TSTP Solution File: COM138+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM138+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 10:47:57 EDT 2024
% Result : Theorem 2.54s 0.74s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 424
% Syntax : Number of formulae : 1513 ( 180 unt; 0 def)
% Number of atoms : 5692 (2460 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 6261 (2082 ~;2890 |; 753 &)
% ( 335 <=>; 201 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 356 ( 354 usr; 336 prp; 0-4 aty)
% Number of functors : 95 ( 95 usr; 8 con; 0-4 aty)
% Number of variables : 4821 (4254 !; 567 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5873,plain,
$false,
inference(avatar_sat_refutation,[],[f553,f558,f563,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,f763,f767,f771,f775,f779,f783,f787,f791,f795,f799,f803,f807,f819,f825,f829,f833,f837,f841,f845,f849,f853,f857,f861,f865,f869,f873,f877,f881,f885,f889,f893,f897,f901,f905,f909,f913,f928,f932,f936,f940,f944,f948,f952,f962,f966,f970,f976,f983,f987,f991,f1000,f1004,f1008,f1015,f1019,f1023,f1027,f1031,f1035,f1039,f1043,f1047,f1051,f1058,f1090,f1094,f1106,f1110,f1116,f1122,f1126,f1130,f1134,f1138,f1142,f1146,f1157,f1161,f1176,f1189,f1193,f1197,f1218,f1222,f1226,f1230,f1234,f1238,f1242,f1257,f1267,f1271,f1275,f1285,f1294,f1308,f1312,f1332,f1344,f1349,f1362,f1366,f1379,f1386,f1392,f1396,f1408,f1413,f1417,f1421,f1425,f1429,f1433,f1442,f1553,f1558,f1562,f1582,f1586,f1600,f1604,f1655,f1659,f1663,f1730,f1734,f1738,f1742,f1747,f1752,f1792,f1806,f1810,f1844,f1858,f1873,f1890,f1896,f1900,f1914,f1918,f1922,f1934,f1954,f1958,f1985,f1989,f1993,f2005,f2014,f2062,f2078,f2082,f2086,f2090,f2113,f2155,f2159,f2163,f2167,f2239,f2243,f2247,f2251,f2326,f2336,f2340,f2344,f2379,f2383,f2393,f2397,f2412,f2416,f2421,f2425,f2436,f2443,f2447,f2474,f2478,f2488,f2492,f2506,f2510,f2523,f2536,f2540,f2549,f2553,f2557,f2561,f2565,f2569,f2716,f2725,f2734,f2738,f2784,f2795,f2799,f2803,f2819,f2823,f2847,f2851,f2936,f2946,f2950,f2978,f2982,f3043,f3047,f3097,f3111,f3138,f3142,f3169,f3183,f3187,f3237,f3330,f3359,f3388,f3422,f3426,f3450,f3454,f3458,f3463,f3646,f3656,f3660,f3665,f3669,f3673,f3677,f3747,f3751,f3755,f3798,f3802,f3806,f3810,f3898,f4094,f4098,f4102,f4157,f4180,f4203,f4209,f4223,f4241,f4249,f4256,f4260,f4365,f4369,f4373,f4377,f4529,f4533,f4537,f4541,f4680,f4763,f4767,f4771,f4775,f4779,f4783,f4788,f4792,f4989,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5053,f5057,f5061,f5870]) ).
fof(f5870,plain,
( ~ spl93_13
| spl93_333 ),
inference(avatar_contradiction_clause,[],[f5865]) ).
fof(f5865,plain,
( $false
| ~ spl93_13
| spl93_333 ),
inference(resolution,[],[f5052,f604]) ).
fof(f604,plain,
( ! [X3] : visFreeVar(X3,vvar(X3))
| ~ spl93_13 ),
inference(avatar_component_clause,[],[f603]) ).
fof(f603,plain,
( spl93_13
<=> ! [X3] : visFreeVar(X3,vvar(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_13])]) ).
fof(f5052,plain,
( ~ visFreeVar(sK14,vvar(sK14))
| spl93_333 ),
inference(avatar_component_clause,[],[f5050]) ).
fof(f5050,plain,
( spl93_333
<=> visFreeVar(sK14,vvar(sK14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_333])]) ).
fof(f5061,plain,
( spl93_335
| ~ spl93_23
| ~ spl93_208 ),
inference(avatar_split_clause,[],[f2127,f2111,f643,f5059]) ).
fof(f5059,plain,
( spl93_335
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK87(vabs(X0,X1,X2)),vabs(X0,X1,X2))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_335])]) ).
fof(f643,plain,
( spl93_23
<=> ! [X4,X5,X0] : ~ visFreeVar(X4,vabs(X4,X0,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_23])]) ).
fof(f2111,plain,
( spl93_208
<=> ! [X0,X3,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK87(vabs(X0,X1,X2)),sK88(vabs(X0,X1,X2)),sK89(vabs(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_208])]) ).
fof(f2127,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK87(vabs(X0,X1,X2)),vabs(X0,X1,X2))
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3)) )
| ~ spl93_23
| ~ spl93_208 ),
inference(superposition,[],[f644,f2112]) ).
fof(f2112,plain,
( ! [X2,X3,X0,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK87(vabs(X0,X1,X2)),sK88(vabs(X0,X1,X2)),sK89(vabs(X0,X1,X2))) )
| ~ spl93_208 ),
inference(avatar_component_clause,[],[f2111]) ).
fof(f644,plain,
( ! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5))
| ~ spl93_23 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f5057,plain,
( spl93_334
| ~ spl93_17
| ~ spl93_193 ),
inference(avatar_split_clause,[],[f1923,f1920,f619,f5055]) ).
fof(f5055,plain,
( spl93_334
<=> ! [X5,X4,X0,X3,X2,X1] : vsomeExp(vsubst(X0,vabs(X1,X2,X3),X4)) = vreduce(vapp(vabs(X0,X5,X4),vabs(X1,X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_334])]) ).
fof(f619,plain,
( spl93_17
<=> ! [X2,X0,X1] : visValue(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_17])]) ).
fof(f1920,plain,
( spl93_193
<=> ! [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,[spl93_193])]) ).
fof(f1923,plain,
( ! [X2,X3,X0,X1,X4,X5] : vsomeExp(vsubst(X0,vabs(X1,X2,X3),X4)) = vreduce(vapp(vabs(X0,X5,X4),vabs(X1,X2,X3)))
| ~ spl93_17
| ~ spl93_193 ),
inference(resolution,[],[f1921,f620]) ).
fof(f620,plain,
( ! [X2,X0,X1] : visValue(vabs(X0,X1,X2))
| ~ spl93_17 ),
inference(avatar_component_clause,[],[f619]) ).
fof(f1921,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ visValue(vabs(X0,X1,X2))
| vsomeExp(vsubst(X3,vabs(X0,X1,X2),X4)) = vreduce(vapp(vabs(X3,X5,X4),vabs(X0,X1,X2))) )
| ~ spl93_193 ),
inference(avatar_component_clause,[],[f1920]) ).
fof(f5053,plain,
( ~ spl93_333
| spl93_1
| ~ spl93_203 ),
inference(avatar_split_clause,[],[f4990,f2071,f550,f5050]) ).
fof(f550,plain,
( spl93_1
<=> visFreeVar(sK14,vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_1])]) ).
fof(f2071,plain,
( spl93_203
<=> sK14 = sK17 ),
introduced(avatar_definition,[new_symbols(naming,[spl93_203])]) ).
fof(f4990,plain,
( ~ visFreeVar(sK14,vvar(sK14))
| spl93_1
| ~ spl93_203 ),
inference(superposition,[],[f552,f2073]) ).
fof(f2073,plain,
( sK14 = sK17
| ~ spl93_203 ),
inference(avatar_component_clause,[],[f2071]) ).
fof(f552,plain,
( ~ visFreeVar(sK14,vvar(sK17))
| spl93_1 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f5048,plain,
( spl93_332
| ~ spl93_162
| ~ spl93_172 ),
inference(avatar_split_clause,[],[f1635,f1602,f1423,f5046]) ).
fof(f5046,plain,
( spl93_332
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vapp(vsubst(X0,X1,X2),vvar(X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X3)))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_332])]) ).
fof(f1423,plain,
( spl93_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,[spl93_162])]) ).
fof(f1602,plain,
( spl93_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,[spl93_172])]) ).
fof(f1635,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vapp(vsubst(X0,X1,X2),vvar(X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X3)))
| X0 = X3 )
| ~ spl93_162
| ~ spl93_172 ),
inference(superposition,[],[f1424,f1603]) ).
fof(f1603,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl93_172 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f1424,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl93_162 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f5044,plain,
( spl93_331
| ~ spl93_163
| ~ spl93_171 ),
inference(avatar_split_clause,[],[f1613,f1598,f1427,f5042]) ).
fof(f5042,plain,
( spl93_331
<=> ! [X4,X0,X3,X2,X1] :
( visFreeVar(X4,vapp(vvar(X2),vsubst(X0,X1,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X2)))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_331])]) ).
fof(f1427,plain,
( spl93_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,[spl93_163])]) ).
fof(f1598,plain,
( spl93_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,[spl93_171])]) ).
fof(f1613,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vapp(vvar(X2),vsubst(X0,X1,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,vvar(X2)))
| X0 = X2 )
| ~ spl93_163
| ~ spl93_171 ),
inference(superposition,[],[f1428,f1599]) ).
fof(f1599,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl93_171 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f1428,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl93_163 ),
inference(avatar_component_clause,[],[f1427]) ).
fof(f5040,plain,
( spl93_330
| ~ spl93_44
| ~ spl93_170 ),
inference(avatar_split_clause,[],[f1593,f1584,f733,f5038]) ).
fof(f5038,plain,
( spl93_330
<=> ! [X0,X1] :
( vempty = X0
| sK54(vlookup(X1,X0),X0,X1) = X1
| sK57(vlookup(X1,X0),X0,X1) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_330])]) ).
fof(f733,plain,
( spl93_44
<=> ! [X2,X0,X1] :
( sK57(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_44])]) ).
fof(f1584,plain,
( spl93_170
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK54(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_170])]) ).
fof(f1593,plain,
( ! [X0,X1] :
( vempty = X0
| sK54(vlookup(X1,X0),X0,X1) = X1
| sK57(vlookup(X1,X0),X0,X1) = X1 )
| ~ spl93_44
| ~ spl93_170 ),
inference(resolution,[],[f1585,f734]) ).
fof(f734,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| sK57(X0,X1,X2) = X2 )
| ~ spl93_44 ),
inference(avatar_component_clause,[],[f733]) ).
fof(f1585,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK54(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl93_170 ),
inference(avatar_component_clause,[],[f1584]) ).
fof(f5036,plain,
( spl93_329
| ~ spl93_42
| ~ spl93_169 ),
inference(avatar_split_clause,[],[f1588,f1580,f725,f5034]) ).
fof(f5034,plain,
( spl93_329
<=> ! [X5,X4,X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X4,X5,vbind(X0,X1,X2)),vvar(X0),X3)
| X0 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_329])]) ).
fof(f725,plain,
( spl93_42
<=> ! [X6,X0,X3] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_42])]) ).
fof(f1580,plain,
( spl93_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,[spl93_169])]) ).
fof(f1588,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X4,X5,vbind(X0,X1,X2)),vvar(X0),X3)
| X0 = X4 )
| ~ spl93_42
| ~ spl93_169 ),
inference(superposition,[],[f1581,f726]) ).
fof(f726,plain,
( ! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0))
| ~ spl93_42 ),
inference(avatar_component_clause,[],[f725]) ).
fof(f1581,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl93_169 ),
inference(avatar_component_clause,[],[f1580]) ).
fof(f5032,plain,
( spl93_328
| ~ spl93_160
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1495,f1419,f1415,f5030]) ).
fof(f5030,plain,
( spl93_328
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X0)))) = vapp(X1,vapp(vsubst(X0,X1,X2),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_328])]) ).
fof(f1415,plain,
( spl93_160
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_160])]) ).
fof(f1419,plain,
( spl93_161
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_161])]) ).
fof(f1495,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(X2,vvar(X0)))) = vapp(X1,vapp(vsubst(X0,X1,X2),X1))
| ~ spl93_160
| ~ spl93_161 ),
inference(superposition,[],[f1416,f1420]) ).
fof(f1420,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl93_161 ),
inference(avatar_component_clause,[],[f1419]) ).
fof(f1416,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl93_160 ),
inference(avatar_component_clause,[],[f1415]) ).
fof(f5028,plain,
( spl93_327
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1484,f1419,f5026]) ).
fof(f5026,plain,
( spl93_327
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_327])]) ).
fof(f1484,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(X2,vvar(X0)),vvar(X0))) = vapp(vapp(vsubst(X0,X1,X2),X1),X1)
| ~ spl93_161 ),
inference(superposition,[],[f1420,f1420]) ).
fof(f5024,plain,
( spl93_326
| ~ spl93_160
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1483,f1419,f1415,f5022]) ).
fof(f5022,plain,
( spl93_326
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),vvar(X0))) = vapp(vapp(X1,vsubst(X0,X1,X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_326])]) ).
fof(f1483,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vapp(vvar(X0),X2),vvar(X0))) = vapp(vapp(X1,vsubst(X0,X1,X2)),X1)
| ~ spl93_160
| ~ spl93_161 ),
inference(superposition,[],[f1420,f1416]) ).
fof(f5020,plain,
( spl93_325
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1447,f1415,f5018]) ).
fof(f5018,plain,
( spl93_325
<=> ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X0),X2))) = vapp(X1,vapp(X1,vsubst(X0,X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_325])]) ).
fof(f1447,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vapp(vvar(X0),X2))) = vapp(X1,vapp(X1,vsubst(X0,X1,X2)))
| ~ spl93_160 ),
inference(superposition,[],[f1416,f1416]) ).
fof(f4989,plain,
( spl93_2
| ~ spl93_310 ),
inference(avatar_split_clause,[],[f4784,f4371,f555]) ).
fof(f555,plain,
( spl93_2
<=> vtcheck(sK16,vvar(sK17),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_2])]) ).
fof(f4371,plain,
( spl93_310
<=> ! [X0] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(sK16,vvar(sK17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_310])]) ).
fof(f4784,plain,
( vtcheck(sK16,vvar(sK17),sK18)
| ~ spl93_310 ),
inference(equality_resolution,[],[f4372]) ).
fof(f4372,plain,
( ! [X0] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(sK16,vvar(sK17),X0) )
| ~ spl93_310 ),
inference(avatar_component_clause,[],[f4371]) ).
fof(f4792,plain,
( spl93_324
| ~ spl93_160
| ~ spl93_163 ),
inference(avatar_split_clause,[],[f1542,f1427,f1415,f4790]) ).
fof(f4790,plain,
( spl93_324
<=> ! [X3,X4,X0,X5,X2,X1] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X1,X0,vapp(vvar(X1),X2))))
| ~ visFreeVar(X3,vsubst(X4,X5,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_324])]) ).
fof(f1542,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X1,X0,vapp(vvar(X1),X2))))
| ~ visFreeVar(X3,vsubst(X4,X5,X0)) )
| ~ spl93_160
| ~ spl93_163 ),
inference(superposition,[],[f1428,f1416]) ).
fof(f4788,plain,
( spl93_323
| ~ spl93_161
| ~ spl93_162 ),
inference(avatar_split_clause,[],[f1528,f1423,f1419,f4786]) ).
fof(f4786,plain,
( spl93_323
<=> ! [X3,X4,X0,X5,X2,X1] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X0,X1,vapp(X2,vvar(X0)))))
| ~ visFreeVar(X3,vsubst(X4,X5,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_323])]) ).
fof(f1528,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X3,vsubst(X4,X5,vsubst(X0,X1,vapp(X2,vvar(X0)))))
| ~ visFreeVar(X3,vsubst(X4,X5,X1)) )
| ~ spl93_161
| ~ spl93_162 ),
inference(superposition,[],[f1424,f1420]) ).
fof(f4783,plain,
( spl93_322
| ~ spl93_60
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1507,f1419,f801,f4781]) ).
fof(f4781,plain,
( spl93_322
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| visFreeVar(X3,vsubst(X0,X1,X2))
| visFreeVar(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_322])]) ).
fof(f801,plain,
( spl93_60
<=> ! [X4,X2,X3] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_60])]) ).
fof(f1507,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| visFreeVar(X3,vsubst(X0,X1,X2))
| visFreeVar(X3,X1) )
| ~ spl93_60
| ~ spl93_161 ),
inference(superposition,[],[f802,f1420]) ).
fof(f802,plain,
( ! [X2,X3,X4] :
( ~ visFreeVar(X3,vapp(X2,X4))
| visFreeVar(X3,X2)
| visFreeVar(X3,X4) )
| ~ spl93_60 ),
inference(avatar_component_clause,[],[f801]) ).
fof(f4779,plain,
( spl93_321
| ~ spl93_60
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1468,f1415,f801,f4777]) ).
fof(f4777,plain,
( spl93_321
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| visFreeVar(X3,X0)
| visFreeVar(X3,vsubst(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_321])]) ).
fof(f1468,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| visFreeVar(X3,X0)
| visFreeVar(X3,vsubst(X1,X0,X2)) )
| ~ spl93_60
| ~ spl93_160 ),
inference(superposition,[],[f802,f1416]) ).
fof(f4775,plain,
( spl93_320
| ~ spl93_39
| ~ spl93_159 ),
inference(avatar_split_clause,[],[f1437,f1411,f708,f4773]) ).
fof(f4773,plain,
( spl93_320
<=> ! [X0,X3,X2,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_320])]) ).
fof(f708,plain,
( spl93_39
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_39])]) ).
fof(f1411,plain,
( spl93_159
<=> ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_159])]) ).
fof(f1437,plain,
( ! [X2,X3,X0,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X3) )
| ~ spl93_39
| ~ spl93_159 ),
inference(resolution,[],[f1412,f709]) ).
fof(f709,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) )
| ~ spl93_39 ),
inference(avatar_component_clause,[],[f708]) ).
fof(f1412,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl93_159 ),
inference(avatar_component_clause,[],[f1411]) ).
fof(f4771,plain,
( spl93_319
| ~ spl93_40
| ~ spl93_159 ),
inference(avatar_split_clause,[],[f1436,f1411,f712,f4769]) ).
fof(f4769,plain,
( spl93_319
<=> ! [X0,X3,X2,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_319])]) ).
fof(f712,plain,
( spl93_40
<=> ! [X4,X2,X3] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_40])]) ).
fof(f1436,plain,
( ! [X2,X3,X0,X1] :
( vgensym(vabs(X0,X1,vapp(X2,X3))) = X0
| ~ visFreeVar(vgensym(vabs(X0,X1,vapp(X2,X3))),X2) )
| ~ spl93_40
| ~ spl93_159 ),
inference(resolution,[],[f1412,f713]) ).
fof(f713,plain,
( ! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) )
| ~ spl93_40 ),
inference(avatar_component_clause,[],[f712]) ).
fof(f4767,plain,
( spl93_318
| ~ spl93_48
| ~ spl93_82 ),
inference(avatar_split_clause,[],[f922,f899,f749,f4765]) ).
fof(f4765,plain,
( spl93_318
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(vgensym(vapp(X0,vabs(X1,X2,X3))),X3)
| vgensym(vapp(X0,vabs(X1,X2,X3))) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_318])]) ).
fof(f749,plain,
( spl93_48
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_48])]) ).
fof(f899,plain,
( spl93_82
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_82])]) ).
fof(f922,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(vgensym(vapp(X0,vabs(X1,X2,X3))),X3)
| vgensym(vapp(X0,vabs(X1,X2,X3))) = X1 )
| ~ spl93_48
| ~ spl93_82 ),
inference(resolution,[],[f900,f750]) ).
fof(f750,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl93_48 ),
inference(avatar_component_clause,[],[f749]) ).
fof(f900,plain,
( ! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 )
| ~ spl93_82 ),
inference(avatar_component_clause,[],[f899]) ).
fof(f4763,plain,
( spl93_317
| ~ spl93_53
| ~ spl93_82 ),
inference(avatar_split_clause,[],[f921,f899,f773,f4761]) ).
fof(f4761,plain,
( spl93_317
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(vgensym(vapp(vabs(X0,X1,X2),X3)),X2)
| vgensym(vapp(vabs(X0,X1,X2),X3)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_317])]) ).
fof(f773,plain,
( spl93_53
<=> ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_53])]) ).
fof(f921,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(vgensym(vapp(vabs(X0,X1,X2),X3)),X2)
| vgensym(vapp(vabs(X0,X1,X2),X3)) = X0 )
| ~ spl93_53
| ~ spl93_82 ),
inference(resolution,[],[f900,f774]) ).
fof(f774,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl93_53 ),
inference(avatar_component_clause,[],[f773]) ).
fof(f4680,plain,
( spl93_316
| ~ spl93_44
| ~ spl93_303 ),
inference(avatar_split_clause,[],[f4245,f4216,f733,f4677]) ).
fof(f4677,plain,
( spl93_316
<=> sK17 = sK57(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_316])]) ).
fof(f4216,plain,
( spl93_303
<=> sP7(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_303])]) ).
fof(f4245,plain,
( sK17 = sK57(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17)
| ~ spl93_44
| ~ spl93_303 ),
inference(resolution,[],[f4218,f734]) ).
fof(f4218,plain,
( sP7(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17)
| ~ spl93_303 ),
inference(avatar_component_clause,[],[f4216]) ).
fof(f4541,plain,
( spl93_315
| ~ spl93_161
| ~ spl93_168 ),
inference(avatar_split_clause,[],[f1575,f1560,f1419,f4539]) ).
fof(f4539,plain,
( spl93_315
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vapp(vsubst(X0,X1,X2),X1)
| vsubst(X0,X1,vvar(X0)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_315])]) ).
fof(f1560,plain,
( spl93_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,[spl93_168])]) ).
fof(f1575,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vapp(vsubst(X0,X1,X2),X1)
| vsubst(X0,X1,vvar(X0)) = X4 )
| ~ spl93_161
| ~ spl93_168 ),
inference(superposition,[],[f1561,f1420]) ).
fof(f1561,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl93_168 ),
inference(avatar_component_clause,[],[f1560]) ).
fof(f4537,plain,
( spl93_314
| ~ spl93_160
| ~ spl93_167 ),
inference(avatar_split_clause,[],[f1566,f1556,f1415,f4535]) ).
fof(f4535,plain,
( spl93_314
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vapp(X1,vsubst(X0,X1,X2))
| vsubst(X0,X1,vvar(X0)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_314])]) ).
fof(f1556,plain,
( spl93_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,[spl93_167])]) ).
fof(f1566,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vapp(X1,vsubst(X0,X1,X2))
| vsubst(X0,X1,vvar(X0)) = X3 )
| ~ spl93_160
| ~ spl93_167 ),
inference(superposition,[],[f1557,f1416]) ).
fof(f1557,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl93_167 ),
inference(avatar_component_clause,[],[f1556]) ).
fof(f4533,plain,
( spl93_313
| ~ spl93_83
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1482,f1419,f903,f4531]) ).
fof(f4531,plain,
( spl93_313
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),vvar(X0))) = vapp(vabs(X0,X2,X3),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_313])]) ).
fof(f903,plain,
( spl93_83
<=> ! [X7,X8,X6,X3] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_83])]) ).
fof(f1482,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),vvar(X0))) = vapp(vabs(X0,X2,X3),X1)
| ~ spl93_83
| ~ spl93_161 ),
inference(superposition,[],[f1420,f904]) ).
fof(f904,plain,
( ! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8))
| ~ spl93_83 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f4529,plain,
( spl93_312
| ~ spl93_83
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1446,f1415,f903,f4527]) ).
fof(f4527,plain,
( spl93_312
<=> ! [X0,X3,X2,X1] : vsubst(X0,X1,vapp(vvar(X0),vabs(X0,X2,X3))) = vapp(X1,vabs(X0,X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_312])]) ).
fof(f1446,plain,
( ! [X2,X3,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vabs(X0,X2,X3))) = vapp(X1,vabs(X0,X2,X3))
| ~ spl93_83
| ~ spl93_160 ),
inference(superposition,[],[f1416,f904]) ).
fof(f4377,plain,
( spl93_311
| ~ spl93_43
| ~ spl93_164 ),
inference(avatar_split_clause,[],[f1549,f1431,f729,f4375]) ).
fof(f4375,plain,
( spl93_311
<=> ! [X0] :
( sP7(vnoType,vempty,X0)
| sK60(X0,vempty,vnoType) = X0
| sK54(vnoType,vempty,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_311])]) ).
fof(f729,plain,
( spl93_43
<=> ! [X2,X0,X1] :
( sK54(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_43])]) ).
fof(f1431,plain,
( spl93_164
<=> ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK60(X0,vempty,vnoType) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_164])]) ).
fof(f1549,plain,
( ! [X0] :
( sP7(vnoType,vempty,X0)
| sK60(X0,vempty,vnoType) = X0
| sK54(vnoType,vempty,X0) = X0 )
| ~ spl93_43
| ~ spl93_164 ),
inference(resolution,[],[f1432,f730]) ).
fof(f730,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| sK54(X0,X1,X2) = X2 )
| ~ spl93_43 ),
inference(avatar_component_clause,[],[f729]) ).
fof(f1432,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK60(X0,vempty,vnoType) = X0 )
| ~ spl93_164 ),
inference(avatar_component_clause,[],[f1431]) ).
fof(f4373,plain,
( spl93_310
| ~ spl93_59
| ~ spl93_204 ),
inference(avatar_split_clause,[],[f4181,f2075,f797,f4371]) ).
fof(f797,plain,
( spl93_59
<=> ! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_59])]) ).
fof(f2075,plain,
( spl93_204
<=> vsomeType(sK18) = vlookup(sK17,sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_204])]) ).
fof(f4181,plain,
( ! [X0] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(sK16,vvar(sK17),X0) )
| ~ spl93_59
| ~ spl93_204 ),
inference(superposition,[],[f798,f2076]) ).
fof(f2076,plain,
( vsomeType(sK18) = vlookup(sK17,sK16)
| ~ spl93_204 ),
inference(avatar_component_clause,[],[f2075]) ).
fof(f798,plain,
( ! [X2,X0,X1] :
( vsomeType(X2) != vlookup(X1,X0)
| vtcheck(X0,vvar(X1),X2) )
| ~ spl93_59 ),
inference(avatar_component_clause,[],[f797]) ).
fof(f4369,plain,
( spl93_309
| ~ spl93_61
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1481,f1419,f805,f4367]) ).
fof(f4367,plain,
( spl93_309
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),vvar(X0))) = vapp(vvar(X2),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_309])]) ).
fof(f805,plain,
( spl93_61
<=> ! [X6,X2,X3] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_61])]) ).
fof(f1481,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),vvar(X0))) = vapp(vvar(X2),X1)
| X0 = X2 )
| ~ spl93_61
| ~ spl93_161 ),
inference(superposition,[],[f1420,f806]) ).
fof(f806,plain,
( ! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 )
| ~ spl93_61 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f4365,plain,
( spl93_308
| ~ spl93_61
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1445,f1415,f805,f4363]) ).
fof(f4363,plain,
( spl93_308
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_308])]) ).
fof(f1445,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 )
| ~ spl93_61
| ~ spl93_160 ),
inference(superposition,[],[f1416,f806]) ).
fof(f4260,plain,
( spl93_307
| ~ spl93_34
| ~ spl93_160
| ~ spl93_172 ),
inference(avatar_split_clause,[],[f1649,f1602,f1415,f687,f4258]) ).
fof(f4258,plain,
( spl93_307
<=> ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_307])]) ).
fof(f687,plain,
( spl93_34
<=> ! [X6,X2] : vsubst(X2,X6,vvar(X2)) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl93_34])]) ).
fof(f1649,plain,
( ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(X1,vvar(X2))
| X0 = X2 )
| ~ spl93_34
| ~ spl93_160
| ~ spl93_172 ),
inference(forward_demodulation,[],[f1628,f688]) ).
fof(f688,plain,
( ! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6
| ~ spl93_34 ),
inference(avatar_component_clause,[],[f687]) ).
fof(f1628,plain,
( ! [X2,X0,X1] :
( vapp(X1,vsubst(X0,X1,vvar(X2))) = vapp(vsubst(X0,X1,vvar(X0)),vvar(X2))
| X0 = X2 )
| ~ spl93_160
| ~ spl93_172 ),
inference(superposition,[],[f1603,f1416]) ).
fof(f4256,plain,
( spl93_306
| ~ spl93_34
| ~ spl93_161
| ~ spl93_171 ),
inference(avatar_split_clause,[],[f1625,f1598,f1419,f687,f4254]) ).
fof(f4254,plain,
( spl93_306
<=> ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),X1)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_306])]) ).
fof(f1625,plain,
( ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),X1)
| X0 = X2 )
| ~ spl93_34
| ~ spl93_161
| ~ spl93_171 ),
inference(forward_demodulation,[],[f1607,f688]) ).
fof(f1607,plain,
( ! [X2,X0,X1] :
( vapp(vsubst(X0,X1,vvar(X2)),X1) = vapp(vvar(X2),vsubst(X0,X1,vvar(X0)))
| X0 = X2 )
| ~ spl93_161
| ~ spl93_171 ),
inference(superposition,[],[f1599,f1420]) ).
fof(f4249,plain,
( spl93_302
| spl93_305
| ~ spl93_192
| ~ spl93_200 ),
inference(avatar_split_clause,[],[f4172,f2002,f1916,f4247,f4212]) ).
fof(f4212,plain,
( spl93_302
<=> vnoType = vsomeType(sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_302])]) ).
fof(f4247,plain,
( spl93_305
<=> ! [X0,X1] :
( sP8(vsomeType(sK18),vbind(X0,X1,vbind(sK14,sK15,sK16)),sK17)
| sK17 = X0
| sP7(vsomeType(sK18),vbind(X0,X1,vbind(sK14,sK15,sK16)),sK17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_305])]) ).
fof(f1916,plain,
( spl93_192
<=> ! [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,[spl93_192])]) ).
fof(f2002,plain,
( spl93_200
<=> vsomeType(sK18) = vlookup(sK17,vbind(sK14,sK15,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_200])]) ).
fof(f4172,plain,
( ! [X0,X1] :
( sP8(vsomeType(sK18),vbind(X0,X1,vbind(sK14,sK15,sK16)),sK17)
| sP7(vsomeType(sK18),vbind(X0,X1,vbind(sK14,sK15,sK16)),sK17)
| vnoType = vsomeType(sK18)
| sK17 = X0 )
| ~ spl93_192
| ~ spl93_200 ),
inference(superposition,[],[f1917,f2004]) ).
fof(f2004,plain,
( vsomeType(sK18) = vlookup(sK17,vbind(sK14,sK15,sK16))
| ~ spl93_200 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f1917,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 )
| ~ spl93_192 ),
inference(avatar_component_clause,[],[f1916]) ).
fof(f4241,plain,
( ~ spl93_9
| ~ spl93_302 ),
inference(avatar_contradiction_clause,[],[f4240]) ).
fof(f4240,plain,
( $false
| ~ spl93_9
| ~ spl93_302 ),
inference(trivial_inequality_removal,[],[f4227]) ).
fof(f4227,plain,
( vnoType != vnoType
| ~ spl93_9
| ~ spl93_302 ),
inference(superposition,[],[f588,f4214]) ).
fof(f4214,plain,
( vnoType = vsomeType(sK18)
| ~ spl93_302 ),
inference(avatar_component_clause,[],[f4212]) ).
fof(f588,plain,
( ! [X0] : vnoType != vsomeType(X0)
| ~ spl93_9 ),
inference(avatar_component_clause,[],[f587]) ).
fof(f587,plain,
( spl93_9
<=> ! [X0] : vnoType != vsomeType(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_9])]) ).
fof(f4223,plain,
( spl93_302
| spl93_303
| spl93_304
| ~ spl93_114
| ~ spl93_200 ),
inference(avatar_split_clause,[],[f4164,f2002,f1088,f4220,f4216,f4212]) ).
fof(f4220,plain,
( spl93_304
<=> sP8(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_304])]) ).
fof(f1088,plain,
( spl93_114
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_114])]) ).
fof(f4164,plain,
( sP8(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17)
| sP7(vsomeType(sK18),vbind(sK14,sK15,sK16),sK17)
| vnoType = vsomeType(sK18)
| ~ spl93_114
| ~ spl93_200 ),
inference(superposition,[],[f1089,f2004]) ).
fof(f1089,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl93_114 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f4209,plain,
( spl93_301
| ~ spl93_169
| ~ spl93_200 ),
inference(avatar_split_clause,[],[f4166,f2002,f1580,f4207]) ).
fof(f4207,plain,
( spl93_301
<=> ! [X2,X0,X1] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(vbind(X1,X2,vbind(sK14,sK15,sK16)),vvar(sK17),X0)
| sK17 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_301])]) ).
fof(f4166,plain,
( ! [X2,X0,X1] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(vbind(X1,X2,vbind(sK14,sK15,sK16)),vvar(sK17),X0)
| sK17 = X1 )
| ~ spl93_169
| ~ spl93_200 ),
inference(superposition,[],[f1581,f2004]) ).
fof(f4203,plain,
( spl93_300
| ~ spl93_59
| ~ spl93_200 ),
inference(avatar_split_clause,[],[f4161,f2002,f797,f4201]) ).
fof(f4201,plain,
( spl93_300
<=> ! [X0] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_300])]) ).
fof(f4161,plain,
( ! [X0] :
( vsomeType(X0) != vsomeType(sK18)
| vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),X0) )
| ~ spl93_59
| ~ spl93_200 ),
inference(superposition,[],[f798,f2004]) ).
fof(f4180,plain,
( spl93_203
| spl93_204
| ~ spl93_92
| ~ spl93_200 ),
inference(avatar_split_clause,[],[f4159,f2002,f950,f2075,f2071]) ).
fof(f950,plain,
( spl93_92
<=> ! [X5,X0,X6,X1] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_92])]) ).
fof(f4159,plain,
( vsomeType(sK18) = vlookup(sK17,sK16)
| sK14 = sK17
| ~ spl93_92
| ~ spl93_200 ),
inference(superposition,[],[f2004,f951]) ).
fof(f951,plain,
( ! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 )
| ~ spl93_92 ),
inference(avatar_component_clause,[],[f950]) ).
fof(f4157,plain,
~ spl93_296,
inference(avatar_contradiction_clause,[],[f4156]) ).
fof(f4156,plain,
( $false
| ~ spl93_296 ),
inference(equality_resolution,[],[f3897]) ).
fof(f3897,plain,
( ! [X0] : vvar(X0) != vvar(sK17)
| ~ spl93_296 ),
inference(avatar_component_clause,[],[f3896]) ).
fof(f3896,plain,
( spl93_296
<=> ! [X0] : vvar(X0) != vvar(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_296])]) ).
fof(f4102,plain,
( spl93_299
| ~ spl93_49
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1504,f1419,f753,f4100]) ).
fof(f4100,plain,
( spl93_299
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vsubst(X0,X1,vapp(X2,vvar(X0)))
| X1 = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_299])]) ).
fof(f753,plain,
( spl93_49
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_49])]) ).
fof(f1504,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vsubst(X0,X1,vapp(X2,vvar(X0)))
| X1 = X4 )
| ~ spl93_49
| ~ spl93_161 ),
inference(superposition,[],[f754,f1420]) ).
fof(f754,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X1 = X3 )
| ~ spl93_49 ),
inference(avatar_component_clause,[],[f753]) ).
fof(f4098,plain,
( spl93_298
| ~ spl93_47
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1462,f1415,f745,f4096]) ).
fof(f4096,plain,
( spl93_298
<=> ! [X4,X0,X3,X2,X1] :
( vapp(X3,X4) != vsubst(X1,X0,vapp(vvar(X1),X2))
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_298])]) ).
fof(f745,plain,
( spl93_47
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_47])]) ).
fof(f1462,plain,
( ! [X2,X3,X0,X1,X4] :
( vapp(X3,X4) != vsubst(X1,X0,vapp(vvar(X1),X2))
| X0 = X3 )
| ~ spl93_47
| ~ spl93_160 ),
inference(superposition,[],[f746,f1416]) ).
fof(f746,plain,
( ! [X2,X3,X0,X1] :
( vapp(X0,X1) != vapp(X2,X3)
| X0 = X2 )
| ~ spl93_47 ),
inference(avatar_component_clause,[],[f745]) ).
fof(f4094,plain,
( spl93_297
| ~ spl93_112
| ~ spl93_157 ),
inference(avatar_split_clause,[],[f1404,f1394,f1049,f4092]) ).
fof(f4092,plain,
( spl93_297
<=> ! [X5,X6,X4,X0,X8,X7,X3,X2,X1] : vabs(X6,X7,X8) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_297])]) ).
fof(f1049,plain,
( spl93_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,[spl93_112])]) ).
fof(f1394,plain,
( spl93_157
<=> ! [X5,X4,X2,X0,X6,X3,X1] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_157])]) ).
fof(f1404,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : vabs(X6,X7,X8) != vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))
| ~ spl93_112
| ~ spl93_157 ),
inference(superposition,[],[f1395,f1050]) ).
fof(f1050,plain,
( ! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7))
| ~ spl93_112 ),
inference(avatar_component_clause,[],[f1049]) ).
fof(f1395,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl93_157 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f3898,plain,
( spl93_296
| ~ spl93_22
| ~ spl93_188 ),
inference(avatar_split_clause,[],[f3766,f1887,f639,f3896]) ).
fof(f639,plain,
( spl93_22
<=> ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_22])]) ).
fof(f1887,plain,
( spl93_188
<=> vvar(sK17) = vapp(sK44(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK45(vbind(sK14,sK15,sK16),sK18,vvar(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_188])]) ).
fof(f3766,plain,
( ! [X0] : vvar(X0) != vvar(sK17)
| ~ spl93_22
| ~ spl93_188 ),
inference(superposition,[],[f640,f1889]) ).
fof(f1889,plain,
( vvar(sK17) = vapp(sK44(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK45(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_188 ),
inference(avatar_component_clause,[],[f1887]) ).
fof(f640,plain,
( ! [X2,X0,X1] : vvar(X0) != vapp(X1,X2)
| ~ spl93_22 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f3810,plain,
( spl93_295
| ~ spl93_39
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1499,f1419,f708,f3808]) ).
fof(f3808,plain,
( spl93_295
<=> ! [X0,X3,X2,X1] :
( visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| ~ visFreeVar(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_295])]) ).
fof(f1499,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(X3,vsubst(X0,X1,vapp(X2,vvar(X0))))
| ~ visFreeVar(X3,X1) )
| ~ spl93_39
| ~ spl93_161 ),
inference(superposition,[],[f709,f1420]) ).
fof(f3806,plain,
( spl93_294
| ~ spl93_40
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1461,f1415,f712,f3804]) ).
fof(f3804,plain,
( spl93_294
<=> ! [X0,X3,X2,X1] :
( visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| ~ visFreeVar(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_294])]) ).
fof(f1461,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(X3,vsubst(X1,X0,vapp(vvar(X1),X2)))
| ~ visFreeVar(X3,X0) )
| ~ spl93_40
| ~ spl93_160 ),
inference(superposition,[],[f713,f1416]) ).
fof(f3802,plain,
( spl93_293
| ~ spl93_34
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1444,f1415,f687,f3800]) ).
fof(f3800,plain,
( spl93_293
<=> ! [X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vvar(X0))) = vapp(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_293])]) ).
fof(f1444,plain,
( ! [X0,X1] : vsubst(X0,X1,vapp(vvar(X0),vvar(X0))) = vapp(X1,X1)
| ~ spl93_34
| ~ spl93_160 ),
inference(superposition,[],[f1416,f688]) ).
fof(f3798,plain,
( spl93_292
| ~ spl93_112
| ~ spl93_155 ),
inference(avatar_split_clause,[],[f1388,f1384,f1049,f3796]) ).
fof(f3796,plain,
( spl93_292
<=> ! [X5,X6,X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_292])]) ).
fof(f1384,plain,
( spl93_155
<=> ! [X4,X0,X3,X2,X1] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_155])]) ).
fof(f1388,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vvar(X4) != vsubst(X5,X6,vsubst(X0,X1,vapp(X2,X3)))
| ~ spl93_112
| ~ spl93_155 ),
inference(superposition,[],[f1385,f1050]) ).
fof(f1385,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl93_155 ),
inference(avatar_component_clause,[],[f1384]) ).
fof(f3755,plain,
( ~ spl93_8
| ~ spl93_286 ),
inference(avatar_contradiction_clause,[],[f3752]) ).
fof(f3752,plain,
( $false
| ~ spl93_8
| ~ spl93_286 ),
inference(resolution,[],[f3664,f584]) ).
fof(f584,plain,
( ! [X0] : ~ visValue(vvar(X0))
| ~ spl93_8 ),
inference(avatar_component_clause,[],[f583]) ).
fof(f583,plain,
( spl93_8
<=> ! [X0] : ~ visValue(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_8])]) ).
fof(f3664,plain,
( visValue(vvar(sK17))
| ~ spl93_286 ),
inference(avatar_component_clause,[],[f3662]) ).
fof(f3662,plain,
( spl93_286
<=> visValue(vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_286])]) ).
fof(f3751,plain,
( spl93_291
| ~ spl93_53
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1081,f1049,f773,f3749]) ).
fof(f3749,plain,
( spl93_291
<=> ! [X0,X3,X2,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_291])]) ).
fof(f1081,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X2))
| ~ spl93_53
| ~ spl93_112 ),
inference(superposition,[],[f774,f1050]) ).
fof(f3747,plain,
( spl93_290
| ~ spl93_48
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1078,f1049,f749,f3745]) ).
fof(f3745,plain,
( spl93_290
<=> ! [X0,X3,X2,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_290])]) ).
fof(f1078,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,X3))),vsubst(X0,X1,X3))
| ~ spl93_48
| ~ spl93_112 ),
inference(superposition,[],[f750,f1050]) ).
fof(f3677,plain,
( spl93_289
| ~ spl93_17
| ~ spl93_184 ),
inference(avatar_split_clause,[],[f1819,f1808,f619,f3675]) ).
fof(f3675,plain,
( spl93_289
<=> ! [X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vvar(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_289])]) ).
fof(f1808,plain,
( spl93_184
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK87(vvar(X0)),sK88(vvar(X0)),sK89(vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_184])]) ).
fof(f1819,plain,
( ! [X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vvar(X0),X1)) )
| ~ spl93_17
| ~ spl93_184 ),
inference(superposition,[],[f620,f1809]) ).
fof(f1809,plain,
( ! [X0,X1] :
( vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK87(vvar(X0)),sK88(vvar(X0)),sK89(vvar(X0))) )
| ~ spl93_184 ),
inference(avatar_component_clause,[],[f1808]) ).
fof(f3673,plain,
( spl93_288
| ~ spl93_8
| ~ spl93_166 ),
inference(avatar_split_clause,[],[f1554,f1551,f583,f3671]) ).
fof(f3671,plain,
( spl93_288
<=> ! [X2,X0,X1,X3] : vnoExp = vreduce(vapp(vabs(X0,X1,X2),vvar(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_288])]) ).
fof(f1551,plain,
( spl93_166
<=> ! [X2,X0,X1,X3] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_166])]) ).
fof(f1554,plain,
( ! [X2,X3,X0,X1] : vnoExp = vreduce(vapp(vabs(X0,X1,X2),vvar(X3)))
| ~ spl93_8
| ~ spl93_166 ),
inference(resolution,[],[f1552,f584]) ).
fof(f1552,plain,
( ! [X2,X3,X0,X1] :
( visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl93_166 ),
inference(avatar_component_clause,[],[f1551]) ).
fof(f3669,plain,
( spl93_287
| ~ spl93_48
| ~ spl93_161 ),
inference(avatar_split_clause,[],[f1503,f1419,f749,f3667]) ).
fof(f3667,plain,
( spl93_287
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,vvar(X0)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_287])]) ).
fof(f1503,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X0,X1,vapp(X2,vvar(X0)))),X1)
| ~ spl93_48
| ~ spl93_161 ),
inference(superposition,[],[f750,f1420]) ).
fof(f3665,plain,
( spl93_286
| ~ spl93_17
| ~ spl93_282 ),
inference(avatar_split_clause,[],[f3606,f3460,f619,f3662]) ).
fof(f3460,plain,
( spl93_282
<=> vvar(sK17) = vabs(sK47(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK48(vbind(sK14,sK15,sK16),sK18,vvar(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_282])]) ).
fof(f3606,plain,
( visValue(vvar(sK17))
| ~ spl93_17
| ~ spl93_282 ),
inference(superposition,[],[f620,f3462]) ).
fof(f3462,plain,
( vvar(sK17) = vabs(sK47(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK48(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_282 ),
inference(avatar_component_clause,[],[f3460]) ).
fof(f3660,plain,
( spl93_285
| ~ spl93_53
| ~ spl93_160 ),
inference(avatar_split_clause,[],[f1467,f1415,f773,f3658]) ).
fof(f3658,plain,
( spl93_285
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X1,X0,vapp(vvar(X1),X2))),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_285])]) ).
fof(f1467,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vsubst(X1,X0,vapp(vvar(X1),X2))),X0)
| ~ spl93_53
| ~ spl93_160 ),
inference(superposition,[],[f774,f1416]) ).
fof(f3656,plain,
( spl93_284
| ~ spl93_112
| ~ spl93_118 ),
inference(avatar_split_clause,[],[f1147,f1114,f1049,f3654]) ).
fof(f3654,plain,
( spl93_284
<=> ! [X5,X4,X0,X3,X2,X1] : ~ visValue(vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_284])]) ).
fof(f1114,plain,
( spl93_118
<=> ! [X2,X0,X1,X3] : ~ visValue(vsubst(X0,X1,vapp(X2,X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_118])]) ).
fof(f1147,plain,
( ! [X2,X3,X0,X1,X4,X5] : ~ visValue(vsubst(X4,X5,vsubst(X0,X1,vapp(X2,X3))))
| ~ spl93_112
| ~ spl93_118 ),
inference(superposition,[],[f1115,f1050]) ).
fof(f1115,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl93_118 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f3646,plain,
( spl93_283
| ~ spl93_158 ),
inference(avatar_split_clause,[],[f1409,f1406,f3644]) ).
fof(f3644,plain,
( spl93_283
<=> ! [X2,X0,X1] : vtcheck(vbind(X0,X1,X2),vvar(X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_283])]) ).
fof(f1406,plain,
( spl93_158
<=> ! [X0,X3,X2,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_158])]) ).
fof(f1409,plain,
( ! [X2,X0,X1] : vtcheck(vbind(X0,X1,X2),vvar(X0),X1)
| ~ spl93_158 ),
inference(equality_resolution,[],[f1407]) ).
fof(f1407,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl93_158 ),
inference(avatar_component_clause,[],[f1406]) ).
fof(f3463,plain,
( spl93_282
| ~ spl93_122
| ~ spl93_131 ),
inference(avatar_split_clause,[],[f1380,f1186,f1132,f3460]) ).
fof(f1132,plain,
( spl93_122
<=> ! [X2,X0,X1] :
( vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_122])]) ).
fof(f1186,plain,
( spl93_131
<=> sP5(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_131])]) ).
fof(f1380,plain,
( vvar(sK17) = vabs(sK47(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK48(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_122
| ~ spl93_131 ),
inference(resolution,[],[f1188,f1133]) ).
fof(f1133,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X2 )
| ~ spl93_122 ),
inference(avatar_component_clause,[],[f1132]) ).
fof(f1188,plain,
( sP5(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| ~ spl93_131 ),
inference(avatar_component_clause,[],[f1186]) ).
fof(f3458,plain,
( spl93_281
| ~ spl93_112
| ~ spl93_153 ),
inference(avatar_split_clause,[],[f1374,f1364,f1049,f3456]) ).
fof(f3456,plain,
( spl93_281
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,vvar(sK17),vapp(vabs(sK14,X1,X2),X3)) = vapp(vabs(sK14,X1,vsubst(X0,vvar(sK17),X2)),vsubst(X0,vvar(sK17),X3))
| sK14 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_281])]) ).
fof(f1364,plain,
( spl93_153
<=> ! [X2,X0,X1] :
( vabs(sK14,X0,vsubst(X1,vvar(sK17),X2)) = vsubst(X1,vvar(sK17),vabs(sK14,X0,X2))
| sK14 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_153])]) ).
fof(f1374,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,vvar(sK17),vapp(vabs(sK14,X1,X2),X3)) = vapp(vabs(sK14,X1,vsubst(X0,vvar(sK17),X2)),vsubst(X0,vvar(sK17),X3))
| sK14 = X0 )
| ~ spl93_112
| ~ spl93_153 ),
inference(superposition,[],[f1050,f1365]) ).
fof(f1365,plain,
( ! [X2,X0,X1] :
( vabs(sK14,X0,vsubst(X1,vvar(sK17),X2)) = vsubst(X1,vvar(sK17),vabs(sK14,X0,X2))
| sK14 = X1 )
| ~ spl93_153 ),
inference(avatar_component_clause,[],[f1364]) ).
fof(f3454,plain,
( spl93_280
| ~ spl93_112
| ~ spl93_153 ),
inference(avatar_split_clause,[],[f1373,f1364,f1049,f3452]) ).
fof(f3452,plain,
( spl93_280
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,vvar(sK17),vapp(X3,vabs(sK14,X1,X2))) = vapp(vsubst(X0,vvar(sK17),X3),vabs(sK14,X1,vsubst(X0,vvar(sK17),X2)))
| sK14 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_280])]) ).
fof(f1373,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,vvar(sK17),vapp(X3,vabs(sK14,X1,X2))) = vapp(vsubst(X0,vvar(sK17),X3),vabs(sK14,X1,vsubst(X0,vvar(sK17),X2)))
| sK14 = X0 )
| ~ spl93_112
| ~ spl93_153 ),
inference(superposition,[],[f1050,f1365]) ).
fof(f3450,plain,
( spl93_279
| ~ spl93_160
| ~ spl93_268 ),
inference(avatar_split_clause,[],[f3270,f3136,f1415,f3448]) ).
fof(f3448,plain,
( spl93_279
<=> ! [X0,X3,X2,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(sK17))) = vapp(X1,vvar(sK17))
| X0 = X2
| vvar(sK17) = vsubst(X2,X3,vvar(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_279])]) ).
fof(f3136,plain,
( spl93_268
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| vvar(sK17) = vsubst(X1,X2,vvar(sK17))
| vvar(sK17) = vsubst(X0,X3,vvar(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_268])]) ).
fof(f3270,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X0),vvar(sK17))) = vapp(X1,vvar(sK17))
| X0 = X2
| vvar(sK17) = vsubst(X2,X3,vvar(sK17)) )
| ~ spl93_160
| ~ spl93_268 ),
inference(superposition,[],[f1416,f3137]) ).
fof(f3137,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| vvar(sK17) = vsubst(X1,X2,vvar(sK17))
| vvar(sK17) = vsubst(X0,X3,vvar(sK17)) )
| ~ spl93_268 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f3426,plain,
( spl93_278
| spl93_1
| ~ spl93_201 ),
inference(avatar_split_clause,[],[f2056,f2012,f550,f3424]) ).
fof(f3424,plain,
( spl93_278
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK14,X0)
| sK14 = X1
| vabs(sK14,X2,vsubst(X1,vapp(vvar(sK17),X0),X3)) = vsubst(X1,vapp(vvar(sK17),X0),vabs(sK14,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_278])]) ).
fof(f2012,plain,
( spl93_201
<=> ! [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,[spl93_201])]) ).
fof(f2056,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(sK14,X0)
| sK14 = X1
| vabs(sK14,X2,vsubst(X1,vapp(vvar(sK17),X0),X3)) = vsubst(X1,vapp(vvar(sK17),X0),vabs(sK14,X2,X3)) )
| spl93_1
| ~ spl93_201 ),
inference(resolution,[],[f2013,f552]) ).
fof(f2013,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X0,X4)
| visFreeVar(X0,X3)
| X0 = X2
| vabs(X0,X1,vsubst(X2,vapp(X3,X4),X5)) = vsubst(X2,vapp(X3,X4),vabs(X0,X1,X5)) )
| ~ spl93_201 ),
inference(avatar_component_clause,[],[f2012]) ).
fof(f3422,plain,
( spl93_277
| spl93_1
| ~ spl93_201 ),
inference(avatar_split_clause,[],[f2040,f2012,f550,f3420]) ).
fof(f3420,plain,
( spl93_277
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK14,X0)
| sK14 = X1
| vabs(sK14,X2,vsubst(X1,vapp(X0,vvar(sK17)),X3)) = vsubst(X1,vapp(X0,vvar(sK17)),vabs(sK14,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_277])]) ).
fof(f2040,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(sK14,X0)
| sK14 = X1
| vabs(sK14,X2,vsubst(X1,vapp(X0,vvar(sK17)),X3)) = vsubst(X1,vapp(X0,vvar(sK17)),vabs(sK14,X2,X3)) )
| spl93_1
| ~ spl93_201 ),
inference(resolution,[],[f2013,f552]) ).
fof(f3388,plain,
( spl93_276
| spl93_1
| ~ spl93_196 ),
inference(avatar_split_clause,[],[f1979,f1956,f550,f3386]) ).
fof(f3386,plain,
( spl93_276
<=> ! [X2,X4,X0,X3,X1] :
( sK14 = X0
| vabs(sK14,X1,vsubst(X0,vabs(X2,X3,vvar(sK17)),X4)) = vsubst(X0,vabs(X2,X3,vvar(sK17)),vabs(sK14,X1,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_276])]) ).
fof(f1956,plain,
( spl93_196
<=> ! [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,[spl93_196])]) ).
fof(f1979,plain,
( ! [X2,X3,X0,X1,X4] :
( sK14 = X0
| vabs(sK14,X1,vsubst(X0,vabs(X2,X3,vvar(sK17)),X4)) = vsubst(X0,vabs(X2,X3,vvar(sK17)),vabs(sK14,X1,X4)) )
| spl93_1
| ~ spl93_196 ),
inference(resolution,[],[f1957,f552]) ).
fof(f1957,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( visFreeVar(X0,X5)
| X0 = X2
| vabs(X0,X1,vsubst(X2,vabs(X3,X4,X5),X6)) = vsubst(X2,vabs(X3,X4,X5),vabs(X0,X1,X6)) )
| ~ spl93_196 ),
inference(avatar_component_clause,[],[f1956]) ).
fof(f3359,plain,
( spl93_275
| ~ spl93_146
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1350,f1347,f1292,f3357]) ).
fof(f3357,plain,
( spl93_275
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_275])]) ).
fof(f1292,plain,
( spl93_146
<=> ! [X0,X3,X2,X1] :
( vsubst(sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3),vabs(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vsubst(sK69(X0,X1,X2,X3),vvar(sK70(X0,X1,X2,X3)),sK71(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_146])]) ).
fof(f1347,plain,
( spl93_151
<=> ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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,[spl93_151])]) ).
fof(f1350,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_146
| ~ spl93_151 ),
inference(resolution,[],[f1348,f1293]) ).
fof(f1293,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| vsubst(sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3),vabs(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vsubst(sK69(X0,X1,X2,X3),vvar(sK70(X0,X1,X2,X3)),sK71(X0,X1,X2,X3)))) = X0 )
| ~ spl93_146 ),
inference(avatar_component_clause,[],[f1292]) ).
fof(f1348,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(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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) )
| ~ spl93_151 ),
inference(avatar_component_clause,[],[f1347]) ).
fof(f3330,plain,
( spl93_274
| ~ spl93_146
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1333,f1330,f1292,f3328]) ).
fof(f3328,plain,
( spl93_274
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_274])]) ).
fof(f1330,plain,
( spl93_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)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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,[spl93_149])]) ).
fof(f1333,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_146
| ~ spl93_149 ),
inference(resolution,[],[f1331,f1293]) ).
fof(f1331,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(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl93_149 ),
inference(avatar_component_clause,[],[f1330]) ).
fof(f3237,plain,
( spl93_273
| ~ spl93_142
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1351,f1347,f1265,f3235]) ).
fof(f3235,plain,
( spl93_273
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_273])]) ).
fof(f1265,plain,
( spl93_142
<=> ! [X0,X3,X2,X1] :
( sK70(X0,X1,X2,X3) = vgensym(vapp(vapp(sK67(X0,X1,X2,X3),sK71(X0,X1,X2,X3)),vvar(sK66(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_142])]) ).
fof(f1351,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_142
| ~ spl93_151 ),
inference(resolution,[],[f1348,f1266]) ).
fof(f1266,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK70(X0,X1,X2,X3) = vgensym(vapp(vapp(sK67(X0,X1,X2,X3),sK71(X0,X1,X2,X3)),vvar(sK66(X0,X1,X2,X3)))) )
| ~ spl93_142 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f3187,plain,
( spl93_272
| ~ spl93_146
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1321,f1310,f1292,f3185]) ).
fof(f3185,plain,
( spl93_272
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_272])]) ).
fof(f1310,plain,
( spl93_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)
| sK84(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,[spl93_148])]) ).
fof(f1321,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_146
| ~ spl93_148 ),
inference(resolution,[],[f1311,f1293]) ).
fof(f1311,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)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl93_148 ),
inference(avatar_component_clause,[],[f1310]) ).
fof(f3183,plain,
( spl93_271
| ~ spl93_146
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1313,f1306,f1292,f3181]) ).
fof(f3181,plain,
( spl93_271
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_271])]) ).
fof(f1306,plain,
( spl93_147
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_147])]) ).
fof(f1313,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK66(vsubst(X0,X1,X2),X2,X1,X0),sK67(vsubst(X0,X1,X2),X2,X1,X0),vabs(sK70(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),vsubst(sK69(vsubst(X0,X1,X2),X2,X1,X0),vvar(sK70(vsubst(X0,X1,X2),X2,X1,X0)),sK71(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_146
| ~ spl93_147 ),
inference(resolution,[],[f1307,f1293]) ).
fof(f1307,plain,
( ! [X2,X0,X1] :
( sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl93_147 ),
inference(avatar_component_clause,[],[f1306]) ).
fof(f3169,plain,
( spl93_270
| ~ spl93_83
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1357,f1347,f903,f3167]) ).
fof(f3167,plain,
( spl93_270
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vsubst(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),vapp(sK83(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3))))
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_270])]) ).
fof(f1357,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vsubst(sK84(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),vapp(sK83(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3))))
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl93_83
| ~ spl93_151 ),
inference(superposition,[],[f1348,f904]) ).
fof(f3142,plain,
( spl93_269
| ~ spl93_136
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1352,f1347,f1224,f3140]) ).
fof(f3140,plain,
( spl93_269
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_269])]) ).
fof(f1224,plain,
( spl93_136
<=> ! [X0,X3,X2,X1] :
( vabs(sK69(X0,X1,X2,X3),sK68(X0,X1,X2,X3),sK71(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_136])]) ).
fof(f1352,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl93_136
| ~ spl93_151 ),
inference(resolution,[],[f1348,f1225]) ).
fof(f1225,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| vabs(sK69(X0,X1,X2,X3),sK68(X0,X1,X2,X3),sK71(X0,X1,X2,X3)) = X1 )
| ~ spl93_136 ),
inference(avatar_component_clause,[],[f1224]) ).
fof(f3138,plain,
( spl93_268
| ~ spl93_252 ),
inference(avatar_split_clause,[],[f2853,f2793,f3136]) ).
fof(f2793,plain,
( spl93_252
<=> ! [X0,X1] :
( vvar(sK17) = vsubst(X0,X1,vvar(sK17))
| sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_252])]) ).
fof(f2853,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| vvar(sK17) = vsubst(X1,X2,vvar(sK17))
| vvar(sK17) = vsubst(X0,X3,vvar(sK17)) )
| ~ spl93_252 ),
inference(superposition,[],[f2794,f2794]) ).
fof(f2794,plain,
( ! [X0,X1] :
( vvar(sK17) = vsubst(X0,X1,vvar(sK17))
| sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) = X0 )
| ~ spl93_252 ),
inference(avatar_component_clause,[],[f2793]) ).
fof(f3111,plain,
( spl93_267
| ~ spl93_142
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1334,f1330,f1265,f3109]) ).
fof(f3109,plain,
( spl93_267
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_267])]) ).
fof(f1334,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_142
| ~ spl93_149 ),
inference(resolution,[],[f1331,f1266]) ).
fof(f3097,plain,
( spl93_266
| ~ spl93_83
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1340,f1330,f903,f3095]) ).
fof(f3095,plain,
( spl93_266
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| vabs(X0,X2,X3) = vapp(sK83(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)))
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_266])]) ).
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)
| vabs(X0,X2,X3) = vapp(sK83(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)),sK86(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)))
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl93_83
| ~ spl93_149 ),
inference(superposition,[],[f1331,f904]) ).
fof(f3047,plain,
( spl93_265
| ~ spl93_66
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1354,f1347,f835,f3045]) ).
fof(f3045,plain,
( spl93_265
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_265])]) ).
fof(f835,plain,
( spl93_66
<=> ! [X0,X3,X2,X1] :
( sK66(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_66])]) ).
fof(f1354,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl93_66
| ~ spl93_151 ),
inference(resolution,[],[f1348,f836]) ).
fof(f836,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK66(X0,X1,X2,X3) = X3 )
| ~ spl93_66 ),
inference(avatar_component_clause,[],[f835]) ).
fof(f3043,plain,
( spl93_264
| ~ spl93_67
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1353,f1347,f839,f3041]) ).
fof(f3041,plain,
( spl93_264
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_264])]) ).
fof(f839,plain,
( spl93_67
<=> ! [X0,X3,X2,X1] :
( sK67(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_67])]) ).
fof(f1353,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl93_67
| ~ spl93_151 ),
inference(resolution,[],[f1348,f840]) ).
fof(f840,plain,
( ! [X2,X3,X0,X1] :
( ~ sP12(X0,X1,X2,X3)
| sK67(X0,X1,X2,X3) = X2 )
| ~ spl93_67 ),
inference(avatar_component_clause,[],[f839]) ).
fof(f2982,plain,
( spl93_263
| ~ spl93_142
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1322,f1310,f1265,f2980]) ).
fof(f2980,plain,
( spl93_263
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_263])]) ).
fof(f1322,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_142
| ~ spl93_148 ),
inference(resolution,[],[f1311,f1266]) ).
fof(f2978,plain,
( spl93_262
| ~ spl93_142
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1314,f1306,f1265,f2976]) ).
fof(f2976,plain,
( spl93_262
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_262])]) ).
fof(f1314,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK70(vsubst(X0,X1,X2),X2,X1,X0) = vgensym(vapp(vapp(sK67(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)),vvar(sK66(vsubst(X0,X1,X2),X2,X1,X0)))) )
| ~ spl93_142
| ~ spl93_147 ),
inference(resolution,[],[f1307,f1266]) ).
fof(f2950,plain,
( spl93_261
| ~ spl93_136
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1335,f1330,f1224,f2948]) ).
fof(f2948,plain,
( spl93_261
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_261])]) ).
fof(f1335,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl93_136
| ~ spl93_149 ),
inference(resolution,[],[f1331,f1225]) ).
fof(f2946,plain,
( spl93_260
| ~ spl93_132
| ~ spl93_134 ),
inference(avatar_split_clause,[],[f1243,f1216,f1191,f2944]) ).
fof(f2944,plain,
( spl93_260
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2))
| vsomeType(sK50(X0,X1,X2)) = vlookup(sK51(sK48(X0,X1,X2),sK50(X0,X1,X2),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0)),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0))
| sP6(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_260])]) ).
fof(f1191,plain,
( spl93_132
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK51(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_132])]) ).
fof(f1216,plain,
( spl93_134
<=> ! [X2,X0,X1] :
( vtcheck(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK48(X0,X1,X2),sK50(X0,X1,X2))
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_134])]) ).
fof(f1243,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2))
| vsomeType(sK50(X0,X1,X2)) = vlookup(sK51(sK48(X0,X1,X2),sK50(X0,X1,X2),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0)),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0))
| sP6(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2)) )
| ~ spl93_132
| ~ spl93_134 ),
inference(resolution,[],[f1217,f1192]) ).
fof(f1192,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK51(X0,X1,X2),X2)
| sP6(X2,X1,X0) )
| ~ spl93_132 ),
inference(avatar_component_clause,[],[f1191]) ).
fof(f1217,plain,
( ! [X2,X0,X1] :
( vtcheck(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK48(X0,X1,X2),sK50(X0,X1,X2))
| ~ sP5(X0,X1,X2) )
| ~ spl93_134 ),
inference(avatar_component_clause,[],[f1216]) ).
fof(f2936,plain,
( spl93_259
| ~ spl93_61
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1356,f1347,f805,f2934]) ).
fof(f2934,plain,
( spl93_259
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK84(X0,X1,vvar(X2),vvar(X2)),sK85(X0,X1,vvar(X2),vvar(X2)),vapp(sK83(X0,X1,vvar(X2),vvar(X2)),sK86(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,[spl93_259])]) ).
fof(f1356,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vsubst(sK84(X0,X1,vvar(X2),vvar(X2)),sK85(X0,X1,vvar(X2),vvar(X2)),vapp(sK83(X0,X1,vvar(X2),vvar(X2)),sK86(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 )
| ~ spl93_61
| ~ spl93_151 ),
inference(superposition,[],[f1348,f806]) ).
fof(f2851,plain,
( spl93_258
| ~ spl93_136
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1323,f1310,f1224,f2849]) ).
fof(f2849,plain,
( spl93_258
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(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(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_258])]) ).
fof(f1323,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(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(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl93_136
| ~ spl93_148 ),
inference(resolution,[],[f1311,f1225]) ).
fof(f2847,plain,
( spl93_257
| ~ spl93_136
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1315,f1306,f1224,f2845]) ).
fof(f2845,plain,
( spl93_257
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_257])]) ).
fof(f1315,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| vabs(sK69(vsubst(X0,X1,X2),X2,X1,X0),sK68(vsubst(X0,X1,X2),X2,X1,X0),sK71(vsubst(X0,X1,X2),X2,X1,X0)) = X2 )
| ~ spl93_136
| ~ spl93_147 ),
inference(resolution,[],[f1307,f1225]) ).
fof(f2823,plain,
( spl93_256
| ~ spl93_83
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1328,f1310,f903,f2821]) ).
fof(f2821,plain,
( spl93_256
<=> ! [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)
| sK84(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,[spl93_256])]) ).
fof(f1328,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)
| sK84(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) )
| ~ spl93_83
| ~ spl93_148 ),
inference(superposition,[],[f1311,f904]) ).
fof(f2819,plain,
( spl93_255
| ~ spl93_83
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1320,f1306,f903,f2817]) ).
fof(f2817,plain,
( spl93_255
<=> ! [X0,X3,X2,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = 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,[spl93_255])]) ).
fof(f1320,plain,
( ! [X2,X3,X0,X1] :
( sP12(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP13(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP11(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sK85(X0,X1,vabs(X0,X2,X3),vabs(X0,X2,X3)) = X1
| sP10(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0)
| sP9(vabs(X0,X2,X3),vabs(X0,X2,X3),X1,X0) )
| ~ spl93_83
| ~ spl93_147 ),
inference(superposition,[],[f1307,f904]) ).
fof(f2803,plain,
( spl93_254
| ~ spl93_105
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1281,f1273,f1021,f2801]) ).
fof(f2801,plain,
( spl93_254
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( vsubst(X0,sK67(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK67(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK69(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK67(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK67(X1,X2,X3,X4),vabs(sK69(X1,X2,X3,X4),X6,X5))
| sK69(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_254])]) ).
fof(f1021,plain,
( spl93_105
<=> ! [X0,X3,X2,X1] :
( visFreeVar(sK69(X0,X1,X2,X3),sK67(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_105])]) ).
fof(f1273,plain,
( spl93_144
<=> ! [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,[spl93_144])]) ).
fof(f1281,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vsubst(X0,sK67(X1,X2,X3,X4),vabs(vgensym(vapp(vapp(sK67(X1,X2,X3,X4),X5),vvar(X0))),X6,vsubst(sK69(X1,X2,X3,X4),vvar(vgensym(vapp(vapp(sK67(X1,X2,X3,X4),X5),vvar(X0)))),X5))) = vsubst(X0,sK67(X1,X2,X3,X4),vabs(sK69(X1,X2,X3,X4),X6,X5))
| sK69(X1,X2,X3,X4) = X0
| ~ sP12(X1,X2,X3,X4) )
| ~ spl93_105
| ~ spl93_144 ),
inference(resolution,[],[f1274,f1022]) ).
fof(f1022,plain,
( ! [X2,X3,X0,X1] :
( visFreeVar(sK69(X0,X1,X2,X3),sK67(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) )
| ~ spl93_105 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1274,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 )
| ~ spl93_144 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f2799,plain,
( spl93_253
| ~ spl93_123
| ~ spl93_134 ),
inference(avatar_split_clause,[],[f1244,f1216,f1136,f2797]) ).
fof(f2797,plain,
( spl93_253
<=> ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2))
| sK48(X0,X1,X2) = vvar(sK51(sK48(X0,X1,X2),sK50(X0,X1,X2),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0)))
| sP6(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_253])]) ).
fof(f1136,plain,
( spl93_123
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK51(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_123])]) ).
fof(f1244,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| sP5(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2))
| sK48(X0,X1,X2) = vvar(sK51(sK48(X0,X1,X2),sK50(X0,X1,X2),vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0)))
| sP6(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK50(X0,X1,X2),sK48(X0,X1,X2)) )
| ~ spl93_123
| ~ spl93_134 ),
inference(resolution,[],[f1217,f1137]) ).
fof(f1137,plain,
( ! [X2,X0,X1] :
( ~ vtcheck(X2,X0,X1)
| sP5(X2,X1,X0)
| vvar(sK51(X0,X1,X2)) = X0
| sP6(X2,X1,X0) )
| ~ spl93_123 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f2795,plain,
( spl93_252
| ~ spl93_61
| ~ spl93_130 ),
inference(avatar_split_clause,[],[f1304,f1182,f805,f2793]) ).
fof(f1182,plain,
( spl93_130
<=> vvar(sK17) = vvar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_130])]) ).
fof(f1304,plain,
( ! [X0,X1] :
( vvar(sK17) = vsubst(X0,X1,vvar(sK17))
| sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) = X0 )
| ~ spl93_61
| ~ spl93_130 ),
inference(superposition,[],[f806,f1184]) ).
fof(f1184,plain,
( vvar(sK17) = vvar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)))
| ~ spl93_130 ),
inference(avatar_component_clause,[],[f1182]) ).
fof(f2784,plain,
( spl93_251
| ~ spl93_33
| ~ spl93_145 ),
inference(avatar_split_clause,[],[f1290,f1283,f683,f2782]) ).
fof(f2782,plain,
( spl93_251
<=> ! [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(sK40(vabs(X0,X1,X2),vnoExp),sK41(vabs(X0,X1,X2),vnoExp),sK42(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK43(vabs(X0,X1,X2),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_251])]) ).
fof(f683,plain,
( spl93_33
<=> ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_33])]) ).
fof(f1283,plain,
( spl93_145
<=> ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_145])]) ).
fof(f1290,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(sK40(vabs(X0,X1,X2),vnoExp),sK41(vabs(X0,X1,X2),vnoExp),sK42(vabs(X0,X1,X2),vnoExp))
| vabs(X0,X1,X2) = vvar(sK43(vabs(X0,X1,X2),vnoExp)) )
| ~ spl93_33
| ~ spl93_145 ),
inference(superposition,[],[f1284,f684]) ).
fof(f684,plain,
( ! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2))
| ~ spl93_33 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f1284,plain,
( ! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0 )
| ~ spl93_145 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f2738,plain,
( spl93_250
| ~ spl93_66
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1337,f1330,f835,f2736]) ).
fof(f2736,plain,
( spl93_250
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_250])]) ).
fof(f1337,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl93_66
| ~ spl93_149 ),
inference(resolution,[],[f1331,f836]) ).
fof(f2734,plain,
( spl93_249
| ~ spl93_67
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1336,f1330,f839,f2732]) ).
fof(f2732,plain,
( spl93_249
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_249])]) ).
fof(f1336,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))) = X2
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK67(vsubst(X0,X1,X2),X2,X1,X0) = X1 )
| ~ spl93_67
| ~ spl93_149 ),
inference(resolution,[],[f1331,f840]) ).
fof(f2725,plain,
( spl93_248
| ~ spl93_34
| ~ spl93_151 ),
inference(avatar_split_clause,[],[f1355,f1347,f687,f2723]) ).
fof(f2723,plain,
( spl93_248
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK84(X0,X1,vvar(X0),X1),sK85(X0,X1,vvar(X0),X1),vapp(sK83(X0,X1,vvar(X0),X1),sK86(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,[spl93_248])]) ).
fof(f1355,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| vsubst(sK84(X0,X1,vvar(X0),X1),sK85(X0,X1,vvar(X0),X1),vapp(sK83(X0,X1,vvar(X0),X1),sK86(X0,X1,vvar(X0),X1))) = X1
| sP11(X1,vvar(X0),X1,X0)
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl93_34
| ~ spl93_151 ),
inference(superposition,[],[f1348,f688]) ).
fof(f2716,plain,
( spl93_247
| ~ spl93_61
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1339,f1330,f805,f2714]) ).
fof(f2714,plain,
( spl93_247
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| vvar(X2) = vapp(sK83(X0,X1,vvar(X2),vvar(X2)),sK86(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,[spl93_247])]) ).
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)
| vvar(X2) = vapp(sK83(X0,X1,vvar(X2),vvar(X2)),sK86(X0,X1,vvar(X2),vvar(X2)))
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl93_61
| ~ spl93_149 ),
inference(superposition,[],[f1331,f806]) ).
fof(f2569,plain,
( spl93_246
| ~ spl93_66
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1325,f1310,f835,f2567]) ).
fof(f2567,plain,
( spl93_246
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_246])]) ).
fof(f1325,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(X0,X1,X2,vsubst(X0,X1,X2)) = X0
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl93_66
| ~ spl93_148 ),
inference(resolution,[],[f1311,f836]) ).
fof(f2565,plain,
( spl93_245
| ~ spl93_67
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1324,f1310,f839,f2563]) ).
fof(f2563,plain,
( spl93_245
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(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) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_245])]) ).
fof(f1324,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK84(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) = X1 )
| ~ spl93_67
| ~ spl93_148 ),
inference(resolution,[],[f1311,f840]) ).
fof(f2561,plain,
( spl93_244
| ~ spl93_66
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1317,f1306,f835,f2559]) ).
fof(f2559,plain,
( spl93_244
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_244])]) ).
fof(f1317,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0)
| sK66(vsubst(X0,X1,X2),X2,X1,X0) = X0 )
| ~ spl93_66
| ~ spl93_147 ),
inference(resolution,[],[f1307,f836]) ).
fof(f2557,plain,
( spl93_243
| ~ spl93_67
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1316,f1306,f839,f2555]) ).
fof(f2555,plain,
( spl93_243
<=> ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = 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) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_243])]) ).
fof(f1316,plain,
( ! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = 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) = X1 )
| ~ spl93_67
| ~ spl93_147 ),
inference(resolution,[],[f1307,f840]) ).
fof(f2553,plain,
( spl93_242
| ~ spl93_82
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1278,f1273,f899,f2551]) ).
fof(f2551,plain,
( spl93_242
<=> ! [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,[spl93_242])]) ).
fof(f1278,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 )
| ~ spl93_82
| ~ spl93_144 ),
inference(resolution,[],[f1274,f900]) ).
fof(f2549,plain,
( spl93_241
| ~ spl93_133
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1276,f1273,f1195,f2547]) ).
fof(f2547,plain,
( spl93_241
<=> ! [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,[spl93_241])]) ).
fof(f1195,plain,
( spl93_133
<=> ! [X6,X4,X7,X5,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = vsubst(X6,X7,vabs(X4,X5,X8))
| visFreeVar(X4,X7)
| X4 = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_133])]) ).
fof(f1276,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 )
| ~ spl93_133
| ~ spl93_144 ),
inference(resolution,[],[f1274,f1196]) ).
fof(f1196,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 )
| ~ spl93_133 ),
inference(avatar_component_clause,[],[f1195]) ).
fof(f2540,plain,
( spl93_240
| ~ spl93_134
| ~ spl93_139 ),
inference(avatar_split_clause,[],[f1245,f1236,f1216,f2538]) ).
fof(f2538,plain,
( spl93_240
<=> ! [X4,X0,X3,X2,X1] :
( vtcheck(vbind(X0,X1,vbind(sK47(vbind(X0,X1,X2),X3,X4),sK49(vbind(X0,X1,X2),X3,X4),X2)),sK48(vbind(X0,X1,X2),X3,X4),sK50(vbind(X0,X1,X2),X3,X4))
| sK47(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_240])]) ).
fof(f1236,plain,
( spl93_139
<=> ! [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,[spl93_139])]) ).
fof(f1245,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,vbind(sK47(vbind(X0,X1,X2),X3,X4),sK49(vbind(X0,X1,X2),X3,X4),X2)),sK48(vbind(X0,X1,X2),X3,X4),sK50(vbind(X0,X1,X2),X3,X4))
| sK47(vbind(X0,X1,X2),X3,X4) = X0
| ~ sP5(vbind(X0,X1,X2),X3,X4) )
| ~ spl93_134
| ~ spl93_139 ),
inference(resolution,[],[f1237,f1217]) ).
fof(f1237,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 )
| ~ spl93_139 ),
inference(avatar_component_clause,[],[f1236]) ).
fof(f2536,plain,
( spl93_239
| ~ spl93_101
| ~ spl93_132 ),
inference(avatar_split_clause,[],[f1200,f1191,f1002,f2534]) ).
fof(f2534,plain,
( spl93_239
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| vsomeType(varrow(sK46(X0,X1,X2),X1)) = vlookup(sK51(sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_239])]) ).
fof(f1002,plain,
( spl93_101
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_101])]) ).
fof(f1200,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| vsomeType(varrow(sK46(X0,X1,X2),X1)) = vlookup(sK51(sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1),X0),X0)
| sP6(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl93_101
| ~ spl93_132 ),
inference(resolution,[],[f1192,f1003]) ).
fof(f1003,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) )
| ~ spl93_101 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f2523,plain,
( spl93_238
| ~ spl93_62
| ~ spl93_145 ),
inference(avatar_split_clause,[],[f1286,f1283,f817,f2521]) ).
fof(f2521,plain,
( spl93_238
<=> ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0
| vapp(sK25(vreduce(X0),X0),sK24(vreduce(X0),X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_238])]) ).
fof(f817,plain,
( spl93_62
<=> ! [X0,X1] :
( vapp(sK25(X0,X1),sK24(X0,X1)) = X1
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_62])]) ).
fof(f1286,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0
| vapp(sK25(vreduce(X0),X0),sK24(vreduce(X0),X0)) = X0 )
| ~ spl93_62
| ~ spl93_145 ),
inference(resolution,[],[f1284,f818]) ).
fof(f818,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vapp(sK25(X0,X1),sK24(X0,X1)) = X1 )
| ~ spl93_62 ),
inference(avatar_component_clause,[],[f817]) ).
fof(f2510,plain,
( spl93_237
| ~ spl93_52
| ~ spl93_145 ),
inference(avatar_split_clause,[],[f1287,f1283,f769,f2508]) ).
fof(f2508,plain,
( spl93_237
<=> ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0
| sK26(vreduce(X0),X0) = vreduce(sK25(vreduce(X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_237])]) ).
fof(f769,plain,
( spl93_52
<=> ! [X0,X1] :
( sK26(X0,X1) = vreduce(sK25(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_52])]) ).
fof(f1287,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0
| sK26(vreduce(X0),X0) = vreduce(sK25(vreduce(X0),X0)) )
| ~ spl93_52
| ~ spl93_145 ),
inference(resolution,[],[f1284,f770]) ).
fof(f770,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| sK26(X0,X1) = vreduce(sK25(X0,X1)) )
| ~ spl93_52 ),
inference(avatar_component_clause,[],[f769]) ).
fof(f2506,plain,
( spl93_236
| ~ spl93_45
| ~ spl93_180 ),
inference(avatar_split_clause,[],[f1929,f1744,f737,f2504]) ).
fof(f2504,plain,
( spl93_236
<=> ! [X0,X1] :
( varrow(X0,X1) != sK18
| sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_236])]) ).
fof(f737,plain,
( spl93_45
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_45])]) ).
fof(f1744,plain,
( spl93_180
<=> sK18 = varrow(sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK50(vbind(sK14,sK15,sK16),sK18,vvar(sK17))) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_180])]) ).
fof(f1929,plain,
( ! [X0,X1] :
( varrow(X0,X1) != sK18
| sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) = X0 )
| ~ spl93_45
| ~ spl93_180 ),
inference(superposition,[],[f738,f1746]) ).
fof(f1746,plain,
( sK18 = varrow(sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK50(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_180 ),
inference(avatar_component_clause,[],[f1744]) ).
fof(f738,plain,
( ! [X2,X3,X0,X1] :
( varrow(X0,X1) != varrow(X2,X3)
| X0 = X2 )
| ~ spl93_45 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f2492,plain,
( spl93_235
| ~ spl93_61
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1327,f1310,f805,f2490]) ).
fof(f2490,plain,
( spl93_235
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK84(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,[spl93_235])]) ).
fof(f1327,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)
| sK84(X0,X1,vvar(X2),vvar(X2)) = X0
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl93_61
| ~ spl93_148 ),
inference(superposition,[],[f1311,f806]) ).
fof(f2488,plain,
( spl93_234
| ~ spl93_61
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1319,f1306,f805,f2486]) ).
fof(f2486,plain,
( spl93_234
<=> ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK85(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_234])]) ).
fof(f1319,plain,
( ! [X2,X0,X1] :
( sP12(vvar(X2),vvar(X2),X1,X0)
| sP13(vvar(X2),vvar(X2),X1,X0)
| sP11(vvar(X2),vvar(X2),X1,X0)
| sK85(X0,X1,vvar(X2),vvar(X2)) = X1
| sP10(vvar(X2),vvar(X2),X1,X0)
| sP9(vvar(X2),vvar(X2),X1,X0)
| X0 = X2 )
| ~ spl93_61
| ~ spl93_147 ),
inference(superposition,[],[f1307,f806]) ).
fof(f2478,plain,
( spl93_233
| ~ spl93_34
| ~ spl93_149 ),
inference(avatar_split_clause,[],[f1338,f1330,f687,f2476]) ).
fof(f2476,plain,
( spl93_233
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK83(X0,X1,vvar(X0),X1),sK86(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_233])]) ).
fof(f1338,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| vvar(X0) = vapp(sK83(X0,X1,vvar(X0),X1),sK86(X0,X1,vvar(X0),X1))
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl93_34
| ~ spl93_149 ),
inference(superposition,[],[f1331,f688]) ).
fof(f2474,plain,
( spl93_232
| ~ spl93_101
| ~ spl93_123 ),
inference(avatar_split_clause,[],[f1150,f1136,f1002,f2472]) ).
fof(f2472,plain,
( spl93_232
<=> ! [X2,X0,X1] :
( sP5(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| sK44(X0,X1,X2) = vvar(sK51(sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_232])]) ).
fof(f1150,plain,
( ! [X2,X0,X1] :
( sP5(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| sK44(X0,X1,X2) = vvar(sK51(sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1),X0))
| sP6(X0,varrow(sK46(X0,X1,X2),X1),sK44(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl93_101
| ~ spl93_123 ),
inference(resolution,[],[f1137,f1003]) ).
fof(f2447,plain,
( spl93_231
| ~ spl93_39
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1280,f1273,f708,f2445]) ).
fof(f2445,plain,
( spl93_231
<=> ! [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,[spl93_231])]) ).
fof(f1280,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) )
| ~ spl93_39
| ~ spl93_144 ),
inference(resolution,[],[f1274,f709]) ).
fof(f2443,plain,
( spl93_230
| ~ spl93_40
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1279,f1273,f712,f2441]) ).
fof(f2441,plain,
( spl93_230
<=> ! [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,[spl93_230])]) ).
fof(f1279,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) )
| ~ spl93_40
| ~ spl93_144 ),
inference(resolution,[],[f1274,f713]) ).
fof(f2436,plain,
( spl93_229
| ~ spl93_16
| ~ spl93_145 ),
inference(avatar_split_clause,[],[f1289,f1283,f615,f2434]) ).
fof(f2434,plain,
( spl93_229
<=> ! [X0] :
( sP3(vnoExp,vvar(X0))
| sP2(vnoExp,vvar(X0))
| sP1(vnoExp,vvar(X0))
| sP0(vnoExp,vvar(X0))
| sP4(vnoExp,vvar(X0))
| vvar(X0) = vabs(sK40(vvar(X0),vnoExp),sK41(vvar(X0),vnoExp),sK42(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK43(vvar(X0),vnoExp)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_229])]) ).
fof(f615,plain,
( spl93_16
<=> ! [X0] : vnoExp = vreduce(vvar(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_16])]) ).
fof(f1289,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(sK40(vvar(X0),vnoExp),sK41(vvar(X0),vnoExp),sK42(vvar(X0),vnoExp))
| vvar(X0) = vvar(sK43(vvar(X0),vnoExp)) )
| ~ spl93_16
| ~ spl93_145 ),
inference(superposition,[],[f1284,f616]) ).
fof(f616,plain,
( ! [X0] : vnoExp = vreduce(vvar(X0))
| ~ spl93_16 ),
inference(avatar_component_clause,[],[f615]) ).
fof(f2425,plain,
( spl93_228
| ~ spl93_101
| ~ spl93_139 ),
inference(avatar_split_clause,[],[f1247,f1236,f1002,f2423]) ).
fof(f2423,plain,
( spl93_228
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK44(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK46(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,[spl93_228])]) ).
fof(f1247,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK44(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),varrow(sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),X5))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl93_101
| ~ spl93_139 ),
inference(resolution,[],[f1237,f1003]) ).
fof(f2421,plain,
( spl93_227
| ~ spl93_103
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1214,f1195,f1013,f2419]) ).
fof(f2419,plain,
( spl93_227
<=> ! [X5,X3,X4,X0,X6,X2,X1] :
( vabs(sK61(X0,X1,X2,X3),X4,vsubst(X5,sK64(X0,X1,X2,X3),X6)) = vsubst(X5,sK64(X0,X1,X2,X3),vabs(sK61(X0,X1,X2,X3),X4,X6))
| sK61(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_227])]) ).
fof(f1013,plain,
( spl93_103
<=> ! [X0,X3,X2,X1] :
( ~ visFreeVar(sK61(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_103])]) ).
fof(f1214,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vabs(sK61(X0,X1,X2,X3),X4,vsubst(X5,sK64(X0,X1,X2,X3),X6)) = vsubst(X5,sK64(X0,X1,X2,X3),vabs(sK61(X0,X1,X2,X3),X4,X6))
| sK61(X0,X1,X2,X3) = X5
| ~ sP13(X0,X1,X2,X3) )
| ~ spl93_103
| ~ spl93_133 ),
inference(resolution,[],[f1196,f1014]) ).
fof(f1014,plain,
( ! [X2,X3,X0,X1] :
( ~ visFreeVar(sK61(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) )
| ~ spl93_103 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f2416,plain,
( spl93_226
| ~ spl93_94
| ~ spl93_132 ),
inference(avatar_split_clause,[],[f1199,f1191,f964,f2414]) ).
fof(f2414,plain,
( spl93_226
<=> ! [X2,X0,X1] :
( sP5(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| vsomeType(sK46(X0,X1,X2)) = vlookup(sK51(sK45(X0,X1,X2),sK46(X0,X1,X2),X0),X0)
| sP6(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_226])]) ).
fof(f964,plain,
( spl93_94
<=> ! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_94])]) ).
fof(f1199,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| vsomeType(sK46(X0,X1,X2)) = vlookup(sK51(sK45(X0,X1,X2),sK46(X0,X1,X2),X0),X0)
| sP6(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl93_94
| ~ spl93_132 ),
inference(resolution,[],[f1192,f965]) ).
fof(f965,plain,
( ! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl93_94 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f2412,plain,
( spl93_225
| ~ spl93_37
| ~ spl93_130 ),
inference(avatar_split_clause,[],[f1302,f1182,f700,f2410]) ).
fof(f2410,plain,
( spl93_225
<=> ! [X0] :
( vvar(X0) != vvar(sK17)
| sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_225])]) ).
fof(f700,plain,
( spl93_37
<=> ! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_37])]) ).
fof(f1302,plain,
( ! [X0] :
( vvar(X0) != vvar(sK17)
| sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) = X0 )
| ~ spl93_37
| ~ spl93_130 ),
inference(superposition,[],[f701,f1184]) ).
fof(f701,plain,
( ! [X0,X1] :
( vvar(X0) != vvar(X1)
| X0 = X1 )
| ~ spl93_37 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f2397,plain,
( spl93_224
| ~ spl93_94
| ~ spl93_139 ),
inference(avatar_split_clause,[],[f1246,f1236,f964,f2395]) ).
fof(f2395,plain,
( spl93_224
<=> ! [X5,X3,X4,X2,X0,X6,X1] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK45(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK46(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,[spl93_224])]) ).
fof(f1246,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),sK45(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6),sK46(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6))
| X0 = X2
| ~ sP6(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6) )
| ~ spl93_94
| ~ spl93_139 ),
inference(resolution,[],[f1237,f965]) ).
fof(f2393,plain,
( spl93_223
| ~ spl93_109
| ~ spl93_132 ),
inference(avatar_split_clause,[],[f1201,f1191,f1037,f2391]) ).
fof(f2391,plain,
( spl93_223
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK51(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,[spl93_223])]) ).
fof(f1037,plain,
( spl93_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,[spl93_109])]) ).
fof(f1201,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vsomeType(varrow(X1,X2)) = vlookup(sK51(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) )
| ~ spl93_109
| ~ spl93_132 ),
inference(resolution,[],[f1192,f1038]) ).
fof(f1038,plain,
( ! [X2,X3,X0,X1,X4] :
( vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4))
| ~ vtcheck(vbind(X1,X3,X0),X2,X4) )
| ~ spl93_109 ),
inference(avatar_component_clause,[],[f1037]) ).
fof(f2383,plain,
( spl93_222
| ~ spl93_109
| ~ spl93_123 ),
inference(avatar_split_clause,[],[f1151,f1136,f1037,f2381]) ).
fof(f2381,plain,
( spl93_222
<=> ! [X4,X0,X3,X2,X1] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK51(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,[spl93_222])]) ).
fof(f1151,plain,
( ! [X2,X3,X0,X1,X4] :
( sP5(X0,varrow(X1,X2),vabs(X3,X1,X4))
| vabs(X3,X1,X4) = vvar(sK51(vabs(X3,X1,X4),varrow(X1,X2),X0))
| sP6(X0,varrow(X1,X2),vabs(X3,X1,X4))
| ~ vtcheck(vbind(X3,X1,X0),X4,X2) )
| ~ spl93_109
| ~ spl93_123 ),
inference(resolution,[],[f1137,f1038]) ).
fof(f2379,plain,
( spl93_221
| ~ spl93_94
| ~ spl93_123 ),
inference(avatar_split_clause,[],[f1149,f1136,f964,f2377]) ).
fof(f2377,plain,
( spl93_221
<=> ! [X2,X0,X1] :
( sP5(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK51(sK45(X0,X1,X2),sK46(X0,X1,X2),X0))
| sP6(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_221])]) ).
fof(f1149,plain,
( ! [X2,X0,X1] :
( sP5(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| sK45(X0,X1,X2) = vvar(sK51(sK45(X0,X1,X2),sK46(X0,X1,X2),X0))
| sP6(X0,sK46(X0,X1,X2),sK45(X0,X1,X2))
| ~ sP6(X0,X1,X2) )
| ~ spl93_94
| ~ spl93_123 ),
inference(resolution,[],[f1137,f965]) ).
fof(f2344,plain,
( spl93_220
| ~ spl93_34
| ~ spl93_148 ),
inference(avatar_split_clause,[],[f1326,f1310,f687,f2342]) ).
fof(f2342,plain,
( spl93_220
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK84(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_220])]) ).
fof(f1326,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK84(X0,X1,vvar(X0),X1) = X0
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl93_34
| ~ spl93_148 ),
inference(superposition,[],[f1311,f688]) ).
fof(f2340,plain,
( spl93_219
| ~ spl93_34
| ~ spl93_147 ),
inference(avatar_split_clause,[],[f1318,f1306,f687,f2338]) ).
fof(f2338,plain,
( spl93_219
<=> ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK85(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_219])]) ).
fof(f1318,plain,
( ! [X0,X1] :
( sP12(X1,vvar(X0),X1,X0)
| sP13(X1,vvar(X0),X1,X0)
| sP11(X1,vvar(X0),X1,X0)
| sK85(X0,X1,vvar(X0),X1) = X1
| sP10(X1,vvar(X0),X1,X0)
| sP9(X1,vvar(X0),X1,X0) )
| ~ spl93_34
| ~ spl93_147 ),
inference(superposition,[],[f1307,f688]) ).
fof(f2336,plain,
( spl93_218
| ~ spl93_13
| ~ spl93_144 ),
inference(avatar_split_clause,[],[f1277,f1273,f603,f2334]) ).
fof(f2334,plain,
( spl93_218
<=> ! [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,[spl93_218])]) ).
fof(f1277,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 )
| ~ spl93_13
| ~ spl93_144 ),
inference(resolution,[],[f1274,f604]) ).
fof(f2326,plain,
( spl93_217
| ~ spl93_101
| ~ spl93_115 ),
inference(avatar_split_clause,[],[f1101,f1092,f1002,f2324]) ).
fof(f2324,plain,
( spl93_217
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK44(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK46(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,[spl93_217])]) ).
fof(f1092,plain,
( spl93_115
<=> ! [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,[spl93_115])]) ).
fof(f1101,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK44(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),varrow(sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),X4))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl93_101
| ~ spl93_115 ),
inference(resolution,[],[f1093,f1003]) ).
fof(f1093,plain,
( ! [X2,X3,X1,X6,X4,X5] :
( ~ vtcheck(vbind(X2,X3,vbind(X2,X1,X4)),X5,X6)
| vtcheck(vbind(X2,X3,X4),X5,X6) )
| ~ spl93_115 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f2251,plain,
( spl93_216
| ~ spl93_116
| ~ spl93_140 ),
inference(avatar_split_clause,[],[f1250,f1240,f1104,f2249]) ).
fof(f2249,plain,
( spl93_216
<=> ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_216])]) ).
fof(f1104,plain,
( spl93_116
<=> ! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_116])]) ).
fof(f1240,plain,
( spl93_140
<=> ! [X4,X0] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_140])]) ).
fof(f1250,plain,
( ! [X2,X0,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vnoExp = vreduce(vapp(X0,X2))
| vabs(sK87(X0),sK88(X0),sK89(X0)) = X0 )
| ~ spl93_116
| ~ spl93_140 ),
inference(resolution,[],[f1241,f1105]) ).
fof(f1105,plain,
( ! [X0,X1] :
( visSomeExp(vreduce(X1))
| vnoExp = vreduce(vapp(X1,X0))
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1 )
| ~ spl93_116 ),
inference(avatar_component_clause,[],[f1104]) ).
fof(f1241,plain,
( ! [X0,X4] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0 )
| ~ spl93_140 ),
inference(avatar_component_clause,[],[f1240]) ).
fof(f2247,plain,
( spl93_215
| ~ spl93_117
| ~ spl93_140 ),
inference(avatar_split_clause,[],[f1249,f1240,f1108,f2245]) ).
fof(f2245,plain,
( spl93_215
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_215])]) ).
fof(f1108,plain,
( spl93_117
<=> ! [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,[spl93_117])]) ).
fof(f1249,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| ~ visValue(X0)
| vsomeExp(vsubst(X2,X0,X3)) = vreduce(vapp(vabs(X2,X4,X3),X0)) )
| ~ spl93_117
| ~ spl93_140 ),
inference(resolution,[],[f1241,f1109]) ).
fof(f1109,plain,
( ! [X0,X6,X4,X5] :
( visSomeExp(vreduce(X5))
| ~ visValue(X5)
| vsomeExp(vsubst(X4,X5,X6)) = vreduce(vapp(vabs(X4,X0,X6),X5)) )
| ~ spl93_117 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f2243,plain,
( spl93_214
| ~ spl93_124
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1162,f1155,f1140,f2241]) ).
fof(f2241,plain,
( spl93_214
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_214])]) ).
fof(f1140,plain,
( spl93_124
<=> ! [X2,X0,X1] :
( vbind(sK53(X0,X1,X2),sK52(X0,X1,X2),sK55(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_124])]) ).
fof(f1155,plain,
( spl93_126
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_126])]) ).
fof(f1162,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1 )
| ~ spl93_124
| ~ spl93_126 ),
inference(resolution,[],[f1156,f1141]) ).
fof(f1141,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vbind(sK53(X0,X1,X2),sK52(X0,X1,X2),sK55(X0,X1,X2)) = X1 )
| ~ spl93_124 ),
inference(avatar_component_clause,[],[f1140]) ).
fof(f1156,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0 )
| ~ spl93_126 ),
inference(avatar_component_clause,[],[f1155]) ).
fof(f2239,plain,
( spl93_213
| ~ spl93_94
| ~ spl93_115 ),
inference(avatar_split_clause,[],[f1100,f1092,f964,f2237]) ).
fof(f2237,plain,
( spl93_213
<=> ! [X3,X4,X0,X5,X2,X1] :
( vtcheck(vbind(X0,X1,X2),sK45(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK46(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,[spl93_213])]) ).
fof(f1100,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vtcheck(vbind(X0,X1,X2),sK45(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5),sK46(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5))
| ~ sP6(vbind(X0,X1,vbind(X0,X3,X2)),X4,X5) )
| ~ spl93_94
| ~ spl93_115 ),
inference(resolution,[],[f1093,f965]) ).
fof(f2167,plain,
( spl93_212
| ~ spl93_116
| ~ spl93_127 ),
inference(avatar_split_clause,[],[f1169,f1159,f1104,f2165]) ).
fof(f2165,plain,
( spl93_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(sK87(X3),sK88(X3),sK89(X3)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_212])]) ).
fof(f1159,plain,
( spl93_127
<=> ! [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,[spl93_127])]) ).
fof(f1169,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(sK87(X3),sK88(X3),sK89(X3)) = X3 )
| ~ spl93_116
| ~ spl93_127 ),
inference(resolution,[],[f1160,f1105]) ).
fof(f1160,plain,
( ! [X3,X0,X4,X5] :
( ~ visSomeExp(vreduce(X0))
| vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(vreduce(X0)))) = vreduce(vapp(vabs(X3,X4,X5),X0)) )
| ~ spl93_127 ),
inference(avatar_component_clause,[],[f1159]) ).
fof(f2163,plain,
( spl93_211
| ~ spl93_117
| ~ spl93_127 ),
inference(avatar_split_clause,[],[f1168,f1159,f1108,f2161]) ).
fof(f2161,plain,
( spl93_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,[spl93_211])]) ).
fof(f1168,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)) )
| ~ spl93_117
| ~ spl93_127 ),
inference(resolution,[],[f1160,f1109]) ).
fof(f2159,plain,
( spl93_210
| ~ spl93_92
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1167,f1155,f950,f2157]) ).
fof(f2157,plain,
( spl93_210
<=> ! [X0,X3,X2,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK60(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_210])]) ).
fof(f1167,plain,
( ! [X2,X3,X0,X1] :
( sP8(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sP7(vlookup(X0,X3),vbind(X1,X2,X3),X0)
| sK60(X0,vbind(X1,X2,X3),vlookup(X0,X3)) = X0
| X0 = X1 )
| ~ spl93_92
| ~ spl93_126 ),
inference(superposition,[],[f1156,f951]) ).
fof(f2155,plain,
( spl93_209
| ~ spl93_114
| ~ spl93_124 ),
inference(avatar_split_clause,[],[f1152,f1140,f1088,f2153]) ).
fof(f2153,plain,
( spl93_209
<=> ! [X0,X1] :
( vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_209])]) ).
fof(f1152,plain,
( ! [X0,X1] :
( vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) )
| ~ spl93_114
| ~ spl93_124 ),
inference(resolution,[],[f1141,f1089]) ).
fof(f2113,plain,
( spl93_208
| spl93_5
| ~ spl93_33
| ~ spl93_116 ),
inference(avatar_split_clause,[],[f1112,f1104,f683,f570,f2111]) ).
fof(f570,plain,
( spl93_5
<=> visSomeExp(vnoExp) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_5])]) ).
fof(f1112,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X3))
| vabs(X0,X1,X2) = vabs(sK87(vabs(X0,X1,X2)),sK88(vabs(X0,X1,X2)),sK89(vabs(X0,X1,X2))) )
| ~ spl93_33
| ~ spl93_116 ),
inference(superposition,[],[f1105,f684]) ).
fof(f2090,plain,
( spl93_207
| ~ spl93_95
| ~ spl93_140 ),
inference(avatar_split_clause,[],[f1251,f1240,f968,f2088]) ).
fof(f2088,plain,
( spl93_207
<=> ! [X2,X4,X0,X3,X1] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_207])]) ).
fof(f968,plain,
( spl93_95
<=> ! [X4,X0,X2,X1] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_95])]) ).
fof(f1251,plain,
( ! [X2,X3,X0,X1,X4] :
( vreduce(vapp(X0,X1)) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X1))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| visValue(X0)
| vnoExp = vreduce(vapp(vabs(X2,X3,X4),X0)) )
| ~ spl93_95
| ~ spl93_140 ),
inference(resolution,[],[f1241,f969]) ).
fof(f969,plain,
( ! [X2,X0,X1,X4] :
( visSomeExp(vreduce(X4))
| visValue(X4)
| vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4)) )
| ~ spl93_95 ),
inference(avatar_component_clause,[],[f968]) ).
fof(f2086,plain,
( spl93_206
| ~ spl93_109
| ~ spl93_139 ),
inference(avatar_split_clause,[],[f1248,f1236,f1037,f2084]) ).
fof(f2084,plain,
( spl93_206
<=> ! [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,[spl93_206])]) ).
fof(f1248,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) )
| ~ spl93_109
| ~ spl93_139 ),
inference(resolution,[],[f1237,f1038]) ).
fof(f2082,plain,
( spl93_205
| ~ spl93_98
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1163,f1155,f985,f2080]) ).
fof(f2080,plain,
( spl93_205
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_205])]) ).
fof(f985,plain,
( spl93_98
<=> ! [X2,X0,X1] :
( vlookup(sK54(X0,X1,X2),sK55(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_98])]) ).
fof(f1163,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) )
| ~ spl93_98
| ~ spl93_126 ),
inference(resolution,[],[f1156,f986]) ).
fof(f986,plain,
( ! [X2,X0,X1] :
( ~ sP8(X0,X1,X2)
| vlookup(sK54(X0,X1,X2),sK55(X0,X1,X2)) = X0 )
| ~ spl93_98 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f2078,plain,
( spl93_203
| ~ spl93_204
| ~ spl93_92
| spl93_200 ),
inference(avatar_split_clause,[],[f2010,f2002,f950,f2075,f2071]) ).
fof(f2010,plain,
( vsomeType(sK18) != vlookup(sK17,sK16)
| sK14 = sK17
| ~ spl93_92
| spl93_200 ),
inference(superposition,[],[f2003,f951]) ).
fof(f2003,plain,
( vsomeType(sK18) != vlookup(sK17,vbind(sK14,sK15,sK16))
| spl93_200 ),
inference(avatar_component_clause,[],[f2002]) ).
fof(f2062,plain,
( spl93_202
| ~ spl93_99
| ~ spl93_124 ),
inference(avatar_split_clause,[],[f1153,f1140,f989,f2060]) ).
fof(f2060,plain,
( spl93_202
<=> ! [X0,X1] :
( vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_202])]) ).
fof(f989,plain,
( spl93_99
<=> ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_99])]) ).
fof(f1153,plain,
( ! [X0,X1] :
( vbind(sK53(vlookup(X0,X1),X1,X0),sK52(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) = X1
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl93_99
| ~ spl93_124 ),
inference(resolution,[],[f1141,f990]) ).
fof(f990,plain,
( ! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 )
| ~ spl93_99 ),
inference(avatar_component_clause,[],[f989]) ).
fof(f2014,plain,
( spl93_201
| ~ spl93_60
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1205,f1195,f801,f2012]) ).
fof(f1205,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) )
| ~ spl93_60
| ~ spl93_133 ),
inference(resolution,[],[f1196,f802]) ).
fof(f2005,plain,
( spl93_200
| ~ spl93_154
| ~ spl93_165 ),
inference(avatar_split_clause,[],[f1994,f1439,f1376,f2002]) ).
fof(f1376,plain,
( spl93_154
<=> vsomeType(sK18) = vlookup(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vbind(sK14,sK15,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_154])]) ).
fof(f1439,plain,
( spl93_165
<=> sK17 = sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_165])]) ).
fof(f1994,plain,
( vsomeType(sK18) = vlookup(sK17,vbind(sK14,sK15,sK16))
| ~ spl93_154
| ~ spl93_165 ),
inference(forward_demodulation,[],[f1378,f1441]) ).
fof(f1441,plain,
( sK17 = sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16))
| ~ spl93_165 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1378,plain,
( vsomeType(sK18) = vlookup(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vbind(sK14,sK15,sK16))
| ~ spl93_154 ),
inference(avatar_component_clause,[],[f1376]) ).
fof(f1993,plain,
( spl93_199
| ~ spl93_46
| ~ spl93_180 ),
inference(avatar_split_clause,[],[f1927,f1744,f741,f1991]) ).
fof(f1991,plain,
( spl93_199
<=> ! [X0,X1] :
( varrow(X0,X1) != sK18
| sK50(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_199])]) ).
fof(f741,plain,
( spl93_46
<=> ! [X2,X0,X1,X3] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_46])]) ).
fof(f1927,plain,
( ! [X0,X1] :
( varrow(X0,X1) != sK18
| sK50(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) = X1 )
| ~ spl93_46
| ~ spl93_180 ),
inference(superposition,[],[f742,f1746]) ).
fof(f742,plain,
( ! [X2,X3,X0,X1] :
( varrow(X0,X1) != varrow(X2,X3)
| X1 = X3 )
| ~ spl93_46 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f1989,plain,
( spl93_198
| ~ spl93_95
| ~ spl93_127 ),
inference(avatar_split_clause,[],[f1170,f1159,f968,f1987]) ).
fof(f1987,plain,
( spl93_198
<=> ! [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,[spl93_198])]) ).
fof(f1170,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)) )
| ~ spl93_95
| ~ spl93_127 ),
inference(resolution,[],[f1160,f969]) ).
fof(f1985,plain,
( spl93_197
| ~ spl93_98
| ~ spl93_114 ),
inference(avatar_split_clause,[],[f1095,f1088,f985,f1983]) ).
fof(f1983,plain,
( spl93_197
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_197])]) ).
fof(f1095,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) )
| ~ spl93_98
| ~ spl93_114 ),
inference(resolution,[],[f1089,f986]) ).
fof(f1958,plain,
( spl93_196
| ~ spl93_41
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1203,f1195,f721,f1956]) ).
fof(f721,plain,
( spl93_41
<=> ! [X4,X0,X5,X3] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_41])]) ).
fof(f1203,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) )
| ~ spl93_41
| ~ spl93_133 ),
inference(resolution,[],[f1196,f722]) ).
fof(f722,plain,
( ! [X3,X0,X4,X5] :
( ~ visFreeVar(X4,vabs(X3,X0,X5))
| visFreeVar(X4,X5) )
| ~ spl93_41 ),
inference(avatar_component_clause,[],[f721]) ).
fof(f1954,plain,
( spl93_195
| ~ spl93_92
| ~ spl93_99 ),
inference(avatar_split_clause,[],[f996,f989,f950,f1952]) ).
fof(f1952,plain,
( spl93_195
<=> ! [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,[spl93_195])]) ).
fof(f996,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 )
| ~ spl93_92
| ~ spl93_99 ),
inference(superposition,[],[f990,f951]) ).
fof(f1934,plain,
( spl93_194
| ~ spl93_42
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1166,f1155,f725,f1932]) ).
fof(f1932,plain,
( spl93_194
<=> ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK60(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_194])]) ).
fof(f1166,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| sK60(X0,vbind(X0,X1,X2),vsomeType(X1)) = X0 )
| ~ spl93_42
| ~ spl93_126 ),
inference(superposition,[],[f1156,f726]) ).
fof(f1922,plain,
( spl93_193
| spl93_5
| ~ spl93_33
| ~ spl93_117 ),
inference(avatar_split_clause,[],[f1118,f1108,f683,f570,f1920]) ).
fof(f1118,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))) )
| ~ spl93_33
| ~ spl93_117 ),
inference(superposition,[],[f1109,f684]) ).
fof(f1918,plain,
( spl93_192
| ~ spl93_92
| ~ spl93_114 ),
inference(avatar_split_clause,[],[f1099,f1088,f950,f1916]) ).
fof(f1099,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 )
| ~ spl93_92
| ~ spl93_114 ),
inference(superposition,[],[f1089,f951]) ).
fof(f1914,plain,
( spl93_191
| ~ spl93_98
| ~ spl93_99 ),
inference(avatar_split_clause,[],[f992,f989,f985,f1912]) ).
fof(f1912,plain,
( spl93_191
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_191])]) ).
fof(f992,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| vlookup(X0,X1) = vlookup(sK54(vlookup(X0,X1),X1,X0),sK55(vlookup(X0,X1),X1,X0)) )
| ~ spl93_98
| ~ spl93_99 ),
inference(resolution,[],[f990,f986]) ).
fof(f1900,plain,
( spl93_190
| ~ spl93_109
| ~ spl93_115 ),
inference(avatar_split_clause,[],[f1102,f1092,f1037,f1898]) ).
fof(f1898,plain,
( spl93_190
<=> ! [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,[spl93_190])]) ).
fof(f1102,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) )
| ~ spl93_109
| ~ spl93_115 ),
inference(resolution,[],[f1093,f1038]) ).
fof(f1896,plain,
( spl93_189
| ~ spl93_92
| ~ spl93_110 ),
inference(avatar_split_clause,[],[f1061,f1041,f950,f1894]) ).
fof(f1894,plain,
( spl93_189
<=> ! [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,[spl93_189])]) ).
fof(f1041,plain,
( spl93_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,[spl93_110])]) ).
fof(f1061,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 )
| ~ spl93_92
| ~ spl93_110 ),
inference(superposition,[],[f1042,f951]) ).
fof(f1042,plain,
( ! [X2,X3,X0,X1,X4] :
( vnoType != vlookup(X0,X2)
| ~ vtcheck(X2,X3,X4)
| vtcheck(vbind(X0,X1,X2),X3,X4) )
| ~ spl93_110 ),
inference(avatar_component_clause,[],[f1041]) ).
fof(f1890,plain,
( spl93_188
| ~ spl93_96
| ~ spl93_129 ),
inference(avatar_split_clause,[],[f1748,f1178,f974,f1887]) ).
fof(f974,plain,
( spl93_96
<=> ! [X2,X0,X1] :
( vapp(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_96])]) ).
fof(f1178,plain,
( spl93_129
<=> sP6(vbind(sK14,sK15,sK16),sK18,vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_129])]) ).
fof(f1748,plain,
( vvar(sK17) = vapp(sK44(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK45(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_96
| ~ spl93_129 ),
inference(resolution,[],[f1180,f975]) ).
fof(f975,plain,
( ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| vapp(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X2 )
| ~ spl93_96 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1180,plain,
( sP6(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| ~ spl93_129 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f1873,plain,
( spl93_187
| ~ spl93_23
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1202,f1195,f643,f1871]) ).
fof(f1871,plain,
( spl93_187
<=> ! [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,[spl93_187])]) ).
fof(f1202,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 )
| ~ spl93_23
| ~ spl93_133 ),
inference(resolution,[],[f1196,f644]) ).
fof(f1858,plain,
( spl93_186
| ~ spl93_32
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1204,f1195,f679,f1856]) ).
fof(f1856,plain,
( spl93_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,[spl93_186])]) ).
fof(f679,plain,
( spl93_32
<=> ! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_32])]) ).
fof(f1204,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 )
| ~ spl93_32
| ~ spl93_133 ),
inference(resolution,[],[f1196,f680]) ).
fof(f680,plain,
( ! [X2,X3] :
( ~ visFreeVar(X3,vvar(X2))
| X2 = X3 )
| ~ spl93_32 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f1844,plain,
( spl93_185
| ~ spl93_43
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1164,f1155,f729,f1842]) ).
fof(f1842,plain,
( spl93_185
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| sK54(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_185])]) ).
fof(f1164,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0
| sK54(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl93_43
| ~ spl93_126 ),
inference(resolution,[],[f1156,f730]) ).
fof(f1810,plain,
( spl93_184
| spl93_5
| ~ spl93_16
| ~ spl93_116 ),
inference(avatar_split_clause,[],[f1111,f1104,f615,f570,f1808]) ).
fof(f1111,plain,
( ! [X0,X1] :
( visSomeExp(vnoExp)
| vnoExp = vreduce(vapp(vvar(X0),X1))
| vvar(X0) = vabs(sK87(vvar(X0)),sK88(vvar(X0)),sK89(vvar(X0))) )
| ~ spl93_16
| ~ spl93_116 ),
inference(superposition,[],[f1105,f616]) ).
fof(f1806,plain,
( spl93_183
| ~ spl93_42
| ~ spl93_99 ),
inference(avatar_split_clause,[],[f995,f989,f725,f1804]) ).
fof(f1804,plain,
( spl93_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,[spl93_183])]) ).
fof(f995,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) )
| ~ spl93_42
| ~ spl93_99 ),
inference(superposition,[],[f990,f726]) ).
fof(f1792,plain,
( spl93_182
| ~ spl93_11
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1206,f1195,f595,f1790]) ).
fof(f1790,plain,
( spl93_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,[spl93_182])]) ).
fof(f595,plain,
( spl93_11
<=> ! [X1] : ~ visFreeVar(vgensym(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_11])]) ).
fof(f1206,plain,
( ! [X2,X3,X0,X1] :
( vabs(vgensym(X0),X1,vsubst(X2,X0,X3)) = vsubst(X2,X0,vabs(vgensym(X0),X1,X3))
| vgensym(X0) = X2 )
| ~ spl93_11
| ~ spl93_133 ),
inference(resolution,[],[f1196,f596]) ).
fof(f596,plain,
( ! [X1] : ~ visFreeVar(vgensym(X1),X1)
| ~ spl93_11 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f1752,plain,
( spl93_181
| ~ spl93_19
| ~ spl93_141 ),
inference(avatar_split_clause,[],[f1263,f1255,f627,f1750]) ).
fof(f1750,plain,
( spl93_181
<=> ! [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,[spl93_181])]) ).
fof(f627,plain,
( spl93_19
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_19])]) ).
fof(f1255,plain,
( spl93_141
<=> ! [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,[spl93_141])]) ).
fof(f1263,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0) )
| ~ spl93_19
| ~ spl93_141 ),
inference(duplicate_literal_removal,[],[f1260]) ).
fof(f1260,plain,
( ! [X0] :
( sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vnoExp = vreduce(X0)
| vnoExp = vreduce(X0) )
| ~ spl93_19
| ~ spl93_141 ),
inference(resolution,[],[f1256,f628]) ).
fof(f628,plain,
( ! [X0,X1] :
( ~ sP3(X0,X1)
| vnoExp = X0 )
| ~ spl93_19 ),
inference(avatar_component_clause,[],[f627]) ).
fof(f1256,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) )
| ~ spl93_141 ),
inference(avatar_component_clause,[],[f1255]) ).
fof(f1747,plain,
( spl93_180
| ~ spl93_97
| ~ spl93_131 ),
inference(avatar_split_clause,[],[f1381,f1186,f981,f1744]) ).
fof(f981,plain,
( spl93_97
<=> ! [X2,X0,X1] :
( varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_97])]) ).
fof(f1381,plain,
( sK18 = varrow(sK49(vbind(sK14,sK15,sK16),sK18,vvar(sK17)),sK50(vbind(sK14,sK15,sK16),sK18,vvar(sK17)))
| ~ spl93_97
| ~ spl93_131 ),
inference(resolution,[],[f1188,f982]) ).
fof(f982,plain,
( ! [X2,X0,X1] :
( ~ sP5(X0,X1,X2)
| varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1 )
| ~ spl93_97 ),
inference(avatar_component_clause,[],[f981]) ).
fof(f1742,plain,
( spl93_179
| ~ spl93_42
| ~ spl93_114 ),
inference(avatar_split_clause,[],[f1098,f1088,f725,f1740]) ).
fof(f1740,plain,
( spl93_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,[spl93_179])]) ).
fof(f1098,plain,
( ! [X2,X0,X1] :
( sP8(vsomeType(X1),vbind(X0,X1,X2),X0)
| sP7(vsomeType(X1),vbind(X0,X1,X2),X0)
| vnoType = vsomeType(X1) )
| ~ spl93_42
| ~ spl93_114 ),
inference(superposition,[],[f1089,f726]) ).
fof(f1738,plain,
( spl93_178
| ~ spl93_60
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1082,f1049,f801,f1736]) ).
fof(f1736,plain,
( spl93_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,[spl93_178])]) ).
fof(f1082,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)) )
| ~ spl93_60
| ~ spl93_112 ),
inference(superposition,[],[f802,f1050]) ).
fof(f1734,plain,
( spl93_177
| ~ spl93_109
| ~ spl93_111 ),
inference(avatar_split_clause,[],[f1064,f1045,f1037,f1732]) ).
fof(f1732,plain,
( spl93_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,[spl93_177])]) ).
fof(f1045,plain,
( spl93_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,[spl93_111])]) ).
fof(f1064,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) )
| ~ spl93_109
| ~ spl93_111 ),
inference(resolution,[],[f1046,f1038]) ).
fof(f1046,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ vtcheck(X1,X2,varrow(X0,X4))
| ~ vtcheck(X1,X3,X0)
| vtcheck(X1,vapp(X2,X3),X4) )
| ~ spl93_111 ),
inference(avatar_component_clause,[],[f1045]) ).
fof(f1730,plain,
( spl93_176
| ~ spl93_101
| ~ spl93_111 ),
inference(avatar_split_clause,[],[f1063,f1045,f1002,f1728]) ).
fof(f1728,plain,
( spl93_176
<=> ! [X0,X3,X2,X1] :
( ~ vtcheck(X0,X1,sK46(X0,X2,X3))
| vtcheck(X0,vapp(sK44(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_176])]) ).
fof(f1063,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(X0,X1,sK46(X0,X2,X3))
| vtcheck(X0,vapp(sK44(X0,X2,X3),X1),X2)
| ~ sP6(X0,X2,X3) )
| ~ spl93_101
| ~ spl93_111 ),
inference(resolution,[],[f1046,f1003]) ).
fof(f1663,plain,
( spl93_175
| ~ spl93_43
| ~ spl93_114 ),
inference(avatar_split_clause,[],[f1096,f1088,f729,f1661]) ).
fof(f1661,plain,
( spl93_175
<=> ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK54(vlookup(X0,X1),X1,X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_175])]) ).
fof(f1096,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1)
| sK54(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl93_43
| ~ spl93_114 ),
inference(resolution,[],[f1089,f730]) ).
fof(f1659,plain,
( spl93_174
| ~ spl93_83
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1070,f1049,f903,f1657]) ).
fof(f1657,plain,
( spl93_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,[spl93_174])]) ).
fof(f1070,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(X4,vabs(X0,X2,X3))) = vapp(vsubst(X0,X1,X4),vabs(X0,X2,X3))
| ~ spl93_83
| ~ spl93_112 ),
inference(superposition,[],[f1050,f904]) ).
fof(f1655,plain,
( spl93_173
| ~ spl93_83
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1067,f1049,f903,f1653]) ).
fof(f1653,plain,
( spl93_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,[spl93_173])]) ).
fof(f1067,plain,
( ! [X2,X3,X0,X1,X4] : vsubst(X0,X1,vapp(vabs(X0,X2,X3),X4)) = vapp(vabs(X0,X2,X3),vsubst(X0,X1,X4))
| ~ spl93_83
| ~ spl93_112 ),
inference(superposition,[],[f1050,f904]) ).
fof(f1604,plain,
( spl93_172
| ~ spl93_61
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1069,f1049,f805,f1602]) ).
fof(f1069,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(X3,vvar(X2))) = vapp(vsubst(X0,X1,X3),vvar(X2))
| X0 = X2 )
| ~ spl93_61
| ~ spl93_112 ),
inference(superposition,[],[f1050,f806]) ).
fof(f1600,plain,
( spl93_171
| ~ spl93_61
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1066,f1049,f805,f1598]) ).
fof(f1066,plain,
( ! [X2,X3,X0,X1] :
( vsubst(X0,X1,vapp(vvar(X2),X3)) = vapp(vvar(X2),vsubst(X0,X1,X3))
| X0 = X2 )
| ~ spl93_61
| ~ spl93_112 ),
inference(superposition,[],[f1050,f806]) ).
fof(f1586,plain,
( spl93_170
| ~ spl93_43
| ~ spl93_99 ),
inference(avatar_split_clause,[],[f993,f989,f729,f1584]) ).
fof(f993,plain,
( ! [X0,X1] :
( sP7(vlookup(X0,X1),X1,X0)
| vempty = X1
| sK54(vlookup(X0,X1),X1,X0) = X0 )
| ~ spl93_43
| ~ spl93_99 ),
inference(resolution,[],[f990,f730]) ).
fof(f1582,plain,
( spl93_169
| ~ spl93_59
| ~ spl93_92 ),
inference(avatar_split_clause,[],[f958,f950,f797,f1580]) ).
fof(f958,plain,
( ! [X2,X3,X0,X1,X4] :
( vsomeType(X4) != vlookup(X0,X3)
| vtcheck(vbind(X1,X2,X3),vvar(X0),X4)
| X0 = X1 )
| ~ spl93_59
| ~ spl93_92 ),
inference(superposition,[],[f798,f951]) ).
fof(f1562,plain,
( spl93_168
| ~ spl93_49
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1079,f1049,f753,f1560]) ).
fof(f1079,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X3) = X5 )
| ~ spl93_49
| ~ spl93_112 ),
inference(superposition,[],[f754,f1050]) ).
fof(f1558,plain,
( spl93_167
| ~ spl93_47
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1076,f1049,f745,f1556]) ).
fof(f1076,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( vsubst(X0,X1,vapp(X2,X3)) != vapp(X4,X5)
| vsubst(X0,X1,X2) = X4 )
| ~ spl93_47
| ~ spl93_112 ),
inference(superposition,[],[f746,f1050]) ).
fof(f1553,plain,
( spl93_166
| spl93_5
| ~ spl93_16
| ~ spl93_95 ),
inference(avatar_split_clause,[],[f971,f968,f615,f570,f1551]) ).
fof(f971,plain,
( ! [X2,X3,X0,X1] :
( visSomeExp(vnoExp)
| visValue(vvar(X0))
| vnoExp = vreduce(vapp(vabs(X1,X2,X3),vvar(X0))) )
| ~ spl93_16
| ~ spl93_95 ),
inference(superposition,[],[f969,f616]) ).
fof(f1442,plain,
( spl93_165
| ~ spl93_32
| ~ spl93_152 ),
inference(avatar_split_clause,[],[f1400,f1359,f679,f1439]) ).
fof(f1359,plain,
( spl93_152
<=> visFreeVar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vvar(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_152])]) ).
fof(f1400,plain,
( sK17 = sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16))
| ~ spl93_32
| ~ spl93_152 ),
inference(resolution,[],[f1361,f680]) ).
fof(f1361,plain,
( visFreeVar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vvar(sK17))
| ~ spl93_152 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f1433,plain,
( spl93_164
| ~ spl93_18
| ~ spl93_126 ),
inference(avatar_split_clause,[],[f1165,f1155,f623,f1431]) ).
fof(f623,plain,
( spl93_18
<=> ! [X1] : vnoType = vlookup(X1,vempty) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_18])]) ).
fof(f1165,plain,
( ! [X0] :
( sP8(vnoType,vempty,X0)
| sP7(vnoType,vempty,X0)
| sK60(X0,vempty,vnoType) = X0 )
| ~ spl93_18
| ~ spl93_126 ),
inference(superposition,[],[f1156,f624]) ).
fof(f624,plain,
( ! [X1] : vnoType = vlookup(X1,vempty)
| ~ spl93_18 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f1429,plain,
( spl93_163
| ~ spl93_40
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1075,f1049,f712,f1427]) ).
fof(f1075,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X2)) )
| ~ spl93_40
| ~ spl93_112 ),
inference(superposition,[],[f713,f1050]) ).
fof(f1425,plain,
( spl93_162
| ~ spl93_39
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1074,f1049,f708,f1423]) ).
fof(f1074,plain,
( ! [X2,X3,X0,X1,X4] :
( visFreeVar(X4,vsubst(X0,X1,vapp(X2,X3)))
| ~ visFreeVar(X4,vsubst(X0,X1,X3)) )
| ~ spl93_39
| ~ spl93_112 ),
inference(superposition,[],[f709,f1050]) ).
fof(f1421,plain,
( spl93_161
| ~ spl93_34
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1068,f1049,f687,f1419]) ).
fof(f1068,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(X2,vvar(X0))) = vapp(vsubst(X0,X1,X2),X1)
| ~ spl93_34
| ~ spl93_112 ),
inference(superposition,[],[f1050,f688]) ).
fof(f1417,plain,
( spl93_160
| ~ spl93_34
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1065,f1049,f687,f1415]) ).
fof(f1065,plain,
( ! [X2,X0,X1] : vsubst(X0,X1,vapp(vvar(X0),X2)) = vapp(X1,vsubst(X0,X1,X2))
| ~ spl93_34
| ~ spl93_112 ),
inference(superposition,[],[f1050,f688]) ).
fof(f1413,plain,
( spl93_159
| ~ spl93_11
| ~ spl93_82 ),
inference(avatar_split_clause,[],[f920,f899,f595,f1411]) ).
fof(f920,plain,
( ! [X2,X0,X1] :
( ~ visFreeVar(vgensym(vabs(X0,X1,X2)),X2)
| vgensym(vabs(X0,X1,X2)) = X0 )
| ~ spl93_11
| ~ spl93_82 ),
inference(resolution,[],[f900,f596]) ).
fof(f1408,plain,
( spl93_158
| ~ spl93_42
| ~ spl93_59 ),
inference(avatar_split_clause,[],[f811,f797,f725,f1406]) ).
fof(f811,plain,
( ! [X2,X3,X0,X1] :
( vsomeType(X1) != vsomeType(X3)
| vtcheck(vbind(X0,X1,X2),vvar(X0),X3) )
| ~ spl93_42
| ~ spl93_59 ),
inference(superposition,[],[f798,f726]) ).
fof(f1396,plain,
( spl93_157
| ~ spl93_38
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1073,f1049,f704,f1394]) ).
fof(f704,plain,
( spl93_38
<=> ! [X4,X0,X3,X2,X1] : vapp(X3,X4) != vabs(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_38])]) ).
fof(f1073,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : vsubst(X0,X1,vapp(X2,X3)) != vabs(X4,X5,X6)
| ~ spl93_38
| ~ spl93_112 ),
inference(superposition,[],[f705,f1050]) ).
fof(f705,plain,
( ! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2)
| ~ spl93_38 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1392,plain,
( spl93_156
| ~ spl93_18
| ~ spl93_110 ),
inference(avatar_split_clause,[],[f1062,f1041,f623,f1390]) ).
fof(f1390,plain,
( spl93_156
<=> ! [X2,X0,X1,X3] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_156])]) ).
fof(f1062,plain,
( ! [X2,X3,X0,X1] :
( ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl93_18
| ~ spl93_110 ),
inference(trivial_inequality_removal,[],[f1059]) ).
fof(f1059,plain,
( ! [X2,X3,X0,X1] :
( vnoType != vnoType
| ~ vtcheck(vempty,X1,X2)
| vtcheck(vbind(X0,X3,vempty),X1,X2) )
| ~ spl93_18
| ~ spl93_110 ),
inference(superposition,[],[f1042,f624]) ).
fof(f1386,plain,
( spl93_155
| ~ spl93_22
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1072,f1049,f639,f1384]) ).
fof(f1072,plain,
( ! [X2,X3,X0,X1,X4] : vvar(X4) != vsubst(X0,X1,vapp(X2,X3))
| ~ spl93_22
| ~ spl93_112 ),
inference(superposition,[],[f640,f1050]) ).
fof(f1379,plain,
( spl93_129
| spl93_154
| spl93_131
| ~ spl93_3
| ~ spl93_132 ),
inference(avatar_split_clause,[],[f1198,f1191,f560,f1186,f1376,f1178]) ).
fof(f560,plain,
( spl93_3
<=> vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),sK18) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_3])]) ).
fof(f1198,plain,
( sP5(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| vsomeType(sK18) = vlookup(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vbind(sK14,sK15,sK16))
| sP6(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| ~ spl93_3
| ~ spl93_132 ),
inference(resolution,[],[f1192,f562]) ).
fof(f562,plain,
( vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),sK18)
| ~ spl93_3 ),
inference(avatar_component_clause,[],[f560]) ).
fof(f1366,plain,
( spl93_153
| spl93_1
| ~ spl93_133 ),
inference(avatar_split_clause,[],[f1213,f1195,f550,f1364]) ).
fof(f1213,plain,
( ! [X2,X0,X1] :
( vabs(sK14,X0,vsubst(X1,vvar(sK17),X2)) = vsubst(X1,vvar(sK17),vabs(sK14,X0,X2))
| sK14 = X1 )
| spl93_1
| ~ spl93_133 ),
inference(resolution,[],[f1196,f552]) ).
fof(f1362,plain,
( spl93_152
| ~ spl93_13
| ~ spl93_130 ),
inference(avatar_split_clause,[],[f1296,f1182,f603,f1359]) ).
fof(f1296,plain,
( visFreeVar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)),vvar(sK17))
| ~ spl93_13
| ~ spl93_130 ),
inference(superposition,[],[f604,f1184]) ).
fof(f1349,plain,
( spl93_151
| ~ spl93_112
| ~ spl93_150 ),
inference(avatar_split_clause,[],[f1345,f1342,f1049,f1347]) ).
fof(f1342,plain,
( spl93_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)
| vsubst(X0,X1,X2) = vapp(vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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,[spl93_150])]) ).
fof(f1345,plain,
( ! [X2,X0,X1] :
( vsubst(X0,X1,X2) = vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),vapp(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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) )
| ~ spl93_112
| ~ spl93_150 ),
inference(forward_demodulation,[],[f1343,f1050]) ).
fof(f1343,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(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(X0,X1,X2,vsubst(X0,X1,X2))))
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) )
| ~ spl93_150 ),
inference(avatar_component_clause,[],[f1342]) ).
fof(f1344,plain,
spl93_150,
inference(avatar_split_clause,[],[f464,f1342]) ).
fof(f464,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(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK83(X0,X1,X2,vsubst(X0,X1,X2))),vsubst(sK84(X0,X1,X2,vsubst(X0,X1,X2)),sK85(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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,[],[f398]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(vsubst(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK83(X0,X1,X2,X3)),vsubst(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3))) = X3
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| ( vapp(vsubst(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK83(X0,X1,X2,X3)),vsubst(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3))) = X3
& vapp(sK83(X0,X1,X2,X3),sK86(X0,X1,X2,X3)) = X2
& sK85(X0,X1,X2,X3) = X1
& sK84(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,[sK83,sK84,sK85,sK86])],[f279,f280]) ).
fof(f280,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(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK83(X0,X1,X2,X3)),vsubst(sK84(X0,X1,X2,X3),sK85(X0,X1,X2,X3),sK86(X0,X1,X2,X3))) = X3
& vapp(sK83(X0,X1,X2,X3),sK86(X0,X1,X2,X3)) = X2
& sK85(X0,X1,X2,X3) = X1
& sK84(X0,X1,X2,X3) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f279,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,[],[f210]) ).
fof(f210,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,[],[f142,f209,f208,f207,f206,f205]) ).
fof(f205,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(f206,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(f207,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(f208,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(f209,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(f142,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,[],[f141]) ).
fof(f141,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,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( vsubst(X0,X1,X2) = X3
=> ( ? [X4,X5,X6,X7,X8] :
( vabs(X4,X5,vsubst(X6,X7,X8)) = X3
& ~ visFreeVar(X4,X7)
& X4 != X6
& vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
| ? [X9,X10,X11,X12,X13,X14] :
( vsubst(X9,X10,vabs(X13,X11,vsubst(X12,vvar(X13),X14))) = X3
& vgensym(vapp(vapp(X10,X14),vvar(X9))) = X13
& visFreeVar(X12,X10)
& X9 != X12
& vabs(X12,X11,X14) = X2
& X1 = X10
& X0 = X9 )
| ? [X15,X16,X17,X18,X19] :
( vabs(X17,X18,X19) = X3
& X16 = X17
& vabs(X17,X18,X19) = X2
& X1 = X15
& X0 = X16 )
| ? [X20,X21,X22,X23] :
( vapp(vsubst(X21,X22,X20),vsubst(X21,X22,X23)) = X3
& vapp(X20,X23) = X2
& X1 = X22
& X0 = X21 )
| ? [X24,X25,X26] :
( vvar(X26) = X3
& X25 != X26
& vvar(X26) = X2
& X1 = X24
& X0 = X25 )
| ? [X27,X28,X29] :
( X3 = X29
& X27 = X28
& vvar(X28) = X2
& X1 = X29
& X0 = X27 ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X3,X5,X18] :
( vsubst(X0,X3,X5) = X18
=> ( ? [X20,X14,X8,X10,X11] :
( vabs(X20,X14,vsubst(X8,X10,X11)) = X18
& ~ visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X10,X14,X20,X23,X11] :
( vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18
& vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20,X14,X11] :
( vabs(X20,X14,X11) = X18
& X8 = X20
& vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
| ? [X11,X8,X10,X12] :
( vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18
& vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
| ? [X10,X8,X20] :
( vvar(X20) = X18
& X8 != X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 )
| ? [X8,X20,X10] :
( X10 = X18
& X8 = X20
& vvar(X20) = X5
& X3 = X10
& X0 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','subst-INV') ).
fof(f1332,plain,
spl93_149,
inference(avatar_split_clause,[],[f465,f1330]) ).
fof(f465,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(sK83(X0,X1,X2,vsubst(X0,X1,X2)),sK86(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,[],[f397]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| vapp(sK83(X0,X1,X2,X3),sK86(X0,X1,X2,X3)) = X2
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f281]) ).
fof(f1312,plain,
spl93_148,
inference(avatar_split_clause,[],[f467,f1310]) ).
fof(f467,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)
| sK84(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,[],[f395]) ).
fof(f395,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK84(X0,X1,X2,X3) = X0
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f281]) ).
fof(f1308,plain,
spl93_147,
inference(avatar_split_clause,[],[f466,f1306]) ).
fof(f466,plain,
! [X2,X0,X1] :
( sP13(vsubst(X0,X1,X2),X2,X1,X0)
| sP12(vsubst(X0,X1,X2),X2,X1,X0)
| sP11(vsubst(X0,X1,X2),X2,X1,X0)
| sK85(X0,X1,X2,vsubst(X0,X1,X2)) = X1
| sP10(vsubst(X0,X1,X2),X2,X1,X0)
| sP9(vsubst(X0,X1,X2),X2,X1,X0) ),
inference(equality_resolution,[],[f396]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( sP13(X3,X2,X1,X0)
| sP12(X3,X2,X1,X0)
| sP11(X3,X2,X1,X0)
| sK85(X0,X1,X2,X3) = X1
| sP10(X3,X2,X1,X0)
| sP9(X3,X2,X1,X0)
| vsubst(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f281]) ).
fof(f1294,plain,
spl93_146,
inference(avatar_split_clause,[],[f379,f1292]) ).
fof(f379,plain,
! [X2,X3,X0,X1] :
( vsubst(sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3),vabs(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vsubst(sK69(X0,X1,X2,X3),vvar(sK70(X0,X1,X2,X3)),sK71(X0,X1,X2,X3)))) = X0
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2,X3] :
( ( vsubst(sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3),vabs(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vsubst(sK69(X0,X1,X2,X3),vvar(sK70(X0,X1,X2,X3)),sK71(X0,X1,X2,X3)))) = X0
& sK70(X0,X1,X2,X3) = vgensym(vapp(vapp(sK67(X0,X1,X2,X3),sK71(X0,X1,X2,X3)),vvar(sK66(X0,X1,X2,X3))))
& visFreeVar(sK69(X0,X1,X2,X3),sK67(X0,X1,X2,X3))
& sK66(X0,X1,X2,X3) != sK69(X0,X1,X2,X3)
& vabs(sK69(X0,X1,X2,X3),sK68(X0,X1,X2,X3),sK71(X0,X1,X2,X3)) = X1
& sK67(X0,X1,X2,X3) = X2
& sK66(X0,X1,X2,X3) = X3 )
| ~ sP12(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66,sK67,sK68,sK69,sK70,sK71])],[f264,f265]) ).
fof(f265,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(sK66(X0,X1,X2,X3),sK67(X0,X1,X2,X3),vabs(sK70(X0,X1,X2,X3),sK68(X0,X1,X2,X3),vsubst(sK69(X0,X1,X2,X3),vvar(sK70(X0,X1,X2,X3)),sK71(X0,X1,X2,X3)))) = X0
& sK70(X0,X1,X2,X3) = vgensym(vapp(vapp(sK67(X0,X1,X2,X3),sK71(X0,X1,X2,X3)),vvar(sK66(X0,X1,X2,X3))))
& visFreeVar(sK69(X0,X1,X2,X3),sK67(X0,X1,X2,X3))
& sK66(X0,X1,X2,X3) != sK69(X0,X1,X2,X3)
& vabs(sK69(X0,X1,X2,X3),sK68(X0,X1,X2,X3),sK71(X0,X1,X2,X3)) = X1
& sK67(X0,X1,X2,X3) = X2
& sK66(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f264,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,[],[f263]) ).
fof(f263,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,[],[f208]) ).
fof(f1285,plain,
spl93_145,
inference(avatar_split_clause,[],[f448,f1283]) ).
fof(f448,plain,
! [X0] :
( sP3(vreduce(X0),X0)
| sP2(vreduce(X0),X0)
| sP1(vreduce(X0),X0)
| sP0(vreduce(X0),X0)
| sP4(vreduce(X0),X0)
| vabs(sK40(X0,vreduce(X0)),sK41(X0,vreduce(X0)),sK42(X0,vreduce(X0))) = X0
| vvar(sK43(X0,vreduce(X0))) = X0 ),
inference(equality_resolution,[],[f329]) ).
fof(f329,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| vabs(sK40(X0,X1),sK41(X0,X1),sK42(X0,X1)) = X0
| vvar(sK43(X0,X1)) = X0
| vreduce(X0) != X1 ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( sP3(X1,X0)
| sP2(X1,X0)
| sP1(X1,X0)
| sP0(X1,X0)
| sP4(X1,X0)
| ( vnoExp = X1
& vabs(sK40(X0,X1),sK41(X0,X1),sK42(X0,X1)) = X0 )
| ( vnoExp = X1
& vvar(sK43(X0,X1)) = X0 )
| vreduce(X0) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43])],[f233,f235,f234]) ).
fof(f234,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( vnoExp = X1
& vabs(X2,X3,X4) = X0 )
=> ( vnoExp = X1
& vabs(sK40(X0,X1),sK41(X0,X1),sK42(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f235,plain,
! [X0,X1] :
( ? [X5] :
( vnoExp = X1
& vvar(X5) = X0 )
=> ( vnoExp = X1
& vvar(sK43(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f233,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,[],[f198]) ).
fof(f198,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,[],[f123,f197,f196,f195,f194,f193]) ).
fof(f193,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(f194,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(f195,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(f196,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(f197,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(f123,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,[],[f122]) ).
fof(f122,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,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( vreduce(X0) = X1
=> ( ? [X2,X3,X4] :
( vnoExp = X1
& ~ visSomeExp(X4)
& vreduce(X3) = X4
& ! [X5,X6,X7] : vabs(X5,X6,X7) != X3
& vapp(X3,X2) = X0 )
| ? [X8,X9,X10] :
( vsomeExp(vapp(vgetSomeExp(X9),X10)) = X1
& visSomeExp(X9)
& vreduce(X8) = X9
& ! [X11,X12,X13] : vabs(X11,X12,X13) != X8
& vapp(X8,X10) = X0 )
| ? [X14,X15,X16,X17,X18] :
( vnoExp = X1
& ~ visValue(X18)
& ~ visSomeExp(X17)
& vreduce(X18) = X17
& vapp(vabs(X14,X15,X16),X18) = X0 )
| ? [X19,X20,X21,X22,X23] :
( vsomeExp(vsubst(X21,X22,X23)) = X1
& visValue(X22)
& ~ visSomeExp(X20)
& vreduce(X22) = X20
& vapp(vabs(X21,X19,X23),X22) = X0 )
| ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ? [X29,X30,X31] :
( vnoExp = X1
& vabs(X29,X30,X31) = X0 )
| ? [X32] :
( vnoExp = X1
& vvar(X32) = X0 ) ) ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X3,X18] :
( vreduce(X3) = X18
=> ( ? [X12,X11,X26] :
( vnoExp = X18
& ~ visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X11,X26,X12] :
( vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18
& visSomeExp(X26)
& vreduce(X11) = X26
& ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
| ? [X8,X9,X11,X25,X12] :
( vnoExp = X18
& ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X9,X25,X8,X12,X11] :
( vsomeExp(vsubst(X8,X12,X11)) = X18
& visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X12,X8,X9,X11,X25] :
( vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18
& visSomeExp(X25)
& vreduce(X12) = X25
& vapp(vabs(X8,X9,X11),X12) = X3 )
| ? [X8,X9,X10] :
( vnoExp = X18
& vabs(X8,X9,X10) = X3 )
| ? [X8] :
( vnoExp = X18
& vvar(X8) = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-INV') ).
fof(f1275,plain,
spl93_144,
inference(avatar_split_clause,[],[f547,f1273]) ).
fof(f547,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,[],[f546]) ).
fof(f546,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,[],[f545]) ).
fof(f545,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,[],[f544]) ).
fof(f544,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,[],[f543]) ).
fof(f543,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,[],[f436]) ).
fof(f436,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,[],[f192]) ).
fof(f192,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,[],[f191]) ).
fof(f191,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,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ( vabs(X7,X6,X9) = X2
& X1 = X5
& X0 = X4 )
=> ( ( vgensym(vapp(vapp(X5,X9),vvar(X4))) = X8
& visFreeVar(X7,X5)
& X4 != X7 )
=> ( vsubst(X0,X1,X2) = X3
=> vsubst(X4,X5,vabs(X8,X6,vsubst(X7,vvar(X8),X9))) = X3 ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X3,X5,X18,X8,X10,X14,X20,X23,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( vgensym(vapp(vapp(X10,X11),vvar(X8))) = X23
& visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vsubst(X8,X10,vabs(X23,X14,vsubst(X20,vvar(X23),X11))) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst4) ).
fof(f1271,plain,
spl93_143,
inference(avatar_split_clause,[],[f372,f1269]) ).
fof(f1269,plain,
( spl93_143
<=> ! [X0,X3,X2,X1] :
( vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_143])]) ).
fof(f372,plain,
! [X2,X3,X0,X1] :
( vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3))) = X0
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK61(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
& sK61(X0,X1,X2,X3) != sK63(X0,X1,X2,X3)
& vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3)) = X1
& sK64(X0,X1,X2,X3) = X2
& sK63(X0,X1,X2,X3) = X3 )
| ~ sP13(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62,sK63,sK64,sK65])],[f260,f261]) ).
fof(f261,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(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),vsubst(sK63(X0,X1,X2,X3),sK64(X0,X1,X2,X3),sK65(X0,X1,X2,X3))) = X0
& ~ visFreeVar(sK61(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
& sK61(X0,X1,X2,X3) != sK63(X0,X1,X2,X3)
& vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3)) = X1
& sK64(X0,X1,X2,X3) = X2
& sK63(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f260,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,[],[f259]) ).
fof(f259,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,[],[f209]) ).
fof(f1267,plain,
spl93_142,
inference(avatar_split_clause,[],[f378,f1265]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( sK70(X0,X1,X2,X3) = vgensym(vapp(vapp(sK67(X0,X1,X2,X3),sK71(X0,X1,X2,X3)),vvar(sK66(X0,X1,X2,X3))))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1257,plain,
spl93_141,
inference(avatar_split_clause,[],[f548,f1255]) ).
fof(f548,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,[],[f445]) ).
fof(f445,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,[],[f332]) ).
fof(f332,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,[],[f236]) ).
fof(f1242,plain,
spl93_140,
inference(avatar_split_clause,[],[f490,f1240]) ).
fof(f490,plain,
! [X0,X4] :
( vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4)) = vreduce(vapp(X0,X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0 ),
inference(equality_resolution,[],[f489]) ).
fof(f489,plain,
! [X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(vreduce(X0)),X4))
| ~ visSomeExp(vreduce(X0))
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f488]) ).
fof(f488,plain,
! [X3,X0,X1,X4] :
( vreduce(X1) = vsomeExp(vapp(vgetSomeExp(X3),X4))
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(equality_resolution,[],[f411]) ).
fof(f411,plain,
! [X2,X3,X0,X1,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0,X1,X2,X3,X4] :
( vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2
| vreduce(X1) != X2
| ~ visSomeExp(X3)
| vreduce(X0) != X3
| vabs(sK90(X0),sK91(X0),sK92(X0)) = X0
| vapp(X0,X4) != X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90,sK91,sK92])],[f158,f284]) ).
fof(f284,plain,
! [X0] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X0
=> vabs(sK90(X0),sK91(X0),sK92(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f158,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,[],[f157]) ).
fof(f157,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,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X0
& vapp(X0,X4) = X1 )
=> ( ( visSomeExp(X3)
& vreduce(X0) = X3 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vgetSomeExp(X3),X4)) = X2 ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X11,X3,X18,X26,X12] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vgetSomeExp(X26),X12)) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce5) ).
fof(f1238,plain,
spl93_139,
inference(avatar_split_clause,[],[f427,f1236]) ).
fof(f427,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,[],[f174]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 != X2 )
=> vtcheck(vbind(X0,X1,vbind(X2,X3,X4)),X5,X6) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 != X20 )
=> vtcheck(vbind(X20,X21,vbind(X8,X22,X19)),X10,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Swap') ).
fof(f1234,plain,
spl93_138,
inference(avatar_split_clause,[],[f384,f1232]) ).
fof(f1232,plain,
( spl93_138
<=> ! [X0,X3,X2,X1] :
( vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_138])]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X0
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( ( vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X0
& sK73(X0,X1,X2,X3) = sK74(X0,X1,X2,X3)
& vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X1
& sK72(X0,X1,X2,X3) = X2
& sK73(X0,X1,X2,X3) = X3 )
| ~ sP11(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72,sK73,sK74,sK75,sK76])],[f268,f269]) ).
fof(f269,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(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X0
& sK73(X0,X1,X2,X3) = sK74(X0,X1,X2,X3)
& vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X1
& sK72(X0,X1,X2,X3) = X2
& sK73(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f268,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,[],[f267]) ).
fof(f267,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,[],[f207]) ).
fof(f1230,plain,
spl93_137,
inference(avatar_split_clause,[],[f382,f1228]) ).
fof(f1228,plain,
( spl93_137
<=> ! [X0,X3,X2,X1] :
( vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_137])]) ).
fof(f382,plain,
! [X2,X3,X0,X1] :
( vabs(sK74(X0,X1,X2,X3),sK75(X0,X1,X2,X3),sK76(X0,X1,X2,X3)) = X1
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1226,plain,
spl93_136,
inference(avatar_split_clause,[],[f375,f1224]) ).
fof(f375,plain,
! [X2,X3,X0,X1] :
( vabs(sK69(X0,X1,X2,X3),sK68(X0,X1,X2,X3),sK71(X0,X1,X2,X3)) = X1
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1222,plain,
spl93_135,
inference(avatar_split_clause,[],[f369,f1220]) ).
fof(f1220,plain,
( spl93_135
<=> ! [X0,X3,X2,X1] :
( vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_135])]) ).
fof(f369,plain,
! [X2,X3,X0,X1] :
( vabs(sK61(X0,X1,X2,X3),sK62(X0,X1,X2,X3),sK65(X0,X1,X2,X3)) = X1
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f1218,plain,
spl93_134,
inference(avatar_split_clause,[],[f344,f1216]) ).
fof(f344,plain,
! [X2,X0,X1] :
( vtcheck(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK48(X0,X1,X2),sK50(X0,X1,X2))
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1,X2] :
( ( vtcheck(vbind(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK48(X0,X1,X2),sK50(X0,X1,X2))
& varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1
& vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X2 )
| ~ sP5(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50])],[f242,f243]) ).
fof(f243,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(sK47(X0,X1,X2),sK49(X0,X1,X2),X0),sK48(X0,X1,X2),sK50(X0,X1,X2))
& varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1
& vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f242,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,[],[f241]) ).
fof(f241,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,[],[f199]) ).
fof(f199,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(f1197,plain,
spl93_133,
inference(avatar_split_clause,[],[f542,f1195]) ).
fof(f542,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,[],[f541]) ).
fof(f541,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,[],[f540]) ).
fof(f540,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,[],[f539]) ).
fof(f539,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,[],[f435]) ).
fof(f435,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,[],[f190]) ).
fof(f190,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,[],[f189]) ).
fof(f189,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,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X4,X5,X8) = X2
& X1 = X7
& X0 = X6 )
=> ( ( ~ visFreeVar(X4,X7)
& X4 != X6 )
=> ( vsubst(X0,X1,X2) = X3
=> vabs(X4,X5,vsubst(X6,X7,X8)) = X3 ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X0,X3,X5,X18,X20,X14,X8,X10,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( ( ~ visFreeVar(X20,X10)
& X8 != X20 )
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,vsubst(X8,X10,X11)) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst5) ).
fof(f1193,plain,
spl93_132,
inference(avatar_split_clause,[],[f346,f1191]) ).
fof(f346,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vsomeType(X1) = vlookup(sK51(X0,X1,X2),X2)
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1,X2] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| ( vsomeType(X1) = vlookup(sK51(X0,X1,X2),X2)
& vvar(sK51(X0,X1,X2)) = X0 )
| ~ vtcheck(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51])],[f245,f246]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ? [X3] :
( vsomeType(X1) = vlookup(X3,X2)
& vvar(X3) = X0 )
=> ( vsomeType(X1) = vlookup(sK51(X0,X1,X2),X2)
& vvar(sK51(X0,X1,X2)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f245,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,[],[f201]) ).
fof(f201,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,[],[f132,f200,f199]) ).
fof(f200,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(f132,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,[],[f131]) ).
fof(f131,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,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( vtcheck(X2,X0,X1)
=> ( ? [X3,X4,X5] :
( vtcheck(X2,X4,X5)
& vtcheck(X2,X3,varrow(X5,X1))
& vapp(X3,X4) = X0 )
| ? [X6,X7,X8,X9] :
( vtcheck(vbind(X6,X8,X2),X7,X9)
& varrow(X8,X9) = X1
& vabs(X6,X8,X7) = X0 )
| ? [X10] :
( vsomeType(X1) = vlookup(X10,X2)
& vvar(X10) = X0 ) ) ),
inference(rectify,[],[f54]) ).
fof(f54,axiom,
! [X10,X14,X19] :
( vtcheck(X19,X10,X14)
=> ( ? [X11,X12,X9] :
( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14))
& vapp(X11,X12) = X10 )
| ? [X8,X12,X32,X33] :
( vtcheck(vbind(X8,X32,X19),X12,X33)
& varrow(X32,X33) = X14
& vabs(X8,X32,X12) = X10 )
| ? [X8] :
( vlookup(X8,X19) = vsomeType(X14)
& vvar(X8) = X10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-inv') ).
fof(f1189,plain,
( spl93_129
| spl93_130
| spl93_131
| ~ spl93_3
| ~ spl93_123 ),
inference(avatar_split_clause,[],[f1148,f1136,f560,f1186,f1182,f1178]) ).
fof(f1148,plain,
( sP5(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| vvar(sK17) = vvar(sK51(vvar(sK17),sK18,vbind(sK14,sK15,sK16)))
| sP6(vbind(sK14,sK15,sK16),sK18,vvar(sK17))
| ~ spl93_3
| ~ spl93_123 ),
inference(resolution,[],[f1137,f562]) ).
fof(f1176,plain,
spl93_128,
inference(avatar_split_clause,[],[f308,f1174]) ).
fof(f1174,plain,
( spl93_128
<=> ! [X0,X1] :
( vsomeExp(vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),vgetSomeExp(sK23(X0,X1)))) = X0
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_128])]) ).
fof(f308,plain,
! [X0,X1] :
( vsomeExp(vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),vgetSomeExp(sK23(X0,X1)))) = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),vgetSomeExp(sK23(X0,X1)))) = X0
& visSomeExp(sK23(X0,X1))
& sK23(X0,X1) = vreduce(sK19(X0,X1))
& vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),sK19(X0,X1)) = X1 )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20,sK21,sK22,sK23])],[f214,f215]) ).
fof(f215,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(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),vgetSomeExp(sK23(X0,X1)))) = X0
& visSomeExp(sK23(X0,X1))
& sK23(X0,X1) = vreduce(sK19(X0,X1))
& vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),sK19(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f214,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,[],[f213]) ).
fof(f213,plain,
! [X1,X0] :
( ? [X24,X25,X26,X27,X28] :
( vsomeExp(vapp(vabs(X25,X26,X27),vgetSomeExp(X28))) = X1
& visSomeExp(X28)
& vreduce(X24) = X28
& vapp(vabs(X25,X26,X27),X24) = X0 )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f197]) ).
fof(f1161,plain,
spl93_127,
inference(avatar_split_clause,[],[f512,f1159]) ).
fof(f512,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,[],[f511]) ).
fof(f511,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,[],[f510]) ).
fof(f510,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,[],[f426]) ).
fof(f426,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,[],[f172]) ).
fof(f172,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,[],[f171]) ).
fof(f171,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,[],[f101]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X3,X4,X5),X0) = X1
=> ( ( visSomeExp(X6)
& vreduce(X0) = X6 )
=> ( vreduce(X1) = X2
=> vsomeExp(vapp(vabs(X3,X4,X5),vgetSomeExp(X6))) = X2 ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X12,X3,X18,X8,X9,X11,X25] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vapp(vabs(X8,X9,X11),vgetSomeExp(X25))) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce2) ).
fof(f1157,plain,
spl93_126,
inference(avatar_split_clause,[],[f458,f1155]) ).
fof(f458,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| sK60(X0,X1,vlookup(X0,X1)) = X0 ),
inference(equality_resolution,[],[f355]) ).
fof(f355,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| sK60(X0,X1,X2) = X0
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| ( vnoType = X2
& vempty = X1
& sK60(X0,X1,X2) = X0 )
| vlookup(X0,X1) != X2 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f256,f257]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ? [X3] :
( vnoType = X2
& vempty = X1
& X0 = X3 )
=> ( vnoType = X2
& vempty = X1
& sK60(X0,X1,X2) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f256,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,[],[f204]) ).
fof(f204,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,[],[f134,f203,f202]) ).
fof(f202,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(f203,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(f134,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,[],[f133]) ).
fof(f133,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,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( vlookup(X0,X1) = X2
=> ( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X2
& X4 != X5
& vbind(X4,X3,X6) = X1
& X0 = X5 )
| ? [X7,X8,X9,X10] :
( vsomeType(X10) = X2
& X8 = X9
& vbind(X9,X10,X7) = X1
& X0 = X8 )
| ? [X11] :
( vnoType = X2
& vempty = X1
& X0 = X11 ) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X0,X15,X18] :
( vlookup(X0,X15) = X18
=> ( ? [X21,X20,X8,X19] :
( vlookup(X8,X19) = X18
& X8 != X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X19,X8,X20,X21] :
( vsomeType(X21) = X18
& X8 = X20
& vbind(X20,X21,X19) = X15
& X0 = X8 )
| ? [X8] :
( vnoType = X18
& vempty = X15
& X0 = X8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','lookup-INV') ).
fof(f1146,plain,
spl93_125,
inference(avatar_split_clause,[],[f352,f1144]) ).
fof(f1144,plain,
( spl93_125
<=> ! [X2,X0,X1] :
( vbind(sK58(X0,X1,X2),sK59(X0,X1,X2),sK56(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_125])]) ).
fof(f352,plain,
! [X2,X0,X1] :
( vbind(sK58(X0,X1,X2),sK59(X0,X1,X2),sK56(X0,X1,X2)) = X1
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ( vsomeType(sK59(X0,X1,X2)) = X0
& sK57(X0,X1,X2) = sK58(X0,X1,X2)
& vbind(sK58(X0,X1,X2),sK59(X0,X1,X2),sK56(X0,X1,X2)) = X1
& sK57(X0,X1,X2) = X2 )
| ~ sP7(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vsomeType(X6) = X0
& X4 = X5
& vbind(X5,X6,X3) = X1
& X2 = X4 )
=> ( vsomeType(sK59(X0,X1,X2)) = X0
& sK57(X0,X1,X2) = sK58(X0,X1,X2)
& vbind(sK58(X0,X1,X2),sK59(X0,X1,X2),sK56(X0,X1,X2)) = X1
& sK57(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f253,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,[],[f252]) ).
fof(f252,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,[],[f202]) ).
fof(f1142,plain,
spl93_124,
inference(avatar_split_clause,[],[f348,f1140]) ).
fof(f348,plain,
! [X2,X0,X1] :
( vbind(sK53(X0,X1,X2),sK52(X0,X1,X2),sK55(X0,X1,X2)) = X1
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( ( vlookup(sK54(X0,X1,X2),sK55(X0,X1,X2)) = X0
& sK53(X0,X1,X2) != sK54(X0,X1,X2)
& vbind(sK53(X0,X1,X2),sK52(X0,X1,X2),sK55(X0,X1,X2)) = X1
& sK54(X0,X1,X2) = X2 )
| ~ sP8(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54,sK55])],[f249,f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5,X6] :
( vlookup(X5,X6) = X0
& X4 != X5
& vbind(X4,X3,X6) = X1
& X2 = X5 )
=> ( vlookup(sK54(X0,X1,X2),sK55(X0,X1,X2)) = X0
& sK53(X0,X1,X2) != sK54(X0,X1,X2)
& vbind(sK53(X0,X1,X2),sK52(X0,X1,X2),sK55(X0,X1,X2)) = X1
& sK54(X0,X1,X2) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f249,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,[],[f248]) ).
fof(f248,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,[],[f203]) ).
fof(f1138,plain,
spl93_123,
inference(avatar_split_clause,[],[f345,f1136]) ).
fof(f345,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| sP5(X2,X1,X0)
| vvar(sK51(X0,X1,X2)) = X0
| ~ vtcheck(X2,X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1134,plain,
spl93_122,
inference(avatar_split_clause,[],[f342,f1132]) ).
fof(f342,plain,
! [X2,X0,X1] :
( vabs(sK47(X0,X1,X2),sK49(X0,X1,X2),sK48(X0,X1,X2)) = X2
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f1130,plain,
spl93_121,
inference(avatar_split_clause,[],[f324,f1128]) ).
fof(f1128,plain,
( spl93_121
<=> ! [X0,X1] :
( vapp(vabs(sK37(X0,X1),sK35(X0,X1),sK39(X0,X1)),sK38(X0,X1)) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_121])]) ).
fof(f324,plain,
! [X0,X1] :
( vapp(vabs(sK37(X0,X1),sK35(X0,X1),sK39(X0,X1)),sK38(X0,X1)) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( ( vsomeExp(vsubst(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1))) = X0
& visValue(sK38(X0,X1))
& ~ visSomeExp(sK36(X0,X1))
& sK36(X0,X1) = vreduce(sK38(X0,X1))
& vapp(vabs(sK37(X0,X1),sK35(X0,X1),sK39(X0,X1)),sK38(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f230,f231]) ).
fof(f231,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(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1))) = X0
& visValue(sK38(X0,X1))
& ~ visSomeExp(sK36(X0,X1))
& sK36(X0,X1) = vreduce(sK38(X0,X1))
& vapp(vabs(sK37(X0,X1),sK35(X0,X1),sK39(X0,X1)),sK38(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f230,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,[],[f229]) ).
fof(f229,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,[],[f193]) ).
fof(f1126,plain,
spl93_120,
inference(avatar_split_clause,[],[f319,f1124]) ).
fof(f1124,plain,
( spl93_120
<=> ! [X0,X1] :
( vapp(vabs(sK30(X0,X1),sK31(X0,X1),sK32(X0,X1)),sK34(X0,X1)) = X1
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_120])]) ).
fof(f319,plain,
! [X0,X1] :
( vapp(vabs(sK30(X0,X1),sK31(X0,X1),sK32(X0,X1)),sK34(X0,X1)) = X1
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visValue(sK34(X0,X1))
& ~ visSomeExp(sK33(X0,X1))
& sK33(X0,X1) = vreduce(sK34(X0,X1))
& vapp(vabs(sK30(X0,X1),sK31(X0,X1),sK32(X0,X1)),sK34(X0,X1)) = X1 )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33,sK34])],[f226,f227]) ).
fof(f227,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(sK34(X0,X1))
& ~ visSomeExp(sK33(X0,X1))
& sK33(X0,X1) = vreduce(sK34(X0,X1))
& vapp(vabs(sK30(X0,X1),sK31(X0,X1),sK32(X0,X1)),sK34(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f226,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,[],[f225]) ).
fof(f225,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,[],[f194]) ).
fof(f1122,plain,
spl93_119,
inference(avatar_split_clause,[],[f305,f1120]) ).
fof(f1120,plain,
( spl93_119
<=> ! [X0,X1] :
( vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),sK19(X0,X1)) = X1
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_119])]) ).
fof(f305,plain,
! [X0,X1] :
( vapp(vabs(sK20(X0,X1),sK21(X0,X1),sK22(X0,X1)),sK19(X0,X1)) = X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f1116,plain,
( spl93_118
| ~ spl93_12
| ~ spl93_112 ),
inference(avatar_split_clause,[],[f1071,f1049,f599,f1114]) ).
fof(f599,plain,
( spl93_12
<=> ! [X0,X1] : ~ visValue(vapp(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_12])]) ).
fof(f1071,plain,
( ! [X2,X3,X0,X1] : ~ visValue(vsubst(X0,X1,vapp(X2,X3)))
| ~ spl93_12
| ~ spl93_112 ),
inference(superposition,[],[f600,f1050]) ).
fof(f600,plain,
( ! [X0,X1] : ~ visValue(vapp(X0,X1))
| ~ spl93_12 ),
inference(avatar_component_clause,[],[f599]) ).
fof(f1110,plain,
spl93_117,
inference(avatar_split_clause,[],[f509,f1108]) ).
fof(f509,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,[],[f508]) ).
fof(f508,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,[],[f507]) ).
fof(f507,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,[],[f425]) ).
fof(f425,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,[],[f170]) ).
fof(f170,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,[],[f169]) ).
fof(f169,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,[],[f100]) ).
fof(f100,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X4,X0,X6),X5) = X2
=> ( ( visValue(X5)
& ~ visSomeExp(X1)
& vreduce(X5) = X1 )
=> ( vreduce(X2) = X3
=> vsomeExp(vsubst(X4,X5,X6)) = X3 ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X9,X25,X3,X18,X8,X12,X11] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vsomeExp(vsubst(X8,X12,X11)) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce3) ).
fof(f1106,plain,
spl93_116,
inference(avatar_split_clause,[],[f487,f1104]) ).
fof(f487,plain,
! [X0,X1] :
( vnoExp = vreduce(vapp(X1,X0))
| visSomeExp(vreduce(X1))
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1 ),
inference(equality_resolution,[],[f486]) ).
fof(f486,plain,
! [X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(vreduce(X1))
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f485]) ).
fof(f485,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(equality_resolution,[],[f410]) ).
fof(f410,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| visSomeExp(X2)
| vreduce(X1) != X2
| vabs(sK87(X1),sK88(X1),sK89(X1)) = X1
| vapp(X1,X0) != X3 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88,sK89])],[f156,f282]) ).
fof(f282,plain,
! [X1] :
( ? [X5,X6,X7] : vabs(X5,X6,X7) = X1
=> vabs(sK87(X1),sK88(X1),sK89(X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f156,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,[],[f155]) ).
fof(f155,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,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5,X6,X7] : vabs(X5,X6,X7) != X1
& vapp(X1,X0) = X3 )
=> ( ( ~ visSomeExp(X2)
& vreduce(X1) = X2 )
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X12,X11,X26,X3,X18] :
( ( ! [X27,X28,X29] : vabs(X27,X28,X29) != X11
& vapp(X11,X12) = X3 )
=> ( ( ~ visSomeExp(X26)
& vreduce(X11) = X26 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce6) ).
fof(f1094,plain,
spl93_115,
inference(avatar_split_clause,[],[f529,f1092]) ).
fof(f529,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,[],[f432]) ).
fof(f432,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,[],[f184]) ).
fof(f184,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,[],[f183]) ).
fof(f183,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,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vtcheck(vbind(X2,X3,vbind(X0,X1,X4)),X5,X6)
& X0 = X2 )
=> vtcheck(vbind(X2,X3,X4),X5,X6) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X20,X21,X8,X22,X19,X10,X14] :
( ( vtcheck(vbind(X8,X22,vbind(X20,X21,X19)),X10,X14)
& X8 = X20 )
=> vtcheck(vbind(X8,X22,X19),X10,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Context-Duplicate') ).
fof(f1090,plain,
spl93_114,
inference(avatar_split_clause,[],[f456,f1088]) ).
fof(f456,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vnoType = vlookup(X0,X1) ),
inference(equality_resolution,[],[f357]) ).
fof(f357,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vnoType = X2
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f258]) ).
fof(f1058,plain,
( spl93_113
| ~ spl93_40
| ~ spl93_73 ),
inference(avatar_split_clause,[],[f953,f863,f712,f1056]) ).
fof(f1056,plain,
( spl93_113
<=> ! [X2,X0,X1,X3] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_113])]) ).
fof(f863,plain,
( spl93_73
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_73])]) ).
fof(f953,plain,
( ! [X2,X3,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(vapp(X1,X2),X3))),X1)
| ~ spl93_40
| ~ spl93_73 ),
inference(resolution,[],[f864,f713]) ).
fof(f864,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl93_73 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f1051,plain,
spl93_112,
inference(avatar_split_clause,[],[f533,f1049]) ).
fof(f533,plain,
! [X6,X7,X4,X5] : vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = vsubst(X5,X6,vapp(X4,X7)),
inference(equality_resolution,[],[f532]) ).
fof(f532,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,[],[f531]) ).
fof(f531,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,[],[f530]) ).
fof(f530,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,[],[f433]) ).
fof(f433,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,[],[f186]) ).
fof(f186,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,[],[f185]) ).
fof(f185,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,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( vapp(X4,X7) = X2
& X1 = X6
& X0 = X5 )
=> ( vsubst(X0,X1,X2) = X3
=> vapp(vsubst(X5,X6,X4),vsubst(X5,X6,X7)) = X3 ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X0,X3,X5,X18,X11,X8,X10,X12] :
( ( vapp(X11,X12) = X5
& X3 = X10
& X0 = X8 )
=> ( vsubst(X0,X3,X5) = X18
=> vapp(vsubst(X8,X10,X11),vsubst(X8,X10,X12)) = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst2) ).
fof(f1047,plain,
spl93_111,
inference(avatar_split_clause,[],[f412,f1045]) ).
fof(f412,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,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(X1,vapp(X2,X3),X4)
| ~ vtcheck(X1,X3,X0)
| ~ vtcheck(X1,X2,varrow(X0,X4)) ),
inference(flattening,[],[f159]) ).
fof(f159,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,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X1,X3,X0)
& vtcheck(X1,X2,varrow(X0,X4)) )
=> vtcheck(X1,vapp(X2,X3),X4) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X9,X19,X11,X12,X14] :
( ( vtcheck(X19,X12,X9)
& vtcheck(X19,X11,varrow(X9,X14)) )
=> vtcheck(X19,vapp(X11,X12),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-app') ).
fof(f1043,plain,
spl93_110,
inference(avatar_split_clause,[],[f409,f1041]) ).
fof(f409,plain,
! [X2,X3,X0,X1,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X0,X1,X2),X3,X4)
| ~ vtcheck(X2,X3,X4)
| vnoType != vlookup(X0,X2) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2,X3,X4] :
( ( vtcheck(X2,X3,X4)
& vnoType = vlookup(X0,X2) )
=> vtcheck(vbind(X0,X1,X2),X3,X4) ),
inference(rectify,[],[f55]) ).
fof(f55,axiom,
! [X8,X9,X19,X10,X14] :
( ( vtcheck(X19,X10,X14)
& vnoType = vlookup(X8,X19) )
=> vtcheck(vbind(X8,X9,X19),X10,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Weak') ).
fof(f1039,plain,
spl93_109,
inference(avatar_split_clause,[],[f405,f1037]) ).
fof(f405,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,[],[f150]) ).
fof(f150,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,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3,X4] :
( vtcheck(vbind(X1,X3,X0),X2,X4)
=> vtcheck(X0,vabs(X1,X3,X2),varrow(X3,X4)) ),
inference(rectify,[],[f52]) ).
fof(f52,axiom,
! [X19,X8,X10,X9,X14] :
( vtcheck(vbind(X8,X9,X19),X10,X14)
=> vtcheck(X19,vabs(X8,X9,X10),varrow(X9,X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-abs') ).
fof(f1035,plain,
spl93_108,
inference(avatar_split_clause,[],[f393,f1033]) ).
fof(f1033,plain,
( spl93_108
<=> ! [X0,X3,X2,X1] :
( sK80(X0,X1,X2,X3) = sK81(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_108])]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( sK80(X0,X1,X2,X3) = sK81(X0,X1,X2,X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1,X2,X3] :
( ( sK82(X0,X1,X2,X3) = X0
& sK80(X0,X1,X2,X3) = sK81(X0,X1,X2,X3)
& vvar(sK81(X0,X1,X2,X3)) = X1
& sK82(X0,X1,X2,X3) = X2
& sK80(X0,X1,X2,X3) = X3 )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82])],[f276,f277]) ).
fof(f277,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( X0 = X6
& X4 = X5
& vvar(X5) = X1
& X2 = X6
& X3 = X4 )
=> ( sK82(X0,X1,X2,X3) = X0
& sK80(X0,X1,X2,X3) = sK81(X0,X1,X2,X3)
& vvar(sK81(X0,X1,X2,X3)) = X1
& sK82(X0,X1,X2,X3) = X2
& sK80(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f276,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,[],[f275]) ).
fof(f275,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,[],[f205]) ).
fof(f1031,plain,
spl93_107,
inference(avatar_split_clause,[],[f388,f1029]) ).
fof(f1029,plain,
( spl93_107
<=> ! [X0,X3,X2,X1] :
( sK78(X0,X1,X2,X3) != sK79(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_107])]) ).
fof(f388,plain,
! [X2,X3,X0,X1] :
( sK78(X0,X1,X2,X3) != sK79(X0,X1,X2,X3)
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1,X2,X3] :
( ( vvar(sK79(X0,X1,X2,X3)) = X0
& sK78(X0,X1,X2,X3) != sK79(X0,X1,X2,X3)
& vvar(sK79(X0,X1,X2,X3)) = X1
& sK77(X0,X1,X2,X3) = X2
& sK78(X0,X1,X2,X3) = X3 )
| ~ sP10(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK77,sK78,sK79])],[f272,f273]) ).
fof(f273,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5,X6] :
( vvar(X6) = X0
& X5 != X6
& vvar(X6) = X1
& X2 = X4
& X3 = X5 )
=> ( vvar(sK79(X0,X1,X2,X3)) = X0
& sK78(X0,X1,X2,X3) != sK79(X0,X1,X2,X3)
& vvar(sK79(X0,X1,X2,X3)) = X1
& sK77(X0,X1,X2,X3) = X2
& sK78(X0,X1,X2,X3) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f272,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,[],[f271]) ).
fof(f271,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,[],[f206]) ).
fof(f1027,plain,
spl93_106,
inference(avatar_split_clause,[],[f383,f1025]) ).
fof(f1025,plain,
( spl93_106
<=> ! [X0,X3,X2,X1] :
( sK73(X0,X1,X2,X3) = sK74(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_106])]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( sK73(X0,X1,X2,X3) = sK74(X0,X1,X2,X3)
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f1023,plain,
spl93_105,
inference(avatar_split_clause,[],[f377,f1021]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( visFreeVar(sK69(X0,X1,X2,X3),sK67(X0,X1,X2,X3))
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1019,plain,
spl93_104,
inference(avatar_split_clause,[],[f376,f1017]) ).
fof(f1017,plain,
( spl93_104
<=> ! [X0,X3,X2,X1] :
( sK66(X0,X1,X2,X3) != sK69(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_104])]) ).
fof(f376,plain,
! [X2,X3,X0,X1] :
( sK66(X0,X1,X2,X3) != sK69(X0,X1,X2,X3)
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f1015,plain,
spl93_103,
inference(avatar_split_clause,[],[f371,f1013]) ).
fof(f371,plain,
! [X2,X3,X0,X1] :
( ~ visFreeVar(sK61(X0,X1,X2,X3),sK64(X0,X1,X2,X3))
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f1008,plain,
spl93_102,
inference(avatar_split_clause,[],[f370,f1006]) ).
fof(f1006,plain,
( spl93_102
<=> ! [X0,X3,X2,X1] :
( sK61(X0,X1,X2,X3) != sK63(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_102])]) ).
fof(f370,plain,
! [X2,X3,X0,X1] :
( sK61(X0,X1,X2,X3) != sK63(X0,X1,X2,X3)
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f1004,plain,
spl93_101,
inference(avatar_split_clause,[],[f340,f1002]) ).
fof(f340,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0,X1,X2] :
( ( vtcheck(X0,sK45(X0,X1,X2),sK46(X0,X1,X2))
& vtcheck(X0,sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1))
& vapp(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X2 )
| ~ sP6(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46])],[f238,f239]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ? [X3,X4,X5] :
( vtcheck(X0,X4,X5)
& vtcheck(X0,X3,varrow(X5,X1))
& vapp(X3,X4) = X2 )
=> ( vtcheck(X0,sK45(X0,X1,X2),sK46(X0,X1,X2))
& vtcheck(X0,sK44(X0,X1,X2),varrow(sK46(X0,X1,X2),X1))
& vapp(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f238,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,[],[f237]) ).
fof(f237,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,[],[f200]) ).
fof(f1000,plain,
spl93_100,
inference(avatar_split_clause,[],[f328,f998]) ).
fof(f998,plain,
( spl93_100
<=> ! [X0,X1] :
( vsomeExp(vsubst(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1))) = X0
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_100])]) ).
fof(f328,plain,
! [X0,X1] :
( vsomeExp(vsubst(sK37(X0,X1),sK38(X0,X1),sK39(X0,X1))) = X0
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f991,plain,
spl93_99,
inference(avatar_split_clause,[],[f457,f989]) ).
fof(f457,plain,
! [X0,X1] :
( sP8(vlookup(X0,X1),X1,X0)
| sP7(vlookup(X0,X1),X1,X0)
| vempty = X1 ),
inference(equality_resolution,[],[f356]) ).
fof(f356,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| sP7(X2,X1,X0)
| vempty = X1
| vlookup(X0,X1) != X2 ),
inference(cnf_transformation,[],[f258]) ).
fof(f987,plain,
spl93_98,
inference(avatar_split_clause,[],[f350,f985]) ).
fof(f350,plain,
! [X2,X0,X1] :
( vlookup(sK54(X0,X1,X2),sK55(X0,X1,X2)) = X0
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f251]) ).
fof(f983,plain,
spl93_97,
inference(avatar_split_clause,[],[f343,f981]) ).
fof(f343,plain,
! [X2,X0,X1] :
( varrow(sK49(X0,X1,X2),sK50(X0,X1,X2)) = X1
| ~ sP5(X0,X1,X2) ),
inference(cnf_transformation,[],[f244]) ).
fof(f976,plain,
spl93_96,
inference(avatar_split_clause,[],[f339,f974]) ).
fof(f339,plain,
! [X2,X0,X1] :
( vapp(sK44(X0,X1,X2),sK45(X0,X1,X2)) = X2
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f970,plain,
spl93_95,
inference(avatar_split_clause,[],[f506,f968]) ).
fof(f506,plain,
! [X2,X0,X1,X4] :
( vnoExp = vreduce(vapp(vabs(X0,X1,X2),X4))
| visValue(X4)
| visSomeExp(vreduce(X4)) ),
inference(equality_resolution,[],[f505]) ).
fof(f505,plain,
! [X2,X0,X1,X4,X5] :
( vnoExp = vreduce(X5)
| visValue(X4)
| visSomeExp(vreduce(X4))
| vapp(vabs(X0,X1,X2),X4) != X5 ),
inference(equality_resolution,[],[f504]) ).
fof(f504,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,[],[f424]) ).
fof(f424,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,[],[f168]) ).
fof(f168,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,[],[f167]) ).
fof(f167,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,[],[f99]) ).
fof(f99,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( vapp(vabs(X0,X1,X2),X4) = X5
=> ( ( ~ visValue(X4)
& ~ visSomeExp(X3)
& vreduce(X4) = X3 )
=> ( vreduce(X5) = X6
=> vnoExp = X6 ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X8,X9,X11,X25,X12,X3,X18] :
( vapp(vabs(X8,X9,X11),X12) = X3
=> ( ( ~ visValue(X12)
& ~ visSomeExp(X25)
& vreduce(X12) = X25 )
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce4) ).
fof(f966,plain,
spl93_94,
inference(avatar_split_clause,[],[f341,f964]) ).
fof(f341,plain,
! [X2,X0,X1] :
( vtcheck(X0,sK45(X0,X1,X2),sK46(X0,X1,X2))
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f240]) ).
fof(f962,plain,
spl93_93,
inference(avatar_split_clause,[],[f318,f960]) ).
fof(f960,plain,
( spl93_93
<=> ! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK28(X0,X1)),sK29(X0,X1))) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_93])]) ).
fof(f318,plain,
! [X0,X1] :
( vsomeExp(vapp(vgetSomeExp(sK28(X0,X1)),sK29(X0,X1))) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( ( vsomeExp(vapp(vgetSomeExp(sK28(X0,X1)),sK29(X0,X1))) = X0
& visSomeExp(sK28(X0,X1))
& sK28(X0,X1) = vreduce(sK27(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK27(X0,X1)
& vapp(sK27(X0,X1),sK29(X0,X1)) = X1 )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28,sK29])],[f222,f223]) ).
fof(f223,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(sK28(X0,X1)),sK29(X0,X1))) = X0
& visSomeExp(sK28(X0,X1))
& sK28(X0,X1) = vreduce(sK27(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK27(X0,X1)
& vapp(sK27(X0,X1),sK29(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f222,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,[],[f221]) ).
fof(f221,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,[],[f195]) ).
fof(f952,plain,
spl93_92,
inference(avatar_split_clause,[],[f524,f950]) ).
fof(f524,plain,
! [X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X5,vbind(X1,X0,X6))
| X1 = X5 ),
inference(equality_resolution,[],[f523]) ).
fof(f523,plain,
! [X2,X0,X1,X6,X5] :
( vlookup(X5,X6) = vlookup(X2,vbind(X1,X0,X6))
| X1 = X5
| X2 != X5 ),
inference(equality_resolution,[],[f522]) ).
fof(f522,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,[],[f430]) ).
fof(f430,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,[],[f180]) ).
fof(f180,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,[],[f179]) ).
fof(f179,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,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X1,X0,X6) = X3
& X2 = X5 )
=> ( X1 != X5
=> ( vlookup(X2,X3) = X4
=> vlookup(X5,X6) = X4 ) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X21,X20,X0,X15,X18,X8,X19] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 != X20
=> ( vlookup(X0,X15) = X18
=> vlookup(X8,X19) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup2) ).
fof(f948,plain,
spl93_91,
inference(avatar_split_clause,[],[f392,f946]) ).
fof(f946,plain,
( spl93_91
<=> ! [X0,X3,X2,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_91])]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( vvar(sK81(X0,X1,X2,X3)) = X1
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f944,plain,
spl93_90,
inference(avatar_split_clause,[],[f389,f942]) ).
fof(f942,plain,
( spl93_90
<=> ! [X0,X3,X2,X1] :
( vvar(sK79(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_90])]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( vvar(sK79(X0,X1,X2,X3)) = X0
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f940,plain,
spl93_89,
inference(avatar_split_clause,[],[f387,f938]) ).
fof(f938,plain,
( spl93_89
<=> ! [X0,X3,X2,X1] :
( vvar(sK79(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_89])]) ).
fof(f387,plain,
! [X2,X3,X0,X1] :
( vvar(sK79(X0,X1,X2,X3)) = X1
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f936,plain,
spl93_88,
inference(avatar_split_clause,[],[f353,f934]) ).
fof(f934,plain,
( spl93_88
<=> ! [X2,X0,X1] :
( sK57(X0,X1,X2) = sK58(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_88])]) ).
fof(f353,plain,
! [X2,X0,X1] :
( sK57(X0,X1,X2) = sK58(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f932,plain,
spl93_87,
inference(avatar_split_clause,[],[f349,f930]) ).
fof(f930,plain,
( spl93_87
<=> ! [X2,X0,X1] :
( sK53(X0,X1,X2) != sK54(X0,X1,X2)
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_87])]) ).
fof(f349,plain,
! [X2,X0,X1] :
( sK53(X0,X1,X2) != sK54(X0,X1,X2)
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f251]) ).
fof(f928,plain,
( spl93_86
| ~ spl93_39
| ~ spl93_53 ),
inference(avatar_split_clause,[],[f821,f773,f708,f926]) ).
fof(f926,plain,
( spl93_86
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_86])]) ).
fof(f821,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X1)
| ~ spl93_39
| ~ spl93_53 ),
inference(resolution,[],[f774,f709]) ).
fof(f913,plain,
( spl93_85
| ~ spl93_40
| ~ spl93_53 ),
inference(avatar_split_clause,[],[f820,f773,f712,f911]) ).
fof(f911,plain,
( spl93_85
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_85])]) ).
fof(f820,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(vapp(X0,X1),X2)),X0)
| ~ spl93_40
| ~ spl93_53 ),
inference(resolution,[],[f774,f713]) ).
fof(f909,plain,
( spl93_84
| ~ spl93_39
| ~ spl93_48 ),
inference(avatar_split_clause,[],[f809,f749,f708,f907]) ).
fof(f907,plain,
( spl93_84
<=> ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_84])]) ).
fof(f809,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X2)
| ~ spl93_39
| ~ spl93_48 ),
inference(resolution,[],[f750,f709]) ).
fof(f905,plain,
spl93_83,
inference(avatar_split_clause,[],[f538,f903]) ).
fof(f538,plain,
! [X3,X8,X6,X7] : vabs(X6,X7,X8) = vsubst(X6,X3,vabs(X6,X7,X8)),
inference(equality_resolution,[],[f537]) ).
fof(f537,plain,
! [X2,X3,X8,X6,X7] :
( vabs(X6,X7,X8) = vsubst(X2,X3,vabs(X6,X7,X8))
| X2 != X6 ),
inference(equality_resolution,[],[f536]) ).
fof(f536,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,[],[f535]) ).
fof(f535,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,[],[f534]) ).
fof(f534,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,[],[f434]) ).
fof(f434,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,[],[f188]) ).
fof(f188,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,[],[f187]) ).
fof(f187,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,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ( vabs(X6,X7,X8) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 = X6
=> ( vsubst(X2,X3,X4) = X5
=> vabs(X6,X7,X8) = X5 ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X10,X8,X0,X3,X5,X18,X20,X14,X11] :
( ( vabs(X20,X14,X11) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> vabs(X20,X14,X11) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst3) ).
fof(f901,plain,
spl93_82,
inference(avatar_split_clause,[],[f503,f899]) ).
fof(f503,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4 ),
inference(equality_resolution,[],[f502]) ).
fof(f502,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X1,vabs(X3,X0,X5))
| ~ visFreeVar(X4,X5)
| X3 = X4
| X1 != X4 ),
inference(equality_resolution,[],[f421]) ).
fof(f421,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,[],[f166]) ).
fof(f166,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,[],[f165]) ).
fof(f165,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,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( vabs(X3,X0,X5) = X2
& X1 = X4 )
=> ( ( visFreeVar(X1,X2)
=> ( visFreeVar(X4,X5)
& X3 != X4 ) )
& ( ( visFreeVar(X4,X5)
& X3 != X4 )
=> visFreeVar(X1,X2) ) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X14,X0,X3,X8,X13,X10] :
( ( vabs(X8,X14,X10) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X10)
& X8 != X13 ) )
& ( ( visFreeVar(X13,X10)
& X8 != X13 )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar1) ).
fof(f897,plain,
spl93_81,
inference(avatar_split_clause,[],[f419,f895]) ).
fof(f895,plain,
( spl93_81
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_81])]) ).
fof(f419,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f164]) ).
fof(f164,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,[],[f163]) ).
fof(f163,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,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vabs(X0,X1,X2) = vabs(X3,X4,X5) )
& ( vabs(X0,X1,X2) = vabs(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X2,X3,X1,X4,X5] :
( ( ( X3 = X5
& X2 = X4
& X0 = X1 )
=> vabs(X0,X2,X3) = vabs(X1,X4,X5) )
& ( vabs(X0,X2,X3) = vabs(X1,X4,X5)
=> ( X3 = X5
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-abs') ).
fof(f893,plain,
spl93_80,
inference(avatar_split_clause,[],[f418,f891]) ).
fof(f891,plain,
( spl93_80
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_80])]) ).
fof(f418,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f164]) ).
fof(f889,plain,
spl93_79,
inference(avatar_split_clause,[],[f417,f887]) ).
fof(f887,plain,
( spl93_79
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_79])]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vabs(X0,X1,X2) != vabs(X3,X4,X5) ),
inference(cnf_transformation,[],[f164]) ).
fof(f885,plain,
spl93_78,
inference(avatar_split_clause,[],[f415,f883]) ).
fof(f883,plain,
( spl93_78
<=> ! [X3,X4,X0,X5,X2,X1] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_78])]) ).
fof(f415,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 = X5
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f162]) ).
fof(f162,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,[],[f161]) ).
fof(f161,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,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ( X2 = X5
& X1 = X4
& X0 = X3 )
=> vbind(X0,X1,X2) = vbind(X3,X4,X5) )
& ( vbind(X0,X1,X2) = vbind(X3,X4,X5)
=> ( X2 = X5
& X1 = X4
& X0 = X3 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X2,X15,X1,X4,X16] :
( ( ( X15 = X16
& X2 = X4
& X0 = X1 )
=> vbind(X0,X2,X15) = vbind(X1,X4,X16) )
& ( vbind(X0,X2,X15) = vbind(X1,X4,X16)
=> ( X15 = X16
& X2 = X4
& X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-bind') ).
fof(f881,plain,
spl93_77,
inference(avatar_split_clause,[],[f414,f879]) ).
fof(f879,plain,
( spl93_77
<=> ! [X2,X3,X4,X0,X5,X1] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_77])]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X4
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f162]) ).
fof(f877,plain,
spl93_76,
inference(avatar_split_clause,[],[f413,f875]) ).
fof(f875,plain,
( spl93_76
<=> ! [X2,X4,X0,X5,X3,X1] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_76])]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X3
| vbind(X0,X1,X2) != vbind(X3,X4,X5) ),
inference(cnf_transformation,[],[f162]) ).
fof(f873,plain,
spl93_75,
inference(avatar_split_clause,[],[f394,f871]) ).
fof(f871,plain,
( spl93_75
<=> ! [X0,X3,X2,X1] :
( sK82(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_75])]) ).
fof(f394,plain,
! [X2,X3,X0,X1] :
( sK82(X0,X1,X2,X3) = X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f869,plain,
spl93_74,
inference(avatar_split_clause,[],[f391,f867]) ).
fof(f867,plain,
( spl93_74
<=> ! [X0,X3,X2,X1] :
( sK82(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_74])]) ).
fof(f391,plain,
! [X2,X3,X0,X1] :
( sK82(X0,X1,X2,X3) = X2
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f865,plain,
( spl93_73
| ~ spl93_40
| ~ spl93_48 ),
inference(avatar_split_clause,[],[f808,f749,f712,f863]) ).
fof(f808,plain,
( ! [X2,X0,X1] : ~ visFreeVar(vgensym(vapp(X0,vapp(X1,X2))),X1)
| ~ spl93_40
| ~ spl93_48 ),
inference(resolution,[],[f750,f713]) ).
fof(f861,plain,
spl93_72,
inference(avatar_split_clause,[],[f390,f859]) ).
fof(f859,plain,
( spl93_72
<=> ! [X0,X3,X2,X1] :
( sK80(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_72])]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( sK80(X0,X1,X2,X3) = X3
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f278]) ).
fof(f857,plain,
spl93_71,
inference(avatar_split_clause,[],[f386,f855]) ).
fof(f855,plain,
( spl93_71
<=> ! [X0,X3,X2,X1] :
( sK77(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_71])]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( sK77(X0,X1,X2,X3) = X2
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f853,plain,
spl93_70,
inference(avatar_split_clause,[],[f385,f851]) ).
fof(f851,plain,
( spl93_70
<=> ! [X0,X3,X2,X1] :
( sK78(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_70])]) ).
fof(f385,plain,
! [X2,X3,X0,X1] :
( sK78(X0,X1,X2,X3) = X3
| ~ sP10(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f274]) ).
fof(f849,plain,
spl93_69,
inference(avatar_split_clause,[],[f381,f847]) ).
fof(f847,plain,
( spl93_69
<=> ! [X0,X3,X2,X1] :
( sK72(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_69])]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( sK72(X0,X1,X2,X3) = X2
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f845,plain,
spl93_68,
inference(avatar_split_clause,[],[f380,f843]) ).
fof(f843,plain,
( spl93_68
<=> ! [X0,X3,X2,X1] :
( sK73(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_68])]) ).
fof(f380,plain,
! [X2,X3,X0,X1] :
( sK73(X0,X1,X2,X3) = X3
| ~ sP11(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f270]) ).
fof(f841,plain,
spl93_67,
inference(avatar_split_clause,[],[f374,f839]) ).
fof(f374,plain,
! [X2,X3,X0,X1] :
( sK67(X0,X1,X2,X3) = X2
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f837,plain,
spl93_66,
inference(avatar_split_clause,[],[f373,f835]) ).
fof(f373,plain,
! [X2,X3,X0,X1] :
( sK66(X0,X1,X2,X3) = X3
| ~ sP12(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f266]) ).
fof(f833,plain,
spl93_65,
inference(avatar_split_clause,[],[f368,f831]) ).
fof(f831,plain,
( spl93_65
<=> ! [X0,X3,X2,X1] :
( sK64(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_65])]) ).
fof(f368,plain,
! [X2,X3,X0,X1] :
( sK64(X0,X1,X2,X3) = X2
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f829,plain,
spl93_64,
inference(avatar_split_clause,[],[f367,f827]) ).
fof(f827,plain,
( spl93_64
<=> ! [X0,X3,X2,X1] :
( sK63(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_64])]) ).
fof(f367,plain,
! [X2,X3,X0,X1] :
( sK63(X0,X1,X2,X3) = X3
| ~ sP13(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f262]) ).
fof(f825,plain,
spl93_63,
inference(avatar_split_clause,[],[f314,f823]) ).
fof(f823,plain,
( spl93_63
<=> ! [X0,X1] :
( vapp(sK27(X0,X1),sK29(X0,X1)) = X1
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_63])]) ).
fof(f314,plain,
! [X0,X1] :
( vapp(sK27(X0,X1),sK29(X0,X1)) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f819,plain,
spl93_62,
inference(avatar_split_clause,[],[f309,f817]) ).
fof(f309,plain,
! [X0,X1] :
( vapp(sK25(X0,X1),sK24(X0,X1)) = X1
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0,X1] :
( ( vnoExp = X0
& ~ visSomeExp(sK26(X0,X1))
& sK26(X0,X1) = vreduce(sK25(X0,X1))
& ! [X5,X6,X7] : vabs(X5,X6,X7) != sK25(X0,X1)
& vapp(sK25(X0,X1),sK24(X0,X1)) = X1 )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25,sK26])],[f218,f219]) ).
fof(f219,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(sK26(X0,X1))
& sK26(X0,X1) = vreduce(sK25(X0,X1))
& ! [X7,X6,X5] : vabs(X5,X6,X7) != sK25(X0,X1)
& vapp(sK25(X0,X1),sK24(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f218,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,[],[f217]) ).
fof(f217,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,[],[f196]) ).
fof(f807,plain,
spl93_61,
inference(avatar_split_clause,[],[f516,f805]) ).
fof(f516,plain,
! [X2,X3,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X2 = X6 ),
inference(equality_resolution,[],[f515]) ).
fof(f515,plain,
! [X2,X3,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X1 != X2 ),
inference(equality_resolution,[],[f514]) ).
fof(f514,plain,
! [X2,X3,X0,X1,X6] :
( vvar(X6) = vsubst(X2,X3,vvar(X6))
| X1 = X6
| X0 != X3
| X1 != X2 ),
inference(equality_resolution,[],[f513]) ).
fof(f513,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,[],[f428]) ).
fof(f428,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,[],[f176]) ).
fof(f176,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,[],[f175]) ).
fof(f175,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,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X6) = X4
& X0 = X3
& X1 = X2 )
=> ( X1 != X6
=> ( vsubst(X2,X3,X4) = X5
=> vvar(X6) = X5 ) ) ),
inference(rectify,[],[f30]) ).
fof(f30,axiom,
! [X10,X8,X0,X3,X5,X18,X20] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 != X20
=> ( vsubst(X0,X3,X5) = X18
=> vvar(X20) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst1) ).
fof(f803,plain,
spl93_60,
inference(avatar_split_clause,[],[f480,f801]) ).
fof(f480,plain,
! [X2,X3,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X3,vapp(X2,X4)) ),
inference(equality_resolution,[],[f479]) ).
fof(f479,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,vapp(X2,X4))
| X0 != X3 ),
inference(equality_resolution,[],[f408]) ).
fof(f408,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X3,X4)
| visFreeVar(X3,X2)
| ~ visFreeVar(X0,X1)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,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,[],[f151]) ).
fof(f151,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,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3,X4] :
( ( vapp(X2,X4) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) ) )
& ( ( visFreeVar(X3,X4)
| visFreeVar(X3,X2) )
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X0,X3,X11,X13,X12] :
( ( vapp(X11,X12) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) ) )
& ( ( visFreeVar(X13,X12)
| visFreeVar(X13,X11) )
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar2) ).
fof(f799,plain,
spl93_59,
inference(avatar_split_clause,[],[f359,f797]) ).
fof(f359,plain,
! [X2,X0,X1] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2] :
( vtcheck(X0,vvar(X1),X2)
| vsomeType(X2) != vlookup(X1,X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( vsomeType(X2) = vlookup(X1,X0)
=> vtcheck(X0,vvar(X1),X2) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X19,X8,X14] :
( vlookup(X8,X19) = vsomeType(X14)
=> vtcheck(X19,vvar(X8),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-var') ).
fof(f795,plain,
spl93_58,
inference(avatar_split_clause,[],[f354,f793]) ).
fof(f793,plain,
( spl93_58
<=> ! [X2,X0,X1] :
( vsomeType(sK59(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_58])]) ).
fof(f354,plain,
! [X2,X0,X1] :
( vsomeType(sK59(X0,X1,X2)) = X0
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f791,plain,
spl93_57,
inference(avatar_split_clause,[],[f325,f789]) ).
fof(f789,plain,
( spl93_57
<=> ! [X0,X1] :
( sK36(X0,X1) = vreduce(sK38(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_57])]) ).
fof(f325,plain,
! [X0,X1] :
( sK36(X0,X1) = vreduce(sK38(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f787,plain,
spl93_56,
inference(avatar_split_clause,[],[f320,f785]) ).
fof(f785,plain,
( spl93_56
<=> ! [X0,X1] :
( sK33(X0,X1) = vreduce(sK34(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_56])]) ).
fof(f320,plain,
! [X0,X1] :
( sK33(X0,X1) = vreduce(sK34(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f783,plain,
spl93_55,
inference(avatar_split_clause,[],[f316,f781]) ).
fof(f781,plain,
( spl93_55
<=> ! [X0,X1] :
( sK28(X0,X1) = vreduce(sK27(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_55])]) ).
fof(f316,plain,
! [X0,X1] :
( sK28(X0,X1) = vreduce(sK27(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f779,plain,
spl93_54,
inference(avatar_split_clause,[],[f315,f777]) ).
fof(f777,plain,
( spl93_54
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK27(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_54])]) ).
fof(f315,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK27(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f775,plain,
( spl93_53
| ~ spl93_11
| ~ spl93_40 ),
inference(avatar_split_clause,[],[f719,f712,f595,f773]) ).
fof(f719,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X0)
| ~ spl93_11
| ~ spl93_40 ),
inference(resolution,[],[f713,f596]) ).
fof(f771,plain,
spl93_52,
inference(avatar_split_clause,[],[f311,f769]) ).
fof(f311,plain,
! [X0,X1] :
( sK26(X0,X1) = vreduce(sK25(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f767,plain,
spl93_51,
inference(avatar_split_clause,[],[f310,f765]) ).
fof(f765,plain,
( spl93_51
<=> ! [X5,X0,X6,X1,X7] :
( vabs(X5,X6,X7) != sK25(X0,X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_51])]) ).
fof(f310,plain,
! [X0,X1,X6,X7,X5] :
( vabs(X5,X6,X7) != sK25(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f763,plain,
spl93_50,
inference(avatar_split_clause,[],[f306,f761]) ).
fof(f761,plain,
( spl93_50
<=> ! [X0,X1] :
( sK23(X0,X1) = vreduce(sK19(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_50])]) ).
fof(f306,plain,
! [X0,X1] :
( sK23(X0,X1) = vreduce(sK19(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f755,plain,
spl93_49,
inference(avatar_split_clause,[],[f365,f753]) ).
fof(f365,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,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,[],[f139]) ).
fof(f139,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,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> vapp(X0,X1) = vapp(X2,X3) )
& ( vapp(X0,X1) = vapp(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X3,X5,X6,X7] :
( ( ( X5 = X7
& X3 = X6 )
=> vapp(X3,X5) = vapp(X6,X7) )
& ( vapp(X3,X5) = vapp(X6,X7)
=> ( X5 = X7
& X3 = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-app') ).
fof(f751,plain,
( spl93_48
| ~ spl93_11
| ~ spl93_39 ),
inference(avatar_split_clause,[],[f718,f708,f595,f749]) ).
fof(f718,plain,
( ! [X0,X1] : ~ visFreeVar(vgensym(vapp(X0,X1)),X1)
| ~ spl93_11
| ~ spl93_39 ),
inference(resolution,[],[f709,f596]) ).
fof(f747,plain,
spl93_47,
inference(avatar_split_clause,[],[f364,f745]) ).
fof(f364,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| vapp(X0,X1) != vapp(X2,X3) ),
inference(cnf_transformation,[],[f140]) ).
fof(f743,plain,
spl93_46,
inference(avatar_split_clause,[],[f362,f741]) ).
fof(f362,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,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,[],[f137]) ).
fof(f137,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,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ( ( X1 = X3
& X0 = X2 )
=> varrow(X0,X1) = varrow(X2,X3) )
& ( varrow(X0,X1) = varrow(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X2,X4,X30,X31] :
( ( ( X4 = X31
& X2 = X30 )
=> varrow(X2,X4) = varrow(X30,X31) )
& ( varrow(X2,X4) = varrow(X30,X31)
=> ( X4 = X31
& X2 = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-arrow') ).
fof(f739,plain,
spl93_45,
inference(avatar_split_clause,[],[f361,f737]) ).
fof(f361,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| varrow(X0,X1) != varrow(X2,X3) ),
inference(cnf_transformation,[],[f138]) ).
fof(f735,plain,
spl93_44,
inference(avatar_split_clause,[],[f351,f733]) ).
fof(f351,plain,
! [X2,X0,X1] :
( sK57(X0,X1,X2) = X2
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f731,plain,
spl93_43,
inference(avatar_split_clause,[],[f347,f729]) ).
fof(f347,plain,
! [X2,X0,X1] :
( sK54(X0,X1,X2) = X2
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f251]) ).
fof(f727,plain,
spl93_42,
inference(avatar_split_clause,[],[f528,f725]) ).
fof(f528,plain,
! [X3,X0,X6] : vsomeType(X6) = vlookup(X3,vbind(X3,X6,X0)),
inference(equality_resolution,[],[f527]) ).
fof(f527,plain,
! [X2,X3,X0,X6] :
( vsomeType(X6) = vlookup(X3,vbind(X2,X6,X0))
| X2 != X3 ),
inference(equality_resolution,[],[f526]) ).
fof(f526,plain,
! [X2,X3,X0,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| vbind(X2,X6,X0) != X4
| X2 != X3 ),
inference(equality_resolution,[],[f525]) ).
fof(f525,plain,
! [X2,X3,X0,X1,X6,X4] :
( vlookup(X3,X4) = vsomeType(X6)
| X1 != X2
| vbind(X2,X6,X0) != X4
| X1 != X3 ),
inference(equality_resolution,[],[f431]) ).
fof(f431,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,[],[f182]) ).
fof(f182,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,[],[f181]) ).
fof(f181,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,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vbind(X2,X6,X0) = X4
& X1 = X3 )
=> ( X1 = X2
=> ( vlookup(X3,X4) = X5
=> vsomeType(X6) = X5 ) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X19,X8,X20,X0,X15,X18,X21] :
( ( vbind(X20,X21,X19) = X15
& X0 = X8 )
=> ( X8 = X20
=> ( vlookup(X0,X15) = X18
=> vsomeType(X21) = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup1) ).
fof(f723,plain,
spl93_41,
inference(avatar_split_clause,[],[f498,f721]) ).
fof(f498,plain,
! [X3,X0,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X4,vabs(X3,X0,X5)) ),
inference(equality_resolution,[],[f497]) ).
fof(f497,plain,
! [X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,vabs(X3,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f423]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4,X5] :
( visFreeVar(X4,X5)
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f166]) ).
fof(f714,plain,
spl93_40,
inference(avatar_split_clause,[],[f484,f712]) ).
fof(f484,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X2) ),
inference(equality_resolution,[],[f483]) ).
fof(f483,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X2)
| X0 != X3 ),
inference(equality_resolution,[],[f406]) ).
fof(f406,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X2)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f152]) ).
fof(f710,plain,
spl93_39,
inference(avatar_split_clause,[],[f482,f708]) ).
fof(f482,plain,
! [X2,X3,X4] :
( visFreeVar(X3,vapp(X2,X4))
| ~ visFreeVar(X3,X4) ),
inference(equality_resolution,[],[f481]) ).
fof(f481,plain,
! [X2,X3,X0,X4] :
( visFreeVar(X0,vapp(X2,X4))
| ~ visFreeVar(X3,X4)
| X0 != X3 ),
inference(equality_resolution,[],[f407]) ).
fof(f407,plain,
! [X2,X3,X0,X1,X4] :
( visFreeVar(X0,X1)
| ~ visFreeVar(X3,X4)
| vapp(X2,X4) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f152]) ).
fof(f706,plain,
spl93_38,
inference(avatar_split_clause,[],[f403,f704]) ).
fof(f403,plain,
! [X2,X3,X0,X1,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2,X3,X4] : vapp(X3,X4) != vabs(X0,X1,X2),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X3,X5,X6] : vabs(X0,X2,X3) != vapp(X5,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-abs-app') ).
fof(f702,plain,
spl93_37,
inference(avatar_split_clause,[],[f300,f700]) ).
fof(f300,plain,
! [X0,X1] :
( X0 = X1
| vvar(X0) != vvar(X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( vvar(X0) = vvar(X1)
| X0 != X1 )
& ( X0 = X1
| vvar(X0) != vvar(X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( X0 = X1
=> vvar(X0) = vvar(X1) )
& ( vvar(X0) = vvar(X1)
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-var') ).
fof(f698,plain,
spl93_36,
inference(avatar_split_clause,[],[f298,f696]) ).
fof(f696,plain,
( spl93_36
<=> ! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_36])]) ).
fof(f298,plain,
! [X0,X1] :
( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( vsomeExp(X0) = vsomeExp(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeExp(X0) != vsomeExp(X1) ) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeExp(X0) = vsomeExp(X1) )
& ( vsomeExp(X0) = vsomeExp(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X3,X5] :
( ( X3 = X5
=> vsomeExp(X3) = vsomeExp(X5) )
& ( vsomeExp(X3) = vsomeExp(X5)
=> X3 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someExp') ).
fof(f694,plain,
spl93_35,
inference(avatar_split_clause,[],[f296,f692]) ).
fof(f692,plain,
( spl93_35
<=> ! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_35])]) ).
fof(f296,plain,
! [X0,X1] :
( X0 = X1
| vsomeType(X0) != vsomeType(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( vsomeType(X0) = vsomeType(X1)
| X0 != X1 )
& ( X0 = X1
| vsomeType(X0) != vsomeType(X1) ) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( X0 = X1
=> vsomeType(X0) = vsomeType(X1) )
& ( vsomeType(X0) = vsomeType(X1)
=> X0 = X1 ) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X2,X4] :
( ( X2 = X4
=> vsomeType(X2) = vsomeType(X4) )
& ( vsomeType(X2) = vsomeType(X4)
=> X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someType') ).
fof(f689,plain,
spl93_34,
inference(avatar_split_clause,[],[f521,f687]) ).
fof(f521,plain,
! [X2,X6] : vsubst(X2,X6,vvar(X2)) = X6,
inference(equality_resolution,[],[f520]) ).
fof(f520,plain,
! [X2,X1,X6] :
( vsubst(X2,X6,vvar(X1)) = X6
| X1 != X2 ),
inference(equality_resolution,[],[f519]) ).
fof(f519,plain,
! [X2,X3,X1,X6] :
( vsubst(X2,X3,vvar(X1)) = X6
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f518]) ).
fof(f518,plain,
! [X2,X3,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| vvar(X1) != X4
| X3 != X6
| X1 != X2 ),
inference(equality_resolution,[],[f517]) ).
fof(f517,plain,
! [X2,X3,X0,X1,X6,X4] :
( vsubst(X2,X3,X4) = X6
| X0 != X1
| vvar(X1) != X4
| X3 != X6
| X0 != X2 ),
inference(equality_resolution,[],[f429]) ).
fof(f429,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,[],[f178]) ).
fof(f178,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,[],[f177]) ).
fof(f177,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,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( vvar(X1) = X4
& X3 = X6
& X0 = X2 )
=> ( X0 = X1
=> ( vsubst(X2,X3,X4) = X5
=> X5 = X6 ) ) ),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X8,X20,X0,X3,X5,X18,X10] :
( ( vvar(X20) = X5
& X3 = X10
& X0 = X8 )
=> ( X8 = X20
=> ( vsubst(X0,X3,X5) = X18
=> X10 = X18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subst0) ).
fof(f685,plain,
spl93_33,
inference(avatar_split_clause,[],[f478,f683]) ).
fof(f478,plain,
! [X2,X0,X1] : vnoExp = vreduce(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f477]) ).
fof(f477,plain,
! [X2,X3,X0,X1] :
( vnoExp = vreduce(X3)
| vabs(X0,X1,X2) != X3 ),
inference(equality_resolution,[],[f404]) ).
fof(f404,plain,
! [X2,X3,X0,X1,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f149]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2,X3,X4] :
( vnoExp = X4
| vreduce(X3) != X4
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2,X3,X4] :
( vabs(X0,X1,X2) = X3
=> ( vreduce(X3) = X4
=> vnoExp = X4 ) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
! [X8,X9,X10,X3,X18] :
( vabs(X8,X9,X10) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce1) ).
fof(f681,plain,
spl93_32,
inference(avatar_split_clause,[],[f473,f679]) ).
fof(f473,plain,
! [X2,X3] :
( X2 = X3
| ~ visFreeVar(X3,vvar(X2)) ),
inference(equality_resolution,[],[f472]) ).
fof(f472,plain,
! [X2,X3,X0] :
( X2 = X3
| ~ visFreeVar(X0,vvar(X2))
| X0 != X3 ),
inference(equality_resolution,[],[f402]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ visFreeVar(X0,X1)
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
| ~ visFreeVar(X0,X1) )
& ( visFreeVar(X0,X1)
| X2 != X3 ) )
| vvar(X2) != X1
| X0 != X3 ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2,X3] :
( ( vvar(X2) = X1
& X0 = X3 )
=> ( ( visFreeVar(X0,X1)
=> X2 = X3 )
& ( X2 = X3
=> visFreeVar(X0,X1) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3,X8,X13] :
( ( vvar(X8) = X3
& X0 = X13 )
=> ( ( visFreeVar(X0,X3)
=> X8 = X13 )
& ( X8 = X13
=> visFreeVar(X0,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isFreeVar0) ).
fof(f677,plain,
spl93_31,
inference(avatar_split_clause,[],[f360,f675]) ).
fof(f675,plain,
( spl93_31
<=> ! [X2,X0,X1,X3] : vvar(X0) != vabs(X1,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_31])]) ).
fof(f360,plain,
! [X2,X3,X0,X1] : vvar(X0) != vabs(X1,X2,X3),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2,X3] : vvar(X0) != vabs(X1,X2,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-abs') ).
fof(f673,plain,
spl93_30,
inference(avatar_split_clause,[],[f327,f671]) ).
fof(f671,plain,
( spl93_30
<=> ! [X0,X1] :
( visValue(sK38(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_30])]) ).
fof(f327,plain,
! [X0,X1] :
( visValue(sK38(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f669,plain,
spl93_29,
inference(avatar_split_clause,[],[f326,f667]) ).
fof(f667,plain,
( spl93_29
<=> ! [X0,X1] :
( ~ visSomeExp(sK36(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_29])]) ).
fof(f326,plain,
! [X0,X1] :
( ~ visSomeExp(sK36(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f665,plain,
spl93_28,
inference(avatar_split_clause,[],[f322,f663]) ).
fof(f663,plain,
( spl93_28
<=> ! [X0,X1] :
( ~ visValue(sK34(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_28])]) ).
fof(f322,plain,
! [X0,X1] :
( ~ visValue(sK34(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f661,plain,
spl93_27,
inference(avatar_split_clause,[],[f321,f659]) ).
fof(f659,plain,
( spl93_27
<=> ! [X0,X1] :
( ~ visSomeExp(sK33(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_27])]) ).
fof(f321,plain,
! [X0,X1] :
( ~ visSomeExp(sK33(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f657,plain,
spl93_26,
inference(avatar_split_clause,[],[f317,f655]) ).
fof(f655,plain,
( spl93_26
<=> ! [X0,X1] :
( visSomeExp(sK28(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_26])]) ).
fof(f317,plain,
! [X0,X1] :
( visSomeExp(sK28(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f653,plain,
spl93_25,
inference(avatar_split_clause,[],[f312,f651]) ).
fof(f651,plain,
( spl93_25
<=> ! [X0,X1] :
( ~ visSomeExp(sK26(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_25])]) ).
fof(f312,plain,
! [X0,X1] :
( ~ visSomeExp(sK26(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f649,plain,
spl93_24,
inference(avatar_split_clause,[],[f307,f647]) ).
fof(f647,plain,
( spl93_24
<=> ! [X0,X1] :
( visSomeExp(sK23(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_24])]) ).
fof(f307,plain,
! [X0,X1] :
( visSomeExp(sK23(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
fof(f645,plain,
spl93_23,
inference(avatar_split_clause,[],[f501,f643]) ).
fof(f501,plain,
! [X0,X4,X5] : ~ visFreeVar(X4,vabs(X4,X0,X5)),
inference(equality_resolution,[],[f500]) ).
fof(f500,plain,
! [X0,X1,X4,X5] :
( ~ visFreeVar(X1,vabs(X4,X0,X5))
| X1 != X4 ),
inference(equality_resolution,[],[f499]) ).
fof(f499,plain,
! [X2,X0,X1,X4,X5] :
( ~ visFreeVar(X1,X2)
| vabs(X4,X0,X5) != X2
| X1 != X4 ),
inference(equality_resolution,[],[f422]) ).
fof(f422,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| ~ visFreeVar(X1,X2)
| vabs(X3,X0,X5) != X2
| X1 != X4 ),
inference(cnf_transformation,[],[f166]) ).
fof(f641,plain,
spl93_22,
inference(avatar_split_clause,[],[f335,f639]) ).
fof(f335,plain,
! [X2,X0,X1] : vvar(X0) != vapp(X1,X2),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] : vvar(X0) != vapp(X1,X2),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3,X5] : vvar(X0) != vapp(X3,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-var-app') ).
fof(f637,plain,
spl93_21,
inference(avatar_split_clause,[],[f334,f635]) ).
fof(f635,plain,
( spl93_21
<=> ! [X2,X0,X1] : vempty != vbind(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_21])]) ).
fof(f334,plain,
! [X2,X0,X1] : vempty != vbind(X0,X1,X2),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] : vempty != vbind(X0,X1,X2),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X2,X15] : vempty != vbind(X0,X2,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-empty-bind') ).
fof(f633,plain,
spl93_20,
inference(avatar_split_clause,[],[f323,f631]) ).
fof(f631,plain,
( spl93_20
<=> ! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_20])]) ).
fof(f323,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f629,plain,
spl93_19,
inference(avatar_split_clause,[],[f313,f627]) ).
fof(f313,plain,
! [X0,X1] :
( vnoExp = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f220]) ).
fof(f625,plain,
spl93_18,
inference(avatar_split_clause,[],[f471,f623]) ).
fof(f471,plain,
! [X1] : vnoType = vlookup(X1,vempty),
inference(equality_resolution,[],[f470]) ).
fof(f470,plain,
! [X0,X1] :
( vnoType = vlookup(X1,vempty)
| X0 != X1 ),
inference(equality_resolution,[],[f469]) ).
fof(f469,plain,
! [X2,X0,X1] :
( vnoType = vlookup(X1,X2)
| vempty != X2
| X0 != X1 ),
inference(equality_resolution,[],[f400]) ).
fof(f400,plain,
! [X2,X3,X0,X1] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(flattening,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2,X3] :
( vnoType = X3
| vlookup(X1,X2) != X3
| vempty != X2
| X0 != X1 ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( vempty = X2
& X0 = X1 )
=> ( vlookup(X1,X2) = X3
=> vnoType = X3 ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X8,X0,X15,X18] :
( ( vempty = X15
& X0 = X8 )
=> ( vlookup(X0,X15) = X18
=> vnoType = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lookup0) ).
fof(f621,plain,
spl93_17,
inference(avatar_split_clause,[],[f468,f619]) ).
fof(f468,plain,
! [X2,X0,X1] : visValue(vabs(X0,X1,X2)),
inference(equality_resolution,[],[f399]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1,X2,X3] :
( visValue(X3)
| vabs(X0,X1,X2) != X3 ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( vabs(X0,X1,X2) = X3
=> visValue(X3) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X8,X9,X10,X3] :
( vabs(X8,X9,X10) = X3
=> visValue(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue0) ).
fof(f617,plain,
spl93_16,
inference(avatar_split_clause,[],[f455,f615]) ).
fof(f455,plain,
! [X0] : vnoExp = vreduce(vvar(X0)),
inference(equality_resolution,[],[f454]) ).
fof(f454,plain,
! [X0,X1] :
( vnoExp = vreduce(X1)
| vvar(X0) != X1 ),
inference(equality_resolution,[],[f338]) ).
fof(f338,plain,
! [X2,X0,X1] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(flattening,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( vnoExp = X2
| vreduce(X1) != X2
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( vvar(X0) = X1
=> ( vreduce(X1) = X2
=> vnoExp = X2 ) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X3,X18] :
( vvar(X8) = X3
=> ( vreduce(X3) = X18
=> vnoExp = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reduce0) ).
fof(f613,plain,
spl93_15,
inference(avatar_split_clause,[],[f453,f611]) ).
fof(f611,plain,
( spl93_15
<=> ! [X2] : vgetSomeExp(vsomeExp(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl93_15])]) ).
fof(f453,plain,
! [X2] : vgetSomeExp(vsomeExp(X2)) = X2,
inference(equality_resolution,[],[f452]) ).
fof(f452,plain,
! [X2,X0] :
( vgetSomeExp(X0) = X2
| vsomeExp(X2) != X0 ),
inference(equality_resolution,[],[f337]) ).
fof(f337,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(flattening,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeExp(X0) != X1
| vsomeExp(X2) != X0 ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( vsomeExp(X2) = X0
=> ( vgetSomeExp(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X24,X18,X10] :
( vsomeExp(X10) = X24
=> ( vgetSomeExp(X24) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeExp0) ).
fof(f609,plain,
spl93_14,
inference(avatar_split_clause,[],[f451,f607]) ).
fof(f607,plain,
( spl93_14
<=> ! [X2] : vgetSomeType(vsomeType(X2)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl93_14])]) ).
fof(f451,plain,
! [X2] : vgetSomeType(vsomeType(X2)) = X2,
inference(equality_resolution,[],[f450]) ).
fof(f450,plain,
! [X2,X0] :
( vgetSomeType(X0) = X2
| vsomeType(X2) != X0 ),
inference(equality_resolution,[],[f336]) ).
fof(f336,plain,
! [X2,X0,X1] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(flattening,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2] :
( X1 = X2
| vgetSomeType(X0) != X1
| vsomeType(X2) != X0 ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( vsomeType(X2) = X0
=> ( vgetSomeType(X0) = X1
=> X1 = X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X17,X18,X10] :
( vsomeType(X10) = X17
=> ( vgetSomeType(X17) = X18
=> X10 = X18 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',getSomeType0) ).
fof(f605,plain,
spl93_13,
inference(avatar_split_clause,[],[f476,f603]) ).
fof(f476,plain,
! [X3] : visFreeVar(X3,vvar(X3)),
inference(equality_resolution,[],[f475]) ).
fof(f475,plain,
! [X3,X0] :
( visFreeVar(X0,vvar(X3))
| X0 != X3 ),
inference(equality_resolution,[],[f474]) ).
fof(f474,plain,
! [X3,X0,X1] :
( visFreeVar(X0,X1)
| vvar(X3) != X1
| X0 != X3 ),
inference(equality_resolution,[],[f401]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( visFreeVar(X0,X1)
| X2 != X3
| vvar(X2) != X1
| X0 != X3 ),
inference(cnf_transformation,[],[f147]) ).
fof(f601,plain,
spl93_12,
inference(avatar_split_clause,[],[f459,f599]) ).
fof(f459,plain,
! [X0,X1] : ~ visValue(vapp(X0,X1)),
inference(equality_resolution,[],[f358]) ).
fof(f358,plain,
! [X2,X0,X1] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2] :
( ~ visValue(X2)
| vapp(X0,X1) != X2 ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( vapp(X0,X1) = X2
=> ~ visValue(X2) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X11,X12,X3] :
( vapp(X11,X12) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue2) ).
fof(f597,plain,
spl93_11,
inference(avatar_split_clause,[],[f442,f595]) ).
fof(f442,plain,
! [X1] : ~ visFreeVar(vgensym(X1),X1),
inference(equality_resolution,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ~ visFreeVar(X0,X1)
| vgensym(X1) != X0 ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( vgensym(X1) = X0
=> ~ visFreeVar(X0,X1) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X13,X10] :
( vgensym(X10) = X13
=> ~ visFreeVar(X13,X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','gensym-is-fresh') ).
fof(f593,plain,
spl93_10,
inference(avatar_split_clause,[],[f293,f591]) ).
fof(f591,plain,
( spl93_10
<=> ! [X0] : vnoExp != vsomeExp(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_10])]) ).
fof(f293,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] : vnoExp != vsomeExp(X0),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X3] : vnoExp != vsomeExp(X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noExp-someExp') ).
fof(f589,plain,
spl93_9,
inference(avatar_split_clause,[],[f292,f587]) ).
fof(f292,plain,
! [X0] : vnoType != vsomeType(X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : vnoType != vsomeType(X0),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X2] : vnoType != vsomeType(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noType-someType') ).
fof(f585,plain,
spl93_8,
inference(avatar_split_clause,[],[f449,f583]) ).
fof(f449,plain,
! [X0] : ~ visValue(vvar(X0)),
inference(equality_resolution,[],[f333]) ).
fof(f333,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ~ visValue(X1)
| vvar(X0) != X1 ),
inference(ennf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( vvar(X0) = X1
=> ~ visValue(X1) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X8,X3] :
( vvar(X8) = X3
=> ~ visValue(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isValue1) ).
fof(f581,plain,
spl93_7,
inference(avatar_split_clause,[],[f444,f579]) ).
fof(f579,plain,
( spl93_7
<=> ! [X0] : visSomeExp(vsomeExp(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_7])]) ).
fof(f444,plain,
! [X0] : visSomeExp(vsomeExp(X0)),
inference(equality_resolution,[],[f304]) ).
fof(f304,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( visSomeExp(X1)
| vsomeExp(X0) != X1 ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( vsomeExp(X0) = X1
=> visSomeExp(X1) ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X10,X24] :
( vsomeExp(X10) = X24
=> visSomeExp(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp1) ).
fof(f577,plain,
spl93_6,
inference(avatar_split_clause,[],[f443,f575]) ).
fof(f575,plain,
( spl93_6
<=> ! [X0] : visSomeType(vsomeType(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_6])]) ).
fof(f443,plain,
! [X0] : visSomeType(vsomeType(X0)),
inference(equality_resolution,[],[f303]) ).
fof(f303,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( visSomeType(X1)
| vsomeType(X0) != X1 ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( vsomeType(X0) = X1
=> visSomeType(X1) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X10,X17] :
( vsomeType(X10) = X17
=> visSomeType(X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType1) ).
fof(f573,plain,
~ spl93_5,
inference(avatar_split_clause,[],[f438,f570]) ).
fof(f438,plain,
~ visSomeExp(vnoExp),
inference(equality_resolution,[],[f295]) ).
fof(f295,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ~ visSomeExp(X0)
| vnoExp != X0 ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( vnoExp = X0
=> ~ visSomeExp(X0) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X24] :
( vnoExp = X24
=> ~ visSomeExp(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeExp0) ).
fof(f568,plain,
~ spl93_4,
inference(avatar_split_clause,[],[f437,f565]) ).
fof(f565,plain,
( spl93_4
<=> visSomeType(vnoType) ),
introduced(avatar_definition,[new_symbols(naming,[spl93_4])]) ).
fof(f437,plain,
~ visSomeType(vnoType),
inference(equality_resolution,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ~ visSomeType(X0)
| vnoType != X0 ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( vnoType = X0
=> ~ visSomeType(X0) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X17] :
( vnoType = X17
=> ~ visSomeType(X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isSomeType0) ).
fof(f563,plain,
spl93_3,
inference(avatar_split_clause,[],[f287,f560]) ).
fof(f287,plain,
vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),sK18),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
( ~ vtcheck(sK16,vvar(sK17),sK18)
& vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),sK18)
& ~ visFreeVar(sK14,vvar(sK17)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16,sK17,sK18])],[f113,f211]) ).
fof(f211,plain,
( ? [X0,X1,X2,X3,X4] :
( ~ vtcheck(X2,vvar(X3),X4)
& vtcheck(vbind(X0,X1,X2),vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) )
=> ( ~ vtcheck(sK16,vvar(sK17),sK18)
& vtcheck(vbind(sK14,sK15,sK16),vvar(sK17),sK18)
& ~ visFreeVar(sK14,vvar(sK17)) ) ),
introduced(choice_axiom,[]) ).
fof(f113,plain,
? [X0,X1,X2,X3,X4] :
( ~ vtcheck(X2,vvar(X3),X4)
& vtcheck(vbind(X0,X1,X2),vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
? [X0,X1,X2,X3,X4] :
( ~ vtcheck(X2,vvar(X3),X4)
& vtcheck(vbind(X0,X1,X2),vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( vtcheck(vbind(X0,X1,X2),vvar(X3),X4)
& ~ visFreeVar(X0,vvar(X3)) )
=> vtcheck(X2,vvar(X3),X4) ),
inference(rectify,[],[f57]) ).
fof(f57,negated_conjecture,
~ ! [X8,X9,X19,X20,X14] :
( ( vtcheck(vbind(X8,X9,X19),vvar(X20),X14)
& ~ visFreeVar(X8,vvar(X20)) )
=> vtcheck(X19,vvar(X20),X14) ),
inference(negated_conjecture,[],[f56]) ).
fof(f56,conjecture,
! [X8,X9,X19,X20,X14] :
( ( vtcheck(vbind(X8,X9,X19),vvar(X20),X14)
& ~ visFreeVar(X8,vvar(X20)) )
=> vtcheck(X19,vvar(X20),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong-var') ).
fof(f558,plain,
~ spl93_2,
inference(avatar_split_clause,[],[f288,f555]) ).
fof(f288,plain,
~ vtcheck(sK16,vvar(sK17),sK18),
inference(cnf_transformation,[],[f212]) ).
fof(f553,plain,
~ spl93_1,
inference(avatar_split_clause,[],[f286,f550]) ).
fof(f286,plain,
~ visFreeVar(sK14,vvar(sK17)),
inference(cnf_transformation,[],[f212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : COM138+1 : TPTP v8.1.2. Released v6.4.0.
% 0.09/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n002.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 05:26:55 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (24863)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.40 % (24868)WARNING: value z3 for option sas not known
% 0.21/0.40 % (24869)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (24870)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)
% 0.21/0.40 % (24867)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.40 % (24866)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.40 % (24871)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.40 % (24868)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)
% 0.21/0.40 % (24872)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.48 TRYING [1]
% 0.21/0.48 TRYING [2]
% 0.21/0.55 TRYING [3]
% 2.54/0.72 % (24870)First to succeed.
% 2.54/0.74 % (24870)Refutation found. Thanks to Tanya!
% 2.54/0.74 % SZS status Theorem for theBenchmark
% 2.54/0.74 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/0.75 % (24870)------------------------------
% 2.54/0.75 % (24870)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.54/0.75 % (24870)Termination reason: Refutation
% 2.54/0.75
% 2.54/0.75 % (24870)Memory used [KB]: 5484
% 2.54/0.75 % (24870)Time elapsed: 0.339 s
% 2.54/0.75 % (24870)Instructions burned: 850 (million)
% 2.54/0.75 % (24870)------------------------------
% 2.54/0.75 % (24870)------------------------------
% 2.54/0.75 % (24863)Success in time 0.37 s
%------------------------------------------------------------------------------