TSTP Solution File: COM149+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM149+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 : n006.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 10:48:00 EDT 2024
% Result : Theorem 1.55s 0.58s
% Output : Refutation 1.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 358
% Syntax : Number of formulae : 1278 ( 179 unt; 0 def)
% Number of atoms : 4887 (2241 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 5347 (1738 ~;2383 |; 755 &)
% ( 268 <=>; 203 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 289 ( 287 usr; 269 prp; 0-4 aty)
% Number of functors : 92 ( 92 usr; 5 con; 0-4 aty)
% Number of variables : 4289 (3728 !; 561 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3162,plain,
$false,
inference(avatar_sat_refutation,[],[f558,f562,f568,f573,f577,f581,f585,f589,f593,f597,f601,f605,f609,f613,f617,f621,f625,f629,f633,f637,f641,f645,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f694,f698,f702,f706,f710,f714,f723,f727,f731,f735,f739,f743,f747,f751,f755,f759,f767,f771,f775,f779,f783,f789,f793,f797,f801,f805,f809,f821,f825,f829,f833,f837,f841,f845,f849,f853,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f917,f932,f939,f943,f947,f951,f955,f965,f969,f973,f977,f984,f991,f995,f999,f1008,f1012,f1016,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1055,f1059,f1063,f1069,f1101,f1105,f1117,f1121,f1127,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1168,f1172,f1187,f1200,f1204,f1208,f1229,f1233,f1237,f1241,f1245,f1249,f1253,f1269,f1279,f1283,f1287,f1297,f1306,f1320,f1324,f1344,f1356,f1361,f1374,f1379,f1384,f1389,f1393,f1402,f1411,f1415,f1419,f1423,f1427,f1431,f1533,f1555,f1560,f1564,f1584,f1588,f1602,f1606,f1656,f1660,f1664,f1732,f1736,f1740,f1744,f1748,f1767,f1795,f1809,f1813,f1847,f1888,f1892,f1912,f1928,f1932,f1936,f1940,f1960,f1984,f1988,f1992,f1998,f2018,f2022,f2047,f2051,f2055,f2059,f2105,f2116,f2120,f2124,f2150,f2154,f2196,f2200,f2204,f2208,f2220,f2293,f2305,f2309,f2311,f2317,f2321,f2398,f2411,f2415,f2419,f2454,f2458,f2476,f2480,f2498,f2503,f2507,f2520,f2524,f2531,f2535,f2561,f2565,f2575,f2579,f2583,f2597,f2610,f2623,f2627,f2639,f2643,f2647,f2651,f2655,f2659,f2803,f2812,f2821,f2825,f2830,f2874,f2885,f2889,f2905,f2909,f2968,f2972,f3016,f3026,f3030,f3035,f3060,f3064,f3108,f3112,f3156]) ).
fof(f3156,plain,
( ~ spl90_7
| ~ spl90_264 ),
inference(avatar_contradiction_clause,[],[f3153]) ).
fof(f3153,plain,
( $false
| ~ spl90_7
| ~ spl90_264 ),
inference(resolution,[],[f3034,f584]) ).
fof(f584,plain,
( ! [X0] : ~ visValue(vvar(X0))
| ~ spl90_7 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f583,plain,
( spl90_7
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_7])]) ).
fof(f3034,plain,
( visValue(vvar(sK15))
| ~ spl90_264 ),
inference(avatar_component_clause,[],[f3032]) ).
fof(f3032,plain,
( spl90_264
<=> visValue(vvar(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_264])]) ).
fof(f3112,plain,
( spl90_268
| ~ spl90_66
| ~ spl90_152 ),
inference(avatar_split_clause,[],[f1366,f1359,f839,f3110]) ).
fof(f3110,plain,
( spl90_268
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_268])]) ).
fof(f839,plain,
( spl90_66
<=> ! [X0,X3,X2,X1] :
( sK63(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_66])]) ).
fof(f1359,plain,
( spl90_152
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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,[spl90_152])]) ).
fof(f1366,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl90_66
| ~ spl90_152 ),
inference(resolution,[],[f1360,f840]) ).
fof(f840,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK63(X0,X1,X2,X3) = X3 )
| ~ spl90_66 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f1360,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl90_152 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f3108,plain,
( spl90_267
| ~ spl90_67
| ~ spl90_152 ),
inference(avatar_split_clause,[],[f1365,f1359,f843,f3106]) ).
fof(f3106,plain,
( spl90_267
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_267])]) ).
fof(f843,plain,
( spl90_67
<=> ! [X0,X3,X2,X1] :
( sK64(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_67])]) ).
fof(f1365,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl90_67
| ~ spl90_152 ),
inference(resolution,[],[f1360,f844]) ).
fof(f844,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK64(X0,X1,X2,X3) = X2 )
| ~ spl90_67 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f3064,plain,
( spl90_266
| ~ spl90_143
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1334,f1322,f1277,f3062]) ).
fof(f3062,plain,
( spl90_266
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK64(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK63(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_266])]) ).
fof(f1277,plain,
( spl90_143
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) = vgensym(vapp(vapp(sK64(X0,X1,X2,X3),sK68(X0,X1,X2,X3)),vvar(sK63(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_143])]) ).
fof(f1322,plain,
( spl90_149
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(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,[spl90_149])]) ).
fof(f1334,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK64(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK63(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl90_143
| ~ spl90_149 ),
inference(resolution,[],[f1323,f1278]) ).
fof(f1278,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK67(X0,X1,X2,X3) = vgensym(vapp(vapp(sK64(X0,X1,X2,X3),sK68(X0,X1,X2,X3)),vvar(sK63(X0,X1,X2,X3)))) )
| ~ spl90_143 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f1323,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl90_149 ),
inference(avatar_component_clause,[],[f1322]) ).
fof(f3060,plain,
( spl90_265
| ~ spl90_143
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1326,f1318,f1277,f3058]) ).
fof(f3058,plain,
( spl90_265
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK64(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK63(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_265])]) ).
fof(f1318,plain,
( spl90_148
<=> ! [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)
| sK82(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,[spl90_148])]) ).
fof(f1326,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK64(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK63(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl90_143
| ~ spl90_148 ),
inference(resolution,[],[f1319,f1278]) ).
fof(f1319,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl90_148 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f3035,plain,
( spl90_264
| ~ spl90_16
| ~ spl90_253 ),
inference(avatar_split_clause,[],[f2910,f2827,f619,f3032]) ).
fof(f619,plain,
( spl90_16
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_16])]) ).
fof(f2827,plain,
( spl90_253
<=> vvar(sK15) = vabs(sK44(vempty,sK14,vvar(sK15)),sK46(vempty,sK14,vvar(sK15)),sK45(vempty,sK14,vvar(sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_253])]) ).
fof(f2910,plain,
( visValue(vvar(sK15))
| ~ spl90_16
| ~ spl90_253 ),
inference(superposition,[],[f620,f2829]) ).
fof(f2829,plain,
( vvar(sK15) = vabs(sK44(vempty,sK14,vvar(sK15)),sK46(vempty,sK14,vvar(sK15)),sK45(vempty,sK14,vvar(sK15)))
| ~ spl90_253 ),
inference(avatar_component_clause,[],[f2827]) ).
fof(f620,plain,
( ! [X2,X0,X1] : visValue(vabs(X0,X1,X2))
| ~ spl90_16 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f3030,plain,
( spl90_263
| ~ spl90_137
| ~ spl90_150 ),
inference(avatar_split_clause,[],[f1347,f1342,f1235,f3028]) ).
fof(f3028,plain,
( spl90_263
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_263])]) ).
fof(f1235,plain,
( spl90_137
<=> ! [X0,X3,X2,X1] :
( vabs(sK66(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK68(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_137])]) ).
fof(f1342,plain,
( spl90_150
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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,[spl90_150])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl90_137
| ~ spl90_150 ),
inference(resolution,[],[f1343,f1236]) ).
fof(f1236,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| vabs(sK66(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK68(X0,X1,X2,X3)) = X1 )
| ~ spl90_137 ),
inference(avatar_component_clause,[],[f1235]) ).
fof(f1343,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl90_150 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f3026,plain,
( spl90_262
| ~ spl90_133
| ~ spl90_135 ),
inference(avatar_split_clause,[],[f1255,f1227,f1202,f3024]) ).
fof(f3024,plain,
( spl90_262
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2))
| vsomeType(sK47(X0,X1,X2)) = vlookup(sK48(sK45(X0,X1,X2),sK47(X0,X1,X2),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0)),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0))
| sP6(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_262])]) ).
fof(f1202,plain,
( spl90_133
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK48(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_133])]) ).
fof(f1227,plain,
( spl90_135
<=> ! [X2,X0,X1] :
( vtcheck(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK45(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_135])]) ).
fof(f1255,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2))
| vsomeType(sK47(X0,X1,X2)) = vlookup(sK48(sK45(X0,X1,X2),sK47(X0,X1,X2),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0)),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0))
| sP6(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2)) )
| ~ spl90_133
| ~ spl90_135 ),
inference(resolution,[],[f1228,f1203]) ).
fof(f1203,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK48(X0,X1,X2),X2)
| sP6(X2,X1,X0) )
| ~ spl90_133 ),
inference(avatar_component_clause,[],[f1202]) ).
fof(f1228,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK45(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP5(X0,X1,X2) )
| ~ spl90_135 ),
inference(avatar_component_clause,[],[f1227]) ).
fof(f3016,plain,
( spl90_261
| ~ spl90_60
| ~ spl90_152 ),
inference(avatar_split_clause,[],[f1368,f1359,f807,f3014]) ).
fof(f3014,plain,
( spl90_261
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK81(X0,X1,vvar(X2),vvar(X2)),sK82(X0,X1,vvar(X2),vvar(X2)),vapp(sK80(X0,X1,vvar(X2),vvar(X2)),sK83(X0,X1,vvar(X2),vvar(X2))))
| sP11(vvar(X2),vvar(X2),X1,X0)
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_261])]) ).
fof(f807,plain,
( spl90_60
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_60])]) ).
fof(f1368,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK81(X0,X1,vvar(X2),vvar(X2)),sK82(X0,X1,vvar(X2),vvar(X2)),vapp(sK80(X0,X1,vvar(X2),vvar(X2)),sK83(X0,X1,vvar(X2),vvar(X2))))
| sP11(vvar(X2),vvar(X2),X1,X0)
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl90_60
| ~ spl90_152 ),
inference(superposition,[],[f1360,f808]) ).
fof(f808,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl90_60 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f2972,plain,
( spl90_260
| ~ spl90_137
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1335,f1322,f1235,f2970]) ).
fof(f2970,plain,
( spl90_260
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_260])]) ).
fof(f1335,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl90_137
| ~ spl90_149 ),
inference(resolution,[],[f1323,f1236]) ).
fof(f2968,plain,
( spl90_259
| ~ spl90_137
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1327,f1318,f1235,f2966]) ).
fof(f2966,plain,
( spl90_259
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_259])]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK65(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl90_137
| ~ spl90_148 ),
inference(resolution,[],[f1319,f1236]) ).
fof(f2909,plain,
( spl90_258
| ~ spl90_83
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1340,f1322,f907,f2907]) ).
fof(f2907,plain,
( spl90_258
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK81(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X0
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_258])]) ).
fof(f907,plain,
( spl90_83
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_83])]) ).
fof(f1340,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK81(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X0
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl90_83
| ~ spl90_149 ),
inference(superposition,[],[f1323,f908]) ).
fof(f908,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl90_83 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f2905,plain,
( spl90_257
| ~ spl90_83
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1332,f1318,f907,f2903]) ).
fof(f2903,plain,
( spl90_257
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK82(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X1
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_257])]) ).
fof(f1332,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK82(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X1
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl90_83
| ~ spl90_148 ),
inference(superposition,[],[f1319,f908]) ).
fof(f2889,plain,
( spl90_256
| ~ spl90_105
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1293,f1285,f1029,f2887]) ).
fof(f2887,plain,
( spl90_256
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,sK64(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK64(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK66(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK64(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK64(X1,X2,X3,X4),vabs(sK66(X1,X2,X3,X4),X6,X5))
| sK66(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_256])]) ).
fof(f1029,plain,
( spl90_105
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK66(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_105])]) ).
fof(f1285,plain,
( spl90_145
<=> ! [X5,X4,X9,X7,X6] :
( vsubst(X4,X5,vabs(vgensym(vapp(vapp(X5,X9),vvar(X4))),X6,vsubst(X7,vvar(vgensym(vapp(vapp(X5,X9),vvar(X4)))),X9))) = vsubst(X4,X5,vabs(X7,X6,X9))
| ~ visFreeVar(X7,X5)
| X4 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_145])]) ).
fof(f1293,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,sK64(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK64(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK66(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK64(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK64(X1,X2,X3,X4),vabs(sK66(X1,X2,X3,X4),X6,X5))
| sK66(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) )
| ~ spl90_105
| ~ spl90_145 ),
inference(resolution,[],[f1286,f1030]) ).
fof(f1030,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(sK66(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) )
| ~ spl90_105 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f1286,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 )
| ~ spl90_145 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f2885,plain,
( spl90_255
| ~ spl90_124
| ~ spl90_135 ),
inference(avatar_split_clause,[],[f1256,f1227,f1147,f2883]) ).
fof(f2883,plain,
( spl90_255
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK48(sK45(X0,X1,X2),sK47(X0,X1,X2),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0)))
| sP6(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_255])]) ).
fof(f1147,plain,
( spl90_124
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK48(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_124])]) ).
fof(f1256,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK48(sK45(X0,X1,X2),sK47(X0,X1,X2),vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0)))
| sP6(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK47(X0,X1,X2),sK45(X0,X1,X2)) )
| ~ spl90_124
| ~ spl90_135 ),
inference(resolution,[],[f1228,f1148]) ).
fof(f1148,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK48(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl90_124 ),
inference(avatar_component_clause,[],[f1147]) ).
fof(f2874,plain,
( spl90_254
| ~ spl90_32
| ~ spl90_146 ),
inference(avatar_split_clause,[],[f1302,f1295,f683,f2872]) ).
fof(f2872,plain,
( spl90_254
<=> ! [X2,X0,X1] :
( sP3(vnoExp,vabs(X0,X1,X2))
| sP2(vnoExp,vabs(X0,X1,X2))
| sP1(vnoExp,vabs(X0,X1,X2))
| sP0(vnoExp,vabs(X0,X1,X2))
| sP4(vnoExp,vabs(X0,X1,X2))
| vabs(X0,X1,X2) = vabs(sK37(vabs(X0,X1,X2),vnoExp),sK38(vabs(X0,X1,X2),vnoExp),sK39(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK40(vabs(X0,X1,X2),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_254])]) ).
fof(f683,plain,
( spl90_32
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_32])]) ).
fof(f1295,plain,
( spl90_146
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_146])]) ).
fof(f1302,plain,
( ! [X2,X0,X1] :
( sP3(vnoExp,vabs(X0,X1,X2))
| sP2(vnoExp,vabs(X0,X1,X2))
| sP1(vnoExp,vabs(X0,X1,X2))
| sP0(vnoExp,vabs(X0,X1,X2))
| sP4(vnoExp,vabs(X0,X1,X2))
| vabs(X0,X1,X2) = vabs(sK37(vabs(X0,X1,X2),vnoExp),sK38(vabs(X0,X1,X2),vnoExp),sK39(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK40(vabs(X0,X1,X2),vnoExp)) )
| ~ spl90_32
| ~ spl90_146 ),
inference(superposition,[],[f1296,f684]) ).
fof(f684,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl90_32 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f1296,plain,
( ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0 )
| ~ spl90_146 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f2830,plain,
( spl90_253
| ~ spl90_123
| ~ spl90_132 ),
inference(avatar_split_clause,[],[f1961,f1197,f1143,f2827]) ).
fof(f1143,plain,
( spl90_123
<=> ! [X2,X0,X1] :
( vabs(sK44(X0,X1,X2),sK46(X0,X1,X2),sK45(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_123])]) ).
fof(f1197,plain,
( spl90_132
<=> sP5(vempty,sK14,vvar(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_132])]) ).
fof(f1961,plain,
( vvar(sK15) = vabs(sK44(vempty,sK14,vvar(sK15)),sK46(vempty,sK14,vvar(sK15)),sK45(vempty,sK14,vvar(sK15)))
| ~ spl90_123
| ~ spl90_132 ),
inference(resolution,[],[f1199,f1144]) ).
fof(f1144,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vabs(sK44(X0,X1,X2),sK46(X0,X1,X2),sK45(X0,X1,X2)) = X2 )
| ~ spl90_123 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f1199,plain,
( sP5(vempty,sK14,vvar(sK15))
| ~ spl90_132 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f2825,plain,
( spl90_252
| ~ spl90_66
| ~ spl90_150 ),
inference(avatar_split_clause,[],[f1349,f1342,f839,f2823]) ).
fof(f2823,plain,
( spl90_252
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_252])]) ).
fof(f1349,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl90_66
| ~ spl90_150 ),
inference(resolution,[],[f1343,f840]) ).
fof(f2821,plain,
( spl90_251
| ~ spl90_67
| ~ spl90_150 ),
inference(avatar_split_clause,[],[f1348,f1342,f843,f2819]) ).
fof(f2819,plain,
( spl90_251
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_251])]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl90_67
| ~ spl90_150 ),
inference(resolution,[],[f1343,f844]) ).
fof(f2812,plain,
( spl90_250
| ~ spl90_33
| ~ spl90_152 ),
inference(avatar_split_clause,[],[f1367,f1359,f687,f2810]) ).
fof(f2810,plain,
( spl90_250
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK81(X0,X1,vvar(X0),X1),sK82(X0,X1,vvar(X0),X1),vapp(sK80(X0,X1,vvar(X0),X1),sK83(X0,X1,vvar(X0),X1))) = X1
| sP11(X1,vvar(X0),X1,X0)
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_250])]) ).
fof(f687,plain,
( spl90_33
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl90_33])]) ).
fof(f1367,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK81(X0,X1,vvar(X0),X1),sK82(X0,X1,vvar(X0),X1),vapp(sK80(X0,X1,vvar(X0),X1),sK83(X0,X1,vvar(X0),X1))) = X1
| sP11(X1,vvar(X0),X1,X0)
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl90_33
| ~ spl90_152 ),
inference(superposition,[],[f1360,f688]) ).
fof(f688,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl90_33 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f2803,plain,
( spl90_249
| ~ spl90_60
| ~ spl90_150 ),
inference(avatar_split_clause,[],[f1351,f1342,f807,f2801]) ).
fof(f2801,plain,
( spl90_249
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vapp(sK80(X0,X1,vvar(X2),vvar(X2)),sK83(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_249])]) ).
fof(f1351,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vapp(sK80(X0,X1,vvar(X2),vvar(X2)),sK83(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl90_60
| ~ spl90_150 ),
inference(superposition,[],[f1343,f808]) ).
fof(f2659,plain,
( spl90_248
| ~ spl90_66
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1337,f1322,f839,f2657]) ).
fof(f2657,plain,
( spl90_248
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_248])]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl90_66
| ~ spl90_149 ),
inference(resolution,[],[f1323,f840]) ).
fof(f2655,plain,
( spl90_247
| ~ spl90_67
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1336,f1322,f843,f2653]) ).
fof(f2653,plain,
( spl90_247
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_247])]) ).
fof(f1336,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK81(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl90_67
| ~ spl90_149 ),
inference(resolution,[],[f1323,f844]) ).
fof(f2651,plain,
( spl90_246
| ~ spl90_66
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1329,f1318,f839,f2649]) ).
fof(f2649,plain,
( spl90_246
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_246])]) ).
fof(f1329,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK63(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl90_66
| ~ spl90_148 ),
inference(resolution,[],[f1319,f840]) ).
fof(f2647,plain,
( spl90_245
| ~ spl90_67
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1328,f1318,f843,f2645]) ).
fof(f2645,plain,
( spl90_245
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_245])]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK82(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK64(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl90_67
| ~ spl90_148 ),
inference(resolution,[],[f1319,f844]) ).
fof(f2643,plain,
( spl90_244
| ~ spl90_82
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1290,f1285,f903,f2641]) ).
fof(f2641,plain,
( spl90_244
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,vabs(X1,X2,X3),vabs(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0))),X5,vsubst(X6,vvar(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0)))),X4))) = vsubst(X0,vabs(X1,X2,X3),vabs(X6,X5,X4))
| X0 = X6
| ~ visFreeVar(X6,X3)
| X1 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_244])]) ).
fof(f903,plain,
( spl90_82
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_82])]) ).
fof(f1290,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,vabs(X1,X2,X3),vabs(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0))),X5,vsubst(X6,vvar(vgensym(vapp(vapp(vabs(X1,X2,X3),X4),vvar(X0)))),X4))) = vsubst(X0,vabs(X1,X2,X3),vabs(X6,X5,X4))
| X0 = X6
| ~ visFreeVar(X6,X3)
| X1 = X6 )
| ~ spl90_82
| ~ spl90_145 ),
inference(resolution,[],[f1286,f904]) ).
fof(f904,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl90_82 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f2639,plain,
( spl90_243
| ~ spl90_134
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1288,f1285,f1206,f2637]) ).
fof(f2637,plain,
( spl90_243
<=> ! [X5,X6,X4,X0,X7,X3,X2,X1] :
( vsubst(X0,X1,vabs(vgensym(vapp(vapp(X1,X2),vvar(X0))),X3,vsubst(X4,vvar(vgensym(vapp(vapp(X1,X2),vvar(X0)))),X2))) = vsubst(X0,X1,vabs(X4,X3,X2))
| X0 = X4
| vabs(X4,X5,vsubst(X6,X1,X7)) = vsubst(X6,X1,vabs(X4,X5,X7))
| X4 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_243])]) ).
fof(f1206,plain,
( spl90_134
<=> ! [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,[spl90_134])]) ).
fof(f1288,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] :
( vsubst(X0,X1,vabs(vgensym(vapp(vapp(X1,X2),vvar(X0))),X3,vsubst(X4,vvar(vgensym(vapp(vapp(X1,X2),vvar(X0)))),X2))) = vsubst(X0,X1,vabs(X4,X3,X2))
| X0 = X4
| vabs(X4,X5,vsubst(X6,X1,X7)) = vsubst(X6,X1,vabs(X4,X5,X7))
| X4 = X6 )
| ~ spl90_134
| ~ spl90_145 ),
inference(resolution,[],[f1286,f1207]) ).
fof(f1207,plain,
( ! [X8,X6,X7,X4,X5] :
( visFreeVar(X4,X7)
| vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X6,X7,vabs(X4,X5,X8))
| X4 = X6 )
| ~ spl90_134 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f2627,plain,
( spl90_242
| ~ spl90_135
| ~ spl90_140 ),
inference(avatar_split_clause,[],[f1257,f1247,f1227,f2625]) ).
fof(f2625,plain,
( spl90_242
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,vbind(sK44(vbind(X0,X1,X2),X3,X4),sK46(vbind(X0,X1,X2),X3,X4),X2)),sK45(vbind(X0,X1,X2),X3,X4),sK47(vbind(X0,X1,X2),X3,X4))
| sK44(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_242])]) ).
fof(f1247,plain,
( spl90_140
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6)
| ~ vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_140])]) ).
fof(f1257,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,vbind(sK44(vbind(X0,X1,X2),X3,X4),sK46(vbind(X0,X1,X2),X3,X4),X2)),sK45(vbind(X0,X1,X2),X3,X4),sK47(vbind(X0,X1,X2),X3,X4))
| sK44(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) )
| ~ spl90_135
| ~ spl90_140 ),
inference(resolution,[],[f1248,f1228]) ).
fof(f1248,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 )
| ~ spl90_140 ),
inference(avatar_component_clause,[],[f1247]) ).
fof(f2623,plain,
( spl90_241
| ~ spl90_101
| ~ spl90_133 ),
inference(avatar_split_clause,[],[f1211,f1202,f1010,f2621]) ).
fof(f2621,plain,
( spl90_241
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| vsomeType(varrow(sK43(X0,X1,X2),X1)) = vlookup(sK48(sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_241])]) ).
fof(f1010,plain,
( spl90_101
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_101])]) ).
fof(f1211,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| vsomeType(varrow(sK43(X0,X1,X2),X1)) = vlookup(sK48(sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl90_101
| ~ spl90_133 ),
inference(resolution,[],[f1203,f1011]) ).
fof(f1011,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) )
| ~ spl90_101 ),
inference(avatar_component_clause,[],[f1010]) ).
fof(f2610,plain,
( spl90_240
| ~ spl90_61
| ~ spl90_146 ),
inference(avatar_split_clause,[],[f1298,f1295,f819,f2608]) ).
fof(f2608,plain,
( spl90_240
<=> ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0
| vapp(sK22(vreduce(X0),X0),sK21(vreduce(X0),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_240])]) ).
fof(f819,plain,
( spl90_61
<=> ! [X0,X1] :
( vapp(sK22(X0,X1),sK21(X0,X1)) = X1
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_61])]) ).
fof(f1298,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0
| vapp(sK22(vreduce(X0),X0),sK21(vreduce(X0),X0)) = X0 )
| ~ spl90_61
| ~ spl90_146 ),
inference(resolution,[],[f1296,f820]) ).
fof(f820,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vapp(sK22(X0,X1),sK21(X0,X1)) = X1 )
| ~ spl90_61 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f2597,plain,
( spl90_239
| ~ spl90_52
| ~ spl90_146 ),
inference(avatar_split_clause,[],[f1299,f1295,f773,f2595]) ).
fof(f2595,plain,
( spl90_239
<=> ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0
| sK23(vreduce(X0),X0) = vreduce(sK22(vreduce(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_239])]) ).
fof(f773,plain,
( spl90_52
<=> ! [X0,X1] :
( sK23(X0,X1) = vreduce(sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_52])]) ).
fof(f1299,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0
| sK23(vreduce(X0),X0) = vreduce(sK22(vreduce(X0),X0)) )
| ~ spl90_52
| ~ spl90_146 ),
inference(resolution,[],[f1296,f774]) ).
fof(f774,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| sK23(X0,X1) = vreduce(sK22(X0,X1)) )
| ~ spl90_52 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f2583,plain,
( spl90_238
| ~ spl90_60
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1339,f1322,f807,f2581]) ).
fof(f2581,plain,
( spl90_238
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK81(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,[spl90_238])]) ).
fof(f1339,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK81(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl90_60
| ~ spl90_149 ),
inference(superposition,[],[f1323,f808]) ).
fof(f2579,plain,
( spl90_237
| ~ spl90_60
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1331,f1318,f807,f2577]) ).
fof(f2577,plain,
( spl90_237
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK82(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,[spl90_237])]) ).
fof(f1331,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK82(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl90_60
| ~ spl90_148 ),
inference(superposition,[],[f1319,f808]) ).
fof(f2575,plain,
( spl90_236
| ~ spl90_46
| ~ spl90_213 ),
inference(avatar_split_clause,[],[f2467,f2217,f745,f2573]) ).
fof(f2573,plain,
( spl90_236
<=> ! [X0,X1] :
( varrow(X0,X1) != sK14
| sK47(vempty,sK14,vvar(sK15)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_236])]) ).
fof(f745,plain,
( spl90_46
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_46])]) ).
fof(f2217,plain,
( spl90_213
<=> sK14 = varrow(sK46(vempty,sK14,vvar(sK15)),sK47(vempty,sK14,vvar(sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_213])]) ).
fof(f2467,plain,
( ! [X0,X1] :
( varrow(X0,X1) != sK14
| sK47(vempty,sK14,vvar(sK15)) = X1 )
| ~ spl90_46
| ~ spl90_213 ),
inference(superposition,[],[f746,f2219]) ).
fof(f2219,plain,
( sK14 = varrow(sK46(vempty,sK14,vvar(sK15)),sK47(vempty,sK14,vvar(sK15)))
| ~ spl90_213 ),
inference(avatar_component_clause,[],[f2217]) ).
fof(f746,plain,
( ! [X2,X3,X0,X1] :
( varrow(X0,X1) != varrow(X2,X3)
| X1 = X3 )
| ~ spl90_46 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f2565,plain,
( spl90_235
| ~ spl90_33
| ~ spl90_150 ),
inference(avatar_split_clause,[],[f1350,f1342,f687,f2563]) ).
fof(f2563,plain,
( spl90_235
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK80(X0,X1,vvar(X0),X1),sK83(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_235])]) ).
fof(f1350,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK80(X0,X1,vvar(X0),X1),sK83(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl90_33
| ~ spl90_150 ),
inference(superposition,[],[f1343,f688]) ).
fof(f2561,plain,
( spl90_234
| ~ spl90_101
| ~ spl90_124 ),
inference(avatar_split_clause,[],[f1161,f1147,f1010,f2559]) ).
fof(f2559,plain,
( spl90_234
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| sK41(X0,X1,X2) = vvar(sK48(sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_234])]) ).
fof(f1161,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| sK41(X0,X1,X2) = vvar(sK48(sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK43(X0,X1,X2),X1),sK41(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl90_101
| ~ spl90_124 ),
inference(resolution,[],[f1148,f1011]) ).
fof(f2535,plain,
( spl90_233
| ~ spl90_38
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1292,f1285,f708,f2533]) ).
fof(f2533,plain,
( spl90_233
<=> ! [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,[spl90_233])]) ).
fof(f708,plain,
( spl90_38
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_38])]) ).
fof(f1292,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) )
| ~ spl90_38
| ~ spl90_145 ),
inference(resolution,[],[f1286,f709]) ).
fof(f709,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl90_38 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f2531,plain,
( spl90_232
| ~ spl90_39
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1291,f1285,f712,f2529]) ).
fof(f2529,plain,
( spl90_232
<=> ! [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,[spl90_232])]) ).
fof(f712,plain,
( spl90_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_39])]) ).
fof(f1291,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) )
| ~ spl90_39
| ~ spl90_145 ),
inference(resolution,[],[f1286,f713]) ).
fof(f713,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl90_39 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f2524,plain,
( spl90_231
| ~ spl90_15
| ~ spl90_146 ),
inference(avatar_split_clause,[],[f1301,f1295,f615,f2522]) ).
fof(f2522,plain,
( spl90_231
<=> ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK37(vvar(X0),vnoExp),sK38(vvar(X0),vnoExp),sK39(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK40(vvar(X0),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_231])]) ).
fof(f615,plain,
( spl90_15
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_15])]) ).
fof(f1301,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(sK37(vvar(X0),vnoExp),sK38(vvar(X0),vnoExp),sK39(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK40(vvar(X0),vnoExp)) )
| ~ spl90_15
| ~ spl90_146 ),
inference(superposition,[],[f1296,f616]) ).
fof(f616,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl90_15 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f2520,plain,
( spl90_230
| ~ spl90_45
| ~ spl90_213 ),
inference(avatar_split_clause,[],[f2465,f2217,f741,f2518]) ).
fof(f2518,plain,
( spl90_230
<=> ! [X0,X1] :
( varrow(X0,X1) != sK14
| sK46(vempty,sK14,vvar(sK15)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_230])]) ).
fof(f741,plain,
( spl90_45
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_45])]) ).
fof(f2465,plain,
( ! [X0,X1] :
( varrow(X0,X1) != sK14
| sK46(vempty,sK14,vvar(sK15)) = X0 )
| ~ spl90_45
| ~ spl90_213 ),
inference(superposition,[],[f742,f2219]) ).
fof(f742,plain,
( ! [X2,X3,X0,X1] :
( varrow(X0,X1) != varrow(X2,X3)
| X0 = X2 )
| ~ spl90_45 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f2507,plain,
( spl90_229
| ~ spl90_101
| ~ spl90_140 ),
inference(avatar_split_clause,[],[f1259,f1247,f1010,f2505]) ).
fof(f2505,plain,
( spl90_229
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK41(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK43(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,[spl90_229])]) ).
fof(f1259,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK41(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK43(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl90_101
| ~ spl90_140 ),
inference(resolution,[],[f1248,f1011]) ).
fof(f2503,plain,
( spl90_228
| ~ spl90_103
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1225,f1206,f1021,f2501]) ).
fof(f2501,plain,
( spl90_228
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( vabs(sK58(X0,X1,X2,X3),X4,vsubst(X5,sK61(X0,X1,X2,X3),X6)) = vsubst(X5,sK61(X0,X1,X2,X3),vabs(sK58(X0,X1,X2,X3),X4,X6))
| sK58(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_228])]) ).
fof(f1021,plain,
( spl90_103
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK58(X0,X1,X2,X3),sK61(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_103])]) ).
fof(f1225,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vabs(sK58(X0,X1,X2,X3),X4,vsubst(X5,sK61(X0,X1,X2,X3),X6)) = vsubst(X5,sK61(X0,X1,X2,X3),vabs(sK58(X0,X1,X2,X3),X4,X6))
| sK58(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) )
| ~ spl90_103
| ~ spl90_134 ),
inference(resolution,[],[f1207,f1022]) ).
fof(f1022,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK58(X0,X1,X2,X3),sK61(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) )
| ~ spl90_103 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f2498,plain,
( spl90_227
| ~ spl90_93
| ~ spl90_133 ),
inference(avatar_split_clause,[],[f1210,f1202,f967,f2496]) ).
fof(f2496,plain,
( spl90_227
<=> ! [X2,X0,X1] :
( sP5(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| vsomeType(sK43(X0,X1,X2)) = vlookup(sK48(sK42(X0,X1,X2),sK43(X0,X1,X2),X0),X0)
| sP6(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_227])]) ).
fof(f967,plain,
( spl90_93
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK42(X0,X1,X2),sK43(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_93])]) ).
fof(f1210,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| vsomeType(sK43(X0,X1,X2)) = vlookup(sK48(sK42(X0,X1,X2),sK43(X0,X1,X2),X0),X0)
| sP6(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl90_93
| ~ spl90_133 ),
inference(resolution,[],[f1203,f968]) ).
fof(f968,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK42(X0,X1,X2),sK43(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl90_93 ),
inference(avatar_component_clause,[],[f967]) ).
fof(f2480,plain,
( spl90_226
| ~ spl90_93
| ~ spl90_140 ),
inference(avatar_split_clause,[],[f1258,f1247,f967,f2478]) ).
fof(f2478,plain,
( spl90_226
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK42(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK43(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,[spl90_226])]) ).
fof(f1258,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK42(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK43(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl90_93
| ~ spl90_140 ),
inference(resolution,[],[f1248,f968]) ).
fof(f2476,plain,
( spl90_225
| ~ spl90_109
| ~ spl90_133 ),
inference(avatar_split_clause,[],[f1212,f1202,f1045,f2474]) ).
fof(f2474,plain,
( spl90_225
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK48(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,[spl90_225])]) ).
fof(f1045,plain,
( spl90_109
<=> ! [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,[spl90_109])]) ).
fof(f1212,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK48(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) )
| ~ spl90_109
| ~ spl90_133 ),
inference(resolution,[],[f1203,f1046]) ).
fof(f1046,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) )
| ~ spl90_109 ),
inference(avatar_component_clause,[],[f1045]) ).
fof(f2458,plain,
( spl90_224
| ~ spl90_109
| ~ spl90_124 ),
inference(avatar_split_clause,[],[f1162,f1147,f1045,f2456]) ).
fof(f2456,plain,
( spl90_224
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK48(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,[spl90_224])]) ).
fof(f1162,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK48(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl90_109
| ~ spl90_124 ),
inference(resolution,[],[f1148,f1046]) ).
fof(f2454,plain,
( spl90_223
| ~ spl90_93
| ~ spl90_124 ),
inference(avatar_split_clause,[],[f1160,f1147,f967,f2452]) ).
fof(f2452,plain,
( spl90_223
<=> ! [X2,X0,X1] :
( sP5(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| sK42(X0,X1,X2) = vvar(sK48(sK42(X0,X1,X2),sK43(X0,X1,X2),X0))
| sP6(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_223])]) ).
fof(f1160,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| sK42(X0,X1,X2) = vvar(sK48(sK42(X0,X1,X2),sK43(X0,X1,X2),X0))
| sP6(X0,sK43(X0,X1,X2),sK42(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl90_93
| ~ spl90_124 ),
inference(resolution,[],[f1148,f968]) ).
fof(f2419,plain,
( spl90_222
| ~ spl90_33
| ~ spl90_149 ),
inference(avatar_split_clause,[],[f1338,f1322,f687,f2417]) ).
fof(f2417,plain,
( spl90_222
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK81(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_222])]) ).
fof(f1338,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK81(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl90_33
| ~ spl90_149 ),
inference(superposition,[],[f1323,f688]) ).
fof(f2415,plain,
( spl90_221
| ~ spl90_33
| ~ spl90_148 ),
inference(avatar_split_clause,[],[f1330,f1318,f687,f2413]) ).
fof(f2413,plain,
( spl90_221
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK82(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_221])]) ).
fof(f1330,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK82(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl90_33
| ~ spl90_148 ),
inference(superposition,[],[f1319,f688]) ).
fof(f2411,plain,
( spl90_220
| ~ spl90_12
| ~ spl90_145 ),
inference(avatar_split_clause,[],[f1289,f1285,f603,f2409]) ).
fof(f2409,plain,
( spl90_220
<=> ! [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,[spl90_220])]) ).
fof(f603,plain,
( spl90_12
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_12])]) ).
fof(f1289,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 )
| ~ spl90_12
| ~ spl90_145 ),
inference(resolution,[],[f1286,f604]) ).
fof(f604,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl90_12 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f2398,plain,
( spl90_219
| ~ spl90_101
| ~ spl90_116 ),
inference(avatar_split_clause,[],[f1112,f1103,f1010,f2396]) ).
fof(f2396,plain,
( spl90_219
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK41(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK43(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,[spl90_219])]) ).
fof(f1103,plain,
( spl90_116
<=> ! [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,[spl90_116])]) ).
fof(f1112,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK41(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK43(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl90_101
| ~ spl90_116 ),
inference(resolution,[],[f1104,f1011]) ).
fof(f1104,plain,
( ! [X2,X3,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6)
| vtcheck(vbind(X2,X3,X4),X5,X6) )
| ~ spl90_116 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f2321,plain,
( spl90_218
| ~ spl90_117
| ~ spl90_141 ),
inference(avatar_split_clause,[],[f1262,f1251,f1115,f2319]) ).
fof(f2319,plain,
( spl90_218
<=> ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK84(X0),sK85(X0),sK86(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_218])]) ).
fof(f1115,plain,
( spl90_117
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_117])]) ).
fof(f1251,plain,
( spl90_141
<=> ! [X4,X0] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_141])]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK84(X0),sK85(X0),sK86(X0)) = X0 )
| ~ spl90_117
| ~ spl90_141 ),
inference(resolution,[],[f1252,f1116]) ).
fof(f1116,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1 )
| ~ spl90_117 ),
inference(avatar_component_clause,[],[f1115]) ).
fof(f1252,plain,
( ! [X0,X4] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 )
| ~ spl90_141 ),
inference(avatar_component_clause,[],[f1251]) ).
fof(f2317,plain,
( spl90_217
| ~ spl90_118
| ~ spl90_141 ),
inference(avatar_split_clause,[],[f1261,f1251,f1119,f2315]) ).
fof(f2315,plain,
( spl90_217
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_217])]) ).
fof(f1119,plain,
( spl90_118
<=> ! [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,[spl90_118])]) ).
fof(f1261,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) )
| ~ spl90_118
| ~ spl90_141 ),
inference(resolution,[],[f1252,f1120]) ).
fof(f1120,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl90_118 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f2311,plain,
~ spl90_192,
inference(avatar_contradiction_clause,[],[f2310]) ).
fof(f2310,plain,
( $false
| ~ spl90_192 ),
inference(equality_resolution,[],[f1939]) ).
fof(f1939,plain,
( ! [X0] : vvar(X0) != vvar(sK15)
| ~ spl90_192 ),
inference(avatar_component_clause,[],[f1938]) ).
fof(f1938,plain,
( spl90_192
<=> ! [X0] : vvar(X0) != vvar(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_192])]) ).
fof(f2309,plain,
( spl90_216
| ~ spl90_125
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1173,f1166,f1151,f2307]) ).
fof(f2307,plain,
( spl90_216
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_216])]) ).
fof(f1151,plain,
( spl90_125
<=> ! [X2,X0,X1] :
( vbind(sK50(X0,X1,X2),sK49(X0,X1,X2),sK52(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_125])]) ).
fof(f1166,plain,
( spl90_127
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_127])]) ).
fof(f1173,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1 )
| ~ spl90_125
| ~ spl90_127 ),
inference(resolution,[],[f1167,f1152]) ).
fof(f1152,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vbind(sK50(X0,X1,X2),sK49(X0,X1,X2),sK52(X0,X1,X2)) = X1 )
| ~ spl90_125 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f1167,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0 )
| ~ spl90_127 ),
inference(avatar_component_clause,[],[f1166]) ).
fof(f2305,plain,
( spl90_215
| ~ spl90_93
| ~ spl90_116 ),
inference(avatar_split_clause,[],[f1111,f1103,f967,f2303]) ).
fof(f2303,plain,
( spl90_215
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK42(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK43(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,[spl90_215])]) ).
fof(f1111,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK42(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK43(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl90_93
| ~ spl90_116 ),
inference(resolution,[],[f1104,f968]) ).
fof(f2293,plain,
( spl90_214
| ~ spl90_94
| ~ spl90_101 ),
inference(avatar_split_clause,[],[f1064,f1010,f971,f2291]) ).
fof(f2291,plain,
( spl90_214
<=> ! [X4,X0,X3,X2,X1] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK41(vbind(X0,X1,X2),X3,X4),varrow(sK43(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK41(vbind(X0,X1,X2),X3,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_214])]) ).
fof(f971,plain,
( spl90_94
<=> ! [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,[spl90_94])]) ).
fof(f1064,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ sP6(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,sK41(vbind(X0,X1,X2),X3,X4),varrow(sK43(vbind(X0,X1,X2),X3,X4),X3))
| visFreeVar(X0,sK41(vbind(X0,X1,X2),X3,X4)) )
| ~ spl90_94
| ~ spl90_101 ),
inference(resolution,[],[f1011,f972]) ).
fof(f972,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| vtcheck(X2,X3,X4)
| visFreeVar(X0,X3) )
| ~ spl90_94 ),
inference(avatar_component_clause,[],[f971]) ).
fof(f2220,plain,
( spl90_213
| ~ spl90_97
| ~ spl90_132 ),
inference(avatar_split_clause,[],[f1962,f1197,f989,f2217]) ).
fof(f989,plain,
( spl90_97
<=> ! [X2,X0,X1] :
( varrow(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_97])]) ).
fof(f1962,plain,
( sK14 = varrow(sK46(vempty,sK14,vvar(sK15)),sK47(vempty,sK14,vvar(sK15)))
| ~ spl90_97
| ~ spl90_132 ),
inference(resolution,[],[f1199,f990]) ).
fof(f990,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| varrow(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X1 )
| ~ spl90_97 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f2208,plain,
( spl90_212
| ~ spl90_117
| ~ spl90_128 ),
inference(avatar_split_clause,[],[f1180,f1170,f1115,f2206]) ).
fof(f2206,plain,
( spl90_212
<=> ! [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(sK84(X3),sK85(X3),sK86(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_212])]) ).
fof(f1170,plain,
( spl90_128
<=> ! [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,[spl90_128])]) ).
fof(f1180,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(sK84(X3),sK85(X3),sK86(X3)) = X3 )
| ~ spl90_117
| ~ spl90_128 ),
inference(resolution,[],[f1171,f1116]) ).
fof(f1171,plain,
( ! [X3,X0,X4,X5] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0)) )
| ~ spl90_128 ),
inference(avatar_component_clause,[],[f1170]) ).
fof(f2204,plain,
( spl90_211
| ~ spl90_118
| ~ spl90_128 ),
inference(avatar_split_clause,[],[f1179,f1170,f1119,f2202]) ).
fof(f2202,plain,
( spl90_211
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( vreduce(vapp(vabs(X0,X1,X2),X3)) = vsomeExp(vapp(vabs(X0,X1,X2),vgetSomeExp(vreduce(X3))))
| ~ visValue(X3)
| vsomeExp(vsubst(X4,X3,X5)) = vreduce(vapp(vabs(X4,X6,X5),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_211])]) ).
fof(f1179,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)) )
| ~ spl90_118
| ~ spl90_128 ),
inference(resolution,[],[f1171,f1120]) ).
fof(f2200,plain,
( spl90_210
| ~ spl90_91
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1178,f1166,f953,f2198]) ).
fof(f2198,plain,
( spl90_210
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK57(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_210])]) ).
fof(f953,plain,
( spl90_91
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_91])]) ).
fof(f1178,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK57(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 )
| ~ spl90_91
| ~ spl90_127 ),
inference(superposition,[],[f1167,f954]) ).
fof(f954,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl90_91 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f2196,plain,
( spl90_209
| ~ spl90_115
| ~ spl90_125 ),
inference(avatar_split_clause,[],[f1163,f1151,f1099,f2194]) ).
fof(f2194,plain,
( spl90_209
<=> ! [X0,X1] :
( vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_209])]) ).
fof(f1099,plain,
( spl90_115
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_115])]) ).
fof(f1163,plain,
( ! [X0,X1] :
( vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl90_115
| ~ spl90_125 ),
inference(resolution,[],[f1152,f1100]) ).
fof(f1100,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl90_115 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f2154,plain,
( spl90_208
| spl90_4
| ~ spl90_32
| ~ spl90_117 ),
inference(avatar_split_clause,[],[f1123,f1115,f683,f570,f2152]) ).
fof(f2152,plain,
( spl90_208
<=> ! [X0,X3,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK84(vabs(X0,X1,X2)),sK85(vabs(X0,X1,X2)),sK86(vabs(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_208])]) ).
fof(f570,plain,
( spl90_4
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_4])]) ).
fof(f1123,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK84(vabs(X0,X1,X2)),sK85(vabs(X0,X1,X2)),sK86(vabs(X0,X1,X2))) )
| ~ spl90_32
| ~ spl90_117 ),
inference(superposition,[],[f1116,f684]) ).
fof(f2150,plain,
( spl90_207
| ~ spl90_93
| ~ spl90_94 ),
inference(avatar_split_clause,[],[f978,f971,f967,f2148]) ).
fof(f2148,plain,
( spl90_207
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(X0,sK42(vbind(X1,X2,X0),X3,X4),sK43(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK42(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_207])]) ).
fof(f978,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,sK42(vbind(X1,X2,X0),X3,X4),sK43(vbind(X1,X2,X0),X3,X4))
| visFreeVar(X1,sK42(vbind(X1,X2,X0),X3,X4))
| ~ sP6(vbind(X1,X2,X0),X3,X4) )
| ~ spl90_93
| ~ spl90_94 ),
inference(resolution,[],[f972,f968]) ).
fof(f2124,plain,
( spl90_206
| ~ spl90_95
| ~ spl90_141 ),
inference(avatar_split_clause,[],[f1263,f1251,f975,f2122]) ).
fof(f2122,plain,
( spl90_206
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_206])]) ).
fof(f975,plain,
( spl90_95
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_95])]) ).
fof(f1263,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) )
| ~ spl90_95
| ~ spl90_141 ),
inference(resolution,[],[f1252,f976]) ).
fof(f976,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl90_95 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f2120,plain,
( spl90_205
| ~ spl90_109
| ~ spl90_140 ),
inference(avatar_split_clause,[],[f1260,f1247,f1045,f2118]) ).
fof(f2118,plain,
( spl90_205
<=> ! [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,[spl90_205])]) ).
fof(f1260,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) )
| ~ spl90_109
| ~ spl90_140 ),
inference(resolution,[],[f1248,f1046]) ).
fof(f2116,plain,
( spl90_204
| ~ spl90_98
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1174,f1166,f993,f2114]) ).
fof(f2114,plain,
( spl90_204
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_204])]) ).
fof(f993,plain,
( spl90_98
<=> ! [X2,X0,X1] :
( vlookup(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_98])]) ).
fof(f1174,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) )
| ~ spl90_98
| ~ spl90_127 ),
inference(resolution,[],[f1167,f994]) ).
fof(f994,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X0 )
| ~ spl90_98 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f2105,plain,
( spl90_203
| ~ spl90_99
| ~ spl90_125 ),
inference(avatar_split_clause,[],[f1164,f1151,f997,f2103]) ).
fof(f2103,plain,
( spl90_203
<=> ! [X0,X1] :
( vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_203])]) ).
fof(f997,plain,
( spl90_99
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_99])]) ).
fof(f1164,plain,
( ! [X0,X1] :
( vbind(sK50(vlookup(X0,X1),X1,X0),sK49(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl90_99
| ~ spl90_125 ),
inference(resolution,[],[f1152,f998]) ).
fof(f998,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl90_99 ),
inference(avatar_component_clause,[],[f997]) ).
fof(f2059,plain,
( spl90_202
| ~ spl90_59
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1224,f1206,f803,f2057]) ).
fof(f2057,plain,
( spl90_202
<=> ! [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,[spl90_202])]) ).
fof(f803,plain,
( spl90_59
<=> ! [X4,X2,X3] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_59])]) ).
fof(f1224,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) )
| ~ spl90_59
| ~ spl90_134 ),
inference(resolution,[],[f1207,f804]) ).
fof(f804,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl90_59 ),
inference(avatar_component_clause,[],[f803]) ).
fof(f2055,plain,
( spl90_201
| ~ spl90_36
| ~ spl90_131 ),
inference(avatar_split_clause,[],[f1314,f1193,f700,f2053]) ).
fof(f2053,plain,
( spl90_201
<=> ! [X0] :
( vvar(X0) != vvar(sK15)
| sK48(vvar(sK15),sK14,vempty) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_201])]) ).
fof(f700,plain,
( spl90_36
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_36])]) ).
fof(f1193,plain,
( spl90_131
<=> vvar(sK15) = vvar(sK48(vvar(sK15),sK14,vempty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_131])]) ).
fof(f1314,plain,
( ! [X0] :
( vvar(X0) != vvar(sK15)
| sK48(vvar(sK15),sK14,vempty) = X0 )
| ~ spl90_36
| ~ spl90_131 ),
inference(superposition,[],[f701,f1195]) ).
fof(f1195,plain,
( vvar(sK15) = vvar(sK48(vvar(sK15),sK14,vempty))
| ~ spl90_131 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f701,plain,
( ! [X0,X1] :
( vvar(X0) != vvar(X1)
| X0 = X1 )
| ~ spl90_36 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f2051,plain,
( spl90_200
| ~ spl90_95
| ~ spl90_128 ),
inference(avatar_split_clause,[],[f1181,f1170,f975,f2049]) ).
fof(f2049,plain,
( spl90_200
<=> ! [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,[spl90_200])]) ).
fof(f1181,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)) )
| ~ spl90_95
| ~ spl90_128 ),
inference(resolution,[],[f1171,f976]) ).
fof(f2047,plain,
( spl90_199
| ~ spl90_98
| ~ spl90_115 ),
inference(avatar_split_clause,[],[f1106,f1099,f993,f2045]) ).
fof(f2045,plain,
( spl90_199
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_199])]) ).
fof(f1106,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) )
| ~ spl90_98
| ~ spl90_115 ),
inference(resolution,[],[f1100,f994]) ).
fof(f2022,plain,
( spl90_198
| ~ spl90_40
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1222,f1206,f721,f2020]) ).
fof(f2020,plain,
( spl90_198
<=> ! [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,[spl90_198])]) ).
fof(f721,plain,
( spl90_40
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_40])]) ).
fof(f1222,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) )
| ~ spl90_40
| ~ spl90_134 ),
inference(resolution,[],[f1207,f722]) ).
fof(f722,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl90_40 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f2018,plain,
( spl90_197
| ~ spl90_91
| ~ spl90_99 ),
inference(avatar_split_clause,[],[f1004,f997,f953,f2016]) ).
fof(f2016,plain,
( spl90_197
<=> ! [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,[spl90_197])]) ).
fof(f1004,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 )
| ~ spl90_91
| ~ spl90_99 ),
inference(superposition,[],[f998,f954]) ).
fof(f1998,plain,
( spl90_196
| ~ spl90_42
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1177,f1166,f729,f1996]) ).
fof(f1996,plain,
( spl90_196
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK57(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_196])]) ).
fof(f729,plain,
( spl90_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_42])]) ).
fof(f1177,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK57(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 )
| ~ spl90_42
| ~ spl90_127 ),
inference(superposition,[],[f1167,f730]) ).
fof(f730,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl90_42 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f1992,plain,
( spl90_195
| spl90_4
| ~ spl90_32
| ~ spl90_118 ),
inference(avatar_split_clause,[],[f1129,f1119,f683,f570,f1990]) ).
fof(f1990,plain,
( spl90_195
<=> ! [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,[spl90_195])]) ).
fof(f1129,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))) )
| ~ spl90_32
| ~ spl90_118 ),
inference(superposition,[],[f1120,f684]) ).
fof(f1988,plain,
( spl90_194
| ~ spl90_91
| ~ spl90_115 ),
inference(avatar_split_clause,[],[f1110,f1099,f953,f1986]) ).
fof(f1986,plain,
( spl90_194
<=> ! [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,[spl90_194])]) ).
fof(f1110,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 )
| ~ spl90_91
| ~ spl90_115 ),
inference(superposition,[],[f1100,f954]) ).
fof(f1984,plain,
( spl90_193
| ~ spl90_98
| ~ spl90_99 ),
inference(avatar_split_clause,[],[f1000,f997,f993,f1982]) ).
fof(f1982,plain,
( spl90_193
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_193])]) ).
fof(f1000,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK51(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0)) )
| ~ spl90_98
| ~ spl90_99 ),
inference(resolution,[],[f998,f994]) ).
fof(f1960,plain,
( ~ spl90_8
| ~ spl90_154 ),
inference(avatar_contradiction_clause,[],[f1959]) ).
fof(f1959,plain,
( $false
| ~ spl90_8
| ~ spl90_154 ),
inference(trivial_inequality_removal,[],[f1951]) ).
fof(f1951,plain,
( vnoType != vnoType
| ~ spl90_8
| ~ spl90_154 ),
inference(superposition,[],[f588,f1378]) ).
fof(f1378,plain,
( vnoType = vsomeType(sK14)
| ~ spl90_154 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f1376,plain,
( spl90_154
<=> vnoType = vsomeType(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_154])]) ).
fof(f588,plain,
( ! [X0] : vnoType != vsomeType(X0)
| ~ spl90_8 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f587,plain,
( spl90_8
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_8])]) ).
fof(f1940,plain,
( spl90_192
| ~ spl90_21
| ~ spl90_181 ),
inference(avatar_split_clause,[],[f1853,f1764,f639,f1938]) ).
fof(f639,plain,
( spl90_21
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_21])]) ).
fof(f1764,plain,
( spl90_181
<=> vvar(sK15) = vapp(sK41(vempty,sK14,vvar(sK15)),sK42(vempty,sK14,vvar(sK15))) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_181])]) ).
fof(f1853,plain,
( ! [X0] : vvar(X0) != vvar(sK15)
| ~ spl90_21
| ~ spl90_181 ),
inference(superposition,[],[f640,f1766]) ).
fof(f1766,plain,
( vvar(sK15) = vapp(sK41(vempty,sK14,vvar(sK15)),sK42(vempty,sK14,vvar(sK15)))
| ~ spl90_181 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f640,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl90_21 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f1936,plain,
( spl90_191
| ~ spl90_109
| ~ spl90_116 ),
inference(avatar_split_clause,[],[f1113,f1103,f1045,f1934]) ).
fof(f1934,plain,
( spl90_191
<=> ! [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,[spl90_191])]) ).
fof(f1113,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) )
| ~ spl90_109
| ~ spl90_116 ),
inference(resolution,[],[f1104,f1046]) ).
fof(f1932,plain,
( spl90_190
| ~ spl90_91
| ~ spl90_110 ),
inference(avatar_split_clause,[],[f1072,f1049,f953,f1930]) ).
fof(f1930,plain,
( spl90_190
<=> ! [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,[spl90_190])]) ).
fof(f1049,plain,
( spl90_110
<=> ! [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,[spl90_110])]) ).
fof(f1072,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 )
| ~ spl90_91
| ~ spl90_110 ),
inference(superposition,[],[f1050,f954]) ).
fof(f1050,plain,
( ! [X2,X3,X0,X1,X4] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,X3,X4)
| vtcheck(vbind(X0,X1,X2),X3,X4) )
| ~ spl90_110 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1928,plain,
( spl90_189
| ~ spl90_94
| ~ spl90_109 ),
inference(avatar_split_clause,[],[f1065,f1045,f971,f1926]) ).
fof(f1926,plain,
( spl90_189
<=> ! [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,[spl90_189])]) ).
fof(f1065,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)) )
| ~ spl90_94
| ~ spl90_109 ),
inference(resolution,[],[f1046,f972]) ).
fof(f1912,plain,
( spl90_188
| ~ spl90_22
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1221,f1206,f643,f1910]) ).
fof(f1910,plain,
( spl90_188
<=> ! [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,[spl90_188])]) ).
fof(f643,plain,
( spl90_22
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_22])]) ).
fof(f1221,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 )
| ~ spl90_22
| ~ spl90_134 ),
inference(resolution,[],[f1207,f644]) ).
fof(f644,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl90_22 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f1892,plain,
( spl90_187
| ~ spl90_94
| ~ spl90_135 ),
inference(avatar_split_clause,[],[f1254,f1227,f971,f1890]) ).
fof(f1890,plain,
( spl90_187
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK45(X0,X1,X2),sK47(X0,X1,X2))
| visFreeVar(sK44(X0,X1,X2),sK45(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_187])]) ).
fof(f1254,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vtcheck(X0,sK45(X0,X1,X2),sK47(X0,X1,X2))
| visFreeVar(sK44(X0,X1,X2),sK45(X0,X1,X2)) )
| ~ spl90_94
| ~ spl90_135 ),
inference(resolution,[],[f1228,f972]) ).
fof(f1888,plain,
( spl90_186
| ~ spl90_31
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1223,f1206,f679,f1886]) ).
fof(f1886,plain,
( spl90_186
<=> ! [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,[spl90_186])]) ).
fof(f679,plain,
( spl90_31
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_31])]) ).
fof(f1223,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 )
| ~ spl90_31
| ~ spl90_134 ),
inference(resolution,[],[f1207,f680]) ).
fof(f680,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl90_31 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f1847,plain,
( spl90_185
| ~ spl90_43
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1175,f1166,f733,f1845]) ).
fof(f1845,plain,
( spl90_185
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| sK51(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_185])]) ).
fof(f733,plain,
( spl90_43
<=> ! [X2,X0,X1] :
( sK51(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_43])]) ).
fof(f1175,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0
| sK51(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl90_43
| ~ spl90_127 ),
inference(resolution,[],[f1167,f734]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK51(X0,X1,X2) = X2 )
| ~ spl90_43 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f1813,plain,
( spl90_184
| spl90_4
| ~ spl90_15
| ~ spl90_117 ),
inference(avatar_split_clause,[],[f1122,f1115,f615,f570,f1811]) ).
fof(f1811,plain,
( spl90_184
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK84(vvar(X0)),sK85(vvar(X0)),sK86(vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_184])]) ).
fof(f1122,plain,
( ! [X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK84(vvar(X0)),sK85(vvar(X0)),sK86(vvar(X0))) )
| ~ spl90_15
| ~ spl90_117 ),
inference(superposition,[],[f1116,f616]) ).
fof(f1809,plain,
( spl90_183
| ~ spl90_42
| ~ spl90_99 ),
inference(avatar_split_clause,[],[f1003,f997,f729,f1807]) ).
fof(f1807,plain,
( spl90_183
<=> ! [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,[spl90_183])]) ).
fof(f1003,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) )
| ~ spl90_42
| ~ spl90_99 ),
inference(superposition,[],[f998,f730]) ).
fof(f1795,plain,
( spl90_182
| ~ spl90_10
| ~ spl90_134 ),
inference(avatar_split_clause,[],[f1214,f1206,f595,f1793]) ).
fof(f1793,plain,
( spl90_182
<=> ! [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,[spl90_182])]) ).
fof(f595,plain,
( spl90_10
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_10])]) ).
fof(f1214,plain,
( ! [X2,X3,X0,X1] :
( vabs(vgensym(X0),X1,vsubst(X2,X0,X3)) = vsubst(X2,X0,vabs(vgensym(X0),X1,X3))
| vgensym(X0) = X2 )
| ~ spl90_10
| ~ spl90_134 ),
inference(resolution,[],[f1207,f596]) ).
fof(f596,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl90_10 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f1767,plain,
( spl90_181
| ~ spl90_96
| ~ spl90_130 ),
inference(avatar_split_clause,[],[f1380,f1189,f982,f1764]) ).
fof(f982,plain,
( spl90_96
<=> ! [X2,X0,X1] :
( vapp(sK41(X0,X1,X2),sK42(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_96])]) ).
fof(f1189,plain,
( spl90_130
<=> sP6(vempty,sK14,vvar(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_130])]) ).
fof(f1380,plain,
( vvar(sK15) = vapp(sK41(vempty,sK14,vvar(sK15)),sK42(vempty,sK14,vvar(sK15)))
| ~ spl90_96
| ~ spl90_130 ),
inference(resolution,[],[f1191,f983]) ).
fof(f983,plain,
( ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| vapp(sK41(X0,X1,X2),sK42(X0,X1,X2)) = X2 )
| ~ spl90_96 ),
inference(avatar_component_clause,[],[f982]) ).
fof(f1191,plain,
( sP6(vempty,sK14,vvar(sK15))
| ~ spl90_130 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f1748,plain,
( spl90_180
| ~ spl90_18
| ~ spl90_142 ),
inference(avatar_split_clause,[],[f1275,f1267,f627,f1746]) ).
fof(f1746,plain,
( spl90_180
<=> ! [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,[spl90_180])]) ).
fof(f627,plain,
( spl90_18
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_18])]) ).
fof(f1267,plain,
( spl90_142
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_142])]) ).
fof(f1275,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl90_18
| ~ spl90_142 ),
inference(duplicate_literal_removal,[],[f1272]) ).
fof(f1272,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0)
| vnoExp = vreduce(X0) )
| ~ spl90_18
| ~ spl90_142 ),
inference(resolution,[],[f1268,f628]) ).
fof(f628,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl90_18 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f1268,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) )
| ~ spl90_142 ),
inference(avatar_component_clause,[],[f1267]) ).
fof(f1744,plain,
( spl90_179
| ~ spl90_42
| ~ spl90_115 ),
inference(avatar_split_clause,[],[f1109,f1099,f729,f1742]) ).
fof(f1742,plain,
( spl90_179
<=> ! [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,[spl90_179])]) ).
fof(f1109,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1) )
| ~ spl90_42
| ~ spl90_115 ),
inference(superposition,[],[f1100,f730]) ).
fof(f1740,plain,
( spl90_178
| ~ spl90_59
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1093,f1057,f803,f1738]) ).
fof(f1738,plain,
( spl90_178
<=> ! [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,[spl90_178])]) ).
fof(f1057,plain,
( spl90_112
<=> ! [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,[spl90_112])]) ).
fof(f1093,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)) )
| ~ spl90_59
| ~ spl90_112 ),
inference(superposition,[],[f804,f1058]) ).
fof(f1058,plain,
( ! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7))
| ~ spl90_112 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f1736,plain,
( spl90_177
| ~ spl90_109
| ~ spl90_111 ),
inference(avatar_split_clause,[],[f1075,f1053,f1045,f1734]) ).
fof(f1734,plain,
( spl90_177
<=> ! [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,[spl90_177])]) ).
fof(f1053,plain,
( spl90_111
<=> ! [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,[spl90_111])]) ).
fof(f1075,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) )
| ~ spl90_109
| ~ spl90_111 ),
inference(resolution,[],[f1054,f1046]) ).
fof(f1054,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vapp(X2,X3),X4) )
| ~ spl90_111 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f1732,plain,
( spl90_176
| ~ spl90_101
| ~ spl90_111 ),
inference(avatar_split_clause,[],[f1074,f1053,f1010,f1730]) ).
fof(f1730,plain,
( spl90_176
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(X0,X1,sK43(X0,X2,X3))
| vtcheck(X0,vapp(sK41(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_176])]) ).
fof(f1074,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(X0,X1,sK43(X0,X2,X3))
| vtcheck(X0,vapp(sK41(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) )
| ~ spl90_101
| ~ spl90_111 ),
inference(resolution,[],[f1054,f1011]) ).
fof(f1664,plain,
( spl90_175
| ~ spl90_43
| ~ spl90_115 ),
inference(avatar_split_clause,[],[f1107,f1099,f733,f1662]) ).
fof(f1662,plain,
( spl90_175
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK51(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_175])]) ).
fof(f1107,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK51(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl90_43
| ~ spl90_115 ),
inference(resolution,[],[f1100,f734]) ).
fof(f1660,plain,
( spl90_174
| ~ spl90_83
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1081,f1057,f907,f1658]) ).
fof(f1658,plain,
( spl90_174
<=> ! [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,[spl90_174])]) ).
fof(f1081,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3))
| ~ spl90_83
| ~ spl90_112 ),
inference(superposition,[],[f1058,f908]) ).
fof(f1656,plain,
( spl90_173
| ~ spl90_83
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1078,f1057,f907,f1654]) ).
fof(f1654,plain,
( spl90_173
<=> ! [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,[spl90_173])]) ).
fof(f1078,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4))
| ~ spl90_83
| ~ spl90_112 ),
inference(superposition,[],[f1058,f908]) ).
fof(f1606,plain,
( spl90_172
| ~ spl90_60
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1080,f1057,f807,f1604]) ).
fof(f1604,plain,
( spl90_172
<=> ! [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,[spl90_172])]) ).
fof(f1080,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl90_60
| ~ spl90_112 ),
inference(superposition,[],[f1058,f808]) ).
fof(f1602,plain,
( spl90_171
| ~ spl90_60
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1077,f1057,f807,f1600]) ).
fof(f1600,plain,
( spl90_171
<=> ! [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,[spl90_171])]) ).
fof(f1077,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl90_60
| ~ spl90_112 ),
inference(superposition,[],[f1058,f808]) ).
fof(f1588,plain,
( spl90_170
| ~ spl90_43
| ~ spl90_99 ),
inference(avatar_split_clause,[],[f1001,f997,f733,f1586]) ).
fof(f1586,plain,
( spl90_170
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK51(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_170])]) ).
fof(f1001,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK51(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl90_43
| ~ spl90_99 ),
inference(resolution,[],[f998,f734]) ).
fof(f1584,plain,
( spl90_169
| ~ spl90_58
| ~ spl90_91 ),
inference(avatar_split_clause,[],[f961,f953,f799,f1582]) ).
fof(f1582,plain,
( spl90_169
<=> ! [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,[spl90_169])]) ).
fof(f799,plain,
( spl90_58
<=> ! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_58])]) ).
fof(f961,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl90_58
| ~ spl90_91 ),
inference(superposition,[],[f800,f954]) ).
fof(f800,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl90_58 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f1564,plain,
( spl90_168
| ~ spl90_48
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1090,f1057,f753,f1562]) ).
fof(f1562,plain,
( spl90_168
<=> ! [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,[spl90_168])]) ).
fof(f753,plain,
( spl90_48
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_48])]) ).
fof(f1090,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl90_48
| ~ spl90_112 ),
inference(superposition,[],[f754,f1058]) ).
fof(f754,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl90_48 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f1560,plain,
( spl90_167
| ~ spl90_47
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1088,f1057,f749,f1558]) ).
fof(f1558,plain,
( spl90_167
<=> ! [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,[spl90_167])]) ).
fof(f749,plain,
( spl90_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_47])]) ).
fof(f1088,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl90_47
| ~ spl90_112 ),
inference(superposition,[],[f750,f1058]) ).
fof(f750,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl90_47 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f1555,plain,
( spl90_166
| spl90_4
| ~ spl90_15
| ~ spl90_95 ),
inference(avatar_split_clause,[],[f979,f975,f615,f570,f1553]) ).
fof(f1553,plain,
( spl90_166
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_166])]) ).
fof(f979,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl90_15
| ~ spl90_95 ),
inference(superposition,[],[f976,f616]) ).
fof(f1533,plain,
( spl90_165
| ~ spl90_31
| ~ spl90_153 ),
inference(avatar_split_clause,[],[f1404,f1371,f679,f1530]) ).
fof(f1530,plain,
( spl90_165
<=> sK15 = sK48(vvar(sK15),sK14,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_165])]) ).
fof(f1371,plain,
( spl90_153
<=> visFreeVar(sK48(vvar(sK15),sK14,vempty),vvar(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_153])]) ).
fof(f1404,plain,
( sK15 = sK48(vvar(sK15),sK14,vempty)
| ~ spl90_31
| ~ spl90_153 ),
inference(resolution,[],[f1373,f680]) ).
fof(f1373,plain,
( visFreeVar(sK48(vvar(sK15),sK14,vempty),vvar(sK15))
| ~ spl90_153 ),
inference(avatar_component_clause,[],[f1371]) ).
fof(f1431,plain,
( spl90_164
| ~ spl90_17
| ~ spl90_127 ),
inference(avatar_split_clause,[],[f1176,f1166,f623,f1429]) ).
fof(f1429,plain,
( spl90_164
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK57(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_164])]) ).
fof(f623,plain,
( spl90_17
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_17])]) ).
fof(f1176,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK57(X0,vempty,vnoType) = X0 )
| ~ spl90_17
| ~ spl90_127 ),
inference(superposition,[],[f1167,f624]) ).
fof(f624,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl90_17 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f1427,plain,
( spl90_163
| ~ spl90_39
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1086,f1057,f712,f1425]) ).
fof(f1425,plain,
( spl90_163
<=> ! [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,[spl90_163])]) ).
fof(f1086,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl90_39
| ~ spl90_112 ),
inference(superposition,[],[f713,f1058]) ).
fof(f1423,plain,
( spl90_162
| ~ spl90_38
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1085,f1057,f708,f1421]) ).
fof(f1421,plain,
( spl90_162
<=> ! [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,[spl90_162])]) ).
fof(f1085,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl90_38
| ~ spl90_112 ),
inference(superposition,[],[f709,f1058]) ).
fof(f1419,plain,
( spl90_161
| ~ spl90_33
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1079,f1057,f687,f1417]) ).
fof(f1417,plain,
( spl90_161
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_161])]) ).
fof(f1079,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl90_33
| ~ spl90_112 ),
inference(superposition,[],[f1058,f688]) ).
fof(f1415,plain,
( spl90_160
| ~ spl90_33
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1076,f1057,f687,f1413]) ).
fof(f1413,plain,
( spl90_160
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_160])]) ).
fof(f1076,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl90_33
| ~ spl90_112 ),
inference(superposition,[],[f1058,f688]) ).
fof(f1411,plain,
( spl90_159
| ~ spl90_10
| ~ spl90_82 ),
inference(avatar_split_clause,[],[f924,f903,f595,f1409]) ).
fof(f1409,plain,
( spl90_159
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_159])]) ).
fof(f924,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl90_10
| ~ spl90_82 ),
inference(resolution,[],[f904,f596]) ).
fof(f1402,plain,
( spl90_158
| ~ spl90_42
| ~ spl90_58 ),
inference(avatar_split_clause,[],[f813,f799,f729,f1400]) ).
fof(f1400,plain,
( spl90_158
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_158])]) ).
fof(f813,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl90_42
| ~ spl90_58 ),
inference(superposition,[],[f800,f730]) ).
fof(f1393,plain,
( spl90_157
| ~ spl90_37
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1084,f1057,f704,f1391]) ).
fof(f1391,plain,
( spl90_157
<=> ! [X5,X4,X2,X0,X6,X3,X1] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_157])]) ).
fof(f704,plain,
( spl90_37
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_37])]) ).
fof(f1084,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl90_37
| ~ spl90_112 ),
inference(superposition,[],[f705,f1058]) ).
fof(f705,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl90_37 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1389,plain,
( spl90_156
| ~ spl90_17
| ~ spl90_110 ),
inference(avatar_split_clause,[],[f1073,f1049,f623,f1387]) ).
fof(f1387,plain,
( spl90_156
<=> ! [X2,X0,X1,X3] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_156])]) ).
fof(f1073,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl90_17
| ~ spl90_110 ),
inference(trivial_inequality_removal,[],[f1070]) ).
fof(f1070,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl90_17
| ~ spl90_110 ),
inference(superposition,[],[f1050,f624]) ).
fof(f1384,plain,
( spl90_155
| ~ spl90_21
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1083,f1057,f639,f1382]) ).
fof(f1382,plain,
( spl90_155
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_155])]) ).
fof(f1083,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl90_21
| ~ spl90_112 ),
inference(superposition,[],[f640,f1058]) ).
fof(f1379,plain,
( spl90_130
| spl90_132
| spl90_154
| ~ spl90_1
| ~ spl90_17
| ~ spl90_133 ),
inference(avatar_split_clause,[],[f1213,f1202,f623,f555,f1376,f1197,f1189]) ).
fof(f555,plain,
( spl90_1
<=> vtcheck(vempty,vvar(sK15),sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_1])]) ).
fof(f1213,plain,
( vnoType = vsomeType(sK14)
| sP5(vempty,sK14,vvar(sK15))
| sP6(vempty,sK14,vvar(sK15))
| ~ spl90_1
| ~ spl90_17
| ~ spl90_133 ),
inference(forward_demodulation,[],[f1209,f624]) ).
fof(f1209,plain,
( sP5(vempty,sK14,vvar(sK15))
| vsomeType(sK14) = vlookup(sK48(vvar(sK15),sK14,vempty),vempty)
| sP6(vempty,sK14,vvar(sK15))
| ~ spl90_1
| ~ spl90_133 ),
inference(resolution,[],[f1203,f557]) ).
fof(f557,plain,
( vtcheck(vempty,vvar(sK15),sK14)
| ~ spl90_1 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f1374,plain,
( spl90_153
| ~ spl90_12
| ~ spl90_131 ),
inference(avatar_split_clause,[],[f1308,f1193,f603,f1371]) ).
fof(f1308,plain,
( visFreeVar(sK48(vvar(sK15),sK14,vempty),vvar(sK15))
| ~ spl90_12
| ~ spl90_131 ),
inference(superposition,[],[f604,f1195]) ).
fof(f1361,plain,
( spl90_152
| ~ spl90_112
| ~ spl90_151 ),
inference(avatar_split_clause,[],[f1357,f1354,f1057,f1359]) ).
fof(f1354,plain,
( spl90_151
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vapp(vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK80(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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,[spl90_151])]) ).
fof(f1357,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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) )
| ~ spl90_112
| ~ spl90_151 ),
inference(forward_demodulation,[],[f1355,f1058]) ).
fof(f1355,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(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK80(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl90_151 ),
inference(avatar_component_clause,[],[f1354]) ).
fof(f1356,plain,
spl90_151,
inference(avatar_split_clause,[],[f469,f1354]) ).
fof(f469,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(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK80(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK81(X0,X1,X2,vsubst(X0,X1,X2)),sK82(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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,[],[f402]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(vsubst(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK80(X0,X1,X2,X3)),vsubst(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK83(X0,X1,X2,X3))) = X3
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ( vapp(vsubst(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK80(X0,X1,X2,X3)),vsubst(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK83(X0,X1,X2,X3))) = X3
& vapp(sK80(X0,X1,X2,X3),sK83(X0,X1,X2,X3)) = X2
& sK82(X0,X1,X2,X3) = X1
& sK81(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,[sK80,sK81,sK82,sK83])],[f283,f284]) ).
fof(f284,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(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK80(X0,X1,X2,X3)),vsubst(sK81(X0,X1,X2,X3),sK82(X0,X1,X2,X3),sK83(X0,X1,X2,X3))) = X3
& vapp(sK80(X0,X1,X2,X3),sK83(X0,X1,X2,X3)) = X2
& sK82(X0,X1,X2,X3) = X1
& sK81(X0,X1,X2,X3) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f283,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,[],[f214]) ).
fof(f214,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,[],[f144,f213,f212,f211,f210,f209]) ).
fof(f209,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(f210,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(f211,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(f212,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(f213,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(f144,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,[],[f143]) ).
fof(f143,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,[],[f85]) ).
fof(f85,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(f1344,plain,
spl90_150,
inference(avatar_split_clause,[],[f470,f1342]) ).
fof(f470,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(sK80(X0,X1,X2,vsubst(X0,X1,X2)),sK83(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,[],[f401]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(sK80(X0,X1,X2,X3),sK83(X0,X1,X2,X3)) = X2
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f285]) ).
fof(f1324,plain,
spl90_149,
inference(avatar_split_clause,[],[f472,f1322]) ).
fof(f472,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)
| sK81(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,[],[f399]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK81(X0,X1,X2,X3) = X0
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f285]) ).
fof(f1320,plain,
spl90_148,
inference(avatar_split_clause,[],[f471,f1318]) ).
fof(f471,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)
| sK82(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,[],[f400]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK82(X0,X1,X2,X3) = X1
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f285]) ).
fof(f1306,plain,
spl90_147,
inference(avatar_split_clause,[],[f383,f1304]) ).
fof(f1304,plain,
( spl90_147
<=> ! [X0,X3,X2,X1] :
( vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vabs(sK67(X0,X1,X2,X3),sK65(X0,X1,X2,X3),vsubst(sK66(X0,X1,X2,X3),vvar(sK67(X0,X1,X2,X3)),sK68(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_147])]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vabs(sK67(X0,X1,X2,X3),sK65(X0,X1,X2,X3),vsubst(sK66(X0,X1,X2,X3),vvar(sK67(X0,X1,X2,X3)),sK68(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( ( vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vabs(sK67(X0,X1,X2,X3),sK65(X0,X1,X2,X3),vsubst(sK66(X0,X1,X2,X3),vvar(sK67(X0,X1,X2,X3)),sK68(X0,X1,X2,X3)))) = X0
& sK67(X0,X1,X2,X3) = vgensym(vapp(vapp(sK64(X0,X1,X2,X3),sK68(X0,X1,X2,X3)),vvar(sK63(X0,X1,X2,X3))))
& visFreeVar(sK66(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
& sK63(X0,X1,X2,X3) != sK66(X0,X1,X2,X3)
& vabs(sK66(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK68(X0,X1,X2,X3)) = X1
& sK64(X0,X1,X2,X3) = X2
& sK63(X0,X1,X2,X3) = X3 )
| ~ sP12(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64,sK65,sK66,sK67,sK68])],[f268,f269]) ).
fof(f269,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(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),vabs(sK67(X0,X1,X2,X3),sK65(X0,X1,X2,X3),vsubst(sK66(X0,X1,X2,X3),vvar(sK67(X0,X1,X2,X3)),sK68(X0,X1,X2,X3)))) = X0
& sK67(X0,X1,X2,X3) = vgensym(vapp(vapp(sK64(X0,X1,X2,X3),sK68(X0,X1,X2,X3)),vvar(sK63(X0,X1,X2,X3))))
& visFreeVar(sK66(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
& sK63(X0,X1,X2,X3) != sK66(X0,X1,X2,X3)
& vabs(sK66(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK68(X0,X1,X2,X3)) = X1
& sK64(X0,X1,X2,X3) = X2
& sK63(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f268,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,[],[f267]) ).
fof(f267,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,[],[f212]) ).
fof(f1297,plain,
spl90_146,
inference(avatar_split_clause,[],[f453,f1295]) ).
fof(f453,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK37(X0,vreduce(X0)),sK38(X0,vreduce(X0)),sK39(X0,vreduce(X0))) = X0
| vvar(sK40(X0,vreduce(X0))) = X0 ),
inference(equality_resolution,[],[f333]) ).
fof(f333,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| vabs(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1)) = X0
| vvar(sK40(X0,X1)) = X0
| vreduce(X0) != X1 ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ( vnoExp = X1
& vabs(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1)) = X0 )
| ( vnoExp = X1
& vvar(sK40(X0,X1)) = X0 )
| vreduce(X0) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40])],[f237,f239,f238]) ).
fof(f238,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& vabs(X2,X3,X4) = X0 )
=> ( vnoExp = X1
& vabs(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f239,plain,
! [X0,X1] :
( ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
=> ( vnoExp = X1
& vvar(sK40(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f237,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,[],[f202]) ).
fof(f202,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,[],[f125,f201,f200,f199,f198,f197]) ).
fof(f197,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(f198,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(f199,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(f200,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(f201,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(f125,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,[],[f124]) ).
fof(f124,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,[],[f72]) ).
fof(f72,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(f1287,plain,
spl90_145,
inference(avatar_split_clause,[],[f552,f1285]) ).
fof(f552,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,[],[f551]) ).
fof(f551,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,[],[f550]) ).
fof(f550,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,[],[f549]) ).
fof(f549,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,[],[f548]) ).
fof(f548,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,[],[f441]) ).
fof(f441,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,[],[f196]) ).
fof(f196,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,[],[f195]) ).
fof(f195,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,[],[f113]) ).
fof(f113,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(f1283,plain,
spl90_144,
inference(avatar_split_clause,[],[f376,f1281]) ).
fof(f1281,plain,
( spl90_144
<=> ! [X0,X3,X2,X1] :
( vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),vsubst(sK60(X0,X1,X2,X3),sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_144])]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),vsubst(sK60(X0,X1,X2,X3),sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),vsubst(sK60(X0,X1,X2,X3),sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK58(X0,X1,X2,X3),sK61(X0,X1,X2,X3))
& sK58(X0,X1,X2,X3) != sK60(X0,X1,X2,X3)
& vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),sK62(X0,X1,X2,X3)) = X1
& sK61(X0,X1,X2,X3) = X2
& sK60(X0,X1,X2,X3) = X3 )
| ~ sP13(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59,sK60,sK61,sK62])],[f264,f265]) ).
fof(f265,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(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),vsubst(sK60(X0,X1,X2,X3),sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK58(X0,X1,X2,X3),sK61(X0,X1,X2,X3))
& sK58(X0,X1,X2,X3) != sK60(X0,X1,X2,X3)
& vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),sK62(X0,X1,X2,X3)) = X1
& sK61(X0,X1,X2,X3) = X2
& sK60(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f264,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,[],[f263]) ).
fof(f263,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,[],[f213]) ).
fof(f1279,plain,
spl90_143,
inference(avatar_split_clause,[],[f382,f1277]) ).
fof(f382,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) = vgensym(vapp(vapp(sK64(X0,X1,X2,X3),sK68(X0,X1,X2,X3)),vvar(sK63(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1269,plain,
spl90_142,
inference(avatar_split_clause,[],[f553,f1267]) ).
fof(f553,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,[],[f450]) ).
fof(f450,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,[],[f336]) ).
fof(f336,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,[],[f240]) ).
fof(f1253,plain,
spl90_141,
inference(avatar_split_clause,[],[f495,f1251]) ).
fof(f495,plain,
! [X0,X4] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f493]) ).
fof(f493,plain,
! [X3,X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(X3),X4))
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f416]) ).
fof(f416,plain,
! [X2,X3,X0,X1,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88,sK89])],[f162,f288]) ).
fof(f288,plain,
! [X0] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
=> vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
| vapp(X0,X4) != X1 ),
inference(flattening,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
| vapp(X0,X4) != X1 ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X0
& vapp(X0,X4) = X1 )
=> ( ( visSomeExp(X3)
& vreduce(X0) = X3 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2 ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X11,X3,X18,X26,X12] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce5) ).
fof(f1249,plain,
spl90_140,
inference(avatar_split_clause,[],[f432,f1247]) ).
fof(f432,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,[],[f178]) ).
fof(f178,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,[],[f177]) ).
fof(f177,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,[],[f104]) ).
fof(f104,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(f1245,plain,
spl90_139,
inference(avatar_split_clause,[],[f388,f1243]) ).
fof(f1243,plain,
( spl90_139
<=> ! [X0,X3,X2,X1] :
( vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_139])]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X0
& sK70(X0,X1,X2,X3) = sK71(X0,X1,X2,X3)
& vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
& sK69(X0,X1,X2,X3) = X2
& sK70(X0,X1,X2,X3) = X3 )
| ~ sP11(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69,sK70,sK71,sK72,sK73])],[f272,f273]) ).
fof(f273,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(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X0
& sK70(X0,X1,X2,X3) = sK71(X0,X1,X2,X3)
& vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
& sK69(X0,X1,X2,X3) = X2
& sK70(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f272,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,[],[f271]) ).
fof(f271,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,[],[f211]) ).
fof(f1241,plain,
spl90_138,
inference(avatar_split_clause,[],[f386,f1239]) ).
fof(f1239,plain,
( spl90_138
<=> ! [X0,X3,X2,X1] :
( vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_138])]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( vabs(sK71(X0,X1,X2,X3),sK72(X0,X1,X2,X3),sK73(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1237,plain,
spl90_137,
inference(avatar_split_clause,[],[f379,f1235]) ).
fof(f379,plain,
! [X2,X3,X0,X1] :
( vabs(sK66(X0,X1,X2,X3),sK65(X0,X1,X2,X3),sK68(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1233,plain,
spl90_136,
inference(avatar_split_clause,[],[f373,f1231]) ).
fof(f1231,plain,
( spl90_136
<=> ! [X0,X3,X2,X1] :
( vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),sK62(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_136])]) ).
fof(f373,plain,
! [X2,X3,X0,X1] :
( vabs(sK58(X0,X1,X2,X3),sK59(X0,X1,X2,X3),sK62(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1229,plain,
spl90_135,
inference(avatar_split_clause,[],[f348,f1227]) ).
fof(f348,plain,
! [X2,X0,X1] :
( vtcheck(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK45(X0,X1,X2),sK47(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ( vtcheck(vbind(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK45(X0,X1,X2),sK47(X0,X1,X2))
& varrow(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X1
& vabs(sK44(X0,X1,X2),sK46(X0,X1,X2),sK45(X0,X1,X2)) = X2 )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47])],[f246,f247]) ).
fof(f247,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(sK44(X0,X1,X2),sK46(X0,X1,X2),X0),sK45(X0,X1,X2),sK47(X0,X1,X2))
& varrow(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X1
& vabs(sK44(X0,X1,X2),sK46(X0,X1,X2),sK45(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f246,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,[],[f245]) ).
fof(f245,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,[],[f203]) ).
fof(f203,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(f1208,plain,
spl90_134,
inference(avatar_split_clause,[],[f547,f1206]) ).
fof(f547,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,[],[f546]) ).
fof(f546,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,[],[f545]) ).
fof(f545,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,[],[f544]) ).
fof(f544,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,[],[f440]) ).
fof(f440,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,[],[f194]) ).
fof(f194,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,[],[f193]) ).
fof(f193,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,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
=> ( ( ~ visFreeVar(X4,X7)
& X4 != X6 )
=> ( vsubst(X0,X1,X2) = X3
=> vabs(X4,X5,vsubst(X6,X7,X8)) = X3 ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X3,X5,X18,X20,X14,X8,X10,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( ~ visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,vsubst(X8,X10,X11)) = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subst5) ).
fof(f1204,plain,
spl90_133,
inference(avatar_split_clause,[],[f350,f1202]) ).
fof(f350,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK48(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ( vsomeType(X1) = vlookup(sK48(X0,X1,X2),X2)
& vvar(sK48(X0,X1,X2)) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f249,f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ? [X3] :
( vsomeType(X1) = vlookup(X3,X2)
& vvar(X3) = X0 )
=> ( vsomeType(X1) = vlookup(sK48(X0,X1,X2),X2)
& vvar(sK48(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f249,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,[],[f205]) ).
fof(f205,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,[],[f134,f204,f203]) ).
fof(f204,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(f134,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,[],[f133]) ).
fof(f133,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,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X10,X14,X19] :
( vtcheck(X19,X10,X14)
=> ( ? [X11,X12,X9] :
( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14))
& vapp(X11,X12) = X10 )
| ? [X8,X12,X32,X33] :
( vtcheck(vbind(X8,X32,X19),X12,X33)
& varrow(X32,X33) = X14
& vabs(X8,X32,X12) = X10 )
| ? [X8] :
( vlookup(X8,X19) = vsomeType(X14)
& vvar(X8) = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-inv') ).
fof(f1200,plain,
( spl90_130
| spl90_131
| spl90_132
| ~ spl90_1
| ~ spl90_124 ),
inference(avatar_split_clause,[],[f1159,f1147,f555,f1197,f1193,f1189]) ).
fof(f1159,plain,
( sP5(vempty,sK14,vvar(sK15))
| vvar(sK15) = vvar(sK48(vvar(sK15),sK14,vempty))
| sP6(vempty,sK14,vvar(sK15))
| ~ spl90_1
| ~ spl90_124 ),
inference(resolution,[],[f1148,f557]) ).
fof(f1187,plain,
spl90_129,
inference(avatar_split_clause,[],[f312,f1185]) ).
fof(f1185,plain,
( spl90_129
<=> ! [X0,X1] :
( vsomeExp(vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),vgetSomeExp(sK20(X0,X1)))) = X0
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_129])]) ).
fof(f312,plain,
! [X0,X1] :
( vsomeExp(vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),vgetSomeExp(sK20(X0,X1)))) = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),vgetSomeExp(sK20(X0,X1)))) = X0
& visSomeExp(sK20(X0,X1))
& sK20(X0,X1) = vreduce(sK16(X0,X1))
& vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),sK16(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19,sK20])],[f218,f219]) ).
fof(f219,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(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),vgetSomeExp(sK20(X0,X1)))) = X0
& visSomeExp(sK20(X0,X1))
& sK20(X0,X1) = vreduce(sK16(X0,X1))
& vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),sK16(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f218,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,[],[f217]) ).
fof(f217,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,[],[f201]) ).
fof(f1172,plain,
spl90_128,
inference(avatar_split_clause,[],[f517,f1170]) ).
fof(f517,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,[],[f516]) ).
fof(f516,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,[],[f515]) ).
fof(f515,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,[],[f431]) ).
fof(f431,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,[],[f176]) ).
fof(f176,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,[],[f175]) ).
fof(f175,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,[],[f103]) ).
fof(f103,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(f1168,plain,
spl90_127,
inference(avatar_split_clause,[],[f463,f1166]) ).
fof(f463,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK57(X0,X1,vlookup(X0,X1)) = X0 ),
inference(equality_resolution,[],[f359]) ).
fof(f359,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| sK57(X0,X1,X2) = X0
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ( vnoType = X2
& vempty = X1
& sK57(X0,X1,X2) = X0 )
| vlookup(X0,X1) != X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f260,f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
=> ( vnoType = X2
& vempty = X1
& sK57(X0,X1,X2) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f260,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,[],[f208]) ).
fof(f208,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,[],[f136,f207,f206]) ).
fof(f206,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(f207,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(f136,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,[],[f135]) ).
fof(f135,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,[],[f80]) ).
fof(f80,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(f1157,plain,
spl90_126,
inference(avatar_split_clause,[],[f356,f1155]) ).
fof(f1155,plain,
( spl90_126
<=> ! [X2,X0,X1] :
( vbind(sK55(X0,X1,X2),sK56(X0,X1,X2),sK53(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_126])]) ).
fof(f356,plain,
! [X2,X0,X1] :
( vbind(sK55(X0,X1,X2),sK56(X0,X1,X2),sK53(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1,X2] :
( ( vsomeType(sK56(X0,X1,X2)) = X0
& sK54(X0,X1,X2) = sK55(X0,X1,X2)
& vbind(sK55(X0,X1,X2),sK56(X0,X1,X2),sK53(X0,X1,X2)) = X1
& sK54(X0,X1,X2) = X2 )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f257,f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
=> ( vsomeType(sK56(X0,X1,X2)) = X0
& sK54(X0,X1,X2) = sK55(X0,X1,X2)
& vbind(sK55(X0,X1,X2),sK56(X0,X1,X2),sK53(X0,X1,X2)) = X1
& sK54(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f257,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,[],[f256]) ).
fof(f256,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,[],[f206]) ).
fof(f1153,plain,
spl90_125,
inference(avatar_split_clause,[],[f352,f1151]) ).
fof(f352,plain,
! [X2,X0,X1] :
( vbind(sK50(X0,X1,X2),sK49(X0,X1,X2),sK52(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ( vlookup(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X0
& sK50(X0,X1,X2) != sK51(X0,X1,X2)
& vbind(sK50(X0,X1,X2),sK49(X0,X1,X2),sK52(X0,X1,X2)) = X1
& sK51(X0,X1,X2) = X2 )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
=> ( vlookup(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X0
& sK50(X0,X1,X2) != sK51(X0,X1,X2)
& vbind(sK50(X0,X1,X2),sK49(X0,X1,X2),sK52(X0,X1,X2)) = X1
& sK51(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f253,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,[],[f252]) ).
fof(f252,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,[],[f207]) ).
fof(f1149,plain,
spl90_124,
inference(avatar_split_clause,[],[f349,f1147]) ).
fof(f349,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK48(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1145,plain,
spl90_123,
inference(avatar_split_clause,[],[f346,f1143]) ).
fof(f346,plain,
! [X2,X0,X1] :
( vabs(sK44(X0,X1,X2),sK46(X0,X1,X2),sK45(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f1141,plain,
spl90_122,
inference(avatar_split_clause,[],[f328,f1139]) ).
fof(f1139,plain,
( spl90_122
<=> ! [X0,X1] :
( vapp(vabs(sK34(X0,X1),sK32(X0,X1),sK36(X0,X1)),sK35(X0,X1)) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_122])]) ).
fof(f328,plain,
! [X0,X1] :
( vapp(vabs(sK34(X0,X1),sK32(X0,X1),sK36(X0,X1)),sK35(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( ( vsomeExp(vsubst(sK34(X0,X1),sK35(X0,X1),sK36(X0,X1))) = X0
& visValue(sK35(X0,X1))
& ~ visSomeExp(sK33(X0,X1))
& sK33(X0,X1) = vreduce(sK35(X0,X1))
& vapp(vabs(sK34(X0,X1),sK32(X0,X1),sK36(X0,X1)),sK35(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35,sK36])],[f234,f235]) ).
fof(f235,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(sK34(X0,X1),sK35(X0,X1),sK36(X0,X1))) = X0
& visValue(sK35(X0,X1))
& ~ visSomeExp(sK33(X0,X1))
& sK33(X0,X1) = vreduce(sK35(X0,X1))
& vapp(vabs(sK34(X0,X1),sK32(X0,X1),sK36(X0,X1)),sK35(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f234,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,[],[f233]) ).
fof(f233,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,[],[f197]) ).
fof(f1137,plain,
spl90_121,
inference(avatar_split_clause,[],[f323,f1135]) ).
fof(f1135,plain,
( spl90_121
<=> ! [X0,X1] :
( vapp(vabs(sK27(X0,X1),sK28(X0,X1),sK29(X0,X1)),sK31(X0,X1)) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_121])]) ).
fof(f323,plain,
! [X0,X1] :
( vapp(vabs(sK27(X0,X1),sK28(X0,X1),sK29(X0,X1)),sK31(X0,X1)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visValue(sK31(X0,X1))
& ~ visSomeExp(sK30(X0,X1))
& sK30(X0,X1) = vreduce(sK31(X0,X1))
& vapp(vabs(sK27(X0,X1),sK28(X0,X1),sK29(X0,X1)),sK31(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29,sK30,sK31])],[f230,f231]) ).
fof(f231,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(sK31(X0,X1))
& ~ visSomeExp(sK30(X0,X1))
& sK30(X0,X1) = vreduce(sK31(X0,X1))
& vapp(vabs(sK27(X0,X1),sK28(X0,X1),sK29(X0,X1)),sK31(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f230,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,[],[f229]) ).
fof(f229,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,[],[f198]) ).
fof(f1133,plain,
spl90_120,
inference(avatar_split_clause,[],[f309,f1131]) ).
fof(f1131,plain,
( spl90_120
<=> ! [X0,X1] :
( vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),sK16(X0,X1)) = X1
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_120])]) ).
fof(f309,plain,
! [X0,X1] :
( vapp(vabs(sK17(X0,X1),sK18(X0,X1),sK19(X0,X1)),sK16(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f1127,plain,
( spl90_119
| ~ spl90_11
| ~ spl90_112 ),
inference(avatar_split_clause,[],[f1082,f1057,f599,f1125]) ).
fof(f1125,plain,
( spl90_119
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_119])]) ).
fof(f599,plain,
( spl90_11
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_11])]) ).
fof(f1082,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl90_11
| ~ spl90_112 ),
inference(superposition,[],[f600,f1058]) ).
fof(f600,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl90_11 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f1121,plain,
spl90_118,
inference(avatar_split_clause,[],[f514,f1119]) ).
fof(f514,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,[],[f513]) ).
fof(f513,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,[],[f512]) ).
fof(f512,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,[],[f430]) ).
fof(f430,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,[],[f174]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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,[],[f102]) ).
fof(f102,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(f1117,plain,
spl90_117,
inference(avatar_split_clause,[],[f492,f1115]) ).
fof(f492,plain,
! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1 ),
inference(equality_resolution,[],[f491]) ).
fof(f491,plain,
! [X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(vreduce(X1))
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f490]) ).
fof(f490,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f415]) ).
fof(f415,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK84(X1),sK85(X1),sK86(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84,sK85,sK86])],[f160,f286]) ).
fof(f286,plain,
! [X1] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
=> vabs(sK84(X1),sK85(X1),sK86(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
| vapp(X1,X0) != X3 ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
| vapp(X1,X0) != X3 ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X1
& vapp(X1,X0) = X3 )
=> ( ( ~ visSomeExp(X2)
& vreduce(X1) = X2 )
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X12,X11,X26,X3,X18] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( ~ visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reduce6) ).
fof(f1105,plain,
spl90_116,
inference(avatar_split_clause,[],[f534,f1103]) ).
fof(f534,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,[],[f437]) ).
fof(f437,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,[],[f188]) ).
fof(f188,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,[],[f187]) ).
fof(f187,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,[],[f109]) ).
fof(f109,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(f1101,plain,
spl90_115,
inference(avatar_split_clause,[],[f461,f1099]) ).
fof(f461,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ),
inference(equality_resolution,[],[f361]) ).
fof(f361,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vnoType = X2
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f262]) ).
fof(f1069,plain,
( spl90_114
| ~ spl90_38
| ~ spl90_64 ),
inference(avatar_split_clause,[],[f934,f831,f708,f1067]) ).
fof(f1067,plain,
( spl90_114
<=> ! [X2,X0,X1,X3] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_114])]) ).
fof(f831,plain,
( spl90_64
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_64])]) ).
fof(f934,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X2)
| ~ spl90_38
| ~ spl90_64 ),
inference(resolution,[],[f832,f709]) ).
fof(f832,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl90_64 ),
inference(avatar_component_clause,[],[f831]) ).
fof(f1063,plain,
( spl90_113
| ~ spl90_39
| ~ spl90_64 ),
inference(avatar_split_clause,[],[f933,f831,f712,f1061]) ).
fof(f1061,plain,
( spl90_113
<=> ! [X2,X0,X1,X3] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_113])]) ).
fof(f933,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X1)
| ~ spl90_39
| ~ spl90_64 ),
inference(resolution,[],[f832,f713]) ).
fof(f1059,plain,
spl90_112,
inference(avatar_split_clause,[],[f538,f1057]) ).
fof(f538,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f537]) ).
fof(f537,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,[],[f536]) ).
fof(f536,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,[],[f535]) ).
fof(f535,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,[],[f438]) ).
fof(f438,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,[],[f190]) ).
fof(f190,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,[],[f189]) ).
fof(f189,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,[],[f110]) ).
fof(f110,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(f1055,plain,
spl90_111,
inference(avatar_split_clause,[],[f417,f1053]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f163]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X3,X0)
& vtcheck(X1,X2,varrow(X0,X4)) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X9,X19,X11,X12,X14] :
( ( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14)) )
=> vtcheck(X19,vapp(X11,X12),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-app') ).
fof(f1051,plain,
spl90_110,
inference(avatar_split_clause,[],[f414,f1049]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,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(f1047,plain,
spl90_109,
inference(avatar_split_clause,[],[f409,f1045]) ).
fof(f409,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,[],[f152]) ).
fof(f152,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,[],[f91]) ).
fof(f91,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(f1043,plain,
spl90_108,
inference(avatar_split_clause,[],[f397,f1041]) ).
fof(f1041,plain,
( spl90_108
<=> ! [X0,X3,X2,X1] :
( sK77(X0,X1,X2,X3) = sK78(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_108])]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( sK77(X0,X1,X2,X3) = sK78(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1,X2,X3] :
( ( sK79(X0,X1,X2,X3) = X0
& sK77(X0,X1,X2,X3) = sK78(X0,X1,X2,X3)
& vvar(sK78(X0,X1,X2,X3)) = X1
& sK79(X0,X1,X2,X3) = X2
& sK77(X0,X1,X2,X3) = X3 )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78,sK79])],[f280,f281]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( X0 = X6
& X4 = X5
& vvar(X5) = X1
& X2 = X6
& X3 = X4 )
=> ( sK79(X0,X1,X2,X3) = X0
& sK77(X0,X1,X2,X3) = sK78(X0,X1,X2,X3)
& vvar(sK78(X0,X1,X2,X3)) = X1
& sK79(X0,X1,X2,X3) = X2
& sK77(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f280,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,[],[f279]) ).
fof(f279,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,[],[f209]) ).
fof(f1039,plain,
spl90_107,
inference(avatar_split_clause,[],[f392,f1037]) ).
fof(f1037,plain,
( spl90_107
<=> ! [X0,X3,X2,X1] :
( sK75(X0,X1,X2,X3) != sK76(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_107])]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( sK75(X0,X1,X2,X3) != sK76(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( ( vvar(sK76(X0,X1,X2,X3)) = X0
& sK75(X0,X1,X2,X3) != sK76(X0,X1,X2,X3)
& vvar(sK76(X0,X1,X2,X3)) = X1
& sK74(X0,X1,X2,X3) = X2
& sK75(X0,X1,X2,X3) = X3 )
| ~ sP10(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75,sK76])],[f276,f277]) ).
fof(f277,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( vvar(X6) = X0
& X5 != X6
& vvar(X6) = X1
& X2 = X4
& X3 = X5 )
=> ( vvar(sK76(X0,X1,X2,X3)) = X0
& sK75(X0,X1,X2,X3) != sK76(X0,X1,X2,X3)
& vvar(sK76(X0,X1,X2,X3)) = X1
& sK74(X0,X1,X2,X3) = X2
& sK75(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f276,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,[],[f275]) ).
fof(f275,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,[],[f210]) ).
fof(f1035,plain,
spl90_106,
inference(avatar_split_clause,[],[f387,f1033]) ).
fof(f1033,plain,
( spl90_106
<=> ! [X0,X3,X2,X1] :
( sK70(X0,X1,X2,X3) = sK71(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_106])]) ).
fof(f387,plain,
! [X2,X3,X0,X1] :
( sK70(X0,X1,X2,X3) = sK71(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f1031,plain,
spl90_105,
inference(avatar_split_clause,[],[f381,f1029]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( visFreeVar(sK66(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1027,plain,
spl90_104,
inference(avatar_split_clause,[],[f380,f1025]) ).
fof(f1025,plain,
( spl90_104
<=> ! [X0,X3,X2,X1] :
( sK63(X0,X1,X2,X3) != sK66(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_104])]) ).
fof(f380,plain,
! [X2,X3,X0,X1] :
( sK63(X0,X1,X2,X3) != sK66(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1023,plain,
spl90_103,
inference(avatar_split_clause,[],[f375,f1021]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(sK58(X0,X1,X2,X3),sK61(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1016,plain,
spl90_102,
inference(avatar_split_clause,[],[f374,f1014]) ).
fof(f1014,plain,
( spl90_102
<=> ! [X0,X3,X2,X1] :
( sK58(X0,X1,X2,X3) != sK60(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_102])]) ).
fof(f374,plain,
! [X2,X3,X0,X1] :
( sK58(X0,X1,X2,X3) != sK60(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1012,plain,
spl90_101,
inference(avatar_split_clause,[],[f344,f1010]) ).
fof(f344,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ( vtcheck(X0,sK42(X0,X1,X2),sK43(X0,X1,X2))
& vtcheck(X0,sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1))
& vapp(sK41(X0,X1,X2),sK42(X0,X1,X2)) = X2 )
| ~ sP6(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43])],[f242,f243]) ).
fof(f243,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X0,X4,X5)
& vtcheck(X0,X3,varrow(X5,X1))
& vapp(X3,X4) = X2 )
=> ( vtcheck(X0,sK42(X0,X1,X2),sK43(X0,X1,X2))
& vtcheck(X0,sK41(X0,X1,X2),varrow(sK43(X0,X1,X2),X1))
& vapp(sK41(X0,X1,X2),sK42(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f242,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,[],[f241]) ).
fof(f241,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,[],[f204]) ).
fof(f1008,plain,
spl90_100,
inference(avatar_split_clause,[],[f332,f1006]) ).
fof(f1006,plain,
( spl90_100
<=> ! [X0,X1] :
( vsomeExp(vsubst(sK34(X0,X1),sK35(X0,X1),sK36(X0,X1))) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_100])]) ).
fof(f332,plain,
! [X0,X1] :
( vsomeExp(vsubst(sK34(X0,X1),sK35(X0,X1),sK36(X0,X1))) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f999,plain,
spl90_99,
inference(avatar_split_clause,[],[f462,f997]) ).
fof(f462,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ),
inference(equality_resolution,[],[f360]) ).
fof(f360,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vempty = X1
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f262]) ).
fof(f995,plain,
spl90_98,
inference(avatar_split_clause,[],[f354,f993]) ).
fof(f354,plain,
! [X2,X0,X1] :
( vlookup(sK51(X0,X1,X2),sK52(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f991,plain,
spl90_97,
inference(avatar_split_clause,[],[f347,f989]) ).
fof(f347,plain,
! [X2,X0,X1] :
( varrow(sK46(X0,X1,X2),sK47(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f248]) ).
fof(f984,plain,
spl90_96,
inference(avatar_split_clause,[],[f343,f982]) ).
fof(f343,plain,
! [X2,X0,X1] :
( vapp(sK41(X0,X1,X2),sK42(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f977,plain,
spl90_95,
inference(avatar_split_clause,[],[f511,f975]) ).
fof(f511,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f510]) ).
fof(f510,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f509]) ).
fof(f509,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,[],[f429]) ).
fof(f429,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,[],[f172]) ).
fof(f172,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,[],[f171]) ).
fof(f171,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,[],[f101]) ).
fof(f101,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(f973,plain,
spl90_94,
inference(avatar_split_clause,[],[f410,f971]) ).
fof(f410,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X2,X3,X4)
| ~ vtcheck(vbind(X0,X1,X2),X3,X4)
| visFreeVar(X0,X3) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,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(f969,plain,
spl90_93,
inference(avatar_split_clause,[],[f345,f967]) ).
fof(f345,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK42(X0,X1,X2),sK43(X0,X1,X2))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f965,plain,
spl90_92,
inference(avatar_split_clause,[],[f322,f963]) ).
fof(f963,plain,
( spl90_92
<=> ! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK25(X0,X1)),sK26(X0,X1))) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_92])]) ).
fof(f322,plain,
! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK25(X0,X1)),sK26(X0,X1))) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vgetSomeExp(sK25(X0,X1)),sK26(X0,X1))) = X0
& visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK24(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK24(X0,X1)
& vapp(sK24(X0,X1),sK26(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f226,f227]) ).
fof(f227,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(sK25(X0,X1)),sK26(X0,X1))) = X0
& visSomeExp(sK25(X0,X1))
& sK25(X0,X1) = vreduce(sK24(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK24(X0,X1)
& vapp(sK24(X0,X1),sK26(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f226,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,[],[f225]) ).
fof(f225,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,[],[f199]) ).
fof(f955,plain,
spl90_91,
inference(avatar_split_clause,[],[f529,f953]) ).
fof(f529,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f528]) ).
fof(f528,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f527]) ).
fof(f527,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,[],[f435]) ).
fof(f435,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,[],[f184]) ).
fof(f184,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,[],[f183]) ).
fof(f183,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,[],[f107]) ).
fof(f107,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(f951,plain,
spl90_90,
inference(avatar_split_clause,[],[f396,f949]) ).
fof(f949,plain,
( spl90_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK78(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_90])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( vvar(sK78(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f947,plain,
spl90_89,
inference(avatar_split_clause,[],[f393,f945]) ).
fof(f945,plain,
( spl90_89
<=> ! [X0,X3,X2,X1] :
( vvar(sK76(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_89])]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( vvar(sK76(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f943,plain,
spl90_88,
inference(avatar_split_clause,[],[f391,f941]) ).
fof(f941,plain,
( spl90_88
<=> ! [X0,X3,X2,X1] :
( vvar(sK76(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_88])]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( vvar(sK76(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f939,plain,
spl90_87,
inference(avatar_split_clause,[],[f357,f937]) ).
fof(f937,plain,
( spl90_87
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) = sK55(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_87])]) ).
fof(f357,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) = sK55(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f932,plain,
spl90_86,
inference(avatar_split_clause,[],[f353,f930]) ).
fof(f930,plain,
( spl90_86
<=> ! [X2,X0,X1] :
( sK50(X0,X1,X2) != sK51(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_86])]) ).
fof(f353,plain,
! [X2,X0,X1] :
( sK50(X0,X1,X2) != sK51(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f917,plain,
( spl90_85
| ~ spl90_38
| ~ spl90_49 ),
inference(avatar_split_clause,[],[f811,f757,f708,f915]) ).
fof(f915,plain,
( spl90_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_85])]) ).
fof(f757,plain,
( spl90_49
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_49])]) ).
fof(f811,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl90_38
| ~ spl90_49 ),
inference(resolution,[],[f758,f709]) ).
fof(f758,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl90_49 ),
inference(avatar_component_clause,[],[f757]) ).
fof(f913,plain,
( spl90_84
| ~ spl90_39
| ~ spl90_49 ),
inference(avatar_split_clause,[],[f810,f757,f712,f911]) ).
fof(f911,plain,
( spl90_84
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_84])]) ).
fof(f810,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl90_39
| ~ spl90_49 ),
inference(resolution,[],[f758,f713]) ).
fof(f909,plain,
spl90_83,
inference(avatar_split_clause,[],[f543,f907]) ).
fof(f543,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f542]) ).
fof(f542,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f541]) ).
fof(f541,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,[],[f540]) ).
fof(f540,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,[],[f539]) ).
fof(f539,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,[],[f439]) ).
fof(f439,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,[],[f192]) ).
fof(f192,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,[],[f191]) ).
fof(f191,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,[],[f111]) ).
fof(f111,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(f905,plain,
spl90_82,
inference(avatar_split_clause,[],[f508,f903]) ).
fof(f508,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f507]) ).
fof(f507,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X1,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4
| X1 != X4 ),
inference(equality_resolution,[],[f426]) ).
fof(f426,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,[],[f170]) ).
fof(f170,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,[],[f169]) ).
fof(f169,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,[],[f100]) ).
fof(f100,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(f901,plain,
spl90_81,
inference(avatar_split_clause,[],[f424,f899]) ).
fof(f899,plain,
( spl90_81
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_81])]) ).
fof(f424,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
inference(flattening,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vabs(X0,X1,X2) = vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2,X3,X1,X4,X5] :
( ( ( X3 = X5
& X2 = X4
& X0 = X1 )
=> vabs(X0,X2,X3) = vabs(X1,X4,X5) )
& ( vabs(X0,X2,X3) = vabs(X1,X4,X5)
=> ( X3 = X5
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-abs') ).
fof(f897,plain,
spl90_80,
inference(avatar_split_clause,[],[f423,f895]) ).
fof(f895,plain,
( spl90_80
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_80])]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f893,plain,
spl90_79,
inference(avatar_split_clause,[],[f422,f891]) ).
fof(f891,plain,
( spl90_79
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_79])]) ).
fof(f422,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f168]) ).
fof(f889,plain,
spl90_78,
inference(avatar_split_clause,[],[f420,f887]) ).
fof(f887,plain,
( spl90_78
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_78])]) ).
fof(f420,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
inference(flattening,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
| X2 != X5
| X1 != X4
| X0 != X3 )
& ( ( X2 = X5
& X1 = X4
& X0 = X3 )
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vbind(X0,X1,X2) = vbind(X3,X4,X5) )
& ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X15,X1,X4,X16] :
( ( ( X15 = X16
& X2 = X4
& X0 = X1 )
=> vbind(X0,X2,X15) = vbind(X1,X4,X16) )
& ( vbind(X0,X2,X15) = vbind(X1,X4,X16)
=> ( X15 = X16
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','EQ-bind') ).
fof(f885,plain,
spl90_77,
inference(avatar_split_clause,[],[f419,f883]) ).
fof(f883,plain,
( spl90_77
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_77])]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f881,plain,
spl90_76,
inference(avatar_split_clause,[],[f418,f879]) ).
fof(f879,plain,
( spl90_76
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_76])]) ).
fof(f418,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f166]) ).
fof(f877,plain,
( spl90_75
| ~ spl90_38
| ~ spl90_41 ),
inference(avatar_split_clause,[],[f785,f725,f708,f875]) ).
fof(f875,plain,
( spl90_75
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_75])]) ).
fof(f725,plain,
( spl90_41
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_41])]) ).
fof(f785,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl90_38
| ~ spl90_41 ),
inference(resolution,[],[f726,f709]) ).
fof(f726,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl90_41 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f873,plain,
spl90_74,
inference(avatar_split_clause,[],[f398,f871]) ).
fof(f871,plain,
( spl90_74
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_74])]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f869,plain,
spl90_73,
inference(avatar_split_clause,[],[f395,f867]) ).
fof(f867,plain,
( spl90_73
<=> ! [X0,X3,X2,X1] :
( sK79(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_73])]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( sK79(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f865,plain,
spl90_72,
inference(avatar_split_clause,[],[f394,f863]) ).
fof(f863,plain,
( spl90_72
<=> ! [X0,X3,X2,X1] :
( sK77(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_72])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sK77(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f282]) ).
fof(f861,plain,
spl90_71,
inference(avatar_split_clause,[],[f390,f859]) ).
fof(f859,plain,
( spl90_71
<=> ! [X0,X3,X2,X1] :
( sK74(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_71])]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( sK74(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f857,plain,
spl90_70,
inference(avatar_split_clause,[],[f389,f855]) ).
fof(f855,plain,
( spl90_70
<=> ! [X0,X3,X2,X1] :
( sK75(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_70])]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( sK75(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f853,plain,
spl90_69,
inference(avatar_split_clause,[],[f385,f851]) ).
fof(f851,plain,
( spl90_69
<=> ! [X0,X3,X2,X1] :
( sK69(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_69])]) ).
fof(f385,plain,
! [X2,X3,X0,X1] :
( sK69(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f849,plain,
spl90_68,
inference(avatar_split_clause,[],[f384,f847]) ).
fof(f847,plain,
( spl90_68
<=> ! [X0,X3,X2,X1] :
( sK70(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_68])]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( sK70(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f845,plain,
spl90_67,
inference(avatar_split_clause,[],[f378,f843]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( sK64(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f841,plain,
spl90_66,
inference(avatar_split_clause,[],[f377,f839]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( sK63(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f837,plain,
spl90_65,
inference(avatar_split_clause,[],[f372,f835]) ).
fof(f835,plain,
( spl90_65
<=> ! [X0,X3,X2,X1] :
( sK61(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_65])]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( sK61(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f833,plain,
( spl90_64
| ~ spl90_39
| ~ spl90_41 ),
inference(avatar_split_clause,[],[f784,f725,f712,f831]) ).
fof(f784,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl90_39
| ~ spl90_41 ),
inference(resolution,[],[f726,f713]) ).
fof(f829,plain,
spl90_63,
inference(avatar_split_clause,[],[f371,f827]) ).
fof(f827,plain,
( spl90_63
<=> ! [X0,X3,X2,X1] :
( sK60(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_63])]) ).
fof(f371,plain,
! [X2,X3,X0,X1] :
( sK60(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f825,plain,
spl90_62,
inference(avatar_split_clause,[],[f318,f823]) ).
fof(f823,plain,
( spl90_62
<=> ! [X0,X1] :
( vapp(sK24(X0,X1),sK26(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_62])]) ).
fof(f318,plain,
! [X0,X1] :
( vapp(sK24(X0,X1),sK26(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f821,plain,
spl90_61,
inference(avatar_split_clause,[],[f313,f819]) ).
fof(f313,plain,
! [X0,X1] :
( vapp(sK22(X0,X1),sK21(X0,X1)) = X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visSomeExp(sK23(X0,X1))
& sK23(X0,X1) = vreduce(sK22(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK22(X0,X1)
& vapp(sK22(X0,X1),sK21(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22,sK23])],[f222,f223]) ).
fof(f223,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(sK23(X0,X1))
& sK23(X0,X1) = vreduce(sK22(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK22(X0,X1)
& vapp(sK22(X0,X1),sK21(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f222,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,[],[f221]) ).
fof(f221,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,[],[f200]) ).
fof(f809,plain,
spl90_60,
inference(avatar_split_clause,[],[f521,f807]) ).
fof(f521,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f520]) ).
fof(f520,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f519]) ).
fof(f519,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f518]) ).
fof(f518,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,[],[f433]) ).
fof(f433,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,[],[f180]) ).
fof(f180,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,[],[f179]) ).
fof(f179,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,[],[f105]) ).
fof(f105,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(f805,plain,
spl90_59,
inference(avatar_split_clause,[],[f485,f803]) ).
fof(f485,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f484]) ).
fof(f484,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,vapp(X2,X4))
| X0 != X3 ),
inference(equality_resolution,[],[f413]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,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,[],[f155]) ).
fof(f155,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,[],[f93]) ).
fof(f93,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(f801,plain,
spl90_58,
inference(avatar_split_clause,[],[f363,f799]) ).
fof(f363,plain,
! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,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(f797,plain,
spl90_57,
inference(avatar_split_clause,[],[f358,f795]) ).
fof(f795,plain,
( spl90_57
<=> ! [X2,X0,X1] :
( vsomeType(sK56(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_57])]) ).
fof(f358,plain,
! [X2,X0,X1] :
( vsomeType(sK56(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f793,plain,
spl90_56,
inference(avatar_split_clause,[],[f329,f791]) ).
fof(f791,plain,
( spl90_56
<=> ! [X0,X1] :
( sK33(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_56])]) ).
fof(f329,plain,
! [X0,X1] :
( sK33(X0,X1) = vreduce(sK35(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f789,plain,
spl90_55,
inference(avatar_split_clause,[],[f324,f787]) ).
fof(f787,plain,
( spl90_55
<=> ! [X0,X1] :
( sK30(X0,X1) = vreduce(sK31(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_55])]) ).
fof(f324,plain,
! [X0,X1] :
( sK30(X0,X1) = vreduce(sK31(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f783,plain,
spl90_54,
inference(avatar_split_clause,[],[f320,f781]) ).
fof(f781,plain,
( spl90_54
<=> ! [X0,X1] :
( sK25(X0,X1) = vreduce(sK24(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_54])]) ).
fof(f320,plain,
! [X0,X1] :
( sK25(X0,X1) = vreduce(sK24(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f779,plain,
spl90_53,
inference(avatar_split_clause,[],[f319,f777]) ).
fof(f777,plain,
( spl90_53
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK24(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_53])]) ).
fof(f319,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK24(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f775,plain,
spl90_52,
inference(avatar_split_clause,[],[f315,f773]) ).
fof(f315,plain,
! [X0,X1] :
( sK23(X0,X1) = vreduce(sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f771,plain,
spl90_51,
inference(avatar_split_clause,[],[f314,f769]) ).
fof(f769,plain,
( spl90_51
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK22(X0,X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_51])]) ).
fof(f314,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK22(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f767,plain,
spl90_50,
inference(avatar_split_clause,[],[f310,f765]) ).
fof(f765,plain,
( spl90_50
<=> ! [X0,X1] :
( sK20(X0,X1) = vreduce(sK16(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_50])]) ).
fof(f310,plain,
! [X0,X1] :
( sK20(X0,X1) = vreduce(sK16(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f759,plain,
( spl90_49
| ~ spl90_10
| ~ spl90_39 ),
inference(avatar_split_clause,[],[f719,f712,f595,f757]) ).
fof(f719,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl90_10
| ~ spl90_39 ),
inference(resolution,[],[f713,f596]) ).
fof(f755,plain,
spl90_48,
inference(avatar_split_clause,[],[f369,f753]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,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,[],[f141]) ).
fof(f141,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,[],[f84]) ).
fof(f84,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(f751,plain,
spl90_47,
inference(avatar_split_clause,[],[f368,f749]) ).
fof(f368,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f142]) ).
fof(f747,plain,
spl90_46,
inference(avatar_split_clause,[],[f366,f745]) ).
fof(f366,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,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,[],[f139]) ).
fof(f139,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,[],[f83]) ).
fof(f83,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(f743,plain,
spl90_45,
inference(avatar_split_clause,[],[f365,f741]) ).
fof(f365,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f739,plain,
spl90_44,
inference(avatar_split_clause,[],[f355,f737]) ).
fof(f737,plain,
( spl90_44
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_44])]) ).
fof(f355,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f735,plain,
spl90_43,
inference(avatar_split_clause,[],[f351,f733]) ).
fof(f351,plain,
! [X2,X0,X1] :
( sK51(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f731,plain,
spl90_42,
inference(avatar_split_clause,[],[f533,f729]) ).
fof(f533,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f532]) ).
fof(f532,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f531]) ).
fof(f531,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f530]) ).
fof(f530,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f436]) ).
fof(f436,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,[],[f186]) ).
fof(f186,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,[],[f185]) ).
fof(f185,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,[],[f108]) ).
fof(f108,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(f727,plain,
( spl90_41
| ~ spl90_10
| ~ spl90_38 ),
inference(avatar_split_clause,[],[f718,f708,f595,f725]) ).
fof(f718,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl90_10
| ~ spl90_38 ),
inference(resolution,[],[f709,f596]) ).
fof(f723,plain,
spl90_40,
inference(avatar_split_clause,[],[f503,f721]) ).
fof(f503,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f502]) ).
fof(f502,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f428]) ).
fof(f428,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f170]) ).
fof(f714,plain,
spl90_39,
inference(avatar_split_clause,[],[f489,f712]) ).
fof(f489,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f488]) ).
fof(f488,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f411]) ).
fof(f411,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f156]) ).
fof(f710,plain,
spl90_38,
inference(avatar_split_clause,[],[f487,f708]) ).
fof(f487,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f486]) ).
fof(f486,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f412]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f156]) ).
fof(f706,plain,
spl90_37,
inference(avatar_split_clause,[],[f407,f704]) ).
fof(f407,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f89]) ).
fof(f89,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(f702,plain,
spl90_36,
inference(avatar_split_clause,[],[f304,f700]) ).
fof(f304,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,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(f698,plain,
spl90_35,
inference(avatar_split_clause,[],[f302,f696]) ).
fof(f696,plain,
( spl90_35
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_35])]) ).
fof(f302,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,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(f694,plain,
spl90_34,
inference(avatar_split_clause,[],[f300,f692]) ).
fof(f692,plain,
( spl90_34
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_34])]) ).
fof(f300,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,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(f689,plain,
spl90_33,
inference(avatar_split_clause,[],[f526,f687]) ).
fof(f526,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f525]) ).
fof(f525,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f524]) ).
fof(f524,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f523]) ).
fof(f523,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f522]) ).
fof(f522,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f434]) ).
fof(f434,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,[],[f182]) ).
fof(f182,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,[],[f181]) ).
fof(f181,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,[],[f106]) ).
fof(f106,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(f685,plain,
spl90_32,
inference(avatar_split_clause,[],[f483,f683]) ).
fof(f483,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f482]) ).
fof(f482,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f408]) ).
fof(f408,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,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(f681,plain,
spl90_31,
inference(avatar_split_clause,[],[f478,f679]) ).
fof(f478,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f477]) ).
fof(f477,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f406]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,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(f677,plain,
spl90_30,
inference(avatar_split_clause,[],[f364,f675]) ).
fof(f675,plain,
( spl90_30
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_30])]) ).
fof(f364,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(f673,plain,
spl90_29,
inference(avatar_split_clause,[],[f331,f671]) ).
fof(f671,plain,
( spl90_29
<=> ! [X0,X1] :
( visValue(sK35(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_29])]) ).
fof(f331,plain,
! [X0,X1] :
( visValue(sK35(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f669,plain,
spl90_28,
inference(avatar_split_clause,[],[f330,f667]) ).
fof(f667,plain,
( spl90_28
<=> ! [X0,X1] :
( ~ visSomeExp(sK33(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_28])]) ).
fof(f330,plain,
! [X0,X1] :
( ~ visSomeExp(sK33(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f665,plain,
spl90_27,
inference(avatar_split_clause,[],[f326,f663]) ).
fof(f663,plain,
( spl90_27
<=> ! [X0,X1] :
( ~ visValue(sK31(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_27])]) ).
fof(f326,plain,
! [X0,X1] :
( ~ visValue(sK31(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f661,plain,
spl90_26,
inference(avatar_split_clause,[],[f325,f659]) ).
fof(f659,plain,
( spl90_26
<=> ! [X0,X1] :
( ~ visSomeExp(sK30(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_26])]) ).
fof(f325,plain,
! [X0,X1] :
( ~ visSomeExp(sK30(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f657,plain,
spl90_25,
inference(avatar_split_clause,[],[f321,f655]) ).
fof(f655,plain,
( spl90_25
<=> ! [X0,X1] :
( visSomeExp(sK25(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_25])]) ).
fof(f321,plain,
! [X0,X1] :
( visSomeExp(sK25(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f653,plain,
spl90_24,
inference(avatar_split_clause,[],[f316,f651]) ).
fof(f651,plain,
( spl90_24
<=> ! [X0,X1] :
( ~ visSomeExp(sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_24])]) ).
fof(f316,plain,
! [X0,X1] :
( ~ visSomeExp(sK23(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f649,plain,
spl90_23,
inference(avatar_split_clause,[],[f311,f647]) ).
fof(f647,plain,
( spl90_23
<=> ! [X0,X1] :
( visSomeExp(sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_23])]) ).
fof(f311,plain,
! [X0,X1] :
( visSomeExp(sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f645,plain,
spl90_22,
inference(avatar_split_clause,[],[f506,f643]) ).
fof(f506,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f505]) ).
fof(f505,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f504]) ).
fof(f504,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f427]) ).
fof(f427,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f170]) ).
fof(f641,plain,
spl90_21,
inference(avatar_split_clause,[],[f339,f639]) ).
fof(f339,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f75]) ).
fof(f75,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(f637,plain,
spl90_20,
inference(avatar_split_clause,[],[f338,f635]) ).
fof(f635,plain,
( spl90_20
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_20])]) ).
fof(f338,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f74]) ).
fof(f74,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(f633,plain,
spl90_19,
inference(avatar_split_clause,[],[f327,f631]) ).
fof(f631,plain,
( spl90_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_19])]) ).
fof(f327,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f629,plain,
spl90_18,
inference(avatar_split_clause,[],[f317,f627]) ).
fof(f317,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f625,plain,
spl90_17,
inference(avatar_split_clause,[],[f476,f623]) ).
fof(f476,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f475]) ).
fof(f475,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f474]) ).
fof(f474,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f404]) ).
fof(f404,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,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(f621,plain,
spl90_16,
inference(avatar_split_clause,[],[f473,f619]) ).
fof(f473,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f403]) ).
fof(f403,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,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(f617,plain,
spl90_15,
inference(avatar_split_clause,[],[f460,f615]) ).
fof(f460,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f459]) ).
fof(f459,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f342]) ).
fof(f342,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,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(f613,plain,
spl90_14,
inference(avatar_split_clause,[],[f458,f611]) ).
fof(f611,plain,
( spl90_14
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl90_14])]) ).
fof(f458,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f457]) ).
fof(f457,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f341]) ).
fof(f341,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,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(f609,plain,
spl90_13,
inference(avatar_split_clause,[],[f456,f607]) ).
fof(f607,plain,
( spl90_13
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl90_13])]) ).
fof(f456,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f455]) ).
fof(f455,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f340]) ).
fof(f340,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,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(f605,plain,
spl90_12,
inference(avatar_split_clause,[],[f481,f603]) ).
fof(f481,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f480]) ).
fof(f480,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f405]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f149]) ).
fof(f601,plain,
spl90_11,
inference(avatar_split_clause,[],[f464,f599]) ).
fof(f464,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f362]) ).
fof(f362,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,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(f597,plain,
spl90_10,
inference(avatar_split_clause,[],[f447,f595]) ).
fof(f447,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f306]) ).
fof(f306,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,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(f593,plain,
spl90_9,
inference(avatar_split_clause,[],[f297,f591]) ).
fof(f591,plain,
( spl90_9
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_9])]) ).
fof(f297,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f64]) ).
fof(f64,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(f589,plain,
spl90_8,
inference(avatar_split_clause,[],[f296,f587]) ).
fof(f296,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f63]) ).
fof(f63,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(f585,plain,
spl90_7,
inference(avatar_split_clause,[],[f454,f583]) ).
fof(f454,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f337]) ).
fof(f337,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,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(f581,plain,
spl90_6,
inference(avatar_split_clause,[],[f449,f579]) ).
fof(f579,plain,
( spl90_6
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_6])]) ).
fof(f449,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f308]) ).
fof(f308,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,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(f577,plain,
spl90_5,
inference(avatar_split_clause,[],[f448,f575]) ).
fof(f575,plain,
( spl90_5
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_5])]) ).
fof(f448,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f307]) ).
fof(f307,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,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(f573,plain,
~ spl90_4,
inference(avatar_split_clause,[],[f443,f570]) ).
fof(f443,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,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(f568,plain,
~ spl90_3,
inference(avatar_split_clause,[],[f442,f565]) ).
fof(f565,plain,
( spl90_3
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_3])]) ).
fof(f442,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,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(f562,plain,
spl90_2,
inference(avatar_split_clause,[],[f292,f560]) ).
fof(f560,plain,
( spl90_2
<=> ! [X2] : vsomeExp(X2) != vreduce(vvar(sK15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl90_2])]) ).
fof(f292,plain,
! [X2] : vsomeExp(X2) != vreduce(vvar(sK15)),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
( ! [X2] : vsomeExp(X2) != vreduce(vvar(sK15))
& ~ visValue(vvar(sK15))
& vtcheck(vempty,vvar(sK15),sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f115,f215]) ).
fof(f215,plain,
( ? [X0,X1] :
( ! [X2] : vreduce(vvar(X1)) != vsomeExp(X2)
& ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) )
=> ( ! [X2] : vsomeExp(X2) != vreduce(vvar(sK15))
& ~ visValue(vvar(sK15))
& vtcheck(vempty,vvar(sK15),sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f115,plain,
? [X0,X1] :
( ! [X2] : vreduce(vvar(X1)) != vsomeExp(X2)
& ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
? [X0,X1] :
( ! [X2] : vreduce(vvar(X1)) != vsomeExp(X2)
& ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,plain,
~ ! [X0,X1] :
( ( ~ visValue(vvar(X1))
& vtcheck(vempty,vvar(X1),X0) )
=> ? [X2] : vreduce(vvar(X1)) = vsomeExp(X2) ),
inference(rectify,[],[f58]) ).
fof(f58,negated_conjecture,
~ ! [X14,X8] :
( ( ~ visValue(vvar(X8))
& vtcheck(vempty,vvar(X8),X14) )
=> ? [X34] : vreduce(vvar(X8)) = vsomeExp(X34) ),
inference(negated_conjecture,[],[f57]) ).
fof(f57,conjecture,
! [X14,X8] :
( ( ~ visValue(vvar(X8))
& vtcheck(vempty,vvar(X8),X14) )
=> ? [X34] : vreduce(vvar(X8)) = vsomeExp(X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Progress-T-var') ).
fof(f558,plain,
spl90_1,
inference(avatar_split_clause,[],[f290,f555]) ).
fof(f290,plain,
vtcheck(vempty,vvar(sK15),sK14),
inference(cnf_transformation,[],[f216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : COM149+1 : TPTP v8.1.2. Released v6.4.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 05:03:50 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (1535)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (1538)WARNING: value z3 for option sas not known
% 0.14/0.38 % (1539)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (1536)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (1541)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (1540)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (1537)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (1542)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)
% 0.14/0.38 % (1538)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)
% 0.21/0.44 TRYING [1]
% 0.21/0.45 TRYING [2]
% 0.21/0.53 TRYING [3]
% 1.41/0.57 % (1540)First to succeed.
% 1.55/0.58 % (1540)Refutation found. Thanks to Tanya!
% 1.55/0.58 % SZS status Theorem for theBenchmark
% 1.55/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 1.55/0.59 % (1540)------------------------------
% 1.55/0.59 % (1540)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.55/0.59 % (1540)Termination reason: Refutation
% 1.55/0.59
% 1.55/0.59 % (1540)Memory used [KB]: 3261
% 1.55/0.59 % (1540)Time elapsed: 0.202 s
% 1.55/0.59 % (1540)Instructions burned: 390 (million)
% 1.55/0.59 % (1540)------------------------------
% 1.55/0.59 % (1540)------------------------------
% 1.55/0.59 % (1535)Success in time 0.218 s
%------------------------------------------------------------------------------