=> ( vsubst(X0,X3,X5) = X18
=> vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst2) ).
fof(f1097,plain,
spl95_115,
inference(avatar_split_clause,[],[f439,f1095]) ).
fof(f439,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,[],[f178]) ).
fof(f178,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f177]) ).
fof(f177,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,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X3,X0)
& vtcheck(X1,X2,varrow(X0,X4)) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X9,X19,X11,X12,X14] :
( ( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14)) )
=> vtcheck(X19,vapp(X11,X12),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
fof(f1093,plain,
spl95_114,
inference(avatar_split_clause,[],[f436,f1091]) ).
fof(f436,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f172]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f171]) ).
fof(f171,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,X3,X4)
& vnoType = vlookup(X0,X2) )
=> vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(X19,X10,X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak') ).
fof(f1089,plain,
spl95_113,
inference(avatar_split_clause,[],[f429,f1087]) ).
fof(f429,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,[],[f162]) ).
fof(f162,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,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X1,X3,X0),X2,X4)
=> vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4)) ),
inference(rectify,[],[f52]) ).
fof(f52,axiom,
! [X19,X8,X10,X9,X14] :
( vtcheck(vbind(X8,X9,X19),X10,X14)
=> vtcheck(X19,vabs(X8,X9,X10),varrow(X9,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-abs') ).
fof(f1084,plain,
spl95_112,
inference(avatar_split_clause,[],[f417,f1082]) ).
fof(f1082,plain,
( spl95_112
<=> ! [X0,X3,X2,X1] :
( sK82(X0,X1,X2,X3) = sK83(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_112])]) ).
fof(f417,plain,
! [X2,X3,X0,X1] :
( sK82(X0,X1,X2,X3) = sK83(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1,X2,X3] :
( ( sK84(X0,X1,X2,X3) = X0
& sK82(X0,X1,X2,X3) = sK83(X0,X1,X2,X3)
& vvar(sK83(X0,X1,X2,X3)) = X1
& sK84(X0,X1,X2,X3) = X2
& sK82(X0,X1,X2,X3) = X3 )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82,sK83,sK84])],[f300,f301]) ).
fof(f301,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( X0 = X6
& X4 = X5
& vvar(X5) = X1
& X2 = X6
& X3 = X4 )
=> ( sK84(X0,X1,X2,X3) = X0
& sK82(X0,X1,X2,X3) = sK83(X0,X1,X2,X3)
& vvar(sK83(X0,X1,X2,X3)) = X1
& sK84(X0,X1,X2,X3) = X2
& sK82(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f300,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,[],[f299]) ).
fof(f299,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,[],[f229]) ).
fof(f1080,plain,
spl95_111,
inference(avatar_split_clause,[],[f412,f1078]) ).
fof(f1078,plain,
( spl95_111
<=> ! [X0,X3,X2,X1] :
( sK80(X0,X1,X2,X3) != sK81(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_111])]) ).
fof(f412,plain,
! [X2,X3,X0,X1] :
( sK80(X0,X1,X2,X3) != sK81(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f298]) ).
fof(f298,plain,
! [X0,X1,X2,X3] :
( ( vvar(sK81(X0,X1,X2,X3)) = X0
& sK80(X0,X1,X2,X3) != sK81(X0,X1,X2,X3)
& vvar(sK81(X0,X1,X2,X3)) = X1
& sK79(X0,X1,X2,X3) = X2
& sK80(X0,X1,X2,X3) = X3 )
| ~ sP10(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80,sK81])],[f296,f297]) ).
fof(f297,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( vvar(X6) = X0
& X5 != X6
& vvar(X6) = X1
& X2 = X4
& X3 = X5 )
=> ( vvar(sK81(X0,X1,X2,X3)) = X0
& sK80(X0,X1,X2,X3) != sK81(X0,X1,X2,X3)
& vvar(sK81(X0,X1,X2,X3)) = X1
& sK79(X0,X1,X2,X3) = X2
& sK80(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f296,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,[],[f295]) ).
fof(f295,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,[],[f230]) ).
fof(f1076,plain,
spl95_110,
inference(avatar_split_clause,[],[f407,f1074]) ).
fof(f1074,plain,
( spl95_110
<=> ! [X0,X3,X2,X1] :
( sK75(X0,X1,X2,X3) = sK76(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_110])]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( sK75(X0,X1,X2,X3) = sK76(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f1072,plain,
spl95_109,
inference(avatar_split_clause,[],[f401,f1070]) ).
fof(f1070,plain,
( spl95_109
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_109])]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( visFreeVar(sK71(X0,X1,X2,X3),sK69(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f1068,plain,
spl95_108,
inference(avatar_split_clause,[],[f400,f1066]) ).
fof(f1066,plain,
( spl95_108
<=> ! [X0,X3,X2,X1] :
( sK68(X0,X1,X2,X3) != sK71(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_108])]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( sK68(X0,X1,X2,X3) != sK71(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f1064,plain,
spl95_107,
inference(avatar_split_clause,[],[f395,f1062]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(sK63(X0,X1,X2,X3),sK66(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f1060,plain,
spl95_106,
inference(avatar_split_clause,[],[f394,f1058]) ).
fof(f1058,plain,
( spl95_106
<=> ! [X0,X3,X2,X1] :
( sK63(X0,X1,X2,X3) != sK65(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_106])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sK63(X0,X1,X2,X3) != sK65(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f1056,plain,
spl95_105,
inference(avatar_split_clause,[],[f364,f1054]) ).
fof(f364,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0,X1,X2] :
( ( vtcheck(X0,sK47(X0,X1,X2),sK48(X0,X1,X2))
& vtcheck(X0,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
& vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X2 )
| ~ sP6(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48])],[f262,f263]) ).
fof(f263,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X0,X4,X5)
& vtcheck(X0,X3,varrow(X5,X1))
& vapp(X3,X4) = X2 )
=> ( vtcheck(X0,sK47(X0,X1,X2),sK48(X0,X1,X2))
& vtcheck(X0,sK46(X0,X1,X2),varrow(sK48(X0,X1,X2),X1))
& vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f262,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,[],[f261]) ).
fof(f261,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,[],[f224]) ).
fof(f1052,plain,
spl95_104,
inference(avatar_split_clause,[],[f352,f1050]) ).
fof(f1050,plain,
( spl95_104
<=> ! [X0,X1] :
( vsomeExp(vsubst(sK39(X0,X1),sK40(X0,X1),sK41(X0,X1))) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_104])]) ).
fof(f352,plain,
! [X0,X1] :
( vsomeExp(vsubst(sK39(X0,X1),sK40(X0,X1),sK41(X0,X1))) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f1043,plain,
( spl95_102
| spl95_103
| ~ spl95_4
| ~ spl95_96 ),
inference(avatar_split_clause,[],[f1013,f1003,f596,f1040,f1036]) ).
fof(f1013,plain,
( vtcheck(sK15,vabs(sK18,sK19,veabs),sK20)
| visFreeVar(sK16,vabs(sK18,sK19,veabs))
| ~ spl95_4
| ~ spl95_96 ),
inference(resolution,[],[f1004,f598]) ).
fof(f1034,plain,
spl95_101,
inference(avatar_split_clause,[],[f487,f1032]) ).
fof(f487,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ),
inference(equality_resolution,[],[f380]) ).
fof(f380,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vempty = X1
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f282]) ).
fof(f1030,plain,
spl95_100,
inference(avatar_split_clause,[],[f374,f1028]) ).
fof(f374,plain,
! [X2,X0,X1] :
( vlookup(sK56(X0,X1,X2),sK57(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
fof(f1026,plain,
spl95_99,
inference(avatar_split_clause,[],[f367,f1024]) ).
fof(f1024,plain,
( spl95_99
<=> ! [X2,X0,X1] :
( varrow(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_99])]) ).
fof(f367,plain,
! [X2,X0,X1] :
( varrow(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f268]) ).
fof(f1022,plain,
spl95_98,
inference(avatar_split_clause,[],[f363,f1020]) ).
fof(f363,plain,
! [X2,X0,X1] :
( vapp(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f264]) ).
fof(f1009,plain,
spl95_97,
inference(avatar_split_clause,[],[f536,f1007]) ).
fof(f536,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f535]) ).
fof(f535,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f534]) ).
fof(f534,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,[],[f451]) ).
fof(f451,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,[],[f186]) ).
fof(f186,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,[],[f185]) ).
fof(f185,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,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X0,X1,X2),X4) = X5
=> ( ( ~ visValue(X4)
& ~ visSomeExp(X3)
& vreduce(X4) = X3 )
=> ( vreduce(X5) = X6
=> vnoExp = X6 ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X8,X9,X11,X25,X12,X3,X18] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce4) ).
fof(f1005,plain,
spl95_96,
inference(avatar_split_clause,[],[f431,f1003]) ).
fof(f431,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(vbind(X0,X1,X2),X3,X4)
& ~ visFreeVar(X0,X3) )
=> vtcheck(X2,X3,X4) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(vbind(X8,X9,X19),X10,X14)
& ~ visFreeVar(X8,X10) )
=> vtcheck(X19,X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Strong') ).
fof(f1001,plain,
spl95_95,
inference(avatar_split_clause,[],[f430,f999]) ).
fof(f430,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,X3,X4)
& ~ visFreeVar(X0,X3) )
=> vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(X19,X10,X14)
& ~ visFreeVar(X8,X10) )
=> vtcheck(vbind(X8,X9,X19),X10,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-FreeVar') ).
fof(f997,plain,
spl95_94,
inference(avatar_split_clause,[],[f365,f995]) ).
fof(f365,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK47(X0,X1,X2),sK48(X0,X1,X2))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f264]) ).
fof(f993,plain,
spl95_93,
inference(avatar_split_clause,[],[f342,f991]) ).
fof(f991,plain,
( spl95_93
<=> ! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK30(X0,X1)),sK31(X0,X1))) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_93])]) ).
fof(f342,plain,
! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK30(X0,X1)),sK31(X0,X1))) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vgetSomeExp(sK30(X0,X1)),sK31(X0,X1))) = X0
& visSomeExp(sK30(X0,X1))
& sK30(X0,X1) = vreduce(sK29(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK29(X0,X1)
& vapp(sK29(X0,X1),sK31(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f246,f247]) ).
fof(f247,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(sK30(X0,X1)),sK31(X0,X1))) = X0
& visSomeExp(sK30(X0,X1))
& sK30(X0,X1) = vreduce(sK29(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK29(X0,X1)
& vapp(sK29(X0,X1),sK31(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f246,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,[],[f245]) ).
fof(f245,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,[],[f219]) ).
fof(f983,plain,
spl95_92,
inference(avatar_split_clause,[],[f554,f981]) ).
fof(f554,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f553]) ).
fof(f553,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f552]) ).
fof(f552,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,[],[f459]) ).
fof(f459,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,[],[f202]) ).
fof(f202,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,[],[f201]) ).
fof(f201,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,[],[f116]) ).
fof(f116,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X1,X0,X6) = X3
& X2 = X5 )
=> ( X1 != X5
=> ( vlookup(X2,X3) = X4
=> vlookup(X5,X6) = X4 ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X21,X20,X0,X15,X18,X8,X19] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 != X20
=> ( vlookup(X0,X15) = X18
=> vlookup(X8,X19) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup2) ).
fof(f979,plain,
spl95_91,
inference(avatar_split_clause,[],[f416,f977]) ).
fof(f977,plain,
( spl95_91
<=> ! [X0,X3,X2,X1] :
( vvar(sK83(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_91])]) ).
fof(f416,plain,
! [X2,X3,X0,X1] :
( vvar(sK83(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f975,plain,
spl95_90,
inference(avatar_split_clause,[],[f413,f973]) ).
fof(f973,plain,
( spl95_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_90])]) ).
fof(f413,plain,
! [X2,X3,X0,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f298]) ).
fof(f971,plain,
spl95_89,
inference(avatar_split_clause,[],[f411,f969]) ).
fof(f969,plain,
( spl95_89
<=> ! [X0,X3,X2,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_89])]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f298]) ).
fof(f967,plain,
spl95_88,
inference(avatar_split_clause,[],[f377,f965]) ).
fof(f965,plain,
( spl95_88
<=> ! [X2,X0,X1] :
( sK59(X0,X1,X2) = sK60(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_88])]) ).
fof(f377,plain,
! [X2,X0,X1] :
( sK59(X0,X1,X2) = sK60(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f963,plain,
spl95_87,
inference(avatar_split_clause,[],[f373,f961]) ).
fof(f961,plain,
( spl95_87
<=> ! [X2,X0,X1] :
( sK55(X0,X1,X2) != sK56(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_87])]) ).
fof(f373,plain,
! [X2,X0,X1] :
( sK55(X0,X1,X2) != sK56(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
fof(f959,plain,
( spl95_86
| ~ spl95_39
| ~ spl95_53 ),
inference(avatar_split_clause,[],[f852,f804,f739,f957]) ).
fof(f957,plain,
( spl95_86
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_86])]) ).
fof(f804,plain,
( spl95_53
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_53])]) ).
fof(f852,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl95_39
| ~ spl95_53 ),
inference(resolution,[],[f805,f740]) ).
fof(f805,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl95_53 ),
inference(avatar_component_clause,[],[f804]) ).
fof(f944,plain,
( spl95_85
| ~ spl95_40
| ~ spl95_53 ),
inference(avatar_split_clause,[],[f851,f804,f743,f942]) ).
fof(f942,plain,
( spl95_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_85])]) ).
fof(f851,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl95_40
| ~ spl95_53 ),
inference(resolution,[],[f805,f744]) ).
fof(f940,plain,
( spl95_84
| ~ spl95_39
| ~ spl95_48 ),
inference(avatar_split_clause,[],[f840,f780,f739,f938]) ).
fof(f938,plain,
( spl95_84
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_84])]) ).
fof(f780,plain,
( spl95_48
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_48])]) ).
fof(f840,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl95_39
| ~ spl95_48 ),
inference(resolution,[],[f781,f740]) ).
fof(f781,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl95_48 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f936,plain,
spl95_83,
inference(avatar_split_clause,[],[f569,f934]) ).
fof(f569,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f568]) ).
fof(f568,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f567]) ).
fof(f567,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,[],[f566]) ).
fof(f566,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,[],[f565]) ).
fof(f565,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,[],[f464]) ).
fof(f464,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,[],[f212]) ).
fof(f212,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,[],[f211]) ).
fof(f211,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,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X6,X7,X8) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 = X6
=> ( vsubst(X2,X3,X4) = X5
=> vabs(X6,X7,X8) = X5 ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X10,X8,X0,X3,X5,X18,X20,X14,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,X11) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst3) ).
fof(f932,plain,
spl95_82,
inference(avatar_split_clause,[],[f533,f930]) ).
fof(f533,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f532]) ).
fof(f532,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X1,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4
| X1 != X4 ),
inference(equality_resolution,[],[f448]) ).
fof(f448,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,[],[f184]) ).
fof(f184,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,[],[f183]) ).
fof(f183,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,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X3,X0,X5) = X2
& X1 = X4 )
=> ( ( visFreeVar(X1,X2)
=> ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ( visFreeVar(X4,X5)
& X3 != X4 )
=> visFreeVar(X1,X2) ) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X14,X0,X3,X8,X13,X10] :
( ( vabs(X8,X14,X10) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X10)
& X8 != X13 ) )
& ( ( visFreeVar(X13,X10)
& X8 != X13 )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f928,plain,
spl95_81,
inference(avatar_split_clause,[],[f446,f926]) ).
fof(f926,plain,
( spl95_81
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_81])]) ).
fof(f446,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,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,[],[f181]) ).
fof(f181,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,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vabs(X0,X1,X2) = vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2,X3,X1,X4,X5] :
( ( ( X3 = X5
& X2 = X4
& X0 = X1 )
=> vabs(X0,X2,X3) = vabs(X1,X4,X5) )
& ( vabs(X0,X2,X3) = vabs(X1,X4,X5)
=> ( X3 = X5
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
fof(f924,plain,
spl95_80,
inference(avatar_split_clause,[],[f445,f922]) ).
fof(f922,plain,
( spl95_80
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_80])]) ).
fof(f445,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f182]) ).
fof(f920,plain,
spl95_79,
inference(avatar_split_clause,[],[f444,f918]) ).
fof(f918,plain,
( spl95_79
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_79])]) ).
fof(f444,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f182]) ).
fof(f916,plain,
spl95_78,
inference(avatar_split_clause,[],[f442,f914]) ).
fof(f914,plain,
( spl95_78
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_78])]) ).
fof(f442,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,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,[],[f179]) ).
fof(f179,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,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vbind(X0,X1,X2) = vbind(X3,X4,X5) )
& ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X15,X1,X4,X16] :
( ( ( X15 = X16
& X2 = X4
& X0 = X1 )
=> vbind(X0,X2,X15) = vbind(X1,X4,X16) )
& ( vbind(X0,X2,X15) = vbind(X1,X4,X16)
=> ( X15 = X16
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
fof(f912,plain,
spl95_77,
inference(avatar_split_clause,[],[f441,f910]) ).
fof(f910,plain,
( spl95_77
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_77])]) ).
fof(f441,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f180]) ).
fof(f908,plain,
spl95_76,
inference(avatar_split_clause,[],[f440,f906]) ).
fof(f906,plain,
( spl95_76
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_76])]) ).
fof(f440,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f180]) ).
fof(f904,plain,
spl95_75,
inference(avatar_split_clause,[],[f418,f902]) ).
fof(f902,plain,
( spl95_75
<=> ! [X0,X3,X2,X1] :
( sK84(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_75])]) ).
fof(f418,plain,
! [X2,X3,X0,X1] :
( sK84(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f900,plain,
spl95_74,
inference(avatar_split_clause,[],[f415,f898]) ).
fof(f898,plain,
( spl95_74
<=> ! [X0,X3,X2,X1] :
( sK84(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_74])]) ).
fof(f415,plain,
! [X2,X3,X0,X1] :
( sK84(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f896,plain,
( spl95_73
| ~ spl95_40
| ~ spl95_48 ),
inference(avatar_split_clause,[],[f839,f780,f743,f894]) ).
fof(f894,plain,
( spl95_73
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_73])]) ).
fof(f839,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl95_40
| ~ spl95_48 ),
inference(resolution,[],[f781,f744]) ).
fof(f892,plain,
spl95_72,
inference(avatar_split_clause,[],[f414,f890]) ).
fof(f890,plain,
( spl95_72
<=> ! [X0,X3,X2,X1] :
( sK82(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_72])]) ).
fof(f414,plain,
! [X2,X3,X0,X1] :
( sK82(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f302]) ).
fof(f888,plain,
spl95_71,
inference(avatar_split_clause,[],[f410,f886]) ).
fof(f886,plain,
( spl95_71
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_71])]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f298]) ).
fof(f884,plain,
spl95_70,
inference(avatar_split_clause,[],[f409,f882]) ).
fof(f882,plain,
( spl95_70
<=> ! [X0,X3,X2,X1] :
( sK80(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_70])]) ).
fof(f409,plain,
! [X2,X3,X0,X1] :
( sK80(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f298]) ).
fof(f880,plain,
spl95_69,
inference(avatar_split_clause,[],[f405,f878]) ).
fof(f878,plain,
( spl95_69
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_69])]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f876,plain,
spl95_68,
inference(avatar_split_clause,[],[f404,f874]) ).
fof(f874,plain,
( spl95_68
<=> ! [X0,X3,X2,X1] :
( sK75(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_68])]) ).
fof(f404,plain,
! [X2,X3,X0,X1] :
( sK75(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f294]) ).
fof(f872,plain,
spl95_67,
inference(avatar_split_clause,[],[f398,f870]) ).
fof(f870,plain,
( spl95_67
<=> ! [X0,X3,X2,X1] :
( sK69(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_67])]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sK69(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f868,plain,
spl95_66,
inference(avatar_split_clause,[],[f397,f866]) ).
fof(f866,plain,
( spl95_66
<=> ! [X0,X3,X2,X1] :
( sK68(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_66])]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( sK68(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f290]) ).
fof(f864,plain,
spl95_65,
inference(avatar_split_clause,[],[f392,f862]) ).
fof(f862,plain,
( spl95_65
<=> ! [X0,X3,X2,X1] :
( sK66(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_65])]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( sK66(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f860,plain,
spl95_64,
inference(avatar_split_clause,[],[f391,f858]) ).
fof(f858,plain,
( spl95_64
<=> ! [X0,X3,X2,X1] :
( sK65(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_64])]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( sK65(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f286]) ).
fof(f856,plain,
spl95_63,
inference(avatar_split_clause,[],[f338,f854]) ).
fof(f854,plain,
( spl95_63
<=> ! [X0,X1] :
( vapp(sK29(X0,X1),sK31(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_63])]) ).
fof(f338,plain,
! [X0,X1] :
( vapp(sK29(X0,X1),sK31(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f850,plain,
spl95_62,
inference(avatar_split_clause,[],[f333,f848]) ).
fof(f848,plain,
( spl95_62
<=> ! [X0,X1] :
( vapp(sK27(X0,X1),sK26(X0,X1)) = X1
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_62])]) ).
fof(f333,plain,
! [X0,X1] :
( vapp(sK27(X0,X1),sK26(X0,X1)) = X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visSomeExp(sK28(X0,X1))
& sK28(X0,X1) = vreduce(sK27(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK27(X0,X1)
& vapp(sK27(X0,X1),sK26(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27,sK28])],[f242,f243]) ).
fof(f243,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(sK28(X0,X1))
& sK28(X0,X1) = vreduce(sK27(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK27(X0,X1)
& vapp(sK27(X0,X1),sK26(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f242,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,[],[f241]) ).
fof(f241,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,[],[f220]) ).
fof(f838,plain,
spl95_61,
inference(avatar_split_clause,[],[f546,f836]) ).
fof(f546,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f545]) ).
fof(f545,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f544]) ).
fof(f544,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f543]) ).
fof(f543,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,[],[f457]) ).
fof(f457,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,[],[f198]) ).
fof(f198,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,[],[f197]) ).
fof(f197,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,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X6) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 != X6
=> ( vsubst(X2,X3,X4) = X5
=> vvar(X6) = X5 ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X10,X8,X0,X3,X5,X18,X20] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 != X20
=> ( vsubst(X0,X3,X5) = X18
=> vvar(X20) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst1) ).
fof(f834,plain,
spl95_60,
inference(avatar_split_clause,[],[f510,f832]) ).
fof(f510,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f509]) ).
fof(f509,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,vapp(X2,X4))
| X0 != X3 ),
inference(equality_resolution,[],[f434]) ).
fof(f434,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,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,[],[f167]) ).
fof(f167,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,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4] :
( ( vapp(X2,X4) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) ) )
& ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) )
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X3,X11,X13,X12] :
( ( vapp(X11,X12) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) ) )
& ( ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f830,plain,
spl95_59,
inference(avatar_split_clause,[],[f383,f828]) ).
fof(f383,plain,
! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( vsomeType(X2) = vlookup(X1,X0)
=> vtcheck(X0,vvar(X1),X2) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X19,X8,X14] :
( vlookup(X8,X19) = vsomeType(X14)
=> vtcheck(X19,vvar(X8),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-var') ).
fof(f826,plain,
spl95_58,
inference(avatar_split_clause,[],[f378,f824]) ).
fof(f824,plain,
( spl95_58
<=> ! [X2,X0,X1] :
( vsomeType(sK61(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_58])]) ).
fof(f378,plain,
! [X2,X0,X1] :
( vsomeType(sK61(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f822,plain,
spl95_57,
inference(avatar_split_clause,[],[f349,f820]) ).
fof(f820,plain,
( spl95_57
<=> ! [X0,X1] :
( sK38(X0,X1) = vreduce(sK40(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_57])]) ).
fof(f349,plain,
! [X0,X1] :
( sK38(X0,X1) = vreduce(sK40(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f818,plain,
spl95_56,
inference(avatar_split_clause,[],[f344,f816]) ).
fof(f816,plain,
( spl95_56
<=> ! [X0,X1] :
( sK35(X0,X1) = vreduce(sK36(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_56])]) ).
fof(f344,plain,
! [X0,X1] :
( sK35(X0,X1) = vreduce(sK36(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f814,plain,
spl95_55,
inference(avatar_split_clause,[],[f340,f812]) ).
fof(f812,plain,
( spl95_55
<=> ! [X0,X1] :
( sK30(X0,X1) = vreduce(sK29(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_55])]) ).
fof(f340,plain,
! [X0,X1] :
( sK30(X0,X1) = vreduce(sK29(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f810,plain,
spl95_54,
inference(avatar_split_clause,[],[f339,f808]) ).
fof(f808,plain,
( spl95_54
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK29(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_54])]) ).
fof(f339,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK29(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f806,plain,
( spl95_53
| ~ spl95_11
| ~ spl95_40 ),
inference(avatar_split_clause,[],[f750,f743,f626,f804]) ).
fof(f750,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl95_11
| ~ spl95_40 ),
inference(resolution,[],[f744,f627]) ).
fof(f802,plain,
spl95_52,
inference(avatar_split_clause,[],[f335,f800]) ).
fof(f800,plain,
( spl95_52
<=> ! [X0,X1] :
( sK28(X0,X1) = vreduce(sK27(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_52])]) ).
fof(f335,plain,
! [X0,X1] :
( sK28(X0,X1) = vreduce(sK27(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f798,plain,
spl95_51,
inference(avatar_split_clause,[],[f334,f796]) ).
fof(f796,plain,
( spl95_51
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK27(X0,X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_51])]) ).
fof(f334,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK27(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f794,plain,
spl95_50,
inference(avatar_split_clause,[],[f330,f792]) ).
fof(f792,plain,
( spl95_50
<=> ! [X0,X1] :
( sK25(X0,X1) = vreduce(sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_50])]) ).
fof(f330,plain,
! [X0,X1] :
( sK25(X0,X1) = vreduce(sK21(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f786,plain,
spl95_49,
inference(avatar_split_clause,[],[f389,f784]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,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,[],[f151]) ).
fof(f151,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,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X5,X6,X7] :
( ( ( X5 = X7
& X3 = X6 )
=> vapp(X3,X5) = vapp(X6,X7) )
& ( vapp(X3,X5) = vapp(X6,X7)
=> ( X5 = X7
& X3 = X6 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-app') ).
fof(f782,plain,
( spl95_48
| ~ spl95_11
| ~ spl95_39 ),
inference(avatar_split_clause,[],[f749,f739,f626,f780]) ).
fof(f749,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl95_11
| ~ spl95_39 ),
inference(resolution,[],[f740,f627]) ).
fof(f778,plain,
spl95_47,
inference(avatar_split_clause,[],[f388,f776]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f152]) ).
fof(f774,plain,
spl95_46,
inference(avatar_split_clause,[],[f386,f772]) ).
fof(f772,plain,
( spl95_46
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_46])]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f150,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,[],[f149]) ).
fof(f149,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,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> varrow(X0,X1) = varrow(X2,X3) )
& ( varrow(X0,X1) = varrow(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X2,X4,X30,X31] :
( ( ( X4 = X31
& X2 = X30 )
=> varrow(X2,X4) = varrow(X30,X31) )
& ( varrow(X2,X4) = varrow(X30,X31)
=> ( X4 = X31
& X2 = X30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-arrow') ).
fof(f770,plain,
spl95_45,
inference(avatar_split_clause,[],[f385,f768]) ).
fof(f768,plain,
( spl95_45
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_45])]) ).
fof(f385,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f150]) ).
fof(f766,plain,
spl95_44,
inference(avatar_split_clause,[],[f375,f764]) ).
fof(f764,plain,
( spl95_44
<=> ! [X2,X0,X1] :
( sK59(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_44])]) ).
fof(f375,plain,
! [X2,X0,X1] :
( sK59(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f279]) ).
fof(f762,plain,
spl95_43,
inference(avatar_split_clause,[],[f371,f760]) ).
fof(f371,plain,
! [X2,X0,X1] :
( sK56(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f275]) ).
fof(f758,plain,
spl95_42,
inference(avatar_split_clause,[],[f558,f756]) ).
fof(f558,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f557]) ).
fof(f557,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f556]) ).
fof(f556,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f555]) ).
fof(f555,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f460]) ).
fof(f460,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,[],[f204]) ).
fof(f204,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,[],[f203]) ).
fof(f203,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,[],[f117]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X2,X6,X0) = X4
& X1 = X3 )
=> ( X1 = X2
=> ( vlookup(X3,X4) = X5
=> vsomeType(X6) = X5 ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X19,X8,X20,X0,X15,X18,X21] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 = X20
=> ( vlookup(X0,X15) = X18
=> vsomeType(X21) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup1) ).
fof(f754,plain,
spl95_41,
inference(avatar_split_clause,[],[f528,f752]) ).
fof(f528,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f527]) ).
fof(f527,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f450]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f184]) ).
fof(f745,plain,
spl95_40,
inference(avatar_split_clause,[],[f514,f743]) ).
fof(f514,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f513]) ).
fof(f513,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f432]) ).
fof(f432,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f168]) ).
fof(f741,plain,
spl95_39,
inference(avatar_split_clause,[],[f512,f739]) ).
fof(f512,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f511]) ).
fof(f511,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f433]) ).
fof(f433,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f168]) ).
fof(f737,plain,
spl95_38,
inference(avatar_split_clause,[],[f427,f735]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X3,X5,X6] : vabs(X0,X2,X3) != vapp(X5,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f733,plain,
spl95_37,
inference(avatar_split_clause,[],[f324,f731]) ).
fof(f731,plain,
( spl95_37
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_37])]) ).
fof(f324,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( ( vvar(X0) = vvar(X1)
| X0 != X1 )
& ( X0 = X1
| vvar(X0) != vvar(X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( X0 = X1
=> vvar(X0) = vvar(X1) )
& ( vvar(X0) = vvar(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-var') ).
fof(f729,plain,
spl95_36,
inference(avatar_split_clause,[],[f322,f727]) ).
fof(f727,plain,
( spl95_36
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_36])]) ).
fof(f322,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeExp(X0) = vsomeExp(X1) )
& ( vsomeExp(X0) = vsomeExp(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X3,X5] :
( ( X3 = X5
=> vsomeExp(X3) = vsomeExp(X5) )
& ( vsomeExp(X3) = vsomeExp(X5)
=> X3 = X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someExp') ).
fof(f725,plain,
spl95_35,
inference(avatar_split_clause,[],[f320,f723]) ).
fof(f723,plain,
( spl95_35
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_35])]) ).
fof(f320,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeType(X0) = vsomeType(X1) )
& ( vsomeType(X0) = vsomeType(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X2,X4] :
( ( X2 = X4
=> vsomeType(X2) = vsomeType(X4) )
& ( vsomeType(X2) = vsomeType(X4)
=> X2 = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-someType') ).
fof(f720,plain,
spl95_34,
inference(avatar_split_clause,[],[f551,f718]) ).
fof(f551,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f550]) ).
fof(f550,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f549]) ).
fof(f549,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f548]) ).
fof(f548,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f547]) ).
fof(f547,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f458]) ).
fof(f458,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,[],[f200]) ).
fof(f200,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,[],[f199]) ).
fof(f199,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,[],[f115]) ).
fof(f115,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X1) = X4
& X3 = X6
& X0 = X2 )
=> ( X0 = X1
=> ( vsubst(X2,X3,X4) = X5
=> X5 = X6 ) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X8,X20,X0,X3,X5,X18,X10] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> X10 = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst0) ).
fof(f716,plain,
spl95_33,
inference(avatar_split_clause,[],[f508,f714]) ).
fof(f508,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f507]) ).
fof(f507,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f428]) ).
fof(f428,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( vabs(X0,X1,X2) = X3
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X8,X9,X10,X3,X18] :
( vabs(X8,X9,X10) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce1) ).
fof(f712,plain,
spl95_32,
inference(avatar_split_clause,[],[f503,f710]) ).
fof(f503,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f502]) ).
fof(f502,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f426]) ).
fof(f426,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3] :
( ( vvar(X2) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> X2 = X3 )
& ( X2 = X3
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3,X8,X13] :
( ( vvar(X8) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> X8 = X13 )
& ( X8 = X13
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f708,plain,
spl95_31,
inference(avatar_split_clause,[],[f384,f706]) ).
fof(f706,plain,
( spl95_31
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_31])]) ).
fof(f384,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f704,plain,
spl95_30,
inference(avatar_split_clause,[],[f351,f702]) ).
fof(f702,plain,
( spl95_30
<=> ! [X0,X1] :
( visValue(sK40(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_30])]) ).
fof(f351,plain,
! [X0,X1] :
( visValue(sK40(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f700,plain,
spl95_29,
inference(avatar_split_clause,[],[f350,f698]) ).
fof(f698,plain,
( spl95_29
<=> ! [X0,X1] :
( ~ visSomeExp(sK38(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_29])]) ).
fof(f350,plain,
! [X0,X1] :
( ~ visSomeExp(sK38(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
fof(f696,plain,
spl95_28,
inference(avatar_split_clause,[],[f346,f694]) ).
fof(f694,plain,
( spl95_28
<=> ! [X0,X1] :
( ~ visValue(sK36(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_28])]) ).
fof(f346,plain,
! [X0,X1] :
( ~ visValue(sK36(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f692,plain,
spl95_27,
inference(avatar_split_clause,[],[f345,f690]) ).
fof(f690,plain,
( spl95_27
<=> ! [X0,X1] :
( ~ visSomeExp(sK35(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_27])]) ).
fof(f345,plain,
! [X0,X1] :
( ~ visSomeExp(sK35(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f688,plain,
spl95_26,
inference(avatar_split_clause,[],[f341,f686]) ).
fof(f686,plain,
( spl95_26
<=> ! [X0,X1] :
( visSomeExp(sK30(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_26])]) ).
fof(f341,plain,
! [X0,X1] :
( visSomeExp(sK30(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
fof(f684,plain,
spl95_25,
inference(avatar_split_clause,[],[f336,f682]) ).
fof(f682,plain,
( spl95_25
<=> ! [X0,X1] :
( ~ visSomeExp(sK28(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_25])]) ).
fof(f336,plain,
! [X0,X1] :
( ~ visSomeExp(sK28(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f680,plain,
spl95_24,
inference(avatar_split_clause,[],[f331,f678]) ).
fof(f678,plain,
( spl95_24
<=> ! [X0,X1] :
( visSomeExp(sK25(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_24])]) ).
fof(f331,plain,
! [X0,X1] :
( visSomeExp(sK25(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f240]) ).
fof(f676,plain,
spl95_23,
inference(avatar_split_clause,[],[f531,f674]) ).
fof(f531,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f530]) ).
fof(f530,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f529]) ).
fof(f529,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f449]) ).
fof(f449,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f184]) ).
fof(f672,plain,
spl95_22,
inference(avatar_split_clause,[],[f359,f670]) ).
fof(f359,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3,X5] : vvar(X0) != vapp(X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f668,plain,
spl95_21,
inference(avatar_split_clause,[],[f358,f666]) ).
fof(f666,plain,
( spl95_21
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_21])]) ).
fof(f358,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] : vempty != vbind(X0,X1,X2),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X15] : vempty != vbind(X0,X2,X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-empty-bind') ).
fof(f664,plain,
spl95_20,
inference(avatar_split_clause,[],[f347,f662]) ).
fof(f662,plain,
( spl95_20
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_20])]) ).
fof(f347,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f660,plain,
spl95_19,
inference(avatar_split_clause,[],[f337,f658]) ).
fof(f337,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f656,plain,
spl95_18,
inference(avatar_split_clause,[],[f501,f654]) ).
fof(f501,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f500]) ).
fof(f500,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f499]) ).
fof(f499,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f424]) ).
fof(f424,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ( vempty = X2
& X0 = X1 )
=> ( vlookup(X1,X2) = X3
=> vnoType = X3 ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X8,X0,X15,X18] :
( ( vempty = X15
& X0 = X8 )
=> ( vlookup(X0,X15) = X18
=> vnoType = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lookup0) ).
fof(f652,plain,
spl95_17,
inference(avatar_split_clause,[],[f498,f650]) ).
fof(f498,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f423]) ).
fof(f423,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) = X3
=> visValue(X3) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X10,X3] :
( vabs(X8,X9,X10) = X3
=> visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue0) ).
fof(f648,plain,
spl95_16,
inference(avatar_split_clause,[],[f485,f646]) ).
fof(f485,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f484]) ).
fof(f484,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f362]) ).
fof(f362,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f141]) ).
fof(f141,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( vvar(X0) = X1
=> ( vreduce(X1) = X2
=> vnoExp = X2 ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X3,X18] :
( vvar(X8) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce0) ).
fof(f644,plain,
spl95_15,
inference(avatar_split_clause,[],[f483,f642]) ).
fof(f642,plain,
( spl95_15
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl95_15])]) ).
fof(f483,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f482]) ).
fof(f482,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f361]) ).
fof(f361,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( vsomeExp(X2) = X0
=> ( vgetSomeExp(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X24,X18,X10] :
( vsomeExp(X10) = X24
=> ( vgetSomeExp(X24) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeExp0) ).
fof(f640,plain,
spl95_14,
inference(avatar_split_clause,[],[f481,f638]) ).
fof(f638,plain,
( spl95_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl95_14])]) ).
fof(f481,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f480]) ).
fof(f480,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f360]) ).
fof(f360,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( vsomeType(X2) = X0
=> ( vgetSomeType(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X17,X18,X10] :
( vsomeType(X10) = X17
=> ( vgetSomeType(X17) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',getSomeType0) ).
fof(f636,plain,
spl95_13,
inference(avatar_split_clause,[],[f506,f634]) ).
fof(f506,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f505]) ).
fof(f505,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f504]) ).
fof(f504,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f425]) ).
fof(f425,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f159]) ).
fof(f632,plain,
spl95_12,
inference(avatar_split_clause,[],[f489,f630]) ).
fof(f489,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f382]) ).
fof(f382,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( vapp(X0,X1) = X2
=> ~ visValue(X2) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X11,X12,X3] :
( vapp(X11,X12) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue2) ).
fof(f628,plain,
spl95_11,
inference(avatar_split_clause,[],[f472,f626]) ).
fof(f472,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f326]) ).
fof(f326,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( vgensym(X1) = X0
=> ~ visFreeVar(X0,X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X13,X10] :
( vgensym(X10) = X13
=> ~ visFreeVar(X13,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f624,plain,
spl95_10,
inference(avatar_split_clause,[],[f317,f622]) ).
fof(f622,plain,
( spl95_10
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_10])]) ).
fof(f317,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3] : vnoExp != vsomeExp(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
fof(f620,plain,
spl95_9,
inference(avatar_split_clause,[],[f316,f618]) ).
fof(f618,plain,
( spl95_9
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_9])]) ).
fof(f316,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0] : vnoType != vsomeType(X0),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2] : vnoType != vsomeType(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','DIFF-noType-someType') ).
fof(f616,plain,
spl95_8,
inference(avatar_split_clause,[],[f479,f614]) ).
fof(f479,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f357]) ).
fof(f357,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( vvar(X0) = X1
=> ~ visValue(X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X8,X3] :
( vvar(X8) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isValue1) ).
fof(f612,plain,
spl95_7,
inference(avatar_split_clause,[],[f474,f610]) ).
fof(f610,plain,
( spl95_7
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_7])]) ).
fof(f474,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f328]) ).
fof(f328,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( vsomeExp(X0) = X1
=> visSomeExp(X1) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X10,X24] :
( vsomeExp(X10) = X24
=> visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp1) ).
fof(f608,plain,
spl95_6,
inference(avatar_split_clause,[],[f473,f606]) ).
fof(f606,plain,
( spl95_6
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_6])]) ).
fof(f473,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f327]) ).
fof(f327,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( vsomeType(X0) = X1
=> visSomeType(X1) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X10,X17] :
( vsomeType(X10) = X17
=> visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType1) ).
fof(f604,plain,
~ spl95_5,
inference(avatar_split_clause,[],[f312,f601]) ).
fof(f312,plain,
~ vtcheck(sK15,vsubst(sK16,sK17,vabs(sK18,sK19,veabs)),sK20),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
( ~ vtcheck(sK15,vsubst(sK16,sK17,vabs(sK18,sK19,veabs)),sK20)
& vtcheck(vbind(sK16,sK14,sK15),vabs(sK18,sK19,veabs),sK20)
& vtcheck(sK15,sK17,sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18,sK19,sK20])],[f125,f235]) ).
fof(f235,plain,
( ? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0) )
=> ( ~ vtcheck(sK15,vsubst(sK16,sK17,vabs(sK18,sK19,veabs)),sK20)
& vtcheck(vbind(sK16,sK14,sK15),vabs(sK18,sK19,veabs),sK20)
& vtcheck(sK15,sK17,sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
? [X0,X1,X2,X3,X4,X5,X6] :
( ~ vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6)
& vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
~ ! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X0,X1),vabs(X4,X5,veabs),X6)
& vtcheck(X1,X3,X0) )
=> vtcheck(X1,vsubst(X2,X3,vabs(X4,X5,veabs)),X6) ),
inference(rectify,[],[f63]) ).
fof(f63,negated_conjecture,
~ ! [X14,X19,X8,X10,X20,X9,X33] :
( ( vtcheck(vbind(X8,X14,X19),vabs(X20,X9,veabs),X33)
& vtcheck(X19,X10,X14) )
=> vtcheck(X19,vsubst(X8,X10,vabs(X20,X9,veabs)),X33) ),
inference(negated_conjecture,[],[f62]) ).
fof(f62,conjecture,
! [X14,X19,X8,X10,X20,X9,X33] :
( ( vtcheck(vbind(X8,X14,X19),vabs(X20,X9,veabs),X33)
& vtcheck(X19,X10,X14) )
=> vtcheck(X19,vsubst(X8,X10,vabs(X20,X9,veabs)),X33) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-subst-abs') ).
fof(f599,plain,
spl95_4,
inference(avatar_split_clause,[],[f311,f596]) ).
fof(f311,plain,
vtcheck(vbind(sK16,sK14,sK15),vabs(sK18,sK19,veabs),sK20),
inference(cnf_transformation,[],[f236]) ).
fof(f594,plain,
~ spl95_3,
inference(avatar_split_clause,[],[f468,f591]) ).
fof(f468,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( vnoExp = X0
=> ~ visSomeExp(X0) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X24] :
( vnoExp = X24
=> ~ visSomeExp(X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeExp0) ).
fof(f589,plain,
~ spl95_2,
inference(avatar_split_clause,[],[f467,f586]) ).
fof(f586,plain,
( spl95_2
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl95_2])]) ).
fof(f467,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f318]) ).
fof(f318,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( vnoType = X0
=> ~ visSomeType(X0) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X17] :
( vnoType = X17
=> ~ visSomeType(X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isSomeType0) ).
fof(f584,plain,
spl95_1,
inference(avatar_split_clause,[],[f310,f581]) ).
fof(f310,plain,
vtcheck(sK15,sK17,sK14),
inference(cnf_transformation,[],[f236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n002.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 05:26:40 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (23905)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (23908)WARNING: value z3 for option sas not known
% 0.15/0.38 % (23909)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (23906)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (23908)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)
% 0.15/0.38 % (23907)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (23912)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)
% 0.15/0.38 % (23910)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)
% 0.15/0.38 % (23911)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)
% 0.21/0.43 TRYING [1]
% 0.21/0.44 TRYING [2]
% 0.21/0.51 % (23910)First to succeed.
% 0.21/0.52 TRYING [3]
% 0.21/0.52 % (23910)Refutation found. Thanks to Tanya!
% 0.21/0.52 % SZS status Theorem for theBenchmark
% 0.21/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (23910)------------------------------
% 0.21/0.53 % (23910)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.53 % (23910)Termination reason: Refutation
% 0.21/0.53
% 0.21/0.53 % (23910)Memory used [KB]: 2984
% 0.21/0.53 % (23910)Time elapsed: 0.144 s
% 0.21/0.53 % (23910)Instructions burned: 276 (million)
% 0.21/0.53 % (23910)------------------------------
% 0.21/0.53 % (23910)------------------------------
% 0.21/0.53 % (23905)Success in time 0.169 s
%------------------------------------------------------------------------------