TSTP Solution File: SEU196+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU196+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:28:31 EDT 2024
% Result : Theorem 0.15s 0.51s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 613
% Syntax : Number of formulae : 1916 ( 408 unt; 0 def)
% Number of atoms : 6212 ( 933 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 7065 (2769 ~;2975 |; 626 &)
% ( 505 <=>; 189 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 412 ( 410 usr; 387 prp; 0-3 aty)
% Number of functors : 85 ( 85 usr; 7 con; 0-4 aty)
% Number of variables : 3741 (3516 !; 225 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5676,plain,
$false,
inference(avatar_sat_refutation,[],[f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1085,f1090,f1095,f1099,f1103,f1107,f1111,f1115,f1119,f1123,f1128,f1133,f1137,f1141,f1145,f1149,f1153,f1157,f1162,f1166,f1170,f1179,f1183,f1187,f1191,f1195,f1199,f1203,f1207,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1240,f1244,f1248,f1252,f1256,f1260,f1264,f1268,f1296,f1303,f1309,f1314,f1319,f1329,f1340,f1344,f1348,f1353,f1357,f1361,f1365,f1369,f1373,f1377,f1381,f1385,f1389,f1393,f1397,f1403,f1427,f1431,f1435,f1441,f1451,f1456,f1466,f1470,f1474,f1478,f1482,f1486,f1491,f1495,f1499,f1503,f1507,f1511,f1515,f1519,f1525,f1529,f1533,f1537,f1562,f1571,f1627,f1631,f1635,f1639,f1643,f1647,f1651,f1655,f1661,f1665,f1670,f1674,f1678,f1682,f1686,f1690,f1694,f1731,f1765,f1769,f1789,f1833,f1837,f1841,f1845,f1852,f1856,f1860,f1864,f1868,f1872,f1876,f1880,f1884,f1938,f1947,f1951,f1957,f1963,f1967,f1971,f1975,f1979,f1983,f1987,f1991,f2010,f2014,f2075,f2079,f2083,f2087,f2092,f2096,f2100,f2104,f2108,f2154,f2160,f2166,f2170,f2174,f2178,f2182,f2186,f2195,f2199,f2203,f2207,f2211,f2215,f2219,f2223,f2227,f2231,f2236,f2242,f2246,f2358,f2407,f2411,f2455,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2489,f2493,f2497,f2501,f2505,f2509,f2520,f2571,f2580,f2584,f2588,f2592,f2596,f2600,f2604,f2651,f2759,f2763,f2767,f2771,f2775,f2786,f2790,f2794,f2798,f2802,f2806,f2810,f2825,f2902,f2915,f2919,f2923,f2927,f2931,f3010,f3021,f3025,f3029,f3033,f3037,f3041,f3045,f3049,f3086,f3092,f3096,f3105,f3109,f3114,f3118,f3122,f3126,f3146,f3199,f3203,f3207,f3211,f3215,f3219,f3223,f3227,f3231,f3235,f3239,f3243,f3247,f3251,f3255,f3262,f3348,f3352,f3356,f3360,f3499,f3511,f3515,f3519,f3576,f3580,f3584,f3621,f3625,f3629,f3633,f3637,f3641,f3697,f3757,f3761,f3765,f3791,f3795,f3799,f3803,f3807,f3864,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3922,f3926,f3930,f3934,f4043,f4208,f4212,f4216,f4275,f4298,f4303,f4309,f4313,f4317,f4322,f4327,f4331,f4361,f4443,f4447,f4490,f4501,f4506,f4512,f4534,f4540,f4562,f4567,f4571,f4595,f4599,f4631,f4635,f4639,f4643,f4647,f4769,f4783,f4788,f4793,f4797,f4813,f4817,f4869,f4873,f4914,f4918,f4922,f4927,f4960,f4991,f5015,f5024,f5029,f5033,f5037,f5041,f5101,f5116,f5137,f5161,f5165,f5170,f5174,f5198,f5218,f5224,f5230,f5234,f5294,f5300,f5306,f5327,f5381,f5387,f5393,f5399,f5403,f5407,f5449,f5532,f5538,f5552,f5557,f5575,f5577,f5588,f5644,f5648,f5674,f5675]) ).
fof(f5675,plain,
( ~ spl77_1
| ~ spl77_74
| spl77_382 ),
inference(avatar_split_clause,[],[f5584,f5572,f1425,f1047]) ).
fof(f1047,plain,
( spl77_1
<=> relation(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_1])]) ).
fof(f1425,plain,
( spl77_74
<=> ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_74])]) ).
fof(f5572,plain,
( spl77_382
<=> subset(relation_dom_restriction(sK17,sK16),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_382])]) ).
fof(f5584,plain,
( ~ relation(sK17)
| ~ spl77_74
| spl77_382 ),
inference(resolution,[],[f5574,f1426]) ).
fof(f1426,plain,
( ! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) )
| ~ spl77_74 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f5574,plain,
( ~ subset(relation_dom_restriction(sK17,sK16),sK17)
| spl77_382 ),
inference(avatar_component_clause,[],[f5572]) ).
fof(f5674,plain,
( spl77_386
| ~ spl77_24
| ~ spl77_51 ),
inference(avatar_split_clause,[],[f1298,f1266,f1151,f5672]) ).
fof(f5672,plain,
( spl77_386
<=> ! [X0] : ~ empty(sK48(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_386])]) ).
fof(f1151,plain,
( spl77_24
<=> ! [X0] : in(X0,sK48(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_24])]) ).
fof(f1266,plain,
( spl77_51
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_51])]) ).
fof(f1298,plain,
( ! [X0] : ~ empty(sK48(X0))
| ~ spl77_24
| ~ spl77_51 ),
inference(resolution,[],[f1267,f1152]) ).
fof(f1152,plain,
( ! [X0] : in(X0,sK48(X0))
| ~ spl77_24 ),
inference(avatar_component_clause,[],[f1151]) ).
fof(f1267,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl77_51 ),
inference(avatar_component_clause,[],[f1266]) ).
fof(f5648,plain,
( spl77_385
| ~ spl77_17
| ~ spl77_52
| ~ spl77_103 ),
inference(avatar_split_clause,[],[f1743,f1637,f1293,f1121,f5646]) ).
fof(f5646,plain,
( spl77_385
<=> ! [X0] : disjoint(X0,sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_385])]) ).
fof(f1121,plain,
( spl77_17
<=> ! [X2] : ~ in(X2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_17])]) ).
fof(f1293,plain,
( spl77_52
<=> empty_set = sK74 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_52])]) ).
fof(f1637,plain,
( spl77_103
<=> ! [X0,X1] :
( in(sK22(X0,X1),X1)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_103])]) ).
fof(f1743,plain,
( ! [X0] : disjoint(X0,sK74)
| ~ spl77_17
| ~ spl77_52
| ~ spl77_103 ),
inference(forward_demodulation,[],[f1738,f1295]) ).
fof(f1295,plain,
( empty_set = sK74
| ~ spl77_52 ),
inference(avatar_component_clause,[],[f1293]) ).
fof(f1738,plain,
( ! [X0] : disjoint(X0,empty_set)
| ~ spl77_17
| ~ spl77_103 ),
inference(resolution,[],[f1638,f1122]) ).
fof(f1122,plain,
( ! [X2] : ~ in(X2,empty_set)
| ~ spl77_17 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f1638,plain,
( ! [X0,X1] :
( in(sK22(X0,X1),X1)
| disjoint(X0,X1) )
| ~ spl77_103 ),
inference(avatar_component_clause,[],[f1637]) ).
fof(f5644,plain,
( spl77_384
| ~ spl77_17
| ~ spl77_52
| ~ spl77_102 ),
inference(avatar_split_clause,[],[f1737,f1633,f1293,f1121,f5642]) ).
fof(f5642,plain,
( spl77_384
<=> ! [X0] : disjoint(sK74,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_384])]) ).
fof(f1633,plain,
( spl77_102
<=> ! [X0,X1] :
( in(sK22(X0,X1),X0)
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_102])]) ).
fof(f1737,plain,
( ! [X0] : disjoint(sK74,X0)
| ~ spl77_17
| ~ spl77_52
| ~ spl77_102 ),
inference(forward_demodulation,[],[f1732,f1295]) ).
fof(f1732,plain,
( ! [X0] : disjoint(empty_set,X0)
| ~ spl77_17
| ~ spl77_102 ),
inference(resolution,[],[f1634,f1122]) ).
fof(f1634,plain,
( ! [X0,X1] :
( in(sK22(X0,X1),X0)
| disjoint(X0,X1) )
| ~ spl77_102 ),
inference(avatar_component_clause,[],[f1633]) ).
fof(f5588,plain,
( spl77_383
| ~ spl77_1
| ~ spl77_261 ),
inference(avatar_split_clause,[],[f3373,f3346,f1047,f5586]) ).
fof(f5586,plain,
( spl77_383
<=> ! [X0] : relation_dom(relation_dom_restriction(sK17,X0)) = set_difference(relation_dom(sK17),set_difference(relation_dom(sK17),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_383])]) ).
fof(f3346,plain,
( spl77_261
<=> ! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_261])]) ).
fof(f3373,plain,
( ! [X0] : relation_dom(relation_dom_restriction(sK17,X0)) = set_difference(relation_dom(sK17),set_difference(relation_dom(sK17),X0))
| ~ spl77_1
| ~ spl77_261 ),
inference(resolution,[],[f3347,f1049]) ).
fof(f1049,plain,
( relation(sK17)
| ~ spl77_1 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f3347,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0)) )
| ~ spl77_261 ),
inference(avatar_component_clause,[],[f3346]) ).
fof(f5577,plain,
( ~ spl77_1
| ~ spl77_63
| spl77_381 ),
inference(avatar_split_clause,[],[f5576,f5568,f1359,f1047]) ).
fof(f1359,plain,
( spl77_63
<=> ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_63])]) ).
fof(f5568,plain,
( spl77_381
<=> relation(relation_dom_restriction(sK17,sK16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_381])]) ).
fof(f5576,plain,
( ~ relation(sK17)
| ~ spl77_63
| spl77_381 ),
inference(resolution,[],[f5570,f1360]) ).
fof(f1360,plain,
( ! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) )
| ~ spl77_63 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f5570,plain,
( ~ relation(relation_dom_restriction(sK17,sK16))
| spl77_381 ),
inference(avatar_component_clause,[],[f5568]) ).
fof(f5575,plain,
( ~ spl77_381
| ~ spl77_1
| ~ spl77_382
| spl77_2
| ~ spl77_220 ),
inference(avatar_split_clause,[],[f2949,f2913,f1052,f5572,f1047,f5568]) ).
fof(f1052,plain,
( spl77_2
<=> subset(relation_rng(relation_dom_restriction(sK17,sK16)),relation_rng(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_2])]) ).
fof(f2913,plain,
( spl77_220
<=> ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_220])]) ).
fof(f2949,plain,
( ~ subset(relation_dom_restriction(sK17,sK16),sK17)
| ~ relation(sK17)
| ~ relation(relation_dom_restriction(sK17,sK16))
| spl77_2
| ~ spl77_220 ),
inference(resolution,[],[f2914,f1054]) ).
fof(f1054,plain,
( ~ subset(relation_rng(relation_dom_restriction(sK17,sK16)),relation_rng(sK17))
| spl77_2 ),
inference(avatar_component_clause,[],[f1052]) ).
fof(f2914,plain,
( ! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_220 ),
inference(avatar_component_clause,[],[f2913]) ).
fof(f5557,plain,
( spl77_380
| ~ spl77_86
| ~ spl77_379 ),
inference(avatar_split_clause,[],[f5553,f5550,f1489,f5555]) ).
fof(f5555,plain,
( spl77_380
<=> ! [X0,X5,X2,X1] :
( ~ in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK32(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),X5),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_380])]) ).
fof(f1489,plain,
( spl77_86
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_86])]) ).
fof(f5550,plain,
( spl77_379
<=> ! [X0,X5,X2,X1] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK32(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),X5),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_379])]) ).
fof(f5553,plain,
( ! [X2,X0,X1,X5] :
( ~ in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK32(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),X5),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1) )
| ~ spl77_86
| ~ spl77_379 ),
inference(forward_demodulation,[],[f5551,f1490]) ).
fof(f1490,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl77_86 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f5551,plain,
( ! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK32(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),X5),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) )
| ~ spl77_379 ),
inference(avatar_component_clause,[],[f5550]) ).
fof(f5552,plain,
spl77_379,
inference(avatar_split_clause,[],[f950,f5550]) ).
fof(f950,plain,
! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(X5,sK32(X0,X1,X2)),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),X5),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| ~ in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f702,f891,f891,f891]) ).
fof(f891,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f750,f559]) ).
fof(f559,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f168]) ).
fof(f168,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f750,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f702,plain,
! [X2,X0,X1,X5] :
( sP0(X0,X1,X2)
| ~ in(ordered_pair(X5,sK32(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK31(X0,X1,X2),X5),X1)
| ~ in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f425,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK32(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK31(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),X0)
& in(ordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),X1) )
| in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ( in(ordered_pair(sK34(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK34(X0,X1,X7,X8)),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33,sK34])],[f421,f424,f423,f422]) ).
fof(f422,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ! [X5] :
( ~ in(ordered_pair(X5,sK32(X0,X1,X2)),X0)
| ~ in(ordered_pair(sK31(X0,X1,X2),X5),X1) )
| ~ in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,sK32(X0,X1,X2)),X0)
& in(ordered_pair(sK31(X0,X1,X2),X6),X1) )
| in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f423,plain,
! [X0,X1,X2] :
( ? [X6] :
( in(ordered_pair(X6,sK32(X0,X1,X2)),X0)
& in(ordered_pair(sK31(X0,X1,X2),X6),X1) )
=> ( in(ordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),X0)
& in(ordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f424,plain,
! [X0,X1,X7,X8] :
( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
=> ( in(ordered_pair(sK34(X0,X1,X7,X8),X8),X0)
& in(ordered_pair(X7,sK34(X0,X1,X7,X8)),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f421,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X3,X5),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X6,X4),X0)
& in(ordered_pair(X3,X6),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X10,X8),X0)
& in(ordered_pair(X7,X10),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f420]) ).
fof(f420,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X5,X4),X1)
| ~ in(ordered_pair(X3,X5),X0) ) )
& ( ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f5538,plain,
( spl77_378
| ~ spl77_86
| ~ spl77_377 ),
inference(avatar_split_clause,[],[f5534,f5530,f1489,f5536]) ).
fof(f5536,plain,
( spl77_378
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK41(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_378])]) ).
fof(f5530,plain,
( spl77_377
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_377])]) ).
fof(f5534,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK41(X0,X1,X2),X1) )
| ~ spl77_86
| ~ spl77_377 ),
inference(forward_demodulation,[],[f5533,f1490]) ).
fof(f5533,plain,
( ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) )
| ~ spl77_86
| ~ spl77_377 ),
inference(forward_demodulation,[],[f5531,f1490]) ).
fof(f5531,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) )
| ~ spl77_377 ),
inference(avatar_component_clause,[],[f5530]) ).
fof(f5532,plain,
spl77_377,
inference(avatar_split_clause,[],[f964,f5530]) ).
fof(f964,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f719,f891,f891]) ).
fof(f719,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f444,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ( ( ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
& in(sK41(X0,X1,X2),X1) )
| in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42])],[f442,f443]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) )
=> ( ( ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
| ~ in(sK41(X0,X1,X2),X1)
| ~ in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
& in(sK41(X0,X1,X2),X1) )
| in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f442,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X5,X6] :
( ( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1) )
& ( ( in(ordered_pair(X5,X6),X0)
& in(X5,X1) )
| ~ in(ordered_pair(X5,X6),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f441]) ).
fof(f441,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(flattening,[],[f440]) ).
fof(f440,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ? [X3,X4] :
( ( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1)
| ~ in(ordered_pair(X3,X4),X2) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ~ in(ordered_pair(X3,X4),X0)
| ~ in(X3,X1) )
& ( ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| ~ sP2(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0,X1,X2] :
( sP2(X0,X1,X2)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f5449,plain,
( spl77_376
| ~ spl77_54
| ~ spl77_361 ),
inference(avatar_split_clause,[],[f5307,f5196,f1307,f5447]) ).
fof(f5447,plain,
( spl77_376
<=> ! [X0] : ~ proper_subset(relation_field(sK17),set_difference(relation_rng(sK17),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_376])]) ).
fof(f1307,plain,
( spl77_54
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_54])]) ).
fof(f5196,plain,
( spl77_361
<=> ! [X0] : subset(set_difference(relation_rng(sK17),X0),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_361])]) ).
fof(f5307,plain,
( ! [X0] : ~ proper_subset(relation_field(sK17),set_difference(relation_rng(sK17),X0))
| ~ spl77_54
| ~ spl77_361 ),
inference(resolution,[],[f5197,f1308]) ).
fof(f1308,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| ~ proper_subset(X1,X0) )
| ~ spl77_54 ),
inference(avatar_component_clause,[],[f1307]) ).
fof(f5197,plain,
( ! [X0] : subset(set_difference(relation_rng(sK17),X0),relation_field(sK17))
| ~ spl77_361 ),
inference(avatar_component_clause,[],[f5196]) ).
fof(f5407,plain,
( spl77_375
| ~ spl77_86
| ~ spl77_372 ),
inference(avatar_split_clause,[],[f5395,f5391,f1489,f5405]) ).
fof(f5405,plain,
( spl77_375
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_375])]) ).
fof(f5391,plain,
( spl77_372
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_372])]) ).
fof(f5395,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2) )
| ~ spl77_86
| ~ spl77_372 ),
inference(forward_demodulation,[],[f5394,f1490]) ).
fof(f5394,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) )
| ~ spl77_86
| ~ spl77_372 ),
inference(forward_demodulation,[],[f5392,f1490]) ).
fof(f5392,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) )
| ~ spl77_372 ),
inference(avatar_component_clause,[],[f5391]) ).
fof(f5403,plain,
( spl77_374
| ~ spl77_86
| ~ spl77_371 ),
inference(avatar_split_clause,[],[f5389,f5385,f1489,f5401]) ).
fof(f5401,plain,
( spl77_374
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_374])]) ).
fof(f5385,plain,
( spl77_371
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_371])]) ).
fof(f5389,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| sP0(X0,X1,X2) )
| ~ spl77_86
| ~ spl77_371 ),
inference(forward_demodulation,[],[f5388,f1490]) ).
fof(f5388,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) )
| ~ spl77_86
| ~ spl77_371 ),
inference(forward_demodulation,[],[f5386,f1490]) ).
fof(f5386,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) )
| ~ spl77_371 ),
inference(avatar_component_clause,[],[f5385]) ).
fof(f5399,plain,
( spl77_373
| ~ spl77_86
| ~ spl77_370 ),
inference(avatar_split_clause,[],[f5383,f5379,f1489,f5397]) ).
fof(f5397,plain,
( spl77_373
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2))),X0)
| sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_373])]) ).
fof(f5379,plain,
( spl77_370
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_370])]) ).
fof(f5383,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK32(X0,X1,X2),sK31(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2))),X0)
| sP0(X0,X1,X2) )
| ~ spl77_86
| ~ spl77_370 ),
inference(forward_demodulation,[],[f5382,f1490]) ).
fof(f5382,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2))),X0)
| sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) )
| ~ spl77_86
| ~ spl77_370 ),
inference(forward_demodulation,[],[f5380,f1490]) ).
fof(f5380,plain,
( ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) )
| ~ spl77_370 ),
inference(avatar_component_clause,[],[f5379]) ).
fof(f5393,plain,
spl77_372,
inference(avatar_split_clause,[],[f965,f5391]) ).
fof(f965,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f718,f891,f891]) ).
fof(f718,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X0)
| in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f5387,plain,
spl77_371,
inference(avatar_split_clause,[],[f952,f5385]) ).
fof(f952,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X1)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f700,f891,f891]) ).
fof(f700,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(sK31(X0,X1,X2),sK33(X0,X1,X2)),X1)
| in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f5381,plain,
spl77_370,
inference(avatar_split_clause,[],[f951,f5379]) ).
fof(f951,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(unordered_pair(unordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK33(X0,X1,X2),sK33(X0,X1,X2))),X0)
| in(unordered_pair(unordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),unordered_pair(sK31(X0,X1,X2),sK31(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f701,f891,f891]) ).
fof(f701,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(ordered_pair(sK33(X0,X1,X2),sK32(X0,X1,X2)),X0)
| in(ordered_pair(sK31(X0,X1,X2),sK32(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f5327,plain,
( spl77_369
| ~ spl77_86
| ~ spl77_367 ),
inference(avatar_split_clause,[],[f5302,f5298,f1489,f5325]) ).
fof(f5325,plain,
( spl77_369
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK29(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK30(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_369])]) ).
fof(f5298,plain,
( spl77_367
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_367])]) ).
fof(f5302,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK29(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK30(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_367 ),
inference(forward_demodulation,[],[f5301,f1490]) ).
fof(f5301,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_367 ),
inference(forward_demodulation,[],[f5299,f1490]) ).
fof(f5299,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_367 ),
inference(avatar_component_clause,[],[f5298]) ).
fof(f5306,plain,
( spl77_368
| ~ spl77_86
| ~ spl77_366 ),
inference(avatar_split_clause,[],[f5296,f5292,f1489,f5304]) ).
fof(f5304,plain,
( spl77_368
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK30(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_368])]) ).
fof(f5292,plain,
( spl77_366
<=> ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_366])]) ).
fof(f5296,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK29(X0,X1)),unordered_pair(sK29(X0,X1),sK30(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_366 ),
inference(forward_demodulation,[],[f5295,f1490]) ).
fof(f5295,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_366 ),
inference(forward_demodulation,[],[f5293,f1490]) ).
fof(f5293,plain,
( ! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_366 ),
inference(avatar_component_clause,[],[f5292]) ).
fof(f5300,plain,
spl77_367,
inference(avatar_split_clause,[],[f947,f5298]) ).
fof(f947,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f693,f891,f891]) ).
fof(f693,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f417]) ).
fof(f417,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ( ( ~ in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1) )
& ( in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30])],[f415,f416]) ).
fof(f416,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( ~ in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1) )
& ( in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f415,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0) )
& ( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f414]) ).
fof(f414,plain,
! [X0] :
( ! [X1] :
( ( ( relation_inverse(X0) = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X3,X2),X0)
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X3,X2),X0) )
& ( in(ordered_pair(X3,X2),X0)
| ~ in(ordered_pair(X2,X3),X1) ) )
| relation_inverse(X0) != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0] :
( ! [X1] :
( ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( relation_inverse(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> in(ordered_pair(X3,X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_relat_1) ).
fof(f5294,plain,
spl77_366,
inference(avatar_split_clause,[],[f946,f5292]) ).
fof(f946,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK30(X0,X1),sK29(X0,X1)),unordered_pair(sK30(X0,X1),sK30(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK29(X0,X1),sK30(X0,X1)),unordered_pair(sK29(X0,X1),sK29(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f694,f891,f891]) ).
fof(f694,plain,
! [X0,X1] :
( relation_inverse(X0) = X1
| ~ in(ordered_pair(sK30(X0,X1),sK29(X0,X1)),X0)
| ~ in(ordered_pair(sK29(X0,X1),sK30(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f417]) ).
fof(f5234,plain,
( spl77_365
| ~ spl77_86
| ~ spl77_363 ),
inference(avatar_split_clause,[],[f5226,f5222,f1489,f5232]) ).
fof(f5232,plain,
( spl77_365
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_365])]) ).
fof(f5222,plain,
( spl77_363
<=> ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_363])]) ).
fof(f5226,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_363 ),
inference(forward_demodulation,[],[f5225,f1490]) ).
fof(f5225,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_363 ),
inference(forward_demodulation,[],[f5223,f1490]) ).
fof(f5223,plain,
( ! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_363 ),
inference(avatar_component_clause,[],[f5222]) ).
fof(f5230,plain,
( spl77_364
| ~ spl77_86
| ~ spl77_362 ),
inference(avatar_split_clause,[],[f5220,f5216,f1489,f5228]) ).
fof(f5228,plain,
( spl77_364
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_364])]) ).
fof(f5216,plain,
( spl77_362
<=> ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_362])]) ).
fof(f5220,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_362 ),
inference(forward_demodulation,[],[f5219,f1490]) ).
fof(f5219,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK26(X0,X1),sK25(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| X0 = X1
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_362 ),
inference(forward_demodulation,[],[f5217,f1490]) ).
fof(f5217,plain,
( ! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_362 ),
inference(avatar_component_clause,[],[f5216]) ).
fof(f5224,plain,
spl77_363,
inference(avatar_split_clause,[],[f940,f5222]) ).
fof(f940,plain,
! [X0,X1] :
( X0 = X1
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f686,f891,f891]) ).
fof(f686,plain,
! [X0,X1] :
( X0 = X1
| in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f409]) ).
fof(f409,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ( ( ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0) )
& ( in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f407,f408]) ).
fof(f408,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) )
=> ( ( ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0) )
& ( in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f407,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X4,X5),X1) )
& ( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f406]) ).
fof(f406,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ? [X2,X3] :
( ( ~ in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
& ( in(ordered_pair(X2,X3),X1)
| in(ordered_pair(X2,X3),X0) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| X0 != X1 ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f277]) ).
fof(f277,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( X0 = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
<=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_relat_1) ).
fof(f5218,plain,
spl77_362,
inference(avatar_split_clause,[],[f939,f5216]) ).
fof(f939,plain,
! [X0,X1] :
( X0 = X1
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X1)
| ~ in(unordered_pair(unordered_pair(sK25(X0,X1),sK26(X0,X1)),unordered_pair(sK25(X0,X1),sK25(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f687,f891,f891]) ).
fof(f687,plain,
! [X0,X1] :
( X0 = X1
| ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X1)
| ~ in(ordered_pair(sK25(X0,X1),sK26(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f409]) ).
fof(f5198,plain,
( spl77_361
| ~ spl77_34
| ~ spl77_317 ),
inference(avatar_split_clause,[],[f5107,f4488,f1197,f5196]) ).
fof(f1197,plain,
( spl77_34
<=> ! [X0,X1] : subset(set_difference(X0,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_34])]) ).
fof(f4488,plain,
( spl77_317
<=> ! [X0] :
( subset(X0,relation_field(sK17))
| ~ subset(X0,relation_rng(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_317])]) ).
fof(f5107,plain,
( ! [X0] : subset(set_difference(relation_rng(sK17),X0),relation_field(sK17))
| ~ spl77_34
| ~ spl77_317 ),
inference(resolution,[],[f4489,f1198]) ).
fof(f1198,plain,
( ! [X0,X1] : subset(set_difference(X0,X1),X0)
| ~ spl77_34 ),
inference(avatar_component_clause,[],[f1197]) ).
fof(f4489,plain,
( ! [X0] :
( ~ subset(X0,relation_rng(sK17))
| subset(X0,relation_field(sK17)) )
| ~ spl77_317 ),
inference(avatar_component_clause,[],[f4488]) ).
fof(f5174,plain,
( spl77_360
| ~ spl77_86
| ~ spl77_358 ),
inference(avatar_split_clause,[],[f5166,f5163,f1489,f5172]) ).
fof(f5172,plain,
( spl77_360
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X8,sK34(X0,X1,X7,X8)),unordered_pair(sK34(X0,X1,X7,X8),sK34(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_360])]) ).
fof(f5163,plain,
( spl77_358
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X7,X8),X8),unordered_pair(sK34(X0,X1,X7,X8),sK34(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_358])]) ).
fof(f5166,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X8,sK34(X0,X1,X7,X8)),unordered_pair(sK34(X0,X1,X7,X8),sK34(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl77_86
| ~ spl77_358 ),
inference(forward_demodulation,[],[f5164,f1490]) ).
fof(f5164,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X7,X8),X8),unordered_pair(sK34(X0,X1,X7,X8),sK34(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl77_358 ),
inference(avatar_component_clause,[],[f5163]) ).
fof(f5170,plain,
spl77_359,
inference(avatar_split_clause,[],[f1042,f5168]) ).
fof(f5168,plain,
( spl77_359
<=> ! [X2,X0,X1] :
( sK64(X0,X1,X2) = unordered_pair(unordered_pair(sK66(X0,X1,X2),sK65(X0,X1,X2)),unordered_pair(sK65(X0,X1,X2),sK65(X0,X1,X2)))
| sP11(X0,X1,X2)
| in(sK64(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_359])]) ).
fof(f1042,plain,
! [X2,X0,X1] :
( sK64(X0,X1,X2) = unordered_pair(unordered_pair(sK66(X0,X1,X2),sK65(X0,X1,X2)),unordered_pair(sK65(X0,X1,X2),sK65(X0,X1,X2)))
| sP11(X0,X1,X2)
| in(sK64(X0,X1,X2),X2) ),
inference(forward_demodulation,[],[f989,f747]) ).
fof(f747,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f989,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| sK64(X0,X1,X2) = unordered_pair(unordered_pair(sK65(X0,X1,X2),sK66(X0,X1,X2)),unordered_pair(sK65(X0,X1,X2),sK65(X0,X1,X2)))
| in(sK64(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f848,f891]) ).
fof(f848,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| sK64(X0,X1,X2) = ordered_pair(sK65(X0,X1,X2),sK66(X0,X1,X2))
| in(sK64(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f517,plain,
! [X0,X1,X2] :
( ( sP11(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK64(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK64(X0,X1,X2),X2) )
& ( ( sK64(X0,X1,X2) = ordered_pair(sK65(X0,X1,X2),sK66(X0,X1,X2))
& in(sK66(X0,X1,X2),X0)
& in(sK65(X0,X1,X2),X1) )
| in(sK64(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK67(X0,X1,X8),sK68(X0,X1,X8)) = X8
& in(sK68(X0,X1,X8),X0)
& in(sK67(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP11(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK64,sK65,sK66,sK67,sK68])],[f513,f516,f515,f514]) ).
fof(f514,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK64(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK64(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK64(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK64(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f515,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK64(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK64(X0,X1,X2) = ordered_pair(sK65(X0,X1,X2),sK66(X0,X1,X2))
& in(sK66(X0,X1,X2),X0)
& in(sK65(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f516,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK67(X0,X1,X8),sK68(X0,X1,X8)) = X8
& in(sK68(X0,X1,X8),X0)
& in(sK67(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f513,plain,
! [X0,X1,X2] :
( ( sP11(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP11(X0,X1,X2) ) ),
inference(rectify,[],[f512]) ).
fof(f512,plain,
! [X1,X0,X2] :
( ( sP11(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP11(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f359]) ).
fof(f359,plain,
! [X1,X0,X2] :
( sP11(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f5165,plain,
spl77_358,
inference(avatar_split_clause,[],[f954,f5163]) ).
fof(f954,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(sK34(X0,X1,X7,X8),X8),unordered_pair(sK34(X0,X1,X7,X8),sK34(X0,X1,X7,X8))),X0)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f698,f891,f891]) ).
fof(f698,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK34(X0,X1,X7,X8),X8),X0)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f5161,plain,
spl77_357,
inference(avatar_split_clause,[],[f1038,f5159]) ).
fof(f5159,plain,
( spl77_357
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1),sK55(X0,X1)),unordered_pair(sK55(X0,X1),sK55(X0,X1))),X1)
| sP6(X0,X1)
| sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK55(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_357])]) ).
fof(f1038,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1),sK55(X0,X1)),unordered_pair(sK55(X0,X1),sK55(X0,X1))),X1)
| sP6(X0,X1)
| sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK55(X0,X1),X0) ),
inference(inner_rewriting,[],[f1037]) ).
fof(f1037,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK55(X0,X1),sK54(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1)
| sP6(X0,X1)
| sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK54(X0,X1),X0) ),
inference(forward_demodulation,[],[f975,f747]) ).
fof(f975,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK54(X0,X1),X0)
| ~ in(unordered_pair(unordered_pair(sK54(X0,X1),sK55(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1) ),
inference(definition_unfolding,[],[f776,f891]) ).
fof(f776,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK54(X0,X1),X0)
| ~ in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f478,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK54(X0,X1),X0)
| ~ in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) )
& ( ( sK54(X0,X1) = sK55(X0,X1)
& in(sK54(X0,X1),X0) )
| in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55])],[f476,f477]) ).
fof(f477,plain,
! [X0,X1] :
( ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) )
=> ( ( sK54(X0,X1) != sK55(X0,X1)
| ~ in(sK54(X0,X1),X0)
| ~ in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) )
& ( ( sK54(X0,X1) = sK55(X0,X1)
& in(sK54(X0,X1),X0) )
| in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f476,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0) )
& ( ( X4 = X5
& in(X4,X0) )
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(rectify,[],[f475]) ).
fof(f475,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(flattening,[],[f474]) ).
fof(f474,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ? [X2,X3] :
( ( X2 != X3
| ~ in(X2,X0)
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( X2 = X3
& in(X2,X0) )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| X2 != X3
| ~ in(X2,X0) )
& ( ( X2 = X3
& in(X2,X0) )
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ sP6(X0,X1) ) ),
inference(nnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f5137,plain,
( spl77_356
| ~ spl77_86
| ~ spl77_355 ),
inference(avatar_split_clause,[],[f5117,f5114,f1489,f5135]) ).
fof(f5135,plain,
( spl77_356
<=> ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_356])]) ).
fof(f5114,plain,
( spl77_355
<=> ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_355])]) ).
fof(f5117,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(sK42(X0,X1,X2),sK41(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2)
| sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1) )
| ~ spl77_86
| ~ spl77_355 ),
inference(forward_demodulation,[],[f5115,f1490]) ).
fof(f5115,plain,
( ! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) )
| ~ spl77_355 ),
inference(avatar_component_clause,[],[f5114]) ).
fof(f5116,plain,
spl77_355,
inference(avatar_split_clause,[],[f966,f5114]) ).
fof(f966,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1)
| in(unordered_pair(unordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),unordered_pair(sK41(X0,X1,X2),sK41(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f717,f891]) ).
fof(f717,plain,
! [X2,X0,X1] :
( sP2(X0,X1,X2)
| in(sK41(X0,X1,X2),X1)
| in(ordered_pair(sK41(X0,X1,X2),sK42(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f5101,plain,
spl77_354,
inference(avatar_split_clause,[],[f953,f5099]) ).
fof(f5099,plain,
( spl77_354
<=> ! [X1,X0,X8,X9,X2,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_354])]) ).
fof(f953,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ in(unordered_pair(unordered_pair(X9,X8),unordered_pair(X9,X9)),X0)
| ~ in(unordered_pair(unordered_pair(X7,X9),unordered_pair(X7,X7)),X1)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f699,f891,f891,f891]) ).
fof(f699,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X9,X8),X0)
| ~ in(ordered_pair(X7,X9),X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f5041,plain,
( spl77_353
| ~ spl77_86
| ~ spl77_349 ),
inference(avatar_split_clause,[],[f5025,f5022,f1489,f5039]) ).
fof(f5039,plain,
( spl77_353
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK38(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_353])]) ).
fof(f5022,plain,
( spl77_349
<=> ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| in(sK38(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_349])]) ).
fof(f5025,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK39(X0,X1),sK38(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| relation_dom(X0) = X1
| in(sK38(X0,X1),X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_349 ),
inference(forward_demodulation,[],[f5023,f1490]) ).
fof(f5023,plain,
( ! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| in(sK38(X0,X1),X1)
| ~ relation(X0) )
| ~ spl77_349 ),
inference(avatar_component_clause,[],[f5022]) ).
fof(f5037,plain,
( spl77_352
| ~ spl77_86
| ~ spl77_348 ),
inference(avatar_split_clause,[],[f5016,f5013,f1489,f5035]) ).
fof(f5035,plain,
( spl77_352
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK35(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK35(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_352])]) ).
fof(f5013,plain,
( spl77_348
<=> ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK35(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| in(sK35(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_348])]) ).
fof(f5016,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK36(X0,X1),sK36(X0,X1)),unordered_pair(sK36(X0,X1),sK35(X0,X1))),X0)
| relation_rng(X0) = X1
| in(sK35(X0,X1),X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_348 ),
inference(forward_demodulation,[],[f5014,f1490]) ).
fof(f5014,plain,
( ! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK35(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| in(sK35(X0,X1),X1)
| ~ relation(X0) )
| ~ spl77_348 ),
inference(avatar_component_clause,[],[f5013]) ).
fof(f5033,plain,
spl77_351,
inference(avatar_split_clause,[],[f1043,f5031]) ).
fof(f5031,plain,
( spl77_351
<=> ! [X0,X8,X2,X1] :
( unordered_pair(unordered_pair(sK68(X0,X1,X8),sK67(X0,X1,X8)),unordered_pair(sK67(X0,X1,X8),sK67(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_351])]) ).
fof(f1043,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK68(X0,X1,X8),sK67(X0,X1,X8)),unordered_pair(sK67(X0,X1,X8),sK67(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ),
inference(forward_demodulation,[],[f991,f747]) ).
fof(f991,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK67(X0,X1,X8),sK68(X0,X1,X8)),unordered_pair(sK67(X0,X1,X8),sK67(X0,X1,X8))) = X8
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ),
inference(definition_unfolding,[],[f844,f891]) ).
fof(f844,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK67(X0,X1,X8),sK68(X0,X1,X8)) = X8
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f5029,plain,
spl77_350,
inference(avatar_split_clause,[],[f988,f5027]) ).
fof(f5027,plain,
( spl77_350
<=> ! [X4,X0,X5,X2,X1] :
( sP11(X0,X1,X2)
| sK64(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK64(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_350])]) ).
fof(f988,plain,
! [X2,X0,X1,X4,X5] :
( sP11(X0,X1,X2)
| sK64(X0,X1,X2) != unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4))
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK64(X0,X1,X2),X2) ),
inference(definition_unfolding,[],[f849,f891]) ).
fof(f849,plain,
! [X2,X0,X1,X4,X5] :
( sP11(X0,X1,X2)
| ordered_pair(X4,X5) != sK64(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK64(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f5024,plain,
spl77_349,
inference(avatar_split_clause,[],[f961,f5022]) ).
fof(f961,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(unordered_pair(unordered_pair(sK38(X0,X1),sK39(X0,X1)),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| in(sK38(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f710,f891]) ).
fof(f710,plain,
! [X0,X1] :
( relation_dom(X0) = X1
| in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0)
| in(sK38(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f437]) ).
fof(f437,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK38(X0,X1),X3),X0)
| ~ in(sK38(X0,X1),X1) )
& ( in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0)
| in(sK38(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK40(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39,sK40])],[f433,f436,f435,f434]) ).
fof(f434,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK38(X0,X1),X3),X0)
| ~ in(sK38(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK38(X0,X1),X4),X0)
| in(sK38(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f435,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK38(X0,X1),X4),X0)
=> in(ordered_pair(sK38(X0,X1),sK39(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f436,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK40(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f433,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f432]) ).
fof(f432,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f5015,plain,
spl77_348,
inference(avatar_split_clause,[],[f957,f5013]) ).
fof(f957,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(unordered_pair(unordered_pair(sK36(X0,X1),sK35(X0,X1)),unordered_pair(sK36(X0,X1),sK36(X0,X1))),X0)
| in(sK35(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f706,f891]) ).
fof(f706,plain,
! [X0,X1] :
( relation_rng(X0) = X1
| in(ordered_pair(sK36(X0,X1),sK35(X0,X1)),X0)
| in(sK35(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f431]) ).
fof(f431,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK35(X0,X1)),X0)
| ~ in(sK35(X0,X1),X1) )
& ( in(ordered_pair(sK36(X0,X1),sK35(X0,X1)),X0)
| in(sK35(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK37(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37])],[f427,f430,f429,f428]) ).
fof(f428,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK35(X0,X1)),X0)
| ~ in(sK35(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK35(X0,X1)),X0)
| in(sK35(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f429,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK35(X0,X1)),X0)
=> in(ordered_pair(sK36(X0,X1),sK35(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f430,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK37(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f427,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f426]) ).
fof(f426,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f4991,plain,
spl77_347,
inference(avatar_split_clause,[],[f1039,f4989]) ).
fof(f4989,plain,
( spl77_347
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1),sK54(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1)
| sP6(X0,X1)
| sK54(X0,X1) = sK55(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_347])]) ).
fof(f1039,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1),sK54(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1)
| sP6(X0,X1)
| sK54(X0,X1) = sK55(X0,X1) ),
inference(forward_demodulation,[],[f976,f747]) ).
fof(f976,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK54(X0,X1) = sK55(X0,X1)
| in(unordered_pair(unordered_pair(sK54(X0,X1),sK55(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1) ),
inference(definition_unfolding,[],[f775,f891]) ).
fof(f775,plain,
! [X0,X1] :
( sP6(X0,X1)
| sK54(X0,X1) = sK55(X0,X1)
| in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f4960,plain,
( spl77_346
| ~ spl77_86
| ~ spl77_344 ),
inference(avatar_split_clause,[],[f4923,f4920,f1489,f4958]) ).
fof(f4958,plain,
( spl77_346
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK34(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_346])]) ).
fof(f4920,plain,
( spl77_344
<=> ! [X2,X0,X8,X1,X7] :
( in(unordered_pair(unordered_pair(X7,sK34(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_344])]) ).
fof(f4923,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,X7),unordered_pair(X7,sK34(X0,X1,X7,X8))),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl77_86
| ~ spl77_344 ),
inference(forward_demodulation,[],[f4921,f1490]) ).
fof(f4921,plain,
( ! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK34(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) )
| ~ spl77_344 ),
inference(avatar_component_clause,[],[f4920]) ).
fof(f4927,plain,
spl77_345,
inference(avatar_split_clause,[],[f960,f4925]) ).
fof(f4925,plain,
( spl77_345
<=> ! [X0,X1,X3] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),X3),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ in(sK38(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_345])]) ).
fof(f960,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(unordered_pair(unordered_pair(sK38(X0,X1),X3),unordered_pair(sK38(X0,X1),sK38(X0,X1))),X0)
| ~ in(sK38(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f711,f891]) ).
fof(f711,plain,
! [X3,X0,X1] :
( relation_dom(X0) = X1
| ~ in(ordered_pair(sK38(X0,X1),X3),X0)
| ~ in(sK38(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f437]) ).
fof(f4922,plain,
spl77_344,
inference(avatar_split_clause,[],[f955,f4920]) ).
fof(f955,plain,
! [X2,X0,X1,X8,X7] :
( in(unordered_pair(unordered_pair(X7,sK34(X0,X1,X7,X8)),unordered_pair(X7,X7)),X1)
| ~ in(unordered_pair(unordered_pair(X7,X8),unordered_pair(X7,X7)),X2)
| ~ sP0(X0,X1,X2) ),
inference(definition_unfolding,[],[f697,f891,f891]) ).
fof(f697,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK34(X0,X1,X7,X8)),X1)
| ~ in(ordered_pair(X7,X8),X2)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f425]) ).
fof(f4918,plain,
spl77_343,
inference(avatar_split_clause,[],[f926,f4916]) ).
fof(f4916,plain,
( spl77_343
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_343])]) ).
fof(f926,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(definition_unfolding,[],[f656,f891,f891]) ).
fof(f656,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2)
| ~ relation(X3) ),
inference(cnf_transformation,[],[f399]) ).
fof(f399,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(flattening,[],[f398]) ).
fof(f398,plain,
! [X0,X1,X2,X3] :
( ( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(X0,X2) )
& ( ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) ) )
| ~ relation(X3) ),
inference(nnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) )
| ~ relation(X3) ),
inference(ennf_transformation,[],[f172]) ).
fof(f172,axiom,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(ordered_pair(X0,X1),X3)
& in(X0,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f4914,plain,
( spl77_342
| ~ spl77_71
| ~ spl77_312 ),
inference(avatar_split_clause,[],[f4803,f4324,f1391,f4911]) ).
fof(f4911,plain,
( spl77_342
<=> sP14(relation_field(sK17),relation_rng(sK17),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_342])]) ).
fof(f1391,plain,
( spl77_71
<=> ! [X0,X1] : sP14(X1,X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_71])]) ).
fof(f4324,plain,
( spl77_312
<=> relation_field(sK17) = set_union2(relation_rng(sK17),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_312])]) ).
fof(f4803,plain,
( sP14(relation_field(sK17),relation_rng(sK17),relation_field(sK17))
| ~ spl77_71
| ~ spl77_312 ),
inference(superposition,[],[f1392,f4326]) ).
fof(f4326,plain,
( relation_field(sK17) = set_union2(relation_rng(sK17),relation_field(sK17))
| ~ spl77_312 ),
inference(avatar_component_clause,[],[f4324]) ).
fof(f1392,plain,
( ! [X0,X1] : sP14(X1,X0,set_union2(X0,X1))
| ~ spl77_71 ),
inference(avatar_component_clause,[],[f1391]) ).
fof(f4873,plain,
spl77_341,
inference(avatar_split_clause,[],[f1040,f4871]) ).
fof(f4871,plain,
( spl77_341
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1),sK54(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1)
| sP6(X0,X1)
| in(sK54(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_341])]) ).
fof(f1040,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK55(X0,X1),sK54(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1)
| sP6(X0,X1)
| in(sK54(X0,X1),X0) ),
inference(forward_demodulation,[],[f977,f747]) ).
fof(f977,plain,
! [X0,X1] :
( sP6(X0,X1)
| in(sK54(X0,X1),X0)
| in(unordered_pair(unordered_pair(sK54(X0,X1),sK55(X0,X1)),unordered_pair(sK54(X0,X1),sK54(X0,X1))),X1) ),
inference(definition_unfolding,[],[f774,f891]) ).
fof(f774,plain,
! [X0,X1] :
( sP6(X0,X1)
| in(sK54(X0,X1),X0)
| in(ordered_pair(sK54(X0,X1),sK55(X0,X1)),X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f4869,plain,
spl77_340,
inference(avatar_split_clause,[],[f967,f4867]) ).
fof(f4867,plain,
( spl77_340
<=> ! [X5,X0,X6,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_340])]) ).
fof(f967,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f716,f891,f891]) ).
fof(f716,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X2)
| ~ in(ordered_pair(X5,X6),X0)
| ~ in(X5,X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f4817,plain,
( spl77_339
| ~ spl77_86
| ~ spl77_335 ),
inference(avatar_split_clause,[],[f4789,f4786,f1489,f4815]) ).
fof(f4815,plain,
( spl77_339
<=> ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_339])]) ).
fof(f4786,plain,
( spl77_335
<=> ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_335])]) ).
fof(f4789,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_335 ),
inference(forward_demodulation,[],[f4787,f1490]) ).
fof(f4787,plain,
( ! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_335 ),
inference(avatar_component_clause,[],[f4786]) ).
fof(f4813,plain,
( spl77_338
| ~ spl77_86
| ~ spl77_334 ),
inference(avatar_split_clause,[],[f4784,f4781,f1489,f4811]) ).
fof(f4811,plain,
( spl77_338
<=> ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_338])]) ).
fof(f4781,plain,
( spl77_334
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_334])]) ).
fof(f4784,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK28(X0,X1),sK27(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_334 ),
inference(forward_demodulation,[],[f4782,f1490]) ).
fof(f4782,plain,
( ! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) )
| ~ spl77_334 ),
inference(avatar_component_clause,[],[f4781]) ).
fof(f4797,plain,
spl77_337,
inference(avatar_split_clause,[],[f1001,f4795]) ).
fof(f4795,plain,
( spl77_337
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_337])]) ).
fof(f1001,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f949]) ).
fof(f949,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f691,f891,f891]) ).
fof(f691,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X5,X4),X0)
| ~ in(ordered_pair(X4,X5),X1)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f417]) ).
fof(f4793,plain,
spl77_336,
inference(avatar_split_clause,[],[f1000,f4791]) ).
fof(f4791,plain,
( spl77_336
<=> ! [X5,X4,X0] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_336])]) ).
fof(f1000,plain,
! [X0,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),relation_inverse(X0))
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| ~ relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f948]) ).
fof(f948,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ in(unordered_pair(unordered_pair(X5,X4),unordered_pair(X5,X5)),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f692,f891,f891]) ).
fof(f692,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X5,X4),X0)
| relation_inverse(X0) != X1
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f417]) ).
fof(f4788,plain,
spl77_335,
inference(avatar_split_clause,[],[f944,f4786]) ).
fof(f944,plain,
! [X0,X1] :
( subset(X0,X1)
| in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f689,f891]) ).
fof(f689,plain,
! [X0,X1] :
( subset(X0,X1)
| in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f413]) ).
fof(f413,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
& in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27,sK28])],[f411,f412]) ).
fof(f412,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) )
=> ( ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
& in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f411,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f410]) ).
fof(f410,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2,X3] :
( ~ in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) )
| ~ subset(X0,X1) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X0)
=> in(ordered_pair(X2,X3),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_relat_1) ).
fof(f4783,plain,
spl77_334,
inference(avatar_split_clause,[],[f943,f4781]) ).
fof(f943,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK27(X0,X1),sK28(X0,X1)),unordered_pair(sK27(X0,X1),sK27(X0,X1))),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f690,f891]) ).
fof(f690,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(ordered_pair(sK27(X0,X1),sK28(X0,X1)),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f413]) ).
fof(f4769,plain,
spl77_333,
inference(avatar_split_clause,[],[f927,f4767]) ).
fof(f4767,plain,
( spl77_333
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_333])]) ).
fof(f927,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f655,f891,f891]) ).
fof(f655,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f399]) ).
fof(f4647,plain,
( spl77_332
| ~ spl77_192
| ~ spl77_260 ),
inference(avatar_split_clause,[],[f3341,f3259,f2495,f4645]) ).
fof(f4645,plain,
( spl77_332
<=> ! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(X0,relation_field(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_332])]) ).
fof(f2495,plain,
( spl77_192
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_192])]) ).
fof(f3259,plain,
( spl77_260
<=> sP14(relation_dom(sK17),relation_rng(sK17),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_260])]) ).
fof(f3341,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK17))
| in(X0,relation_field(sK17)) )
| ~ spl77_192
| ~ spl77_260 ),
inference(resolution,[],[f3261,f2496]) ).
fof(f2496,plain,
( ! [X2,X0,X1,X4] :
( ~ sP14(X0,X1,X2)
| ~ in(X4,X0)
| in(X4,X2) )
| ~ spl77_192 ),
inference(avatar_component_clause,[],[f2495]) ).
fof(f3261,plain,
( sP14(relation_dom(sK17),relation_rng(sK17),relation_field(sK17))
| ~ spl77_260 ),
inference(avatar_component_clause,[],[f3259]) ).
fof(f4643,plain,
spl77_331,
inference(avatar_split_clause,[],[f881,f4641]) ).
fof(f4641,plain,
( spl77_331
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK72(X0,X1,X2),X0)
| ~ in(sK72(X0,X1,X2),X1)
| ~ in(sK72(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_331])]) ).
fof(f881,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK72(X0,X1,X2),X0)
| ~ in(sK72(X0,X1,X2),X1)
| ~ in(sK72(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f541,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ( ( in(sK72(X0,X1,X2),X0)
| ~ in(sK72(X0,X1,X2),X1)
| ~ in(sK72(X0,X1,X2),X2) )
& ( ( ~ in(sK72(X0,X1,X2),X0)
& in(sK72(X0,X1,X2),X1) )
| in(sK72(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f539,f540]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( in(sK72(X0,X1,X2),X0)
| ~ in(sK72(X0,X1,X2),X1)
| ~ in(sK72(X0,X1,X2),X2) )
& ( ( ~ in(sK72(X0,X1,X2),X0)
& in(sK72(X0,X1,X2),X1) )
| in(sK72(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ? [X3] :
( ( in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1) )
& ( ( ~ in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f538]) ).
fof(f538,plain,
! [X1,X0,X2] :
( ( sP15(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(flattening,[],[f537]) ).
fof(f537,plain,
! [X1,X0,X2] :
( ( sP15(X1,X0,X2)
| ? [X3] :
( ( in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) )
& ( ( ~ in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP15(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X1,X0,X2] :
( sP15(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f4639,plain,
spl77_330,
inference(avatar_split_clause,[],[f871,f4637]) ).
fof(f4637,plain,
( spl77_330
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| in(sK71(X0,X1,X2),X0)
| in(sK71(X0,X1,X2),X1)
| in(sK71(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_330])]) ).
fof(f871,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| in(sK71(X0,X1,X2),X0)
| in(sK71(X0,X1,X2),X1)
| in(sK71(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f535,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ( ( ( ~ in(sK71(X0,X1,X2),X0)
& ~ in(sK71(X0,X1,X2),X1) )
| ~ in(sK71(X0,X1,X2),X2) )
& ( in(sK71(X0,X1,X2),X0)
| in(sK71(X0,X1,X2),X1)
| in(sK71(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71])],[f533,f534]) ).
fof(f534,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) )
=> ( ( ( ~ in(sK71(X0,X1,X2),X0)
& ~ in(sK71(X0,X1,X2),X1) )
| ~ in(sK71(X0,X1,X2),X2) )
& ( in(sK71(X0,X1,X2),X0)
| in(sK71(X0,X1,X2),X1)
| in(sK71(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f533,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ? [X3] :
( ( ( ~ in(X3,X0)
& ~ in(X3,X1) )
| ~ in(X3,X2) )
& ( in(X3,X0)
| in(X3,X1)
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( ~ in(X4,X0)
& ~ in(X4,X1) ) )
& ( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2) ) )
| ~ sP14(X0,X1,X2) ) ),
inference(rectify,[],[f532]) ).
fof(f532,plain,
! [X1,X0,X2] :
( ( sP14(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP14(X1,X0,X2) ) ),
inference(flattening,[],[f531]) ).
fof(f531,plain,
! [X1,X0,X2] :
( ( sP14(X1,X0,X2)
| ? [X3] :
( ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| ~ in(X3,X2) )
& ( in(X3,X1)
| in(X3,X0)
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) )
& ( in(X3,X1)
| in(X3,X0)
| ~ in(X3,X2) ) )
| ~ sP14(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f365]) ).
fof(f365,plain,
! [X1,X0,X2] :
( sP14(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f4635,plain,
spl77_329,
inference(avatar_split_clause,[],[f865,f4633]) ).
fof(f4633,plain,
( spl77_329
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ in(sK70(X0,X1,X2),X0)
| ~ in(sK70(X0,X1,X2),X1)
| ~ in(sK70(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_329])]) ).
fof(f865,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ in(sK70(X0,X1,X2),X0)
| ~ in(sK70(X0,X1,X2),X1)
| ~ in(sK70(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f529,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ( ~ in(sK70(X0,X1,X2),X0)
| ~ in(sK70(X0,X1,X2),X1)
| ~ in(sK70(X0,X1,X2),X2) )
& ( ( in(sK70(X0,X1,X2),X0)
& in(sK70(X0,X1,X2),X1) )
| in(sK70(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70])],[f527,f528]) ).
fof(f528,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK70(X0,X1,X2),X0)
| ~ in(sK70(X0,X1,X2),X1)
| ~ in(sK70(X0,X1,X2),X2) )
& ( ( in(sK70(X0,X1,X2),X0)
& in(sK70(X0,X1,X2),X1) )
| in(sK70(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f527,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f526]) ).
fof(f526,plain,
! [X1,X0,X2] :
( ( sP13(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP13(X1,X0,X2) ) ),
inference(flattening,[],[f525]) ).
fof(f525,plain,
! [X1,X0,X2] :
( ( sP13(X1,X0,X2)
| ? [X3] :
( ( ~ in(X3,X1)
| ~ in(X3,X0)
| ~ in(X3,X2) )
& ( ( in(X3,X1)
& in(X3,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X1)
| ~ in(X3,X0) )
& ( ( in(X3,X1)
& in(X3,X0) )
| ~ in(X3,X2) ) )
| ~ sP13(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X1,X0,X2] :
( sP13(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f4631,plain,
spl77_328,
inference(avatar_split_clause,[],[f855,f4629]) ).
fof(f4629,plain,
( spl77_328
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) = X0
| sK69(X0,X1,X2) = X1
| in(sK69(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_328])]) ).
fof(f855,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) = X0
| sK69(X0,X1,X2) = X1
| in(sK69(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f523,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ( ( ( sK69(X0,X1,X2) != X0
& sK69(X0,X1,X2) != X1 )
| ~ in(sK69(X0,X1,X2),X2) )
& ( sK69(X0,X1,X2) = X0
| sK69(X0,X1,X2) = X1
| in(sK69(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f521,f522]) ).
fof(f522,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) )
=> ( ( ( sK69(X0,X1,X2) != X0
& sK69(X0,X1,X2) != X1 )
| ~ in(sK69(X0,X1,X2),X2) )
& ( sK69(X0,X1,X2) = X0
| sK69(X0,X1,X2) = X1
| in(sK69(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f521,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X0 = X3
| X1 = X3
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f520]) ).
fof(f520,plain,
! [X1,X0,X2] :
( ( sP12(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP12(X1,X0,X2) ) ),
inference(flattening,[],[f519]) ).
fof(f519,plain,
! [X1,X0,X2] :
( ( sP12(X1,X0,X2)
| ? [X3] :
( ( ( X1 != X3
& X0 != X3 )
| ~ in(X3,X2) )
& ( X1 = X3
| X0 = X3
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X1 != X3
& X0 != X3 ) )
& ( X1 = X3
| X0 = X3
| ~ in(X3,X2) ) )
| ~ sP12(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X1,X0,X2] :
( sP12(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f4599,plain,
spl77_327,
inference(avatar_split_clause,[],[f968,f4597]) ).
fof(f4597,plain,
( spl77_327
<=> ! [X6,X0,X5,X2,X1] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_327])]) ).
fof(f968,plain,
! [X2,X0,X1,X6,X5] :
( in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f715,f891,f891]) ).
fof(f715,plain,
! [X2,X0,X1,X6,X5] :
( in(ordered_pair(X5,X6),X0)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f4595,plain,
spl77_326,
inference(avatar_split_clause,[],[f956,f4593]) ).
fof(f4593,plain,
( spl77_326
<=> ! [X0,X1,X3] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK35(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK35(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_326])]) ).
fof(f956,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(unordered_pair(unordered_pair(X3,sK35(X0,X1)),unordered_pair(X3,X3)),X0)
| ~ in(sK35(X0,X1),X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f707,f891]) ).
fof(f707,plain,
! [X3,X0,X1] :
( relation_rng(X0) = X1
| ~ in(ordered_pair(X3,sK35(X0,X1)),X0)
| ~ in(sK35(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f431]) ).
fof(f4571,plain,
( spl77_325
| ~ spl77_86
| ~ spl77_323 ),
inference(avatar_split_clause,[],[f4563,f4560,f1489,f4569]) ).
fof(f4569,plain,
( spl77_325
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK37(X0,X5)),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_325])]) ).
fof(f4560,plain,
( spl77_323
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_323])]) ).
fof(f4563,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK37(X0,X5)),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_323 ),
inference(forward_demodulation,[],[f4561,f1490]) ).
fof(f4561,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) )
| ~ spl77_323 ),
inference(avatar_component_clause,[],[f4560]) ).
fof(f4567,plain,
( spl77_324
| ~ spl77_151
| ~ spl77_218 ),
inference(avatar_split_clause,[],[f2909,f2822,f2081,f4565]) ).
fof(f4565,plain,
( spl77_324
<=> ! [X0] :
( ~ in(X0,relation_rng(sK17))
| in(X0,relation_field(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_324])]) ).
fof(f2081,plain,
( spl77_151
<=> ! [X0,X1,X3] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_151])]) ).
fof(f2822,plain,
( spl77_218
<=> subset(relation_rng(sK17),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_218])]) ).
fof(f2909,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK17))
| in(X0,relation_field(sK17)) )
| ~ spl77_151
| ~ spl77_218 ),
inference(resolution,[],[f2824,f2082]) ).
fof(f2082,plain,
( ! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) )
| ~ spl77_151 ),
inference(avatar_component_clause,[],[f2081]) ).
fof(f2824,plain,
( subset(relation_rng(sK17),relation_field(sK17))
| ~ spl77_218 ),
inference(avatar_component_clause,[],[f2822]) ).
fof(f4562,plain,
spl77_323,
inference(avatar_split_clause,[],[f1004,f4560]) ).
fof(f1004,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f959]) ).
fof(f959,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(sK37(X0,X5),X5),unordered_pair(sK37(X0,X5),sK37(X0,X5))),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f704,f891]) ).
fof(f704,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK37(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f431]) ).
fof(f4540,plain,
( spl77_322
| ~ spl77_21
| ~ spl77_52
| ~ spl77_321 ),
inference(avatar_split_clause,[],[f4536,f4532,f1293,f1139,f4538]) ).
fof(f4538,plain,
( spl77_322
<=> ! [X0,X1] :
( sK74 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_322])]) ).
fof(f1139,plain,
( spl77_21
<=> ! [X0] : cast_to_subset(X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_21])]) ).
fof(f4532,plain,
( spl77_321
<=> ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_321])]) ).
fof(f4536,plain,
( ! [X0,X1] :
( sK74 = X1
| meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_21
| ~ spl77_52
| ~ spl77_321 ),
inference(forward_demodulation,[],[f4535,f1295]) ).
fof(f4535,plain,
( ! [X0,X1] :
( meet_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,union_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_21
| ~ spl77_321 ),
inference(forward_demodulation,[],[f4533,f1140]) ).
fof(f1140,plain,
( ! [X0] : cast_to_subset(X0) = X0
| ~ spl77_21 ),
inference(avatar_component_clause,[],[f1139]) ).
fof(f4533,plain,
( ! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_321 ),
inference(avatar_component_clause,[],[f4532]) ).
fof(f4534,plain,
spl77_321,
inference(avatar_split_clause,[],[f607,f4532]) ).
fof(f607,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f238]) ).
fof(f238,plain,
! [X0,X1] :
( subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f152]) ).
fof(f152,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> subset_difference(X0,cast_to_subset(X0),union_of_subsets(X0,X1)) = meet_of_subsets(X0,complements_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_setfam_1) ).
fof(f4512,plain,
( spl77_320
| ~ spl77_21
| ~ spl77_52
| ~ spl77_319 ),
inference(avatar_split_clause,[],[f4508,f4504,f1293,f1139,f4510]) ).
fof(f4510,plain,
( spl77_320
<=> ! [X0,X1] :
( sK74 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_320])]) ).
fof(f4504,plain,
( spl77_319
<=> ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_319])]) ).
fof(f4508,plain,
( ! [X0,X1] :
( sK74 = X1
| union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_21
| ~ spl77_52
| ~ spl77_319 ),
inference(forward_demodulation,[],[f4507,f1295]) ).
fof(f4507,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,X0,meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_21
| ~ spl77_319 ),
inference(forward_demodulation,[],[f4505,f1140]) ).
fof(f4505,plain,
( ! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_319 ),
inference(avatar_component_clause,[],[f4504]) ).
fof(f4506,plain,
spl77_319,
inference(avatar_split_clause,[],[f606,f4504]) ).
fof(f606,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1))
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f153]) ).
fof(f153,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( empty_set != X1
=> union_of_subsets(X0,complements_of_subsets(X0,X1)) = subset_difference(X0,cast_to_subset(X0),meet_of_subsets(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_setfam_1) ).
fof(f4501,plain,
spl77_318,
inference(avatar_split_clause,[],[f1025,f4499]) ).
fof(f4499,plain,
( spl77_318
<=> ! [X10,X0,X9,X2,X1] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_318])]) ).
fof(f1025,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)),X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP11(X0,X1,X2) ),
inference(equality_resolution,[],[f990]) ).
fof(f990,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),unordered_pair(X9,X9)) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP11(X0,X1,X2) ),
inference(definition_unfolding,[],[f845,f891]) ).
fof(f845,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f4490,plain,
( spl77_317
| ~ spl77_146
| ~ spl77_218 ),
inference(avatar_split_clause,[],[f2906,f2822,f1989,f4488]) ).
fof(f1989,plain,
( spl77_146
<=> ! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_146])]) ).
fof(f2906,plain,
( ! [X0] :
( subset(X0,relation_field(sK17))
| ~ subset(X0,relation_rng(sK17)) )
| ~ spl77_146
| ~ spl77_218 ),
inference(resolution,[],[f2824,f1990]) ).
fof(f1990,plain,
( ! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) )
| ~ spl77_146 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f4447,plain,
spl77_316,
inference(avatar_split_clause,[],[f798,f4445]) ).
fof(f4445,plain,
( spl77_316
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| ~ in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_316])]) ).
fof(f798,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| ~ in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| ~ in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f485]) ).
fof(f485,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ( ( ~ in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| ~ in(sK56(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| in(sK56(X0,X1,X2),X2) )
& element(sK56(X0,X1,X2),powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP8(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f483,f484]) ).
fof(f484,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) )
=> ( ( ~ in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| ~ in(sK56(X0,X1,X2),X2) )
& ( in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| in(sK56(X0,X1,X2),X2) )
& element(sK56(X0,X1,X2),powerset(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f483,plain,
! [X0,X1,X2] :
( ( sP8(X0,X1,X2)
| ? [X3] :
( ( ~ in(subset_complement(X1,X3),X0)
| ~ in(X3,X2) )
& ( in(subset_complement(X1,X3),X0)
| in(X3,X2) )
& element(X3,powerset(X1)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0) )
& ( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X1)) )
| ~ sP8(X0,X1,X2) ) ),
inference(rectify,[],[f482]) ).
fof(f482,plain,
! [X1,X0,X2] :
( ( sP8(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP8(X1,X0,X2) ) ),
inference(flattening,[],[f481]) ).
fof(f481,plain,
! [X1,X0,X2] :
( ( sP8(X1,X0,X2)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| ~ sP8(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X1,X0,X2] :
( sP8(X1,X0,X2)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f4443,plain,
spl77_315,
inference(avatar_split_clause,[],[f797,f4441]) ).
fof(f4441,plain,
( spl77_315
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| in(sK56(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_315])]) ).
fof(f797,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| in(subset_complement(X1,sK56(X0,X1,X2)),X0)
| in(sK56(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f485]) ).
fof(f4361,plain,
( spl77_314
| ~ spl77_86
| ~ spl77_310 ),
inference(avatar_split_clause,[],[f4318,f4315,f1489,f4359]) ).
fof(f4359,plain,
( spl77_314
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK45(X4),sK44(X4)),unordered_pair(sK44(X4),sK44(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_314])]) ).
fof(f4315,plain,
( spl77_310
<=> ! [X4,X0] :
( unordered_pair(unordered_pair(sK44(X4),sK45(X4)),unordered_pair(sK44(X4),sK44(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_310])]) ).
fof(f4318,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK45(X4),sK44(X4)),unordered_pair(sK44(X4),sK44(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_310 ),
inference(forward_demodulation,[],[f4316,f1490]) ).
fof(f4316,plain,
( ! [X0,X4] :
( unordered_pair(unordered_pair(sK44(X4),sK45(X4)),unordered_pair(sK44(X4),sK44(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) )
| ~ spl77_310 ),
inference(avatar_component_clause,[],[f4315]) ).
fof(f4331,plain,
( spl77_313
| ~ spl77_52
| ~ spl77_86
| ~ spl77_307 ),
inference(avatar_split_clause,[],[f4305,f4301,f1489,f1293,f4329]) ).
fof(f4329,plain,
( spl77_313
<=> ! [X0] :
( in(unordered_pair(unordered_pair(sK19(X0),sK18(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| sK74 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_313])]) ).
fof(f4301,plain,
( spl77_307
<=> ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK18(X0),sK19(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_307])]) ).
fof(f4305,plain,
( ! [X0] :
( in(unordered_pair(unordered_pair(sK19(X0),sK18(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| sK74 = X0
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_86
| ~ spl77_307 ),
inference(forward_demodulation,[],[f4304,f1490]) ).
fof(f4304,plain,
( ! [X0] :
( sK74 = X0
| in(unordered_pair(unordered_pair(sK18(X0),sK19(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_307 ),
inference(forward_demodulation,[],[f4302,f1295]) ).
fof(f4302,plain,
( ! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK18(X0),sK19(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| ~ relation(X0) )
| ~ spl77_307 ),
inference(avatar_component_clause,[],[f4301]) ).
fof(f4327,plain,
( spl77_312
| ~ spl77_104
| ~ spl77_218 ),
inference(avatar_split_clause,[],[f2904,f2822,f1641,f4324]) ).
fof(f1641,plain,
( spl77_104
<=> ! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_104])]) ).
fof(f2904,plain,
( relation_field(sK17) = set_union2(relation_rng(sK17),relation_field(sK17))
| ~ spl77_104
| ~ spl77_218 ),
inference(resolution,[],[f2824,f1642]) ).
fof(f1642,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 )
| ~ spl77_104 ),
inference(avatar_component_clause,[],[f1641]) ).
fof(f4322,plain,
( spl77_311
| ~ spl77_52
| ~ spl77_306 ),
inference(avatar_split_clause,[],[f4299,f4296,f1293,f4320]) ).
fof(f4320,plain,
( spl77_311
<=> ! [X2,X0,X1] :
( sK74 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_311])]) ).
fof(f4296,plain,
( spl77_306
<=> ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_306])]) ).
fof(f4299,plain,
( ! [X2,X0,X1] :
( sK74 = X0
| in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0)) )
| ~ spl77_52
| ~ spl77_306 ),
inference(forward_demodulation,[],[f4297,f1295]) ).
fof(f4297,plain,
( ! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 )
| ~ spl77_306 ),
inference(avatar_component_clause,[],[f4296]) ).
fof(f4317,plain,
spl77_310,
inference(avatar_split_clause,[],[f971,f4315]) ).
fof(f971,plain,
! [X0,X4] :
( unordered_pair(unordered_pair(sK44(X4),sK45(X4)),unordered_pair(sK44(X4),sK44(X4))) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f729,f891]) ).
fof(f729,plain,
! [X0,X4] :
( ordered_pair(sK44(X4),sK45(X4)) = X4
| ~ in(X4,X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f449]) ).
fof(f449,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK43(X0)
& in(sK43(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK44(X4),sK45(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f446,f448,f447]) ).
fof(f447,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK43(X0)
& in(sK43(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f448,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK44(X4),sK45(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f446,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f445]) ).
fof(f445,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f4313,plain,
spl77_309,
inference(avatar_split_clause,[],[f930,f4311]) ).
fof(f4311,plain,
( spl77_309
<=> ! [X0,X3,X2,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_309])]) ).
fof(f930,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f657,f891,f891]) ).
fof(f657,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(ennf_transformation,[],[f131]) ).
fof(f131,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X2,X3) = ordered_pair(X0,X1)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f4309,plain,
spl77_308,
inference(avatar_split_clause,[],[f929,f4307]) ).
fof(f4307,plain,
( spl77_308
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_308])]) ).
fof(f929,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f658,f891,f891]) ).
fof(f658,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| ordered_pair(X2,X3) != ordered_pair(X0,X1) ),
inference(cnf_transformation,[],[f269]) ).
fof(f4303,plain,
spl77_307,
inference(avatar_split_clause,[],[f894,f4301]) ).
fof(f894,plain,
! [X0] :
( empty_set = X0
| in(unordered_pair(unordered_pair(sK18(X0),sK19(X0)),unordered_pair(sK18(X0),sK18(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f567,f891]) ).
fof(f567,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK18(X0),sK19(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( empty_set = X0
| in(ordered_pair(sK18(X0),sK19(X0)),X0)
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f206,f371]) ).
fof(f371,plain,
! [X0] :
( ? [X1,X2] : in(ordered_pair(X1,X2),X0)
=> in(ordered_pair(sK18(X0),sK19(X0)),X0) ),
introduced(choice_axiom,[]) ).
fof(f206,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(flattening,[],[f205]) ).
fof(f205,plain,
! [X0] :
( empty_set = X0
| ? [X1,X2] : in(ordered_pair(X1,X2),X0)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f160]) ).
fof(f160,axiom,
! [X0] :
( relation(X0)
=> ( ! [X1,X2] : ~ in(ordered_pair(X1,X2),X0)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_relat_1) ).
fof(f4298,plain,
spl77_306,
inference(avatar_split_clause,[],[f576,f4296]) ).
fof(f576,plain,
! [X2,X0,X1] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0)
| ~ element(X1,powerset(X0))
| empty_set = X0 ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( in(X2,subset_complement(X0,X1))
| in(X2,X1)
| ~ element(X2,X0) )
| ~ element(X1,powerset(X0)) )
| empty_set = X0 ),
inference(ennf_transformation,[],[f158]) ).
fof(f158,axiom,
! [X0] :
( empty_set != X0
=> ! [X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,X0)
=> ( ~ in(X2,X1)
=> in(X2,subset_complement(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_subset_1) ).
fof(f4275,plain,
( spl77_305
| ~ spl77_86
| ~ spl77_304 ),
inference(avatar_split_clause,[],[f4217,f4214,f1489,f4273]) ).
fof(f4273,plain,
( spl77_305
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK40(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_305])]) ).
fof(f4214,plain,
( spl77_304
<=> ! [X5,X0] :
( in(unordered_pair(unordered_pair(X5,sK40(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_304])]) ).
fof(f4217,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,sK40(X0,X5))),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl77_86
| ~ spl77_304 ),
inference(forward_demodulation,[],[f4215,f1490]) ).
fof(f4215,plain,
( ! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK40(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) )
| ~ spl77_304 ),
inference(avatar_component_clause,[],[f4214]) ).
fof(f4216,plain,
spl77_304,
inference(avatar_split_clause,[],[f1006,f4214]) ).
fof(f1006,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK40(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f963]) ).
fof(f963,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK40(X0,X5)),unordered_pair(X5,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f708,f891]) ).
fof(f708,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK40(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f437]) ).
fof(f4212,plain,
spl77_303,
inference(avatar_split_clause,[],[f931,f4210]) ).
fof(f4210,plain,
( spl77_303
<=> ! [X0,X3,X2,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_303])]) ).
fof(f931,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(definition_unfolding,[],[f662,f891]) ).
fof(f662,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f401]) ).
fof(f401,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f400]) ).
fof(f400,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f108]) ).
fof(f108,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f4208,plain,
spl77_302,
inference(avatar_split_clause,[],[f928,f4206]) ).
fof(f4206,plain,
( spl77_302
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_302])]) ).
fof(f928,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(definition_unfolding,[],[f654,f891]) ).
fof(f654,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
| ~ relation(X3) ),
inference(cnf_transformation,[],[f399]) ).
fof(f4043,plain,
( spl77_301
| ~ spl77_194
| ~ spl77_278 ),
inference(avatar_split_clause,[],[f3773,f3694,f2503,f4041]) ).
fof(f4041,plain,
( spl77_301
<=> ! [X0] :
( ~ in(X0,sK74)
| ~ in(X0,relation_field(sK17)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_301])]) ).
fof(f2503,plain,
( spl77_194
<=> ! [X4,X0,X2,X1] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_194])]) ).
fof(f3694,plain,
( spl77_278
<=> sP15(relation_field(sK17),relation_rng(sK17),sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_278])]) ).
fof(f3773,plain,
( ! [X0] :
( ~ in(X0,sK74)
| ~ in(X0,relation_field(sK17)) )
| ~ spl77_194
| ~ spl77_278 ),
inference(resolution,[],[f3696,f2504]) ).
fof(f2504,plain,
( ! [X2,X0,X1,X4] :
( ~ sP15(X0,X1,X2)
| ~ in(X4,X2)
| ~ in(X4,X0) )
| ~ spl77_194 ),
inference(avatar_component_clause,[],[f2503]) ).
fof(f3696,plain,
( sP15(relation_field(sK17),relation_rng(sK17),sK74)
| ~ spl77_278 ),
inference(avatar_component_clause,[],[f3694]) ).
fof(f3934,plain,
spl77_300,
inference(avatar_split_clause,[],[f880,f3932]) ).
fof(f3932,plain,
( spl77_300
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(sK72(X0,X1,X2),X0)
| in(sK72(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_300])]) ).
fof(f880,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ in(sK72(X0,X1,X2),X0)
| in(sK72(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f3930,plain,
spl77_299,
inference(avatar_split_clause,[],[f879,f3928]) ).
fof(f3928,plain,
( spl77_299
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK72(X0,X1,X2),X1)
| in(sK72(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_299])]) ).
fof(f879,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| in(sK72(X0,X1,X2),X1)
| in(sK72(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f3926,plain,
spl77_298,
inference(avatar_split_clause,[],[f873,f3924]) ).
fof(f3924,plain,
( spl77_298
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ in(sK71(X0,X1,X2),X0)
| ~ in(sK71(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_298])]) ).
fof(f873,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ in(sK71(X0,X1,X2),X0)
| ~ in(sK71(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f3922,plain,
spl77_297,
inference(avatar_split_clause,[],[f872,f3920]) ).
fof(f3920,plain,
( spl77_297
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ in(sK71(X0,X1,X2),X1)
| ~ in(sK71(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_297])]) ).
fof(f872,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ in(sK71(X0,X1,X2),X1)
| ~ in(sK71(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f3913,plain,
spl77_296,
inference(avatar_split_clause,[],[f864,f3911]) ).
fof(f3911,plain,
( spl77_296
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X0)
| in(sK70(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_296])]) ).
fof(f864,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X0)
| in(sK70(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f3909,plain,
spl77_295,
inference(avatar_split_clause,[],[f863,f3907]) ).
fof(f3907,plain,
( spl77_295
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X1)
| in(sK70(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_295])]) ).
fof(f863,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| in(sK70(X0,X1,X2),X1)
| in(sK70(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f3905,plain,
spl77_294,
inference(avatar_split_clause,[],[f847,f3903]) ).
fof(f3903,plain,
( spl77_294
<=> ! [X2,X0,X1] :
( sP11(X0,X1,X2)
| in(sK66(X0,X1,X2),X0)
| in(sK64(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_294])]) ).
fof(f847,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| in(sK66(X0,X1,X2),X0)
| in(sK64(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f3901,plain,
spl77_293,
inference(avatar_split_clause,[],[f846,f3899]) ).
fof(f3899,plain,
( spl77_293
<=> ! [X2,X0,X1] :
( sP11(X0,X1,X2)
| in(sK65(X0,X1,X2),X1)
| in(sK64(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_293])]) ).
fof(f846,plain,
! [X2,X0,X1] :
( sP11(X0,X1,X2)
| in(sK65(X0,X1,X2),X1)
| in(sK64(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f3897,plain,
spl77_292,
inference(avatar_split_clause,[],[f841,f3895]) ).
fof(f3895,plain,
( spl77_292
<=> ! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_292])]) ).
fof(f841,plain,
! [X2,X0,X1] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f340]) ).
fof(f340,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f339]) ).
fof(f339,plain,
! [X0,X1,X2] :
( subset_difference(X0,X1,X2) = set_difference(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> subset_difference(X0,X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
fof(f3893,plain,
spl77_291,
inference(avatar_split_clause,[],[f824,f3891]) ).
fof(f3891,plain,
( spl77_291
<=> ! [X0,X1,X3] :
( sP10(X0,X1)
| ~ in(X3,X0)
| ~ in(sK59(X0,X1),X3)
| ~ in(sK59(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_291])]) ).
fof(f824,plain,
! [X3,X0,X1] :
( sP10(X0,X1)
| ~ in(X3,X0)
| ~ in(sK59(X0,X1),X3)
| ~ in(sK59(X0,X1),X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f501,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK59(X0,X1),X3) )
| ~ in(sK59(X0,X1),X1) )
& ( ( in(sK60(X0,X1),X0)
& in(sK59(X0,X1),sK60(X0,X1)) )
| in(sK59(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ( in(sK61(X0,X5),X0)
& in(X5,sK61(X0,X5)) )
| ~ in(X5,X1) ) )
| ~ sP10(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61])],[f497,f500,f499,f498]) ).
fof(f498,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) )
=> ( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(sK59(X0,X1),X3) )
| ~ in(sK59(X0,X1),X1) )
& ( ? [X4] :
( in(X4,X0)
& in(sK59(X0,X1),X4) )
| in(sK59(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f499,plain,
! [X0,X1] :
( ? [X4] :
( in(X4,X0)
& in(sK59(X0,X1),X4) )
=> ( in(sK60(X0,X1),X0)
& in(sK59(X0,X1),sK60(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f500,plain,
! [X0,X5] :
( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
=> ( in(sK61(X0,X5),X0)
& in(X5,sK61(X0,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f497,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,X0)
& in(X2,X4) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) ) )
& ( ? [X7] :
( in(X7,X0)
& in(X5,X7) )
| ~ in(X5,X1) ) )
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f496]) ).
fof(f496,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) )
& ( ? [X3] :
( in(X3,X0)
& in(X2,X3) )
| ~ in(X2,X1) ) )
| ~ sP10(X0,X1) ) ),
inference(nnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0,X1] :
( sP10(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f3889,plain,
spl77_290,
inference(avatar_split_clause,[],[f795,f3887]) ).
fof(f3887,plain,
( spl77_290
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_290])]) ).
fof(f795,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(subset_complement(X1,X4),X0)
| ~ element(X4,powerset(X1))
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f485]) ).
fof(f3885,plain,
spl77_289,
inference(avatar_split_clause,[],[f794,f3883]) ).
fof(f3883,plain,
( spl77_289
<=> ! [X2,X4,X0,X1] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP8(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_289])]) ).
fof(f794,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X1,X4),X0)
| ~ in(X4,X2)
| ~ element(X4,powerset(X1))
| ~ sP8(X0,X1,X2) ),
inference(cnf_transformation,[],[f485]) ).
fof(f3881,plain,
spl77_288,
inference(avatar_split_clause,[],[f760,f3879]) ).
fof(f3879,plain,
( spl77_288
<=> ! [X4,X0,X1] :
( sP4(X0,X1)
| in(sK51(X0,X1),X4)
| ~ in(X4,X0)
| in(sK51(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_288])]) ).
fof(f760,plain,
! [X0,X1,X4] :
( sP4(X0,X1)
| in(sK51(X0,X1),X4)
| ~ in(X4,X0)
| in(sK51(X0,X1),X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f470,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ( ~ in(sK51(X0,X1),sK52(X0,X1))
& in(sK52(X0,X1),X0) )
| ~ in(sK51(X0,X1),X1) )
& ( ! [X4] :
( in(sK51(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK51(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ( ~ in(X5,sK53(X0,X5))
& in(sK53(X0,X5),X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52,sK53])],[f466,f469,f468,f467]) ).
fof(f467,plain,
! [X0,X1] :
( ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) )
=> ( ( ? [X3] :
( ~ in(sK51(X0,X1),X3)
& in(X3,X0) )
| ~ in(sK51(X0,X1),X1) )
& ( ! [X4] :
( in(sK51(X0,X1),X4)
| ~ in(X4,X0) )
| in(sK51(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f468,plain,
! [X0,X1] :
( ? [X3] :
( ~ in(sK51(X0,X1),X3)
& in(X3,X0) )
=> ( ~ in(sK51(X0,X1),sK52(X0,X1))
& in(sK52(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f469,plain,
! [X0,X5] :
( ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) )
=> ( ~ in(X5,sK53(X0,X5))
& in(sK53(X0,X5),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f466,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X4] :
( in(X2,X4)
| ~ in(X4,X0) )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ? [X6] :
( ~ in(X5,X6)
& in(X6,X0) ) )
& ( ! [X7] :
( in(X5,X7)
| ~ in(X7,X0) )
| ~ in(X5,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f465]) ).
fof(f465,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ? [X2] :
( ( ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) )
| ~ in(X2,X1) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ? [X3] :
( ~ in(X2,X3)
& in(X3,X0) ) )
& ( ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) )
| ~ in(X2,X1) ) )
| ~ sP4(X0,X1) ) ),
inference(nnf_transformation,[],[f348]) ).
fof(f348,plain,
! [X0,X1] :
( sP4(X0,X1)
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f3864,plain,
( spl77_287
| ~ spl77_79
| ~ spl77_116
| ~ spl77_265 ),
inference(avatar_split_clause,[],[f3604,f3496,f1692,f1454,f3861]) ).
fof(f3861,plain,
( spl77_287
<=> sP13(relation_field(sK17),relation_rng(sK17),relation_rng(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_287])]) ).
fof(f1454,plain,
( spl77_79
<=> ! [X0] : set_difference(X0,sK74) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_79])]) ).
fof(f1692,plain,
( spl77_116
<=> ! [X0,X1] : sP13(X1,X0,set_difference(X0,set_difference(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_116])]) ).
fof(f3496,plain,
( spl77_265
<=> sK74 = set_difference(relation_rng(sK17),relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_265])]) ).
fof(f3604,plain,
( sP13(relation_field(sK17),relation_rng(sK17),relation_rng(sK17))
| ~ spl77_79
| ~ spl77_116
| ~ spl77_265 ),
inference(forward_demodulation,[],[f3588,f1455]) ).
fof(f1455,plain,
( ! [X0] : set_difference(X0,sK74) = X0
| ~ spl77_79 ),
inference(avatar_component_clause,[],[f1454]) ).
fof(f3588,plain,
( sP13(relation_field(sK17),relation_rng(sK17),set_difference(relation_rng(sK17),sK74))
| ~ spl77_116
| ~ spl77_265 ),
inference(superposition,[],[f1693,f3498]) ).
fof(f3498,plain,
( sK74 = set_difference(relation_rng(sK17),relation_field(sK17))
| ~ spl77_265 ),
inference(avatar_component_clause,[],[f3496]) ).
fof(f1693,plain,
( ! [X0,X1] : sP13(X1,X0,set_difference(X0,set_difference(X0,X1)))
| ~ spl77_116 ),
inference(avatar_component_clause,[],[f1692]) ).
fof(f3807,plain,
spl77_286,
inference(avatar_split_clause,[],[f969,f3805]) ).
fof(f3805,plain,
( spl77_286
<=> ! [X5,X0,X6,X2,X1] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_286])]) ).
fof(f969,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X2)
| ~ sP2(X0,X1,X2) ),
inference(definition_unfolding,[],[f714,f891]) ).
fof(f714,plain,
! [X2,X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f444]) ).
fof(f3803,plain,
spl77_285,
inference(avatar_split_clause,[],[f605,f3801]) ).
fof(f3801,plain,
( spl77_285
<=> ! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_285])]) ).
fof(f605,plain,
! [X2,X0,X1] :
( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
! [X0,X1] :
( ! [X2] :
( ( ( disjoint(X1,X2)
| ~ subset(X1,subset_complement(X0,X2)) )
& ( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2) ) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(nnf_transformation,[],[f235]) ).
fof(f235,plain,
! [X0,X1] :
( ! [X2] :
( ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) )
| ~ element(X2,powerset(X0)) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f144]) ).
fof(f144,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( element(X2,powerset(X0))
=> ( disjoint(X1,X2)
<=> subset(X1,subset_complement(X0,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t43_subset_1) ).
fof(f3799,plain,
spl77_284,
inference(avatar_split_clause,[],[f604,f3797]) ).
fof(f3797,plain,
( spl77_284
<=> ! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_284])]) ).
fof(f604,plain,
! [X2,X0,X1] :
( subset(X1,subset_complement(X0,X2))
| ~ disjoint(X1,X2)
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f381]) ).
fof(f3795,plain,
spl77_283,
inference(avatar_split_clause,[],[f575,f3793]) ).
fof(f3793,plain,
( spl77_283
<=> ! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_283])]) ).
fof(f575,plain,
! [X0,X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = relation_rng(relation_composition(X1,X0))
| ~ subset(relation_dom(X0),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f151]) ).
fof(f151,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_dom(X0),relation_rng(X1))
=> relation_rng(X0) = relation_rng(relation_composition(X1,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t47_relat_1) ).
fof(f3791,plain,
spl77_282,
inference(avatar_split_clause,[],[f574,f3789]) ).
fof(f3789,plain,
( spl77_282
<=> ! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_282])]) ).
fof(f574,plain,
! [X0,X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f148,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f3765,plain,
spl77_281,
inference(avatar_split_clause,[],[f840,f3763]) ).
fof(f3763,plain,
( spl77_281
<=> ! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_281])]) ).
fof(f840,plain,
! [X2,X0,X1] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f338]) ).
fof(f338,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(flattening,[],[f337]) ).
fof(f337,plain,
! [X0,X1,X2] :
( element(subset_difference(X0,X1,X2),powerset(X0))
| ~ element(X2,powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0,X1,X2] :
( ( element(X2,powerset(X0))
& element(X1,powerset(X0)) )
=> element(subset_difference(X0,X1,X2),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
fof(f3761,plain,
spl77_280,
inference(avatar_split_clause,[],[f822,f3759]) ).
fof(f3759,plain,
( spl77_280
<=> ! [X0,X1] :
( sP10(X0,X1)
| in(sK59(X0,X1),sK60(X0,X1))
| in(sK59(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_280])]) ).
fof(f822,plain,
! [X0,X1] :
( sP10(X0,X1)
| in(sK59(X0,X1),sK60(X0,X1))
| in(sK59(X0,X1),X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f3757,plain,
spl77_279,
inference(avatar_split_clause,[],[f762,f3755]) ).
fof(f3755,plain,
( spl77_279
<=> ! [X0,X1] :
( sP4(X0,X1)
| ~ in(sK51(X0,X1),sK52(X0,X1))
| ~ in(sK51(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_279])]) ).
fof(f762,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ in(sK51(X0,X1),sK52(X0,X1))
| ~ in(sK51(X0,X1),X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f3697,plain,
( spl77_278
| ~ spl77_72
| ~ spl77_265 ),
inference(avatar_split_clause,[],[f3586,f3496,f1395,f3694]) ).
fof(f1395,plain,
( spl77_72
<=> ! [X0,X1] : sP15(X1,X0,set_difference(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_72])]) ).
fof(f3586,plain,
( sP15(relation_field(sK17),relation_rng(sK17),sK74)
| ~ spl77_72
| ~ spl77_265 ),
inference(superposition,[],[f1396,f3498]) ).
fof(f1396,plain,
( ! [X0,X1] : sP15(X1,X0,set_difference(X0,X1))
| ~ spl77_72 ),
inference(avatar_component_clause,[],[f1395]) ).
fof(f3641,plain,
spl77_277,
inference(avatar_split_clause,[],[f1015,f3639]) ).
fof(f3639,plain,
( spl77_277
<=> ! [X5,X1,X0] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_277])]) ).
fof(f1015,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,X5),unordered_pair(X5,X5)),X1)
| ~ in(X5,X0)
| ~ sP6(X0,X1) ),
inference(equality_resolution,[],[f978]) ).
fof(f978,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f773,f891]) ).
fof(f773,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| X4 != X5
| ~ in(X4,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f3637,plain,
spl77_276,
inference(avatar_split_clause,[],[f985,f3635]) ).
fof(f3635,plain,
( spl77_276
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK62(X0,X1) = X0
| in(sK62(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_276])]) ).
fof(f985,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK62(X0,X1) = X0
| in(sK62(X0,X1),X1) ),
inference(definition_unfolding,[],[f829,f559]) ).
fof(f829,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK62(X0,X1) = X0
| in(sK62(X0,X1),X1) ),
inference(cnf_transformation,[],[f506]) ).
fof(f506,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK62(X0,X1) != X0
| ~ in(sK62(X0,X1),X1) )
& ( sK62(X0,X1) = X0
| in(sK62(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f504,f505]) ).
fof(f505,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK62(X0,X1) != X0
| ~ in(sK62(X0,X1),X1) )
& ( sK62(X0,X1) = X0
| in(sK62(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f504,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f503]) ).
fof(f503,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(f3633,plain,
spl77_275,
inference(avatar_split_clause,[],[f980,f3631]) ).
fof(f3631,plain,
( spl77_275
<=> ! [X4,X0,X5,X1] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_275])]) ).
fof(f980,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f771,f891]) ).
fof(f771,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f3629,plain,
spl77_274,
inference(avatar_split_clause,[],[f979,f3627]) ).
fof(f3627,plain,
( spl77_274
<=> ! [X4,X5,X1,X0] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_274])]) ).
fof(f979,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X1)
| ~ sP6(X0,X1) ),
inference(definition_unfolding,[],[f772,f891]) ).
fof(f772,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f478]) ).
fof(f3625,plain,
spl77_273,
inference(avatar_split_clause,[],[f920,f3623]) ).
fof(f3623,plain,
( spl77_273
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_273])]) ).
fof(f920,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f634,f891]) ).
fof(f634,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f248]) ).
fof(f248,plain,
! [X0,X1,X2] :
( ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f120]) ).
fof(f120,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_rng(X2))
& in(X0,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_relat_1) ).
fof(f3621,plain,
spl77_272,
inference(avatar_split_clause,[],[f919,f3619]) ).
fof(f3619,plain,
( spl77_272
<=> ! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_272])]) ).
fof(f919,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f635,f891]) ).
fof(f635,plain,
! [X2,X0,X1] :
( in(X1,relation_rng(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f249]) ).
fof(f3584,plain,
spl77_271,
inference(avatar_split_clause,[],[f918,f3582]) ).
fof(f3582,plain,
( spl77_271
<=> ! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_271])]) ).
fof(f918,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f632,f891]) ).
fof(f632,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f246]) ).
fof(f246,plain,
! [X0,X1,X2] :
( ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f129]) ).
fof(f129,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X1,relation_field(X2))
& in(X0,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f3580,plain,
spl77_270,
inference(avatar_split_clause,[],[f917,f3578]) ).
fof(f3578,plain,
( spl77_270
<=> ! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_270])]) ).
fof(f917,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| ~ relation(X2) ),
inference(definition_unfolding,[],[f633,f891]) ).
fof(f633,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f247]) ).
fof(f3576,plain,
spl77_269,
inference(avatar_split_clause,[],[f638,f3574]) ).
fof(f3574,plain,
( spl77_269
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_269])]) ).
fof(f638,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f395]) ).
fof(f395,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(flattening,[],[f394]) ).
fof(f394,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(X0,X1) )
& ( ( in(X0,relation_dom(X2))
& in(X0,X1) )
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1))) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f250]) ).
fof(f250,plain,
! [X0,X1,X2] :
( ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f176]) ).
fof(f176,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_dom(relation_dom_restriction(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_relat_1) ).
fof(f3519,plain,
spl77_268,
inference(avatar_split_clause,[],[f834,f3517]) ).
fof(f3517,plain,
( spl77_268
<=> ! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK63(X0,X1),X0)
| ~ in(sK63(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_268])]) ).
fof(f834,plain,
! [X0,X1] :
( powerset(X0) = X1
| ~ subset(sK63(X0,X1),X0)
| ~ in(sK63(X0,X1),X1) ),
inference(cnf_transformation,[],[f510]) ).
fof(f510,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ( ( ~ subset(sK63(X0,X1),X0)
| ~ in(sK63(X0,X1),X1) )
& ( subset(sK63(X0,X1),X0)
| in(sK63(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f508,f509]) ).
fof(f509,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ subset(sK63(X0,X1),X0)
| ~ in(sK63(X0,X1),X1) )
& ( subset(sK63(X0,X1),X0)
| in(sK63(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f508,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| ~ subset(X3,X0) )
& ( subset(X3,X0)
| ~ in(X3,X1) ) )
| powerset(X0) != X1 ) ),
inference(rectify,[],[f507]) ).
fof(f507,plain,
! [X0,X1] :
( ( powerset(X0) = X1
| ? [X2] :
( ( ~ subset(X2,X0)
| ~ in(X2,X1) )
& ( subset(X2,X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ~ subset(X2,X0) )
& ( subset(X2,X0)
| ~ in(X2,X1) ) )
| powerset(X0) != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( powerset(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f3515,plain,
spl77_267,
inference(avatar_split_clause,[],[f833,f3513]) ).
fof(f3513,plain,
( spl77_267
<=> ! [X0,X1] :
( powerset(X0) = X1
| subset(sK63(X0,X1),X0)
| in(sK63(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_267])]) ).
fof(f833,plain,
! [X0,X1] :
( powerset(X0) = X1
| subset(sK63(X0,X1),X0)
| in(sK63(X0,X1),X1) ),
inference(cnf_transformation,[],[f510]) ).
fof(f3511,plain,
spl77_266,
inference(avatar_split_clause,[],[f799,f3509]) ).
fof(f3509,plain,
( spl77_266
<=> ! [X2,X0,X1] :
( sP9(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_266])]) ).
fof(f799,plain,
! [X2,X0,X1] :
( sP9(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0,X1] :
( ! [X2] :
( sP9(X2,X0,X1)
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(definition_folding,[],[f316,f355,f354]) ).
fof(f355,plain,
! [X2,X0,X1] :
( ( complements_of_subsets(X0,X1) = X2
<=> sP8(X1,X0,X2) )
| ~ sP9(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f316,plain,
! [X0,X1] :
( ! [X2] :
( ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( complements_of_subsets(X0,X1) = X2
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f3499,plain,
( spl77_265
| ~ spl77_119
| ~ spl77_218 ),
inference(avatar_split_clause,[],[f2905,f2822,f1767,f3496]) ).
fof(f1767,plain,
( spl77_119
<=> ! [X0,X1] :
( set_difference(X0,X1) = sK74
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_119])]) ).
fof(f2905,plain,
( sK74 = set_difference(relation_rng(sK17),relation_field(sK17))
| ~ spl77_119
| ~ spl77_218 ),
inference(resolution,[],[f2824,f1768]) ).
fof(f1768,plain,
( ! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK74 )
| ~ spl77_119 ),
inference(avatar_component_clause,[],[f1767]) ).
fof(f3360,plain,
spl77_264,
inference(avatar_split_clause,[],[f933,f3358]) ).
fof(f3358,plain,
( spl77_264
<=> ! [X0,X3,X2,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_264])]) ).
fof(f933,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f660,f891]) ).
fof(f660,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f401]) ).
fof(f3356,plain,
spl77_263,
inference(avatar_split_clause,[],[f932,f3354]) ).
fof(f3354,plain,
( spl77_263
<=> ! [X0,X3,X2,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_263])]) ).
fof(f932,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3)) ),
inference(definition_unfolding,[],[f661,f891]) ).
fof(f661,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f401]) ).
fof(f3352,plain,
spl77_262,
inference(avatar_split_clause,[],[f921,f3350]) ).
fof(f3350,plain,
( spl77_262
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_262])]) ).
fof(f921,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,set_difference(X0,X2)),set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f639,f584,f584]) ).
fof(f584,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f154]) ).
fof(f154,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f639,plain,
! [X2,X0,X1] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1,X2] :
( subset(set_intersection2(X0,X2),set_intersection2(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f123]) ).
fof(f123,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_intersection2(X0,X2),set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
fof(f3348,plain,
spl77_261,
inference(avatar_split_clause,[],[f898,f3346]) ).
fof(f898,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_difference(relation_dom(X1),set_difference(relation_dom(X1),X0))
| ~ relation(X1) ),
inference(definition_unfolding,[],[f594,f584]) ).
fof(f594,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X0,X1] :
( relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f181]) ).
fof(f181,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom(relation_dom_restriction(X1,X0)) = set_intersection2(relation_dom(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t90_relat_1) ).
fof(f3262,plain,
( spl77_260
| ~ spl77_71
| ~ spl77_205 ),
inference(avatar_split_clause,[],[f2779,f2648,f1391,f3259]) ).
fof(f2648,plain,
( spl77_205
<=> relation_field(sK17) = set_union2(relation_rng(sK17),relation_dom(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_205])]) ).
fof(f2779,plain,
( sP14(relation_dom(sK17),relation_rng(sK17),relation_field(sK17))
| ~ spl77_71
| ~ spl77_205 ),
inference(superposition,[],[f1392,f2650]) ).
fof(f2650,plain,
( relation_field(sK17) = set_union2(relation_rng(sK17),relation_dom(sK17))
| ~ spl77_205 ),
inference(avatar_component_clause,[],[f2648]) ).
fof(f3255,plain,
spl77_259,
inference(avatar_split_clause,[],[f1045,f3253]) ).
fof(f3253,plain,
( spl77_259
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X1
| ~ in(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_259])]) ).
fof(f1045,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X1
| ~ in(X1,X2) ),
inference(inner_rewriting,[],[f856]) ).
fof(f856,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X1
| ~ in(sK69(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f3251,plain,
spl77_258,
inference(avatar_split_clause,[],[f1044,f3249]) ).
fof(f3249,plain,
( spl77_258
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X0
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_258])]) ).
fof(f1044,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X0
| ~ in(X0,X2) ),
inference(inner_rewriting,[],[f857]) ).
fof(f857,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| sK69(X0,X1,X2) != X0
| ~ in(sK69(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f3247,plain,
spl77_257,
inference(avatar_split_clause,[],[f878,f3245]) ).
fof(f3245,plain,
( spl77_257
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_257])]) ).
fof(f878,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| in(X4,X0)
| ~ in(X4,X1)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f3243,plain,
spl77_256,
inference(avatar_split_clause,[],[f868,f3241]) ).
fof(f3241,plain,
( spl77_256
<=> ! [X2,X4,X0,X1] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_256])]) ).
fof(f868,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| in(X4,X1)
| ~ in(X4,X2)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f3239,plain,
spl77_255,
inference(avatar_split_clause,[],[f862,f3237]) ).
fof(f3237,plain,
( spl77_255
<=> ! [X4,X0,X2,X1] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_255])]) ).
fof(f862,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f3235,plain,
spl77_254,
inference(avatar_split_clause,[],[f852,f3233]) ).
fof(f3233,plain,
( spl77_254
<=> ! [X2,X4,X0,X1] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_254])]) ).
fof(f852,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f3231,plain,
spl77_253,
inference(avatar_split_clause,[],[f843,f3229]) ).
fof(f3229,plain,
( spl77_253
<=> ! [X0,X8,X2,X1] :
( in(sK68(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_253])]) ).
fof(f843,plain,
! [X2,X0,X1,X8] :
( in(sK68(X0,X1,X8),X0)
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f3227,plain,
spl77_252,
inference(avatar_split_clause,[],[f842,f3225]) ).
fof(f3225,plain,
( spl77_252
<=> ! [X0,X8,X2,X1] :
( in(sK67(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_252])]) ).
fof(f842,plain,
! [X2,X0,X1,X8] :
( in(sK67(X0,X1,X8),X1)
| ~ in(X8,X2)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f517]) ).
fof(f3223,plain,
spl77_251,
inference(avatar_split_clause,[],[f823,f3221]) ).
fof(f3221,plain,
( spl77_251
<=> ! [X0,X1] :
( sP10(X0,X1)
| in(sK60(X0,X1),X0)
| in(sK59(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_251])]) ).
fof(f823,plain,
! [X0,X1] :
( sP10(X0,X1)
| in(sK60(X0,X1),X0)
| in(sK59(X0,X1),X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f3219,plain,
spl77_250,
inference(avatar_split_clause,[],[f809,f3217]) ).
fof(f3217,plain,
( spl77_250
<=> ! [X0,X1] :
( X0 = X1
| ~ in(sK57(X0,X1),X1)
| ~ in(sK57(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_250])]) ).
fof(f809,plain,
! [X0,X1] :
( X0 = X1
| ~ in(sK57(X0,X1),X1)
| ~ in(sK57(X0,X1),X0) ),
inference(cnf_transformation,[],[f488]) ).
fof(f488,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK57(X0,X1),X1)
| ~ in(sK57(X0,X1),X0) )
& ( in(sK57(X0,X1),X1)
| in(sK57(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f486,f487]) ).
fof(f487,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK57(X0,X1),X1)
| ~ in(sK57(X0,X1),X0) )
& ( in(sK57(X0,X1),X1)
| in(sK57(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f486,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f329]) ).
fof(f329,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f127]) ).
fof(f127,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f3215,plain,
spl77_249,
inference(avatar_split_clause,[],[f808,f3213]) ).
fof(f3213,plain,
( spl77_249
<=> ! [X0,X1] :
( X0 = X1
| in(sK57(X0,X1),X1)
| in(sK57(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_249])]) ).
fof(f808,plain,
! [X0,X1] :
( X0 = X1
| in(sK57(X0,X1),X1)
| in(sK57(X0,X1),X0) ),
inference(cnf_transformation,[],[f488]) ).
fof(f3211,plain,
spl77_248,
inference(avatar_split_clause,[],[f793,f3209]) ).
fof(f3209,plain,
( spl77_248
<=> ! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP8(X2,X1,X0)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_248])]) ).
fof(f793,plain,
! [X2,X0,X1] :
( complements_of_subsets(X1,X2) = X0
| ~ sP8(X2,X1,X0)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f480]) ).
fof(f480,plain,
! [X0,X1,X2] :
( ( ( complements_of_subsets(X1,X2) = X0
| ~ sP8(X2,X1,X0) )
& ( sP8(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0 ) )
| ~ sP9(X0,X1,X2) ),
inference(rectify,[],[f479]) ).
fof(f479,plain,
! [X2,X0,X1] :
( ( ( complements_of_subsets(X0,X1) = X2
| ~ sP8(X1,X0,X2) )
& ( sP8(X1,X0,X2)
| complements_of_subsets(X0,X1) != X2 ) )
| ~ sP9(X2,X0,X1) ),
inference(nnf_transformation,[],[f355]) ).
fof(f3207,plain,
spl77_247,
inference(avatar_split_clause,[],[f761,f3205]) ).
fof(f3205,plain,
( spl77_247
<=> ! [X0,X1] :
( sP4(X0,X1)
| in(sK52(X0,X1),X0)
| ~ in(sK51(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_247])]) ).
fof(f761,plain,
! [X0,X1] :
( sP4(X0,X1)
| in(sK52(X0,X1),X0)
| ~ in(sK51(X0,X1),X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f3203,plain,
spl77_246,
inference(avatar_split_clause,[],[f713,f3201]) ).
fof(f3201,plain,
( spl77_246
<=> ! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_246])]) ).
fof(f713,plain,
! [X2,X0,X1] :
( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f439]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ( ( relation_dom_restriction(X2,X1) = X0
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0 ) )
| ~ sP3(X0,X1,X2) ),
inference(rectify,[],[f438]) ).
fof(f438,plain,
! [X2,X1,X0] :
( ( ( relation_dom_restriction(X0,X1) = X2
| ~ sP2(X0,X1,X2) )
& ( sP2(X0,X1,X2)
| relation_dom_restriction(X0,X1) != X2 ) )
| ~ sP3(X2,X1,X0) ),
inference(nnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X2,X1,X0] :
( ( relation_dom_restriction(X0,X1) = X2
<=> sP2(X0,X1,X2) )
| ~ sP3(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f3199,plain,
spl77_245,
inference(avatar_split_clause,[],[f696,f3197]) ).
fof(f3197,plain,
( spl77_245
<=> ! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_245])]) ).
fof(f696,plain,
! [X2,X0,X1] :
( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f419]) ).
fof(f419,plain,
! [X0,X1,X2] :
( ( ( relation_composition(X1,X2) = X0
| ~ sP0(X2,X1,X0) )
& ( sP0(X2,X1,X0)
| relation_composition(X1,X2) != X0 ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f418]) ).
fof(f418,plain,
! [X2,X0,X1] :
( ( ( relation_composition(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| relation_composition(X0,X1) != X2 ) )
| ~ sP1(X2,X0,X1) ),
inference(nnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X2,X0,X1] :
( ( relation_composition(X0,X1) = X2
<=> sP0(X1,X0,X2) )
| ~ sP1(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f3146,plain,
( spl77_244
| ~ spl77_52
| ~ spl77_239 ),
inference(avatar_split_clause,[],[f3110,f3107,f1293,f3144]) ).
fof(f3144,plain,
( spl77_244
<=> ! [X0,X1] :
( sK74 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_244])]) ).
fof(f3107,plain,
( spl77_239
<=> ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_239])]) ).
fof(f3110,plain,
( ! [X0,X1] :
( sK74 = X0
| unordered_pair(X1,X1) = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl77_52
| ~ spl77_239 ),
inference(forward_demodulation,[],[f3108,f1295]) ).
fof(f3108,plain,
( ! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) )
| ~ spl77_239 ),
inference(avatar_component_clause,[],[f3107]) ).
fof(f3126,plain,
( spl77_243
| ~ spl77_52
| ~ spl77_234 ),
inference(avatar_split_clause,[],[f3088,f3084,f1293,f3124]) ).
fof(f3124,plain,
( spl77_243
<=> ! [X0,X1] :
( sK74 = X1
| complements_of_subsets(X0,X1) != sK74
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_243])]) ).
fof(f3084,plain,
( spl77_234
<=> ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_234])]) ).
fof(f3088,plain,
( ! [X0,X1] :
( sK74 = X1
| complements_of_subsets(X0,X1) != sK74
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_52
| ~ spl77_234 ),
inference(forward_demodulation,[],[f3087,f1295]) ).
fof(f3087,plain,
( ! [X0,X1] :
( complements_of_subsets(X0,X1) != sK74
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_52
| ~ spl77_234 ),
inference(forward_demodulation,[],[f3085,f1295]) ).
fof(f3085,plain,
( ! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) )
| ~ spl77_234 ),
inference(avatar_component_clause,[],[f3084]) ).
fof(f3122,plain,
spl77_242,
inference(avatar_split_clause,[],[f1041,f3120]) ).
fof(f3120,plain,
( spl77_242
<=> ! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK62(X0,X1) != X0
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_242])]) ).
fof(f1041,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK62(X0,X1) != X0
| ~ in(X0,X1) ),
inference(inner_rewriting,[],[f984]) ).
fof(f984,plain,
! [X0,X1] :
( unordered_pair(X0,X0) = X1
| sK62(X0,X1) != X0
| ~ in(sK62(X0,X1),X1) ),
inference(definition_unfolding,[],[f830,f559]) ).
fof(f830,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK62(X0,X1) != X0
| ~ in(sK62(X0,X1),X1) ),
inference(cnf_transformation,[],[f506]) ).
fof(f3118,plain,
spl77_241,
inference(avatar_split_clause,[],[f925,f3116]) ).
fof(f3116,plain,
( spl77_241
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_241])]) ).
fof(f925,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,set_difference(X1,X2)))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f649,f584]) ).
fof(f649,plain,
! [X2,X0,X1] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f264]) ).
fof(f264,plain,
! [X0,X1,X2] :
( subset(X0,set_intersection2(X1,X2))
| ~ subset(X0,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f115]) ).
fof(f115,axiom,
! [X0,X1,X2] :
( ( subset(X0,X2)
& subset(X0,X1) )
=> subset(X0,set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
fof(f3114,plain,
spl77_240,
inference(avatar_split_clause,[],[f922,f3112]) ).
fof(f3112,plain,
( spl77_240
<=> ! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_240])]) ).
fof(f922,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,unordered_pair(X2,X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f643,f559]) ).
fof(f643,plain,
! [X2,X0,X1] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(flattening,[],[f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
fof(f3109,plain,
spl77_239,
inference(avatar_split_clause,[],[f906,f3107]) ).
fof(f906,plain,
! [X0,X1] :
( unordered_pair(X1,X1) = X0
| empty_set = X0
| ~ subset(X0,unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f614,f559,f559]) ).
fof(f614,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ),
inference(cnf_transformation,[],[f386]) ).
fof(f386,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f385]) ).
fof(f385,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( singleton(X1) != X0
& empty_set != X0 ) )
& ( singleton(X1) = X0
| empty_set = X0
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( singleton(X1) = X0
| empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(f3105,plain,
( spl77_237
| ~ spl77_238
| ~ spl77_61
| ~ spl77_205 ),
inference(avatar_split_clause,[],[f2777,f2648,f1351,f3102,f3098]) ).
fof(f3098,plain,
( spl77_237
<=> empty(relation_dom(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_237])]) ).
fof(f3102,plain,
( spl77_238
<=> empty(relation_field(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_238])]) ).
fof(f1351,plain,
( spl77_61
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_61])]) ).
fof(f2777,plain,
( ~ empty(relation_field(sK17))
| empty(relation_dom(sK17))
| ~ spl77_61
| ~ spl77_205 ),
inference(superposition,[],[f1352,f2650]) ).
fof(f1352,plain,
( ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) )
| ~ spl77_61 ),
inference(avatar_component_clause,[],[f1351]) ).
fof(f3096,plain,
spl77_236,
inference(avatar_split_clause,[],[f666,f3094]) ).
fof(f3094,plain,
( spl77_236
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_236])]) ).
fof(f666,plain,
! [X2,X3,X0,X1] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0,X1,X2,X3] :
( X0 = X3
| X0 = X2
| unordered_pair(X0,X1) != unordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,axiom,
! [X0,X1,X2,X3] :
~ ( X0 != X3
& X0 != X2
& unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
fof(f3092,plain,
spl77_235,
inference(avatar_split_clause,[],[f659,f3090]) ).
fof(f3090,plain,
( spl77_235
<=> ! [X0,X3,X2,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_235])]) ).
fof(f659,plain,
! [X2,X3,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0,X1,X2,X3] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,axiom,
! [X0,X1,X2,X3] :
( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cartesian_product2(X0,X2),cartesian_product2(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(f3086,plain,
spl77_234,
inference(avatar_split_clause,[],[f608,f3084]) ).
fof(f608,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f241]) ).
fof(f241,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f240]) ).
fof(f240,plain,
! [X0,X1] :
( empty_set != complements_of_subsets(X0,X1)
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f149]) ).
fof(f149,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( empty_set = complements_of_subsets(X0,X1)
& empty_set != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f3049,plain,
spl77_233,
inference(avatar_split_clause,[],[f1016,f3047]) ).
fof(f3047,plain,
( spl77_233
<=> ! [X2,X1] :
( sP8(X2,X1,complements_of_subsets(X1,X2))
| ~ sP9(complements_of_subsets(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_233])]) ).
fof(f1016,plain,
! [X2,X1] :
( sP8(X2,X1,complements_of_subsets(X1,X2))
| ~ sP9(complements_of_subsets(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f792]) ).
fof(f792,plain,
! [X2,X0,X1] :
( sP8(X2,X1,X0)
| complements_of_subsets(X1,X2) != X0
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f480]) ).
fof(f3045,plain,
spl77_232,
inference(avatar_split_clause,[],[f1007,f3043]) ).
fof(f3043,plain,
( spl77_232
<=> ! [X2,X1] :
( sP2(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP3(relation_dom_restriction(X2,X1),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_232])]) ).
fof(f1007,plain,
! [X2,X1] :
( sP2(X2,X1,relation_dom_restriction(X2,X1))
| ~ sP3(relation_dom_restriction(X2,X1),X1,X2) ),
inference(equality_resolution,[],[f712]) ).
fof(f712,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| relation_dom_restriction(X2,X1) != X0
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f439]) ).
fof(f3041,plain,
spl77_231,
inference(avatar_split_clause,[],[f1002,f3039]) ).
fof(f3039,plain,
( spl77_231
<=> ! [X2,X1] :
( sP0(X2,X1,relation_composition(X1,X2))
| ~ sP1(relation_composition(X1,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_231])]) ).
fof(f1002,plain,
! [X2,X1] :
( sP0(X2,X1,relation_composition(X1,X2))
| ~ sP1(relation_composition(X1,X2),X1,X2) ),
inference(equality_resolution,[],[f695]) ).
fof(f695,plain,
! [X2,X0,X1] :
( sP0(X2,X1,X0)
| relation_composition(X1,X2) != X0
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f419]) ).
fof(f3037,plain,
spl77_230,
inference(avatar_split_clause,[],[f821,f3035]) ).
fof(f3035,plain,
( spl77_230
<=> ! [X5,X0,X6,X1] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_230])]) ).
fof(f821,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,X0)
| ~ in(X5,X6)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f3033,plain,
spl77_229,
inference(avatar_split_clause,[],[f791,f3031]) ).
fof(f3031,plain,
( spl77_229
<=> ! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_229])]) ).
fof(f791,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f3029,plain,
spl77_228,
inference(avatar_split_clause,[],[f790,f3027]) ).
fof(f3027,plain,
( spl77_228
<=> ! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_228])]) ).
fof(f790,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f314]) ).
fof(f314,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f3025,plain,
spl77_227,
inference(avatar_split_clause,[],[f757,f3023]) ).
fof(f3023,plain,
( spl77_227
<=> ! [X0,X5,X1,X7] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_227])]) ).
fof(f757,plain,
! [X0,X1,X7,X5] :
( in(X5,X7)
| ~ in(X7,X0)
| ~ in(X5,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f3021,plain,
spl77_226,
inference(avatar_split_clause,[],[f738,f3019]) ).
fof(f3019,plain,
( spl77_226
<=> ! [X2,X0,X4] :
( in(X4,sK49(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_226])]) ).
fof(f738,plain,
! [X2,X0,X4] :
( in(X4,sK49(X0,X2))
| ~ subset(X4,X2)
| ~ in(X2,sK48(X0)) ),
inference(cnf_transformation,[],[f459]) ).
fof(f459,plain,
! [X0] :
( ! [X2] :
( ( ! [X4] :
( in(X4,sK49(X0,X2))
| ~ subset(X4,X2) )
& in(sK49(X0,X2),sK48(X0)) )
| ~ in(X2,sK48(X0)) )
& ! [X5,X6] :
( in(X6,sK48(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK48(X0)) )
& in(X0,sK48(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f456,f458,f457]) ).
fof(f457,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK48(X0)) )
| ~ in(X2,sK48(X0)) )
& ! [X6,X5] :
( in(X6,sK48(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK48(X0)) )
& in(X0,sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f458,plain,
! [X0,X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,sK48(X0)) )
=> ( ! [X4] :
( in(X4,sK49(X0,X2))
| ~ subset(X4,X2) )
& in(sK49(X0,X2),sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f456,plain,
! [X0] :
? [X1] :
( ! [X2] :
( ? [X3] :
( ! [X4] :
( in(X4,X3)
| ~ subset(X4,X2) )
& in(X3,X1) )
| ~ in(X2,X1) )
& ! [X5,X6] :
( in(X6,X1)
| ~ subset(X6,X5)
| ~ in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f294]) ).
fof(f294,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(flattening,[],[f293]) ).
fof(f293,plain,
! [X0] :
? [X1] :
( ! [X3] :
( ? [X4] :
( ! [X5] :
( in(X5,X4)
| ~ subset(X5,X3) )
& in(X4,X1) )
| ~ in(X3,X1) )
& ! [X6,X7] :
( in(X7,X1)
| ~ subset(X7,X6)
| ~ in(X6,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f199]) ).
fof(f199,plain,
! [X0] :
? [X1] :
( ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f192]) ).
fof(f192,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
~ ( ! [X4] :
~ ( ! [X5] :
( subset(X5,X3)
=> in(X5,X4) )
& in(X4,X1) )
& in(X3,X1) )
& ! [X6,X7] :
( ( subset(X7,X6)
& in(X6,X1) )
=> in(X7,X1) )
& in(X0,X1) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
~ ( ! [X3] :
~ ( ! [X4] :
( subset(X4,X2)
=> in(X4,X3) )
& in(X3,X1) )
& in(X2,X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_tarski) ).
fof(f3010,plain,
( ~ spl77_225
| ~ spl77_54
| ~ spl77_218 ),
inference(avatar_split_clause,[],[f2903,f2822,f1307,f3007]) ).
fof(f3007,plain,
( spl77_225
<=> proper_subset(relation_field(sK17),relation_rng(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_225])]) ).
fof(f2903,plain,
( ~ proper_subset(relation_field(sK17),relation_rng(sK17))
| ~ spl77_54
| ~ spl77_218 ),
inference(resolution,[],[f2824,f1308]) ).
fof(f2931,plain,
spl77_224,
inference(avatar_split_clause,[],[f970,f2929]) ).
fof(f2929,plain,
( spl77_224
<=> ! [X2,X0,X3] :
( relation(X0)
| sK43(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_224])]) ).
fof(f970,plain,
! [X2,X3,X0] :
( relation(X0)
| sK43(X0) != unordered_pair(unordered_pair(X2,X3),unordered_pair(X2,X2)) ),
inference(definition_unfolding,[],[f731,f891]) ).
fof(f731,plain,
! [X2,X3,X0] :
( relation(X0)
| ordered_pair(X2,X3) != sK43(X0) ),
inference(cnf_transformation,[],[f449]) ).
fof(f2927,plain,
spl77_223,
inference(avatar_split_clause,[],[f897,f2925]) ).
fof(f2925,plain,
( spl77_223
<=> ! [X0,X1] :
( in(sK21(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_223])]) ).
fof(f897,plain,
! [X0,X1] :
( in(sK21(X0,X1),set_difference(X0,set_difference(X0,X1)))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f587,f584]) ).
fof(f587,plain,
! [X0,X1] :
( in(sK21(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( in(sK21(X0,X1),set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f221,f377]) ).
fof(f377,plain,
! [X0,X1] :
( ? [X3] : in(X3,set_intersection2(X0,X1))
=> in(sK21(X0,X1),set_intersection2(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f221,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] : ~ in(X2,set_intersection2(X0,X1)) )
& ( ? [X3] : in(X3,set_intersection2(X0,X1))
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X3] : ~ in(X3,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] : in(X2,set_intersection2(X0,X1)) )
& ~ ( ! [X2] : ~ in(X2,set_intersection2(X0,X1))
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
fof(f2923,plain,
spl77_222,
inference(avatar_split_clause,[],[f644,f2921]) ).
fof(f2921,plain,
( spl77_222
<=> ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_222])]) ).
fof(f644,plain,
! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(flattening,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ~ in(X1,X2)
| ~ in(X1,subset_complement(X0,X2))
| ~ element(X2,powerset(X0)) ),
inference(ennf_transformation,[],[f159]) ).
fof(f159,axiom,
! [X0,X1,X2] :
( element(X2,powerset(X0))
=> ~ ( in(X1,X2)
& in(X1,subset_complement(X0,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_subset_1) ).
fof(f2919,plain,
spl77_221,
inference(avatar_split_clause,[],[f637,f2917]) ).
fof(f2917,plain,
( spl77_221
<=> ! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_221])]) ).
fof(f637,plain,
! [X2,X0,X1] :
( in(X0,relation_dom(X2))
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f395]) ).
fof(f2915,plain,
spl77_220,
inference(avatar_split_clause,[],[f573,f2913]) ).
fof(f573,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_rng(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) )
| ~ subset(X0,X1)
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f122]) ).
fof(f122,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(X0,X1)
=> ( subset(relation_rng(X0),relation_rng(X1))
& subset(relation_dom(X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_relat_1) ).
fof(f2902,plain,
spl77_219,
inference(avatar_split_clause,[],[f572,f2900]) ).
fof(f2900,plain,
( spl77_219
<=> ! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_219])]) ).
fof(f572,plain,
! [X0,X1] :
( subset(relation_dom(X0),relation_dom(X1))
| ~ subset(X0,X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f2825,plain,
( spl77_218
| ~ spl77_33
| ~ spl77_205 ),
inference(avatar_split_clause,[],[f2776,f2648,f1193,f2822]) ).
fof(f1193,plain,
( spl77_33
<=> ! [X0,X1] : subset(X0,set_union2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_33])]) ).
fof(f2776,plain,
( subset(relation_rng(sK17),relation_field(sK17))
| ~ spl77_33
| ~ spl77_205 ),
inference(superposition,[],[f1194,f2650]) ).
fof(f1194,plain,
( ! [X0,X1] : subset(X0,set_union2(X0,X1))
| ~ spl77_33 ),
inference(avatar_component_clause,[],[f1193]) ).
fof(f2810,plain,
spl77_217,
inference(avatar_split_clause,[],[f820,f2808]) ).
fof(f2808,plain,
( spl77_217
<=> ! [X5,X0,X1] :
( in(sK61(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_217])]) ).
fof(f820,plain,
! [X0,X1,X5] :
( in(sK61(X0,X5),X0)
| ~ in(X5,X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f2806,plain,
spl77_216,
inference(avatar_split_clause,[],[f819,f2804]) ).
fof(f2804,plain,
( spl77_216
<=> ! [X5,X0,X1] :
( in(X5,sK61(X0,X5))
| ~ in(X5,X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_216])]) ).
fof(f819,plain,
! [X0,X1,X5] :
( in(X5,sK61(X0,X5))
| ~ in(X5,X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f501]) ).
fof(f2802,plain,
spl77_215,
inference(avatar_split_clause,[],[f796,f2800]) ).
fof(f2800,plain,
( spl77_215
<=> ! [X2,X0,X1] :
( sP8(X0,X1,X2)
| element(sK56(X0,X1,X2),powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_215])]) ).
fof(f796,plain,
! [X2,X0,X1] :
( sP8(X0,X1,X2)
| element(sK56(X0,X1,X2),powerset(X1)) ),
inference(cnf_transformation,[],[f485]) ).
fof(f2798,plain,
spl77_214,
inference(avatar_split_clause,[],[f789,f2796]) ).
fof(f2796,plain,
( spl77_214
<=> ! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_214])]) ).
fof(f789,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f313]) ).
fof(f313,plain,
! [X0,X1] :
( element(meet_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(meet_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_setfam_1) ).
fof(f2794,plain,
spl77_213,
inference(avatar_split_clause,[],[f788,f2792]) ).
fof(f2792,plain,
( spl77_213
<=> ! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_213])]) ).
fof(f788,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f312]) ).
fof(f312,plain,
! [X0,X1] :
( element(union_of_subsets(X0,X1),powerset(X0))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(union_of_subsets(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_setfam_1) ).
fof(f2790,plain,
spl77_212,
inference(avatar_split_clause,[],[f787,f2788]) ).
fof(f2788,plain,
( spl77_212
<=> ! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_212])]) ).
fof(f787,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f311]) ).
fof(f311,plain,
! [X0,X1] :
( union_of_subsets(X0,X1) = union(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> union_of_subsets(X0,X1) = union(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k5_setfam_1) ).
fof(f2786,plain,
spl77_211,
inference(avatar_split_clause,[],[f786,f2784]) ).
fof(f2784,plain,
( spl77_211
<=> ! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_211])]) ).
fof(f786,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0,X1] :
( meet_of_subsets(X0,X1) = set_meet(X1)
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> meet_of_subsets(X0,X1) = set_meet(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_setfam_1) ).
fof(f2775,plain,
spl77_210,
inference(avatar_split_clause,[],[f785,f2773]) ).
fof(f2773,plain,
( spl77_210
<=> ! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_210])]) ).
fof(f785,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f2771,plain,
spl77_209,
inference(avatar_split_clause,[],[f784,f2769]) ).
fof(f2769,plain,
( spl77_209
<=> ! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_209])]) ).
fof(f784,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f308]) ).
fof(f308,plain,
! [X0,X1] :
( set_difference(X0,X1) = subset_complement(X0,X1)
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> set_difference(X0,X1) = subset_complement(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_subset_1) ).
fof(f2767,plain,
spl77_208,
inference(avatar_split_clause,[],[f759,f2765]) ).
fof(f2765,plain,
( spl77_208
<=> ! [X5,X1,X0] :
( in(X5,X1)
| ~ in(X5,sK53(X0,X5))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_208])]) ).
fof(f759,plain,
! [X0,X1,X5] :
( in(X5,X1)
| ~ in(X5,sK53(X0,X5))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f2763,plain,
spl77_207,
inference(avatar_split_clause,[],[f758,f2761]) ).
fof(f2761,plain,
( spl77_207
<=> ! [X5,X1,X0] :
( in(X5,X1)
| in(sK53(X0,X5),X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_207])]) ).
fof(f758,plain,
! [X0,X1,X5] :
( in(X5,X1)
| in(sK53(X0,X5),X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f470]) ).
fof(f2759,plain,
spl77_206,
inference(avatar_split_clause,[],[f736,f2757]) ).
fof(f2757,plain,
( spl77_206
<=> ! [X6,X0,X5] :
( in(X6,sK48(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_206])]) ).
fof(f736,plain,
! [X0,X6,X5] :
( in(X6,sK48(X0))
| ~ subset(X6,X5)
| ~ in(X5,sK48(X0)) ),
inference(cnf_transformation,[],[f459]) ).
fof(f2651,plain,
( spl77_205
| ~ spl77_1
| ~ spl77_195 ),
inference(avatar_split_clause,[],[f2552,f2507,f1047,f2648]) ).
fof(f2507,plain,
( spl77_195
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_195])]) ).
fof(f2552,plain,
( relation_field(sK17) = set_union2(relation_rng(sK17),relation_dom(sK17))
| ~ spl77_1
| ~ spl77_195 ),
inference(resolution,[],[f2508,f1049]) ).
fof(f2508,plain,
( ! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0)) )
| ~ spl77_195 ),
inference(avatar_component_clause,[],[f2507]) ).
fof(f2604,plain,
spl77_204,
inference(avatar_split_clause,[],[f992,f2602]) ).
fof(f2602,plain,
( spl77_204
<=> ! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP13(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_204])]) ).
fof(f992,plain,
! [X2,X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X2
| ~ sP13(X1,X0,X2) ),
inference(definition_unfolding,[],[f867,f584]) ).
fof(f867,plain,
! [X2,X0,X1] :
( set_intersection2(X0,X1) = X2
| ~ sP13(X1,X0,X2) ),
inference(cnf_transformation,[],[f530]) ).
fof(f530,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP13(X1,X0,X2) )
& ( sP13(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f364]) ).
fof(f364,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP13(X1,X0,X2) ),
inference(definition_folding,[],[f22,f363]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f2600,plain,
spl77_203,
inference(avatar_split_clause,[],[f974,f2598]) ).
fof(f2598,plain,
( spl77_203
<=> ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_203])]) ).
fof(f974,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f748,f584,f584]) ).
fof(f748,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f2596,plain,
spl77_202,
inference(avatar_split_clause,[],[f653,f2594]) ).
fof(f2594,plain,
( spl77_202
<=> ! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_202])]) ).
fof(f653,plain,
! [X2,X0,X1] :
( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[],[f397]) ).
fof(f397,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(flattening,[],[f396]) ).
fof(f396,plain,
! [X0,X1,X2] :
( ( subset(unordered_pair(X0,X1),X2)
| ~ in(X1,X2)
| ~ in(X0,X2) )
& ( ( in(X1,X2)
& in(X0,X2) )
| ~ subset(unordered_pair(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,axiom,
! [X0,X1,X2] :
( subset(unordered_pair(X0,X1),X2)
<=> ( in(X1,X2)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_zfmisc_1) ).
fof(f2592,plain,
spl77_201,
inference(avatar_split_clause,[],[f650,f2590]) ).
fof(f2590,plain,
( spl77_201
<=> ! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_201])]) ).
fof(f650,plain,
! [X2,X0,X1] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0,X1,X2] :
( subset(set_union2(X0,X2),X1)
| ~ subset(X2,X1)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f179]) ).
fof(f179,axiom,
! [X0,X1,X2] :
( ( subset(X2,X1)
& subset(X0,X1) )
=> subset(set_union2(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
fof(f2588,plain,
spl77_200,
inference(avatar_split_clause,[],[f636,f2586]) ).
fof(f2586,plain,
( spl77_200
<=> ! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_200])]) ).
fof(f636,plain,
! [X2,X0,X1] :
( in(X0,X1)
| ~ in(X0,relation_dom(relation_dom_restriction(X2,X1)))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f395]) ).
fof(f2584,plain,
spl77_199,
inference(avatar_split_clause,[],[f579,f2582]) ).
fof(f2582,plain,
( spl77_199
<=> ! [X4,X0,X3] :
( in(X4,sK20(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK20(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_199])]) ).
fof(f579,plain,
! [X3,X0,X4] :
( in(X4,sK20(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK20(X0)) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ! [X2] :
( in(powerset(X2),sK20(X0))
| ~ in(X2,sK20(X0)) )
& ! [X3,X4] :
( in(X4,sK20(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK20(X0)) )
& in(X0,sK20(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f374,f375]) ).
fof(f375,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) )
=> ( ! [X2] :
( in(powerset(X2),sK20(X0))
| ~ in(X2,sK20(X0)) )
& ! [X4,X3] :
( in(X4,sK20(X0))
| ~ subset(X4,X3)
| ~ in(X3,sK20(X0)) )
& in(X0,sK20(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f374,plain,
! [X0] :
? [X1] :
( ! [X2] :
( in(powerset(X2),X1)
| ~ in(X2,X1) )
& ! [X3,X4] :
( in(X4,X1)
| ~ subset(X4,X3)
| ~ in(X3,X1) )
& in(X0,X1) ),
inference(rectify,[],[f220]) ).
fof(f220,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(flattening,[],[f219]) ).
fof(f219,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(powerset(X3),X1)
| ~ in(X3,X1) )
& ! [X4,X5] :
( in(X5,X1)
| ~ subset(X5,X4)
| ~ in(X4,X1) )
& in(X0,X1) ),
inference(ennf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
? [X1] :
( ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(pure_predicate_removal,[],[f189]) ).
fof(f189,plain,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X3] :
( in(X3,X1)
=> in(powerset(X3),X1) )
& ! [X4,X5] :
( ( subset(X5,X4)
& in(X4,X1) )
=> in(X5,X1) )
& in(X0,X1) ),
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X0] :
? [X1] :
( ! [X2] :
~ ( ~ in(X2,X1)
& ~ are_equipotent(X2,X1)
& subset(X2,X1) )
& ! [X2] :
( in(X2,X1)
=> in(powerset(X2),X1) )
& ! [X2,X3] :
( ( subset(X3,X2)
& in(X2,X1) )
=> in(X3,X1) )
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t136_zfmisc_1) ).
fof(f2580,plain,
spl77_198,
inference(avatar_split_clause,[],[f571,f2578]) ).
fof(f2578,plain,
( spl77_198
<=> ! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_198])]) ).
fof(f571,plain,
! [X0,X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f145]) ).
fof(f145,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_dom(relation_composition(X0,X1)),relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t44_relat_1) ).
fof(f2571,plain,
spl77_197,
inference(avatar_split_clause,[],[f570,f2569]) ).
fof(f2569,plain,
( spl77_197
<=> ! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_197])]) ).
fof(f570,plain,
! [X0,X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f146]) ).
fof(f146,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> subset(relation_rng(relation_composition(X0,X1)),relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_relat_1) ).
fof(f2520,plain,
( spl77_196
| ~ spl77_1
| ~ spl77_160 ),
inference(avatar_split_clause,[],[f2257,f2164,f1047,f2518]) ).
fof(f2518,plain,
( spl77_196
<=> ! [X0] : relation_dom_restriction(sK17,X0) = relation_composition(identity_relation(X0),sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_196])]) ).
fof(f2164,plain,
( spl77_160
<=> ! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_160])]) ).
fof(f2257,plain,
( ! [X0] : relation_dom_restriction(sK17,X0) = relation_composition(identity_relation(X0),sK17)
| ~ spl77_1
| ~ spl77_160 ),
inference(resolution,[],[f2165,f1049]) ).
fof(f2165,plain,
( ! [X0,X1] :
( ~ relation(X1)
| relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) )
| ~ spl77_160 ),
inference(avatar_component_clause,[],[f2164]) ).
fof(f2509,plain,
( spl77_195
| ~ spl77_87
| ~ spl77_182 ),
inference(avatar_split_clause,[],[f2456,f2453,f1493,f2507]) ).
fof(f1493,plain,
( spl77_87
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_87])]) ).
fof(f2453,plain,
( spl77_182
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_182])]) ).
fof(f2456,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_rng(X0),relation_dom(X0))
| ~ relation(X0) )
| ~ spl77_87
| ~ spl77_182 ),
inference(forward_demodulation,[],[f2454,f1494]) ).
fof(f1494,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl77_87 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f2454,plain,
( ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) )
| ~ spl77_182 ),
inference(avatar_component_clause,[],[f2453]) ).
fof(f2505,plain,
spl77_194,
inference(avatar_split_clause,[],[f877,f2503]) ).
fof(f877,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,X0)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f2501,plain,
spl77_193,
inference(avatar_split_clause,[],[f876,f2499]) ).
fof(f2499,plain,
( spl77_193
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_193])]) ).
fof(f876,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP15(X0,X1,X2) ),
inference(cnf_transformation,[],[f541]) ).
fof(f2497,plain,
spl77_192,
inference(avatar_split_clause,[],[f870,f2495]) ).
fof(f870,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f2493,plain,
spl77_191,
inference(avatar_split_clause,[],[f869,f2491]) ).
fof(f2491,plain,
( spl77_191
<=> ! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_191])]) ).
fof(f869,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X1)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f535]) ).
fof(f2489,plain,
spl77_190,
inference(avatar_split_clause,[],[f861,f2487]) ).
fof(f2487,plain,
( spl77_190
<=> ! [X4,X0,X2,X1] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_190])]) ).
fof(f861,plain,
! [X2,X0,X1,X4] :
( in(X4,X0)
| ~ in(X4,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f2484,plain,
spl77_189,
inference(avatar_split_clause,[],[f860,f2482]) ).
fof(f2482,plain,
( spl77_189
<=> ! [X4,X0,X1,X2] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_189])]) ).
fof(f860,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| ~ sP13(X0,X1,X2) ),
inference(cnf_transformation,[],[f529]) ).
fof(f2480,plain,
spl77_188,
inference(avatar_split_clause,[],[f839,f2478]) ).
fof(f2478,plain,
( spl77_188
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_188])]) ).
fof(f839,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f335]) ).
fof(f335,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f156]) ).
fof(f156,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f2476,plain,
spl77_187,
inference(avatar_split_clause,[],[f783,f2474]) ).
fof(f2474,plain,
( spl77_187
<=> ! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_187])]) ).
fof(f783,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f2472,plain,
spl77_186,
inference(avatar_split_clause,[],[f770,f2470]) ).
fof(f2470,plain,
( spl77_186
<=> ! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP6(X1,X0)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_186])]) ).
fof(f770,plain,
! [X0,X1] :
( identity_relation(X1) = X0
| ~ sP6(X1,X0)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f473]) ).
fof(f473,plain,
! [X0,X1] :
( ( ( identity_relation(X1) = X0
| ~ sP6(X1,X0) )
& ( sP6(X1,X0)
| identity_relation(X1) != X0 ) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f472]) ).
fof(f472,plain,
! [X1,X0] :
( ( ( identity_relation(X0) = X1
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| identity_relation(X0) != X1 ) )
| ~ sP7(X1,X0) ),
inference(nnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X1,X0] :
( ( identity_relation(X0) = X1
<=> sP6(X0,X1) )
| ~ sP7(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f2468,plain,
spl77_185,
inference(avatar_split_clause,[],[f756,f2466]) ).
fof(f2466,plain,
( spl77_185
<=> ! [X0,X1] :
( set_meet(X1) = X0
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_185])]) ).
fof(f756,plain,
! [X0,X1] :
( set_meet(X1) = X0
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f464]) ).
fof(f464,plain,
! [X0,X1] :
( ( ( set_meet(X1) = X0
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| set_meet(X1) != X0 ) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f463]) ).
fof(f463,plain,
! [X1,X0] :
( ( ( set_meet(X0) = X1
| ~ sP4(X0,X1) )
& ( sP4(X0,X1)
| set_meet(X0) != X1 ) )
| ~ sP5(X1,X0) ),
inference(nnf_transformation,[],[f349]) ).
fof(f349,plain,
! [X1,X0] :
( ( set_meet(X0) = X1
<=> sP4(X0,X1) )
| ~ sP5(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f2464,plain,
spl77_184,
inference(avatar_split_clause,[],[f737,f2462]) ).
fof(f2462,plain,
( spl77_184
<=> ! [X2,X0] :
( in(sK49(X0,X2),sK48(X0))
| ~ in(X2,sK48(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_184])]) ).
fof(f737,plain,
! [X2,X0] :
( in(sK49(X0,X2),sK48(X0))
| ~ in(X2,sK48(X0)) ),
inference(cnf_transformation,[],[f459]) ).
fof(f2460,plain,
spl77_183,
inference(avatar_split_clause,[],[f703,f2458]) ).
fof(f2458,plain,
( spl77_183
<=> ! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_183])]) ).
fof(f703,plain,
! [X2,X0,X1] :
( sP1(X2,X0,X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f344]) ).
fof(f344,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( sP1(X2,X0,X1)
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(definition_folding,[],[f280,f343,f342]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( relation_composition(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X5,X4),X1)
& in(ordered_pair(X3,X5),X0) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f2455,plain,
spl77_182,
inference(avatar_split_clause,[],[f683,f2453]) ).
fof(f683,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f2411,plain,
( spl77_181
| ~ spl77_52
| ~ spl77_177 ),
inference(avatar_split_clause,[],[f2237,f2234,f1293,f2409]) ).
fof(f2409,plain,
( spl77_181
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK74
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_181])]) ).
fof(f2234,plain,
( spl77_177
<=> ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_177])]) ).
fof(f2237,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = sK74
| ~ disjoint(X0,X1) )
| ~ spl77_52
| ~ spl77_177 ),
inference(forward_demodulation,[],[f2235,f1295]) ).
fof(f2235,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) )
| ~ spl77_177 ),
inference(avatar_component_clause,[],[f2234]) ).
fof(f2407,plain,
( spl77_180
| ~ spl77_52
| ~ spl77_176 ),
inference(avatar_split_clause,[],[f2232,f2229,f1293,f2405]) ).
fof(f2405,plain,
( spl77_180
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK74
| disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_180])]) ).
fof(f2229,plain,
( spl77_176
<=> ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_176])]) ).
fof(f2232,plain,
( ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) != sK74
| disjoint(X0,X1) )
| ~ spl77_52
| ~ spl77_176 ),
inference(forward_demodulation,[],[f2230,f1295]) ).
fof(f2230,plain,
( ! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) )
| ~ spl77_176 ),
inference(avatar_component_clause,[],[f2229]) ).
fof(f2358,plain,
( ~ spl77_1
| ~ spl77_41
| spl77_166 ),
inference(avatar_split_clause,[],[f2238,f2188,f1226,f1047]) ).
fof(f1226,plain,
( spl77_41
<=> ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_41])]) ).
fof(f2188,plain,
( spl77_166
<=> relation(relation_inverse(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_166])]) ).
fof(f2238,plain,
( ~ relation(sK17)
| ~ spl77_41
| spl77_166 ),
inference(resolution,[],[f2190,f1227]) ).
fof(f1227,plain,
( ! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) )
| ~ spl77_41 ),
inference(avatar_component_clause,[],[f1226]) ).
fof(f2190,plain,
( ~ relation(relation_inverse(sK17))
| spl77_166 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f2246,plain,
( spl77_179
| ~ spl77_52
| ~ spl77_159 ),
inference(avatar_split_clause,[],[f2162,f2158,f1293,f2244]) ).
fof(f2244,plain,
( spl77_179
<=> ! [X0] :
( relation_rng(X0) != sK74
| relation_dom(X0) = sK74
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_179])]) ).
fof(f2158,plain,
( spl77_159
<=> ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_159])]) ).
fof(f2162,plain,
( ! [X0] :
( relation_rng(X0) != sK74
| relation_dom(X0) = sK74
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_159 ),
inference(forward_demodulation,[],[f2161,f1295]) ).
fof(f2161,plain,
( ! [X0] :
( relation_dom(X0) = sK74
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_159 ),
inference(forward_demodulation,[],[f2159,f1295]) ).
fof(f2159,plain,
( ! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl77_159 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f2242,plain,
( spl77_178
| ~ spl77_52
| ~ spl77_158 ),
inference(avatar_split_clause,[],[f2156,f2152,f1293,f2240]) ).
fof(f2240,plain,
( spl77_178
<=> ! [X0] :
( relation_dom(X0) != sK74
| relation_rng(X0) = sK74
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_178])]) ).
fof(f2152,plain,
( spl77_158
<=> ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_158])]) ).
fof(f2156,plain,
( ! [X0] :
( relation_dom(X0) != sK74
| relation_rng(X0) = sK74
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_158 ),
inference(forward_demodulation,[],[f2155,f1295]) ).
fof(f2155,plain,
( ! [X0] :
( relation_rng(X0) = sK74
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_158 ),
inference(forward_demodulation,[],[f2153,f1295]) ).
fof(f2153,plain,
( ! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl77_158 ),
inference(avatar_component_clause,[],[f2152]) ).
fof(f2236,plain,
spl77_177,
inference(avatar_split_clause,[],[f983,f2234]) ).
fof(f983,plain,
! [X0,X1] :
( empty_set = set_difference(X0,set_difference(X0,X1))
| ~ disjoint(X0,X1) ),
inference(definition_unfolding,[],[f814,f584]) ).
fof(f814,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f491]) ).
fof(f491,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set )
& ( set_intersection2(X0,X1) = empty_set
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f2231,plain,
spl77_176,
inference(avatar_split_clause,[],[f982,f2229]) ).
fof(f982,plain,
! [X0,X1] :
( disjoint(X0,X1)
| empty_set != set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f815,f584]) ).
fof(f815,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_intersection2(X0,X1) != empty_set ),
inference(cnf_transformation,[],[f491]) ).
fof(f2227,plain,
spl77_175,
inference(avatar_split_clause,[],[f981,f2225]) ).
fof(f2225,plain,
( spl77_175
<=> ! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_175])]) ).
fof(f981,plain,
! [X0,X1] :
( relation(set_difference(X0,set_difference(X0,X1)))
| ~ relation(X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f802,f584]) ).
fof(f802,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f322]) ).
fof(f322,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f321]) ).
fof(f321,plain,
! [X0,X1] :
( relation(set_intersection2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_intersection2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(f2223,plain,
spl77_174,
inference(avatar_split_clause,[],[f924,f2221]) ).
fof(f2221,plain,
( spl77_174
<=> ! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_174])]) ).
fof(f924,plain,
! [X2,X0,X1] :
( X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f646,f559]) ).
fof(f646,plain,
! [X2,X0,X1] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f259]) ).
fof(f259,plain,
! [X0,X1,X2] :
( X0 = X1
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f180]) ).
fof(f180,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
fof(f2219,plain,
spl77_173,
inference(avatar_split_clause,[],[f923,f2217]) ).
fof(f2217,plain,
( spl77_173
<=> ! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_173])]) ).
fof(f923,plain,
! [X2,X0,X1] :
( X1 = X2
| unordered_pair(X0,X0) != unordered_pair(X1,X2) ),
inference(definition_unfolding,[],[f645,f559]) ).
fof(f645,plain,
! [X2,X0,X1] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(cnf_transformation,[],[f258]) ).
fof(f258,plain,
! [X0,X1,X2] :
( X1 = X2
| singleton(X0) != unordered_pair(X1,X2) ),
inference(ennf_transformation,[],[f188]) ).
fof(f188,axiom,
! [X0,X1,X2] :
( singleton(X0) = unordered_pair(X1,X2)
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
fof(f2215,plain,
spl77_172,
inference(avatar_split_clause,[],[f915,f2213]) ).
fof(f2213,plain,
( spl77_172
<=> ! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_172])]) ).
fof(f915,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,unordered_pair(X1,X1)) != X0 ),
inference(definition_unfolding,[],[f628,f559]) ).
fof(f628,plain,
! [X0,X1] :
( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ),
inference(cnf_transformation,[],[f393]) ).
fof(f393,plain,
! [X0,X1] :
( ( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) )
& ( ~ in(X1,X0)
| set_difference(X0,singleton(X1)) != X0 ) ),
inference(nnf_transformation,[],[f167]) ).
fof(f167,axiom,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
<=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_zfmisc_1) ).
fof(f2211,plain,
spl77_171,
inference(avatar_split_clause,[],[f914,f2209]) ).
fof(f2209,plain,
( spl77_171
<=> ! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_171])]) ).
fof(f914,plain,
! [X0,X1] :
( set_difference(X0,unordered_pair(X1,X1)) = X0
| in(X1,X0) ),
inference(definition_unfolding,[],[f629,f559]) ).
fof(f629,plain,
! [X0,X1] :
( set_difference(X0,singleton(X1)) = X0
| in(X1,X0) ),
inference(cnf_transformation,[],[f393]) ).
fof(f2207,plain,
spl77_170,
inference(avatar_split_clause,[],[f903,f2205]) ).
fof(f2205,plain,
( spl77_170
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_170])]) ).
fof(f903,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(unordered_pair(X0,X0),unordered_pair(X1,X1)) ),
inference(definition_unfolding,[],[f609,f559,f559]) ).
fof(f609,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(cnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f170]) ).
fof(f170,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f2203,plain,
spl77_169,
inference(avatar_split_clause,[],[f901,f2201]) ).
fof(f2201,plain,
( spl77_169
<=> ! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_169])]) ).
fof(f901,plain,
! [X0,X1] :
( set_union2(unordered_pair(X0,X0),X1) = X1
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f601,f559]) ).
fof(f601,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1] :
( set_union2(singleton(X0),X1) = X1
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f150]) ).
fof(f150,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f2199,plain,
spl77_168,
inference(avatar_split_clause,[],[f900,f2197]) ).
fof(f2197,plain,
( spl77_168
<=> ! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_168])]) ).
fof(f900,plain,
! [X0,X1] :
( set_difference(X0,set_difference(X0,X1)) = X0
| ~ subset(X0,X1) ),
inference(definition_unfolding,[],[f596,f584]) ).
fof(f596,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0,X1] :
( set_intersection2(X0,X1) = X0
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f124]) ).
fof(f124,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_intersection2(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
fof(f2195,plain,
( spl77_134
| ~ spl77_166
| ~ spl77_167
| ~ spl77_84
| ~ spl77_117 ),
inference(avatar_split_clause,[],[f1846,f1728,f1480,f2192,f2188,f1931]) ).
fof(f1931,plain,
( spl77_134
<=> empty(relation_inverse(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_134])]) ).
fof(f2192,plain,
( spl77_167
<=> empty(relation_rng(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_167])]) ).
fof(f1480,plain,
( spl77_84
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_84])]) ).
fof(f1728,plain,
( spl77_117
<=> relation_rng(sK17) = relation_dom(relation_inverse(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_117])]) ).
fof(f1846,plain,
( ~ empty(relation_rng(sK17))
| ~ relation(relation_inverse(sK17))
| empty(relation_inverse(sK17))
| ~ spl77_84
| ~ spl77_117 ),
inference(superposition,[],[f1481,f1730]) ).
fof(f1730,plain,
( relation_rng(sK17) = relation_dom(relation_inverse(sK17))
| ~ spl77_117 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f1481,plain,
( ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) )
| ~ spl77_84 ),
inference(avatar_component_clause,[],[f1480]) ).
fof(f2186,plain,
spl77_165,
inference(avatar_split_clause,[],[f896,f2184]) ).
fof(f2184,plain,
( spl77_165
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_165])]) ).
fof(f896,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_difference(X0,set_difference(X0,X1))) ),
inference(definition_unfolding,[],[f588,f584]) ).
fof(f588,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,set_intersection2(X0,X1)) ),
inference(cnf_transformation,[],[f378]) ).
fof(f2182,plain,
spl77_164,
inference(avatar_split_clause,[],[f642,f2180]) ).
fof(f2180,plain,
( spl77_164
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_164])]) ).
fof(f642,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f253]) ).
fof(f253,plain,
! [X0,X1,X2] :
( ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f2178,plain,
spl77_163,
inference(avatar_split_clause,[],[f641,f2176]) ).
fof(f2176,plain,
( spl77_163
<=> ! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_163])]) ).
fof(f641,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f253]) ).
fof(f2174,plain,
spl77_162,
inference(avatar_split_clause,[],[f640,f2172]) ).
fof(f2172,plain,
( spl77_162
<=> ! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_162])]) ).
fof(f640,plain,
! [X2,X0,X1] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f130]) ).
fof(f130,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(set_difference(X0,X2),set_difference(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
fof(f2170,plain,
spl77_161,
inference(avatar_split_clause,[],[f603,f2168]) ).
fof(f2168,plain,
( spl77_161
<=> ! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_161])]) ).
fof(f603,plain,
! [X2,X0,X1] :
( in(X2,X0)
| ~ in(X2,X1)
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
| ~ in(X2,X1) )
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f2166,plain,
spl77_160,
inference(avatar_split_clause,[],[f593,f2164]) ).
fof(f593,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f224]) ).
fof(f224,plain,
! [X0,X1] :
( relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f183]) ).
fof(f183,axiom,
! [X0,X1] :
( relation(X1)
=> relation_dom_restriction(X1,X0) = relation_composition(identity_relation(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t94_relat_1) ).
fof(f2160,plain,
spl77_159,
inference(avatar_split_clause,[],[f569,f2158]) ).
fof(f569,plain,
! [X0] :
( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ( ( empty_set = relation_dom(X0)
| empty_set != relation_rng(X0) )
& ( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0] :
( ( empty_set = relation_dom(X0)
<=> empty_set = relation_rng(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f166]) ).
fof(f166,axiom,
! [X0] :
( relation(X0)
=> ( empty_set = relation_dom(X0)
<=> empty_set = relation_rng(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(f2154,plain,
spl77_158,
inference(avatar_split_clause,[],[f568,f2152]) ).
fof(f568,plain,
! [X0] :
( empty_set = relation_rng(X0)
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f2108,plain,
spl77_157,
inference(avatar_split_clause,[],[f884,f2106]) ).
fof(f2106,plain,
( spl77_157
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_157])]) ).
fof(f884,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f341]) ).
fof(f341,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f161]) ).
fof(f161,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f2104,plain,
spl77_156,
inference(avatar_split_clause,[],[f883,f2102]) ).
fof(f2102,plain,
( spl77_156
<=> ! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP15(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_156])]) ).
fof(f883,plain,
! [X2,X0,X1] :
( set_difference(X0,X1) = X2
| ~ sP15(X1,X0,X2) ),
inference(cnf_transformation,[],[f542]) ).
fof(f542,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) = X2
| ~ sP15(X1,X0,X2) )
& ( sP15(X1,X0,X2)
| set_difference(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f368]) ).
fof(f368,plain,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> sP15(X1,X0,X2) ),
inference(definition_folding,[],[f26,f367]) ).
fof(f26,axiom,
! [X0,X1,X2] :
( set_difference(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f2100,plain,
spl77_155,
inference(avatar_split_clause,[],[f875,f2098]) ).
fof(f2098,plain,
( spl77_155
<=> ! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP14(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_155])]) ).
fof(f875,plain,
! [X2,X0,X1] :
( set_union2(X0,X1) = X2
| ~ sP14(X1,X0,X2) ),
inference(cnf_transformation,[],[f536]) ).
fof(f536,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) = X2
| ~ sP14(X1,X0,X2) )
& ( sP14(X1,X0,X2)
| set_union2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> sP14(X1,X0,X2) ),
inference(definition_folding,[],[f18,f365]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( set_union2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f2096,plain,
spl77_154,
inference(avatar_split_clause,[],[f859,f2094]) ).
fof(f2094,plain,
( spl77_154
<=> ! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP12(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_154])]) ).
fof(f859,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| ~ sP12(X1,X0,X2) ),
inference(cnf_transformation,[],[f524]) ).
fof(f524,plain,
! [X0,X1,X2] :
( ( unordered_pair(X0,X1) = X2
| ~ sP12(X1,X0,X2) )
& ( sP12(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> sP12(X1,X0,X2) ),
inference(definition_folding,[],[f17,f361]) ).
fof(f17,axiom,
! [X0,X1,X2] :
( unordered_pair(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( X1 = X3
| X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f2092,plain,
( ~ spl77_153
| ~ spl77_45
| spl77_135 ),
inference(avatar_split_clause,[],[f2044,f1935,f1242,f2089]) ).
fof(f2089,plain,
( spl77_153
<=> empty(sK17) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_153])]) ).
fof(f1242,plain,
( spl77_45
<=> ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_45])]) ).
fof(f1935,plain,
( spl77_135
<=> relation(relation_rng(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_135])]) ).
fof(f2044,plain,
( ~ empty(sK17)
| ~ spl77_45
| spl77_135 ),
inference(resolution,[],[f1936,f1243]) ).
fof(f1243,plain,
( ! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) )
| ~ spl77_45 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f1936,plain,
( ~ relation(relation_rng(sK17))
| spl77_135 ),
inference(avatar_component_clause,[],[f1935]) ).
fof(f2087,plain,
spl77_152,
inference(avatar_split_clause,[],[f851,f2085]) ).
fof(f2085,plain,
( spl77_152
<=> ! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP11(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_152])]) ).
fof(f851,plain,
! [X2,X0,X1] :
( cartesian_product2(X0,X1) = X2
| ~ sP11(X1,X0,X2) ),
inference(cnf_transformation,[],[f518]) ).
fof(f518,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP11(X1,X0,X2) )
& ( sP11(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP11(X1,X0,X2) ),
inference(definition_folding,[],[f19,f359]) ).
fof(f19,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f2083,plain,
spl77_151,
inference(avatar_split_clause,[],[f816,f2081]) ).
fof(f816,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f495,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK58(X0,X1),X1)
& in(sK58(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f493,f494]) ).
fof(f494,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK58(X0,X1),X1)
& in(sK58(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f493,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f492]) ).
fof(f492,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f332]) ).
fof(f332,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f2079,plain,
spl77_150,
inference(avatar_split_clause,[],[f813,f2077]) ).
fof(f2077,plain,
( spl77_150
<=> ! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_150])]) ).
fof(f813,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f331]) ).
fof(f331,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(flattening,[],[f330]) ).
fof(f330,plain,
! [X0,X1] :
( proper_subset(X0,X1)
| X0 = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f2075,plain,
spl77_149,
inference(avatar_split_clause,[],[f812,f2073]) ).
fof(f2073,plain,
( spl77_149
<=> ! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_149])]) ).
fof(f812,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f490]) ).
fof(f490,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f489]) ).
fof(f489,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f2014,plain,
( spl77_148
| ~ spl77_52
| ~ spl77_138 ),
inference(avatar_split_clause,[],[f1959,f1955,f1293,f2012]) ).
fof(f2012,plain,
( spl77_148
<=> ! [X0] :
( relation_rng(X0) != sK74
| sK74 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_148])]) ).
fof(f1955,plain,
( spl77_138
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_138])]) ).
fof(f1959,plain,
( ! [X0] :
( relation_rng(X0) != sK74
| sK74 = X0
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_138 ),
inference(forward_demodulation,[],[f1958,f1295]) ).
fof(f1958,plain,
( ! [X0] :
( sK74 = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_138 ),
inference(forward_demodulation,[],[f1956,f1295]) ).
fof(f1956,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) )
| ~ spl77_138 ),
inference(avatar_component_clause,[],[f1955]) ).
fof(f2010,plain,
( spl77_147
| ~ spl77_52
| ~ spl77_137 ),
inference(avatar_split_clause,[],[f1953,f1949,f1293,f2008]) ).
fof(f2008,plain,
( spl77_147
<=> ! [X0] :
( relation_dom(X0) != sK74
| sK74 = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_147])]) ).
fof(f1949,plain,
( spl77_137
<=> ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_137])]) ).
fof(f1953,plain,
( ! [X0] :
( relation_dom(X0) != sK74
| sK74 = X0
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_137 ),
inference(forward_demodulation,[],[f1952,f1295]) ).
fof(f1952,plain,
( ! [X0] :
( sK74 = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl77_52
| ~ spl77_137 ),
inference(forward_demodulation,[],[f1950,f1295]) ).
fof(f1950,plain,
( ! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) )
| ~ spl77_137 ),
inference(avatar_component_clause,[],[f1949]) ).
fof(f1991,plain,
spl77_146,
inference(avatar_split_clause,[],[f648,f1989]) ).
fof(f648,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f262]) ).
fof(f262,plain,
! [X0,X1,X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f118]) ).
fof(f118,axiom,
! [X0,X1,X2] :
( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(f1987,plain,
spl77_145,
inference(avatar_split_clause,[],[f647,f1985]) ).
fof(f1985,plain,
( spl77_145
<=> ! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_145])]) ).
fof(f647,plain,
! [X2,X0,X1] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(flattening,[],[f260]) ).
fof(f260,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f164]) ).
fof(f164,axiom,
! [X0,X1,X2] :
( ( disjoint(X1,X2)
& subset(X0,X1) )
=> disjoint(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
fof(f1983,plain,
spl77_144,
inference(avatar_split_clause,[],[f611,f1981]) ).
fof(f1981,plain,
( spl77_144
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK23(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_144])]) ).
fof(f611,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ in(sK23(X0,X1),X1) ),
inference(cnf_transformation,[],[f383]) ).
fof(f383,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ( ~ in(sK23(X0,X1),X1)
& in(sK23(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f243,f382]) ).
fof(f382,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK23(X0,X1),X1)
& in(sK23(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f243,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) ),
inference(ennf_transformation,[],[f96]) ).
fof(f96,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f1979,plain,
spl77_143,
inference(avatar_split_clause,[],[f610,f1977]) ).
fof(f1977,plain,
( spl77_143
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| in(sK23(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_143])]) ).
fof(f610,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| in(sK23(X0,X1),X0) ),
inference(cnf_transformation,[],[f383]) ).
fof(f1975,plain,
spl77_142,
inference(avatar_split_clause,[],[f591,f1973]) ).
fof(f1973,plain,
( spl77_142
<=> ! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_142])]) ).
fof(f591,plain,
! [X2,X0,X1] :
( ~ disjoint(X0,X1)
| ~ in(X2,X1)
| ~ in(X2,X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ( in(sK22(X0,X1),X1)
& in(sK22(X0,X1),X0) )
| disjoint(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f222,f379]) ).
fof(f379,plain,
! [X0,X1] :
( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
=> ( in(sK22(X0,X1),X1)
& in(sK22(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f222,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| ! [X2] :
( ~ in(X2,X1)
| ~ in(X2,X0) ) )
& ( ? [X3] :
( in(X3,X1)
& in(X3,X0) )
| disjoint(X0,X1) ) ),
inference(ennf_transformation,[],[f191]) ).
fof(f191,plain,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X3] :
~ ( in(X3,X1)
& in(X3,X0) )
& ~ disjoint(X0,X1) ) ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X0,X1] :
( ~ ( disjoint(X0,X1)
& ? [X2] :
( in(X2,X1)
& in(X2,X0) ) )
& ~ ( ! [X2] :
~ ( in(X2,X1)
& in(X2,X0) )
& ~ disjoint(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
fof(f1971,plain,
spl77_141,
inference(avatar_split_clause,[],[f586,f1969]) ).
fof(f1969,plain,
( spl77_141
<=> ! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_141])]) ).
fof(f586,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f143]) ).
fof(f143,axiom,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f1967,plain,
spl77_140,
inference(avatar_split_clause,[],[f585,f1965]) ).
fof(f1965,plain,
( spl77_140
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_140])]) ).
fof(f585,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f137]) ).
fof(f137,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f1963,plain,
spl77_139,
inference(avatar_split_clause,[],[f580,f1961]) ).
fof(f1961,plain,
( spl77_139
<=> ! [X2,X0] :
( in(powerset(X2),sK20(X0))
| ~ in(X2,sK20(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_139])]) ).
fof(f580,plain,
! [X2,X0] :
( in(powerset(X2),sK20(X0))
| ~ in(X2,sK20(X0)) ),
inference(cnf_transformation,[],[f376]) ).
fof(f1957,plain,
spl77_138,
inference(avatar_split_clause,[],[f566,f1955]) ).
fof(f566,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_rng(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f204,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(flattening,[],[f203]) ).
fof(f203,plain,
! [X0] :
( empty_set = X0
| ( empty_set != relation_rng(X0)
& empty_set != relation_dom(X0) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f165]) ).
fof(f165,axiom,
! [X0] :
( relation(X0)
=> ( ( empty_set = relation_rng(X0)
| empty_set = relation_dom(X0) )
=> empty_set = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_relat_1) ).
fof(f1951,plain,
spl77_137,
inference(avatar_split_clause,[],[f565,f1949]) ).
fof(f565,plain,
! [X0] :
( empty_set = X0
| empty_set != relation_dom(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f204]) ).
fof(f1947,plain,
spl77_136,
inference(avatar_split_clause,[],[f562,f1945]) ).
fof(f1945,plain,
( spl77_136
<=> ! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_136])]) ).
fof(f562,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0)))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f121]) ).
fof(f121,axiom,
! [X0] :
( relation(X0)
=> subset(X0,cartesian_product2(relation_dom(X0),relation_rng(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_relat_1) ).
fof(f1938,plain,
( ~ spl77_134
| spl77_135
| ~ spl77_47
| ~ spl77_117 ),
inference(avatar_split_clause,[],[f1847,f1728,f1250,f1935,f1931]) ).
fof(f1250,plain,
( spl77_47
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_47])]) ).
fof(f1847,plain,
( relation(relation_rng(sK17))
| ~ empty(relation_inverse(sK17))
| ~ spl77_47
| ~ spl77_117 ),
inference(superposition,[],[f1251,f1730]) ).
fof(f1251,plain,
( ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) )
| ~ spl77_47 ),
inference(avatar_component_clause,[],[f1250]) ).
fof(f1884,plain,
spl77_133,
inference(avatar_split_clause,[],[f1014,f1882]) ).
fof(f1882,plain,
( spl77_133
<=> ! [X1] :
( sP6(X1,identity_relation(X1))
| ~ sP7(identity_relation(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_133])]) ).
fof(f1014,plain,
! [X1] :
( sP6(X1,identity_relation(X1))
| ~ sP7(identity_relation(X1),X1) ),
inference(equality_resolution,[],[f769]) ).
fof(f769,plain,
! [X0,X1] :
( sP6(X1,X0)
| identity_relation(X1) != X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f473]) ).
fof(f1880,plain,
spl77_132,
inference(avatar_split_clause,[],[f1009,f1878]) ).
fof(f1878,plain,
( spl77_132
<=> ! [X1] :
( sP4(X1,set_meet(X1))
| ~ sP5(set_meet(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_132])]) ).
fof(f1009,plain,
! [X1] :
( sP4(X1,set_meet(X1))
| ~ sP5(set_meet(X1),X1) ),
inference(equality_resolution,[],[f755]) ).
fof(f755,plain,
! [X0,X1] :
( sP4(X1,X0)
| set_meet(X1) != X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f464]) ).
fof(f1876,plain,
spl77_131,
inference(avatar_split_clause,[],[f818,f1874]) ).
fof(f1874,plain,
( spl77_131
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ in(sK58(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_131])]) ).
fof(f818,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK58(X0,X1),X1) ),
inference(cnf_transformation,[],[f495]) ).
fof(f1872,plain,
spl77_130,
inference(avatar_split_clause,[],[f817,f1870]) ).
fof(f1870,plain,
( spl77_130
<=> ! [X0,X1] :
( subset(X0,X1)
| in(sK58(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_130])]) ).
fof(f817,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK58(X0,X1),X0) ),
inference(cnf_transformation,[],[f495]) ).
fof(f1868,plain,
spl77_129,
inference(avatar_split_clause,[],[f807,f1866]) ).
fof(f1866,plain,
( spl77_129
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_129])]) ).
fof(f807,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f327]) ).
fof(f327,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X0,X1))
& empty(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_relat_1) ).
fof(f1864,plain,
spl77_128,
inference(avatar_split_clause,[],[f806,f1862]) ).
fof(f1862,plain,
( spl77_128
<=> ! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_128])]) ).
fof(f806,plain,
! [X0,X1] :
( empty(relation_composition(X0,X1))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f1860,plain,
spl77_127,
inference(avatar_split_clause,[],[f805,f1858]) ).
fof(f1858,plain,
( spl77_127
<=> ! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_127])]) ).
fof(f805,plain,
! [X0,X1] :
( relation(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f326,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(flattening,[],[f325]) ).
fof(f325,plain,
! [X0,X1] :
( ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) )
| ~ relation(X1)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0,X1] :
( ( relation(X1)
& empty(X0) )
=> ( relation(relation_composition(X1,X0))
& empty(relation_composition(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_relat_1) ).
fof(f1856,plain,
spl77_126,
inference(avatar_split_clause,[],[f804,f1854]) ).
fof(f1854,plain,
( spl77_126
<=> ! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_126])]) ).
fof(f804,plain,
! [X0,X1] :
( empty(relation_composition(X1,X0))
| ~ relation(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f326]) ).
fof(f1852,plain,
spl77_125,
inference(avatar_split_clause,[],[f803,f1850]) ).
fof(f1850,plain,
( spl77_125
<=> ! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_125])]) ).
fof(f803,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f323]) ).
fof(f323,plain,
! [X0,X1] :
( relation(set_union2(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(f1845,plain,
spl77_124,
inference(avatar_split_clause,[],[f801,f1843]) ).
fof(f1843,plain,
( spl77_124
<=> ! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_124])]) ).
fof(f801,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f320]) ).
fof(f320,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(flattening,[],[f319]) ).
fof(f319,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0,X1] :
( ( relation(X1)
& relation(X0) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f1841,plain,
spl77_123,
inference(avatar_split_clause,[],[f800,f1839]) ).
fof(f1839,plain,
( spl77_123
<=> ! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_123])]) ).
fof(f800,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f317]) ).
fof(f317,plain,
! [X0,X1] :
( ~ empty(cartesian_product2(X0,X1))
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0,X1] :
( ( ~ empty(X1)
& ~ empty(X0) )
=> ~ empty(cartesian_product2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(f1837,plain,
spl77_122,
inference(avatar_split_clause,[],[f751,f1835]) ).
fof(f1835,plain,
( spl77_122
<=> ! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_122])]) ).
fof(f751,plain,
! [X0,X1] :
( in(X1,X0)
| ~ element(X1,X0)
| empty(X0) ),
inference(cnf_transformation,[],[f462]) ).
fof(f462,plain,
! [X0,X1] :
( ( ( ( element(X1,X0)
| ~ empty(X1) )
& ( empty(X1)
| ~ element(X1,X0) ) )
| ~ empty(X0) )
& ( ( ( element(X1,X0)
| ~ in(X1,X0) )
& ( in(X1,X0)
| ~ element(X1,X0) ) )
| empty(X0) ) ),
inference(nnf_transformation,[],[f295]) ).
fof(f295,plain,
! [X0,X1] :
( ( ( element(X1,X0)
<=> empty(X1) )
| ~ empty(X0) )
& ( ( element(X1,X0)
<=> in(X1,X0) )
| empty(X0) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f1833,plain,
spl77_121,
inference(avatar_split_clause,[],[f720,f1831]) ).
fof(f1831,plain,
( spl77_121
<=> ! [X2,X0,X1] :
( sP3(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_121])]) ).
fof(f720,plain,
! [X2,X0,X1] :
( sP3(X2,X1,X0)
| ~ relation(X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ! [X1,X2] :
( sP3(X2,X1,X0)
| ~ relation(X2) )
| ~ relation(X0) ),
inference(definition_folding,[],[f283,f346,f345]) ).
fof(f283,plain,
! [X0] :
( ! [X1,X2] :
( ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) )
| ~ relation(X2) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( relation(X2)
=> ( relation_dom_restriction(X0,X1) = X2
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ( in(ordered_pair(X3,X4),X0)
& in(X3,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11_relat_1) ).
fof(f1789,plain,
( spl77_120
| ~ spl77_1
| ~ spl77_101 ),
inference(avatar_split_clause,[],[f1717,f1629,f1047,f1786]) ).
fof(f1786,plain,
( spl77_120
<=> relation_dom(sK17) = relation_rng(relation_inverse(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_120])]) ).
fof(f1629,plain,
( spl77_101
<=> ! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_101])]) ).
fof(f1717,plain,
( relation_dom(sK17) = relation_rng(relation_inverse(sK17))
| ~ spl77_1
| ~ spl77_101 ),
inference(resolution,[],[f1630,f1049]) ).
fof(f1630,plain,
( ! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) )
| ~ spl77_101 ),
inference(avatar_component_clause,[],[f1629]) ).
fof(f1769,plain,
( spl77_119
| ~ spl77_52
| ~ spl77_109 ),
inference(avatar_split_clause,[],[f1666,f1663,f1293,f1767]) ).
fof(f1663,plain,
( spl77_109
<=> ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_109])]) ).
fof(f1666,plain,
( ! [X0,X1] :
( set_difference(X0,X1) = sK74
| ~ subset(X0,X1) )
| ~ spl77_52
| ~ spl77_109 ),
inference(forward_demodulation,[],[f1664,f1295]) ).
fof(f1664,plain,
( ! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
| ~ spl77_109 ),
inference(avatar_component_clause,[],[f1663]) ).
fof(f1765,plain,
( spl77_118
| ~ spl77_52
| ~ spl77_107 ),
inference(avatar_split_clause,[],[f1656,f1653,f1293,f1763]) ).
fof(f1763,plain,
( spl77_118
<=> ! [X0,X1] :
( set_difference(X0,X1) != sK74
| subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_118])]) ).
fof(f1653,plain,
( spl77_107
<=> ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_107])]) ).
fof(f1656,plain,
( ! [X0,X1] :
( set_difference(X0,X1) != sK74
| subset(X0,X1) )
| ~ spl77_52
| ~ spl77_107 ),
inference(forward_demodulation,[],[f1654,f1295]) ).
fof(f1654,plain,
( ! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) )
| ~ spl77_107 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f1731,plain,
( spl77_117
| ~ spl77_1
| ~ spl77_100 ),
inference(avatar_split_clause,[],[f1701,f1625,f1047,f1728]) ).
fof(f1625,plain,
( spl77_100
<=> ! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_100])]) ).
fof(f1701,plain,
( relation_rng(sK17) = relation_dom(relation_inverse(sK17))
| ~ spl77_1
| ~ spl77_100 ),
inference(resolution,[],[f1626,f1049]) ).
fof(f1626,plain,
( ! [X0] :
( ~ relation(X0)
| relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ spl77_100 ),
inference(avatar_component_clause,[],[f1625]) ).
fof(f1694,plain,
spl77_116,
inference(avatar_split_clause,[],[f1030,f1692]) ).
fof(f1030,plain,
! [X0,X1] : sP13(X1,X0,set_difference(X0,set_difference(X0,X1))),
inference(equality_resolution,[],[f993]) ).
fof(f993,plain,
! [X2,X0,X1] :
( sP13(X1,X0,X2)
| set_difference(X0,set_difference(X0,X1)) != X2 ),
inference(definition_unfolding,[],[f866,f584]) ).
fof(f866,plain,
! [X2,X0,X1] :
( sP13(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f530]) ).
fof(f1690,plain,
spl77_115,
inference(avatar_split_clause,[],[f1022,f1688]) ).
fof(f1688,plain,
( spl77_115
<=> ! [X0,X3] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_115])]) ).
fof(f1022,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,unordered_pair(X0,X0)) ),
inference(equality_resolution,[],[f987]) ).
fof(f987,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f827,f559]) ).
fof(f827,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f506]) ).
fof(f1686,plain,
spl77_114,
inference(avatar_split_clause,[],[f916,f1684]) ).
fof(f1684,plain,
( spl77_114
<=> ! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_114])]) ).
fof(f916,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f631,f559]) ).
fof(f631,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(cnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ disjoint(singleton(X0),X1) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
fof(f1682,plain,
spl77_113,
inference(avatar_split_clause,[],[f910,f1680]) ).
fof(f1680,plain,
( spl77_113
<=> ! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_113])]) ).
fof(f910,plain,
! [X0,X1] :
( subset(unordered_pair(X0,X0),X1)
| ~ in(X0,X1) ),
inference(definition_unfolding,[],[f621,f559]) ).
fof(f621,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f389]) ).
fof(f389,plain,
! [X0,X1] :
( ( subset(singleton(X0),X1)
| ~ in(X0,X1) )
& ( in(X0,X1)
| ~ subset(singleton(X0),X1) ) ),
inference(nnf_transformation,[],[f135]) ).
fof(f135,axiom,
! [X0,X1] :
( subset(singleton(X0),X1)
<=> in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_zfmisc_1) ).
fof(f1678,plain,
spl77_112,
inference(avatar_split_clause,[],[f899,f1676]) ).
fof(f1676,plain,
( spl77_112
<=> ! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_112])]) ).
fof(f899,plain,
! [X0,X1] :
( disjoint(unordered_pair(X0,X0),X1)
| in(X0,X1) ),
inference(definition_unfolding,[],[f595,f559]) ).
fof(f595,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( disjoint(singleton(X0),X1)
| in(X0,X1) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0,X1] :
( ~ in(X0,X1)
=> disjoint(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
fof(f1674,plain,
spl77_111,
inference(avatar_split_clause,[],[f652,f1672]) ).
fof(f1672,plain,
( spl77_111
<=> ! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_111])]) ).
fof(f652,plain,
! [X2,X0,X1] :
( in(X1,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f397]) ).
fof(f1670,plain,
spl77_110,
inference(avatar_split_clause,[],[f651,f1668]) ).
fof(f1668,plain,
( spl77_110
<=> ! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_110])]) ).
fof(f651,plain,
! [X2,X0,X1] :
( in(X0,X2)
| ~ subset(unordered_pair(X0,X1),X2) ),
inference(cnf_transformation,[],[f397]) ).
fof(f1665,plain,
spl77_109,
inference(avatar_split_clause,[],[f625,f1663]) ).
fof(f625,plain,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f391,plain,
! [X0,X1] :
( ( empty_set = set_difference(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| empty_set != set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f134,axiom,
! [X0,X1] :
( empty_set = set_difference(X0,X1)
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f1661,plain,
( spl77_108
| ~ spl77_6
| ~ spl77_9
| ~ spl77_42 ),
inference(avatar_split_clause,[],[f1276,f1230,f1087,f1072,f1658]) ).
fof(f1658,plain,
( spl77_108
<=> sK74 = sK76 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_108])]) ).
fof(f1072,plain,
( spl77_6
<=> empty(sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_6])]) ).
fof(f1087,plain,
( spl77_9
<=> empty(sK76) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_9])]) ).
fof(f1230,plain,
( spl77_42
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_42])]) ).
fof(f1276,plain,
( sK74 = sK76
| ~ spl77_6
| ~ spl77_9
| ~ spl77_42 ),
inference(forward_demodulation,[],[f1275,f1274]) ).
fof(f1274,plain,
( empty_set = sK74
| ~ spl77_6
| ~ spl77_42 ),
inference(resolution,[],[f1231,f1074]) ).
fof(f1074,plain,
( empty(sK74)
| ~ spl77_6 ),
inference(avatar_component_clause,[],[f1072]) ).
fof(f1231,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl77_42 ),
inference(avatar_component_clause,[],[f1230]) ).
fof(f1275,plain,
( empty_set = sK76
| ~ spl77_9
| ~ spl77_42 ),
inference(resolution,[],[f1231,f1089]) ).
fof(f1089,plain,
( empty(sK76)
| ~ spl77_9 ),
inference(avatar_component_clause,[],[f1087]) ).
fof(f1655,plain,
spl77_107,
inference(avatar_split_clause,[],[f624,f1653]) ).
fof(f624,plain,
! [X0,X1] :
( subset(X0,X1)
| empty_set != set_difference(X0,X1) ),
inference(cnf_transformation,[],[f391]) ).
fof(f1651,plain,
spl77_106,
inference(avatar_split_clause,[],[f613,f1649]) ).
fof(f1649,plain,
( spl77_106
<=> ! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_106])]) ).
fof(f613,plain,
! [X0,X1] :
( disjoint(X0,X1)
| set_difference(X0,X1) != X0 ),
inference(cnf_transformation,[],[f384]) ).
fof(f384,plain,
! [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) != X0 )
& ( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f1647,plain,
spl77_105,
inference(avatar_split_clause,[],[f612,f1645]) ).
fof(f1645,plain,
( spl77_105
<=> ! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_105])]) ).
fof(f612,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f384]) ).
fof(f1643,plain,
spl77_104,
inference(avatar_split_clause,[],[f597,f1641]) ).
fof(f597,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0,X1] :
( set_union2(X0,X1) = X1
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f1639,plain,
spl77_103,
inference(avatar_split_clause,[],[f590,f1637]) ).
fof(f590,plain,
! [X0,X1] :
( in(sK22(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1635,plain,
spl77_102,
inference(avatar_split_clause,[],[f589,f1633]) ).
fof(f589,plain,
! [X0,X1] :
( in(sK22(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f380]) ).
fof(f1631,plain,
spl77_101,
inference(avatar_split_clause,[],[f564,f1629]) ).
fof(f564,plain,
! [X0] :
( relation_dom(X0) = relation_rng(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f133]) ).
fof(f133,axiom,
! [X0] :
( relation(X0)
=> ( relation_dom(X0) = relation_rng(relation_inverse(X0))
& relation_rng(X0) = relation_dom(relation_inverse(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_relat_1) ).
fof(f1627,plain,
spl77_100,
inference(avatar_split_clause,[],[f563,f1625]) ).
fof(f563,plain,
! [X0] :
( relation_rng(X0) = relation_dom(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f202]) ).
fof(f1571,plain,
( spl77_99
| ~ spl77_1
| ~ spl77_81 ),
inference(avatar_split_clause,[],[f1544,f1468,f1047,f1568]) ).
fof(f1568,plain,
( spl77_99
<=> sK17 = relation_inverse(relation_inverse(sK17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_99])]) ).
fof(f1468,plain,
( spl77_81
<=> ! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_81])]) ).
fof(f1544,plain,
( sK17 = relation_inverse(relation_inverse(sK17))
| ~ spl77_1
| ~ spl77_81 ),
inference(resolution,[],[f1469,f1049]) ).
fof(f1469,plain,
( ! [X0] :
( ~ relation(X0)
| relation_inverse(relation_inverse(X0)) = X0 )
| ~ spl77_81 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f1562,plain,
( spl77_98
| ~ spl77_52
| ~ spl77_85 ),
inference(avatar_split_clause,[],[f1487,f1484,f1293,f1560]) ).
fof(f1560,plain,
( spl77_98
<=> ! [X0] :
( sK74 = X0
| in(sK46(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_98])]) ).
fof(f1484,plain,
( spl77_85
<=> ! [X0] :
( empty_set = X0
| in(sK46(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_85])]) ).
fof(f1487,plain,
( ! [X0] :
( sK74 = X0
| in(sK46(X0),X0) )
| ~ spl77_52
| ~ spl77_85 ),
inference(forward_demodulation,[],[f1485,f1295]) ).
fof(f1485,plain,
( ! [X0] :
( empty_set = X0
| in(sK46(X0),X0) )
| ~ spl77_85 ),
inference(avatar_component_clause,[],[f1484]) ).
fof(f1537,plain,
spl77_97,
inference(avatar_split_clause,[],[f1028,f1535]) ).
fof(f1535,plain,
( spl77_97
<=> ! [X2,X0,X4] :
( in(X4,X2)
| ~ sP12(X0,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_97])]) ).
fof(f1028,plain,
! [X2,X0,X4] :
( in(X4,X2)
| ~ sP12(X0,X4,X2) ),
inference(equality_resolution,[],[f853]) ).
fof(f853,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f1533,plain,
spl77_96,
inference(avatar_split_clause,[],[f1027,f1531]) ).
fof(f1531,plain,
( spl77_96
<=> ! [X2,X1,X4] :
( in(X4,X2)
| ~ sP12(X4,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_96])]) ).
fof(f1027,plain,
! [X2,X1,X4] :
( in(X4,X2)
| ~ sP12(X4,X1,X2) ),
inference(equality_resolution,[],[f854]) ).
fof(f854,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| ~ sP12(X0,X1,X2) ),
inference(cnf_transformation,[],[f523]) ).
fof(f1529,plain,
spl77_95,
inference(avatar_split_clause,[],[f1024,f1527]) ).
fof(f1527,plain,
( spl77_95
<=> ! [X0,X3] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_95])]) ).
fof(f1024,plain,
! [X3,X0] :
( subset(X3,X0)
| ~ in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f831]) ).
fof(f831,plain,
! [X3,X0,X1] :
( subset(X3,X0)
| ~ in(X3,X1)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f510]) ).
fof(f1525,plain,
spl77_94,
inference(avatar_split_clause,[],[f1023,f1523]) ).
fof(f1523,plain,
( spl77_94
<=> ! [X0,X3] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_94])]) ).
fof(f1023,plain,
! [X3,X0] :
( in(X3,powerset(X0))
| ~ subset(X3,X0) ),
inference(equality_resolution,[],[f832]) ).
fof(f832,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ subset(X3,X0)
| powerset(X0) != X1 ),
inference(cnf_transformation,[],[f510]) ).
fof(f1519,plain,
spl77_93,
inference(avatar_split_clause,[],[f837,f1517]) ).
fof(f1517,plain,
( spl77_93
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_93])]) ).
fof(f837,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f178]) ).
fof(f178,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f1515,plain,
spl77_92,
inference(avatar_split_clause,[],[f836,f1513]) ).
fof(f1513,plain,
( spl77_92
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_92])]) ).
fof(f836,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f511]) ).
fof(f511,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f1511,plain,
spl77_91,
inference(avatar_split_clause,[],[f835,f1509]) ).
fof(f1509,plain,
( spl77_91
<=> ! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_91])]) ).
fof(f835,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f511]) ).
fof(f1507,plain,
spl77_90,
inference(avatar_split_clause,[],[f826,f1505]) ).
fof(f1505,plain,
( spl77_90
<=> ! [X0,X1] :
( union(X0) = X1
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_90])]) ).
fof(f826,plain,
! [X0,X1] :
( union(X0) = X1
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f502]) ).
fof(f502,plain,
! [X0,X1] :
( ( union(X0) = X1
| ~ sP10(X0,X1) )
& ( sP10(X0,X1)
| union(X0) != X1 ) ),
inference(nnf_transformation,[],[f358]) ).
fof(f358,plain,
! [X0,X1] :
( union(X0) = X1
<=> sP10(X0,X1) ),
inference(definition_folding,[],[f25,f357]) ).
fof(f25,axiom,
! [X0,X1] :
( union(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f1503,plain,
spl77_89,
inference(avatar_split_clause,[],[f754,f1501]) ).
fof(f1501,plain,
( spl77_89
<=> ! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_89])]) ).
fof(f754,plain,
! [X0,X1] :
( element(X1,X0)
| ~ empty(X1)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f462]) ).
fof(f1499,plain,
spl77_88,
inference(avatar_split_clause,[],[f753,f1497]) ).
fof(f1497,plain,
( spl77_88
<=> ! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_88])]) ).
fof(f753,plain,
! [X0,X1] :
( empty(X1)
| ~ element(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f462]) ).
fof(f1495,plain,
spl77_87,
inference(avatar_split_clause,[],[f749,f1493]) ).
fof(f749,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f1491,plain,
spl77_86,
inference(avatar_split_clause,[],[f747,f1489]) ).
fof(f1486,plain,
spl77_85,
inference(avatar_split_clause,[],[f733,f1484]) ).
fof(f733,plain,
! [X0] :
( empty_set = X0
| in(sK46(X0),X0) ),
inference(cnf_transformation,[],[f453]) ).
fof(f453,plain,
! [X0] :
( ( empty_set = X0
| in(sK46(X0),X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f451,f452]) ).
fof(f452,plain,
! [X0] :
( ? [X1] : in(X1,X0)
=> in(sK46(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f451,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X2] : ~ in(X2,X0)
| empty_set != X0 ) ),
inference(rectify,[],[f450]) ).
fof(f450,plain,
! [X0] :
( ( empty_set = X0
| ? [X1] : in(X1,X0) )
& ( ! [X1] : ~ in(X1,X0)
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( empty_set = X0
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f1482,plain,
spl77_84,
inference(avatar_split_clause,[],[f728,f1480]) ).
fof(f728,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f1478,plain,
( spl77_83
| ~ spl77_34
| ~ spl77_77 ),
inference(avatar_split_clause,[],[f1445,f1439,f1197,f1476]) ).
fof(f1476,plain,
( spl77_83
<=> ! [X0] : subset(sK74,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_83])]) ).
fof(f1439,plain,
( spl77_77
<=> ! [X0] : sK74 = set_difference(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_77])]) ).
fof(f1445,plain,
( ! [X0] : subset(sK74,X0)
| ~ spl77_34
| ~ spl77_77 ),
inference(superposition,[],[f1198,f1440]) ).
fof(f1440,plain,
( ! [X0] : sK74 = set_difference(X0,X0)
| ~ spl77_77 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f1474,plain,
spl77_82,
inference(avatar_split_clause,[],[f727,f1472]) ).
fof(f1472,plain,
( spl77_82
<=> ! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_82])]) ).
fof(f727,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ~ empty(relation_rng(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_rng(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(f1470,plain,
spl77_81,
inference(avatar_split_clause,[],[f682,f1468]) ).
fof(f682,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0] :
( relation_inverse(relation_inverse(X0)) = X0
| ~ relation(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( relation(X0)
=> relation_inverse(relation_inverse(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k4_relat_1) ).
fof(f1466,plain,
spl77_80,
inference(avatar_split_clause,[],[f679,f1464]) ).
fof(f1464,plain,
( spl77_80
<=> ! [X0] :
( element(sK24(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_80])]) ).
fof(f679,plain,
! [X0] :
( element(sK24(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f405]) ).
fof(f405,plain,
! [X0] :
( ( ~ empty(sK24(X0))
& element(sK24(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f273,f404]) ).
fof(f404,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK24(X0))
& element(sK24(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f273,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f1456,plain,
( spl77_79
| ~ spl77_77
| ~ spl77_78 ),
inference(avatar_split_clause,[],[f1452,f1449,f1439,f1454]) ).
fof(f1449,plain,
( spl77_78
<=> ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_78])]) ).
fof(f1452,plain,
( ! [X0] : set_difference(X0,sK74) = X0
| ~ spl77_77
| ~ spl77_78 ),
inference(forward_demodulation,[],[f1450,f1440]) ).
fof(f1450,plain,
( ! [X0] : set_difference(X0,set_difference(X0,X0)) = X0
| ~ spl77_78 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f1451,plain,
spl77_78,
inference(avatar_split_clause,[],[f973,f1449]) ).
fof(f973,plain,
! [X0] : set_difference(X0,set_difference(X0,X0)) = X0,
inference(definition_unfolding,[],[f745,f584]) ).
fof(f745,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f1441,plain,
( spl77_77
| ~ spl77_39
| ~ spl77_52
| ~ spl77_76 ),
inference(avatar_split_clause,[],[f1437,f1433,f1293,f1218,f1439]) ).
fof(f1218,plain,
( spl77_39
<=> ! [X0] : set_difference(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_39])]) ).
fof(f1433,plain,
( spl77_76
<=> ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_76])]) ).
fof(f1437,plain,
( ! [X0] : sK74 = set_difference(X0,X0)
| ~ spl77_39
| ~ spl77_52
| ~ spl77_76 ),
inference(forward_demodulation,[],[f1436,f1295]) ).
fof(f1436,plain,
( ! [X0] : empty_set = set_difference(X0,X0)
| ~ spl77_39
| ~ spl77_76 ),
inference(forward_demodulation,[],[f1434,f1219]) ).
fof(f1219,plain,
( ! [X0] : set_difference(X0,empty_set) = X0
| ~ spl77_39 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f1434,plain,
( ! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set))
| ~ spl77_76 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f1435,plain,
spl77_76,
inference(avatar_split_clause,[],[f938,f1433]) ).
fof(f938,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f674,f584]) ).
fof(f674,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f125]) ).
fof(f125,axiom,
! [X0] : empty_set = set_intersection2(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
fof(f1431,plain,
spl77_75,
inference(avatar_split_clause,[],[f599,f1429]) ).
fof(f1429,plain,
( spl77_75
<=> ! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_75])]) ).
fof(f599,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0,X1] :
( subset(X0,union(X1))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f182]) ).
fof(f182,axiom,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(f1427,plain,
spl77_74,
inference(avatar_split_clause,[],[f592,f1425]) ).
fof(f592,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0,X1] :
( subset(relation_dom_restriction(X1,X0),X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f177]) ).
fof(f177,axiom,
! [X0,X1] :
( relation(X1)
=> subset(relation_dom_restriction(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t88_relat_1) ).
fof(f1403,plain,
( spl77_73
| ~ spl77_52
| ~ spl77_60 ),
inference(avatar_split_clause,[],[f1349,f1346,f1293,f1401]) ).
fof(f1401,plain,
( spl77_73
<=> ! [X0,X1] :
( sK74 = X0
| sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_73])]) ).
fof(f1346,plain,
( spl77_60
<=> ! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_60])]) ).
fof(f1349,plain,
( ! [X0,X1] :
( sK74 = X0
| sP5(X1,X0) )
| ~ spl77_52
| ~ spl77_60 ),
inference(forward_demodulation,[],[f1347,f1295]) ).
fof(f1347,plain,
( ! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 )
| ~ spl77_60 ),
inference(avatar_component_clause,[],[f1346]) ).
fof(f1397,plain,
spl77_72,
inference(avatar_split_clause,[],[f1032,f1395]) ).
fof(f1032,plain,
! [X0,X1] : sP15(X1,X0,set_difference(X0,X1)),
inference(equality_resolution,[],[f882]) ).
fof(f882,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2)
| set_difference(X0,X1) != X2 ),
inference(cnf_transformation,[],[f542]) ).
fof(f1393,plain,
spl77_71,
inference(avatar_split_clause,[],[f1031,f1391]) ).
fof(f1031,plain,
! [X0,X1] : sP14(X1,X0,set_union2(X0,X1)),
inference(equality_resolution,[],[f874]) ).
fof(f874,plain,
! [X2,X0,X1] :
( sP14(X1,X0,X2)
| set_union2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f536]) ).
fof(f1389,plain,
spl77_70,
inference(avatar_split_clause,[],[f1029,f1387]) ).
fof(f1387,plain,
( spl77_70
<=> ! [X0,X1] : sP12(X1,X0,unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_70])]) ).
fof(f1029,plain,
! [X0,X1] : sP12(X1,X0,unordered_pair(X0,X1)),
inference(equality_resolution,[],[f858]) ).
fof(f858,plain,
! [X2,X0,X1] :
( sP12(X1,X0,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f524]) ).
fof(f1385,plain,
( spl77_69
| ~ spl77_11
| ~ spl77_52
| ~ spl77_54 ),
inference(avatar_split_clause,[],[f1324,f1307,f1293,f1097,f1383]) ).
fof(f1383,plain,
( spl77_69
<=> ! [X0] : ~ proper_subset(X0,sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_69])]) ).
fof(f1097,plain,
( spl77_11
<=> ! [X0] : subset(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_11])]) ).
fof(f1324,plain,
( ! [X0] : ~ proper_subset(X0,sK74)
| ~ spl77_11
| ~ spl77_52
| ~ spl77_54 ),
inference(forward_demodulation,[],[f1320,f1295]) ).
fof(f1320,plain,
( ! [X0] : ~ proper_subset(X0,empty_set)
| ~ spl77_11
| ~ spl77_54 ),
inference(resolution,[],[f1308,f1098]) ).
fof(f1098,plain,
( ! [X0] : subset(empty_set,X0)
| ~ spl77_11 ),
inference(avatar_component_clause,[],[f1097]) ).
fof(f1381,plain,
spl77_68,
inference(avatar_split_clause,[],[f1026,f1379]) ).
fof(f1379,plain,
( spl77_68
<=> ! [X0,X1] : sP11(X1,X0,cartesian_product2(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_68])]) ).
fof(f1026,plain,
! [X0,X1] : sP11(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f850]) ).
fof(f850,plain,
! [X2,X0,X1] :
( sP11(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f518]) ).
fof(f1377,plain,
spl77_67,
inference(avatar_split_clause,[],[f782,f1375]) ).
fof(f1375,plain,
( spl77_67
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_67])]) ).
fof(f782,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f117]) ).
fof(f117,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f1373,plain,
spl77_66,
inference(avatar_split_clause,[],[f781,f1371]) ).
fof(f1371,plain,
( spl77_66
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_66])]) ).
fof(f781,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f305]) ).
fof(f305,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f1369,plain,
spl77_65,
inference(avatar_split_clause,[],[f779,f1367]) ).
fof(f1367,plain,
( spl77_65
<=> ! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_65])]) ).
fof(f779,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f302]) ).
fof(f302,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f1365,plain,
spl77_64,
inference(avatar_split_clause,[],[f778,f1363]) ).
fof(f1363,plain,
( spl77_64
<=> ! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_64])]) ).
fof(f778,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
=> ~ proper_subset(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(f1361,plain,
spl77_63,
inference(avatar_split_clause,[],[f768,f1359]) ).
fof(f768,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0,X1] :
( relation(relation_dom_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_dom_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(f1357,plain,
spl77_62,
inference(avatar_split_clause,[],[f767,f1355]) ).
fof(f1355,plain,
( spl77_62
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_62])]) ).
fof(f767,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f298,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f1353,plain,
spl77_61,
inference(avatar_split_clause,[],[f766,f1351]) ).
fof(f766,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f297]) ).
fof(f297,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f1348,plain,
spl77_60,
inference(avatar_split_clause,[],[f763,f1346]) ).
fof(f763,plain,
! [X0,X1] :
( sP5(X1,X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f471]) ).
fof(f471,plain,
! [X0,X1] :
( ( ( ( set_meet(X0) = X1
| empty_set != X1 )
& ( empty_set = X1
| set_meet(X0) != X1 ) )
| empty_set != X0 )
& ( sP5(X1,X0)
| empty_set = X0 ) ),
inference(nnf_transformation,[],[f350]) ).
fof(f350,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( sP5(X1,X0)
| empty_set = X0 ) ),
inference(definition_folding,[],[f296,f349,f348]) ).
fof(f296,plain,
! [X0,X1] :
( ( ( set_meet(X0) = X1
<=> empty_set = X1 )
| empty_set != X0 )
& ( ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X2,X3)
| ~ in(X3,X0) ) ) )
| empty_set = X0 ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( ( empty_set = X0
=> ( set_meet(X0) = X1
<=> empty_set = X1 ) )
& ( empty_set != X0
=> ( set_meet(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ! [X3] :
( in(X3,X0)
=> in(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_setfam_1) ).
fof(f1344,plain,
spl77_59,
inference(avatar_split_clause,[],[f730,f1342]) ).
fof(f1342,plain,
( spl77_59
<=> ! [X0] :
( relation(X0)
| in(sK43(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_59])]) ).
fof(f730,plain,
! [X0] :
( relation(X0)
| in(sK43(X0),X0) ),
inference(cnf_transformation,[],[f449]) ).
fof(f1340,plain,
( spl77_58
| ~ spl77_20
| ~ spl77_51 ),
inference(avatar_split_clause,[],[f1297,f1266,f1135,f1338]) ).
fof(f1338,plain,
( spl77_58
<=> ! [X0] : ~ empty(sK20(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_58])]) ).
fof(f1135,plain,
( spl77_20
<=> ! [X0] : in(X0,sK20(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_20])]) ).
fof(f1297,plain,
( ! [X0] : ~ empty(sK20(X0))
| ~ spl77_20
| ~ spl77_51 ),
inference(resolution,[],[f1267,f1136]) ).
fof(f1136,plain,
( ! [X0] : in(X0,sK20(X0))
| ~ spl77_20 ),
inference(avatar_component_clause,[],[f1135]) ).
fof(f1329,plain,
( spl77_57
| ~ spl77_52
| ~ spl77_55 ),
inference(avatar_split_clause,[],[f1315,f1311,f1293,f1326]) ).
fof(f1326,plain,
( spl77_57
<=> powerset(sK74) = unordered_pair(sK74,sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_57])]) ).
fof(f1311,plain,
( spl77_55
<=> powerset(empty_set) = unordered_pair(empty_set,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_55])]) ).
fof(f1315,plain,
( powerset(sK74) = unordered_pair(sK74,sK74)
| ~ spl77_52
| ~ spl77_55 ),
inference(forward_demodulation,[],[f1313,f1295]) ).
fof(f1313,plain,
( powerset(empty_set) = unordered_pair(empty_set,empty_set)
| ~ spl77_55 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f1319,plain,
( spl77_56
| ~ spl77_52
| ~ spl77_53 ),
inference(avatar_split_clause,[],[f1305,f1301,f1293,f1317]) ).
fof(f1317,plain,
( spl77_56
<=> ! [X0] :
( ~ subset(X0,sK74)
| sK74 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_56])]) ).
fof(f1301,plain,
( spl77_53
<=> ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_53])]) ).
fof(f1305,plain,
( ! [X0] :
( ~ subset(X0,sK74)
| sK74 = X0 )
| ~ spl77_52
| ~ spl77_53 ),
inference(forward_demodulation,[],[f1304,f1295]) ).
fof(f1304,plain,
( ! [X0] :
( sK74 = X0
| ~ subset(X0,empty_set) )
| ~ spl77_52
| ~ spl77_53 ),
inference(forward_demodulation,[],[f1302,f1295]) ).
fof(f1302,plain,
( ! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) )
| ~ spl77_53 ),
inference(avatar_component_clause,[],[f1301]) ).
fof(f1314,plain,
spl77_55,
inference(avatar_split_clause,[],[f892,f1311]) ).
fof(f892,plain,
powerset(empty_set) = unordered_pair(empty_set,empty_set),
inference(definition_unfolding,[],[f553,f559]) ).
fof(f553,plain,
powerset(empty_set) = singleton(empty_set),
inference(cnf_transformation,[],[f119]) ).
fof(f119,axiom,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
fof(f1309,plain,
spl77_54,
inference(avatar_split_clause,[],[f630,f1307]) ).
fof(f630,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f244]) ).
fof(f244,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f163]) ).
fof(f163,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f1303,plain,
spl77_53,
inference(avatar_split_clause,[],[f577,f1301]) ).
fof(f577,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(ennf_transformation,[],[f142]) ).
fof(f142,axiom,
! [X0] :
( subset(X0,empty_set)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(f1296,plain,
( spl77_52
| ~ spl77_6
| ~ spl77_42 ),
inference(avatar_split_clause,[],[f1274,f1230,f1072,f1293]) ).
fof(f1268,plain,
spl77_51,
inference(avatar_split_clause,[],[f838,f1266]) ).
fof(f838,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f173]) ).
fof(f173,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f1264,plain,
spl77_50,
inference(avatar_split_clause,[],[f777,f1262]) ).
fof(f1262,plain,
( spl77_50
<=> ! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_50])]) ).
fof(f777,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ relation(X1) ),
inference(definition_folding,[],[f300,f352,f351]) ).
fof(f300,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> ( identity_relation(X0) = X1
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( X2 = X3
& in(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f1260,plain,
spl77_49,
inference(avatar_split_clause,[],[f746,f1258]) ).
fof(f1258,plain,
( spl77_49
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_49])]) ).
fof(f746,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f1256,plain,
spl77_48,
inference(avatar_split_clause,[],[f739,f1254]) ).
fof(f1254,plain,
( spl77_48
<=> ! [X0] : element(sK50(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_48])]) ).
fof(f739,plain,
! [X0] : element(sK50(X0),powerset(X0)),
inference(cnf_transformation,[],[f461]) ).
fof(f461,plain,
! [X0] :
( empty(sK50(X0))
& element(sK50(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f101,f460]) ).
fof(f460,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK50(X0))
& element(sK50(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f1252,plain,
spl77_47,
inference(avatar_split_clause,[],[f726,f1250]) ).
fof(f726,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f1248,plain,
spl77_46,
inference(avatar_split_clause,[],[f725,f1246]) ).
fof(f1246,plain,
( spl77_46
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_46])]) ).
fof(f725,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f1244,plain,
spl77_45,
inference(avatar_split_clause,[],[f724,f1242]) ).
fof(f724,plain,
! [X0] :
( relation(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( relation(relation_rng(X0))
& empty(relation_rng(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f77]) ).
fof(f77,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_rng(X0))
& empty(relation_rng(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(f1240,plain,
spl77_44,
inference(avatar_split_clause,[],[f723,f1238]) ).
fof(f1238,plain,
( spl77_44
<=> ! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_44])]) ).
fof(f723,plain,
! [X0] :
( empty(relation_rng(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f1236,plain,
( spl77_43
| ~ spl77_14
| ~ spl77_22 ),
inference(avatar_split_clause,[],[f1172,f1143,f1109,f1234]) ).
fof(f1234,plain,
( spl77_43
<=> ! [X0] : relation(sK50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_43])]) ).
fof(f1109,plain,
( spl77_14
<=> ! [X0] : empty(sK50(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_14])]) ).
fof(f1143,plain,
( spl77_22
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_22])]) ).
fof(f1172,plain,
( ! [X0] : relation(sK50(X0))
| ~ spl77_14
| ~ spl77_22 ),
inference(resolution,[],[f1144,f1110]) ).
fof(f1110,plain,
( ! [X0] : empty(sK50(X0))
| ~ spl77_14 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f1144,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl77_22 ),
inference(avatar_component_clause,[],[f1143]) ).
fof(f1232,plain,
spl77_42,
inference(avatar_split_clause,[],[f722,f1230]) ).
fof(f722,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f169]) ).
fof(f169,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f1228,plain,
spl77_41,
inference(avatar_split_clause,[],[f681,f1226]) ).
fof(f681,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0] :
( relation(relation_inverse(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( relation(X0)
=> relation(relation_inverse(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relat_1) ).
fof(f1224,plain,
spl77_40,
inference(avatar_split_clause,[],[f680,f1222]) ).
fof(f1222,plain,
( spl77_40
<=> ! [X0] :
( ~ empty(sK24(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_40])]) ).
fof(f680,plain,
! [X0] :
( ~ empty(sK24(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f405]) ).
fof(f1220,plain,
spl77_39,
inference(avatar_split_clause,[],[f677,f1218]) ).
fof(f677,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f139]) ).
fof(f139,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
fof(f1216,plain,
spl77_38,
inference(avatar_split_clause,[],[f676,f1214]) ).
fof(f1214,plain,
( spl77_38
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_38])]) ).
fof(f676,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f116]) ).
fof(f116,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(f1212,plain,
spl77_37,
inference(avatar_split_clause,[],[f675,f1210]) ).
fof(f1210,plain,
( spl77_37
<=> ! [X0] : empty_set = set_difference(empty_set,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_37])]) ).
fof(f675,plain,
! [X0] : empty_set = set_difference(empty_set,X0),
inference(cnf_transformation,[],[f155]) ).
fof(f155,axiom,
! [X0] : empty_set = set_difference(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(f1207,plain,
spl77_36,
inference(avatar_split_clause,[],[f1021,f1205]) ).
fof(f1205,plain,
( spl77_36
<=> ! [X3] : in(X3,unordered_pair(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_36])]) ).
fof(f1021,plain,
! [X3] : in(X3,unordered_pair(X3,X3)),
inference(equality_resolution,[],[f1020]) ).
fof(f1020,plain,
! [X3,X1] :
( in(X3,X1)
| unordered_pair(X3,X3) != X1 ),
inference(equality_resolution,[],[f986]) ).
fof(f986,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| unordered_pair(X0,X0) != X1 ),
inference(definition_unfolding,[],[f828,f559]) ).
fof(f828,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f506]) ).
fof(f1203,plain,
spl77_35,
inference(avatar_split_clause,[],[f893,f1201]) ).
fof(f1201,plain,
( spl77_35
<=> ! [X0] : empty_set != unordered_pair(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_35])]) ).
fof(f893,plain,
! [X0] : empty_set != unordered_pair(X0,X0),
inference(definition_unfolding,[],[f557,f559]) ).
fof(f557,plain,
! [X0] : empty_set != singleton(X0),
inference(cnf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] : empty_set != singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
fof(f1199,plain,
spl77_34,
inference(avatar_split_clause,[],[f583,f1197]) ).
fof(f583,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f132]) ).
fof(f132,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f1195,plain,
spl77_33,
inference(avatar_split_clause,[],[f581,f1193]) ).
fof(f581,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[],[f174]) ).
fof(f174,axiom,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
fof(f1191,plain,
spl77_32,
inference(avatar_split_clause,[],[f561,f1189]) ).
fof(f1189,plain,
( spl77_32
<=> ! [X0] : relation_rng(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_32])]) ).
fof(f561,plain,
! [X0] : relation_rng(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f171]) ).
fof(f171,axiom,
! [X0] :
( relation_rng(identity_relation(X0)) = X0
& relation_dom(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f1187,plain,
spl77_31,
inference(avatar_split_clause,[],[f560,f1185]) ).
fof(f1185,plain,
( spl77_31
<=> ! [X0] : relation_dom(identity_relation(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_31])]) ).
fof(f560,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f171]) ).
fof(f1183,plain,
spl77_30,
inference(avatar_split_clause,[],[f558,f1181]) ).
fof(f1181,plain,
( spl77_30
<=> ! [X0] : union(powerset(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl77_30])]) ).
fof(f558,plain,
! [X0] : union(powerset(X0)) = X0,
inference(cnf_transformation,[],[f186]) ).
fof(f186,axiom,
! [X0] : union(powerset(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_zfmisc_1) ).
fof(f1179,plain,
( spl77_29
| ~ spl77_6
| ~ spl77_22 ),
inference(avatar_split_clause,[],[f1173,f1143,f1072,f1176]) ).
fof(f1176,plain,
( spl77_29
<=> relation(sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_29])]) ).
fof(f1173,plain,
( relation(sK74)
| ~ spl77_6
| ~ spl77_22 ),
inference(resolution,[],[f1144,f1074]) ).
fof(f1170,plain,
spl77_28,
inference(avatar_split_clause,[],[f1036,f1168]) ).
fof(f1168,plain,
( spl77_28
<=> ! [X0] : element(X0,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_28])]) ).
fof(f1036,plain,
! [X0] : element(X0,powerset(X0)),
inference(forward_demodulation,[],[f678,f673]) ).
fof(f673,plain,
! [X0] : cast_to_subset(X0) = X0,
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] : cast_to_subset(X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_subset_1) ).
fof(f678,plain,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
inference(cnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] : element(cast_to_subset(X0),powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_subset_1) ).
fof(f1166,plain,
spl77_27,
inference(avatar_split_clause,[],[f1019,f1164]) ).
fof(f1164,plain,
( spl77_27
<=> ! [X0] : sP10(X0,union(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_27])]) ).
fof(f1019,plain,
! [X0] : sP10(X0,union(X0)),
inference(equality_resolution,[],[f825]) ).
fof(f825,plain,
! [X0,X1] :
( sP10(X0,X1)
| union(X0) != X1 ),
inference(cnf_transformation,[],[f502]) ).
fof(f1162,plain,
spl77_26,
inference(avatar_split_clause,[],[f1011,f1159]) ).
fof(f1159,plain,
( spl77_26
<=> empty_set = set_meet(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_26])]) ).
fof(f1011,plain,
empty_set = set_meet(empty_set),
inference(equality_resolution,[],[f1010]) ).
fof(f1010,plain,
! [X0] :
( empty_set = set_meet(X0)
| empty_set != X0 ),
inference(equality_resolution,[],[f765]) ).
fof(f765,plain,
! [X0,X1] :
( set_meet(X0) = X1
| empty_set != X1
| empty_set != X0 ),
inference(cnf_transformation,[],[f471]) ).
fof(f1157,plain,
spl77_25,
inference(avatar_split_clause,[],[f743,f1155]) ).
fof(f1155,plain,
( spl77_25
<=> ! [X0,X1] : ~ empty(unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_25])]) ).
fof(f743,plain,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0,X1] : ~ empty(unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_subset_1) ).
fof(f1153,plain,
spl77_24,
inference(avatar_split_clause,[],[f735,f1151]) ).
fof(f735,plain,
! [X0] : in(X0,sK48(X0)),
inference(cnf_transformation,[],[f459]) ).
fof(f1149,plain,
spl77_23,
inference(avatar_split_clause,[],[f734,f1147]) ).
fof(f1147,plain,
( spl77_23
<=> ! [X0] : element(sK47(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_23])]) ).
fof(f734,plain,
! [X0] : element(sK47(X0),X0),
inference(cnf_transformation,[],[f455]) ).
fof(f455,plain,
! [X0] : element(sK47(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f61,f454]) ).
fof(f454,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK47(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f61,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f1145,plain,
spl77_22,
inference(avatar_split_clause,[],[f721,f1143]) ).
fof(f721,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f1141,plain,
spl77_21,
inference(avatar_split_clause,[],[f673,f1139]) ).
fof(f1137,plain,
spl77_20,
inference(avatar_split_clause,[],[f578,f1135]) ).
fof(f578,plain,
! [X0] : in(X0,sK20(X0)),
inference(cnf_transformation,[],[f376]) ).
fof(f1133,plain,
spl77_19,
inference(avatar_split_clause,[],[f555,f1130]) ).
fof(f1130,plain,
( spl77_19
<=> empty_set = relation_rng(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_19])]) ).
fof(f555,plain,
empty_set = relation_rng(empty_set),
inference(cnf_transformation,[],[f162]) ).
fof(f162,axiom,
( empty_set = relation_rng(empty_set)
& empty_set = relation_dom(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_relat_1) ).
fof(f1128,plain,
spl77_18,
inference(avatar_split_clause,[],[f554,f1125]) ).
fof(f1125,plain,
( spl77_18
<=> empty_set = relation_dom(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_18])]) ).
fof(f554,plain,
empty_set = relation_dom(empty_set),
inference(cnf_transformation,[],[f162]) ).
fof(f1123,plain,
spl77_17,
inference(avatar_split_clause,[],[f1008,f1121]) ).
fof(f1008,plain,
! [X2] : ~ in(X2,empty_set),
inference(equality_resolution,[],[f732]) ).
fof(f732,plain,
! [X2,X0] :
( ~ in(X2,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f453]) ).
fof(f1119,plain,
spl77_16,
inference(avatar_split_clause,[],[f742,f1117]) ).
fof(f1117,plain,
( spl77_16
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_16])]) ).
fof(f742,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f1115,plain,
spl77_15,
inference(avatar_split_clause,[],[f741,f1113]) ).
fof(f1113,plain,
( spl77_15
<=> ! [X0] : ~ proper_subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_15])]) ).
fof(f741,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] : ~ proper_subset(X0,X0),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X0,X1] : ~ proper_subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(f1111,plain,
spl77_14,
inference(avatar_split_clause,[],[f740,f1109]) ).
fof(f740,plain,
! [X0] : empty(sK50(X0)),
inference(cnf_transformation,[],[f461]) ).
fof(f1107,plain,
spl77_13,
inference(avatar_split_clause,[],[f672,f1105]) ).
fof(f1105,plain,
( spl77_13
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_13])]) ).
fof(f672,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f1103,plain,
spl77_12,
inference(avatar_split_clause,[],[f671,f1101]) ).
fof(f1101,plain,
( spl77_12
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_12])]) ).
fof(f671,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f1099,plain,
spl77_11,
inference(avatar_split_clause,[],[f556,f1097]) ).
fof(f556,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[],[f128]) ).
fof(f128,axiom,
! [X0] : subset(empty_set,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(f1095,plain,
spl77_10,
inference(avatar_split_clause,[],[f890,f1092]) ).
fof(f1092,plain,
( spl77_10
<=> relation(sK76) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_10])]) ).
fof(f890,plain,
relation(sK76),
inference(cnf_transformation,[],[f550]) ).
fof(f550,plain,
( relation(sK76)
& empty(sK76) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f97,f549]) ).
fof(f549,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK76)
& empty(sK76) ) ),
introduced(choice_axiom,[]) ).
fof(f97,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f1090,plain,
spl77_9,
inference(avatar_split_clause,[],[f889,f1087]) ).
fof(f889,plain,
empty(sK76),
inference(cnf_transformation,[],[f550]) ).
fof(f1085,plain,
spl77_8,
inference(avatar_split_clause,[],[f888,f1082]) ).
fof(f1082,plain,
( spl77_8
<=> relation(sK75) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_8])]) ).
fof(f888,plain,
relation(sK75),
inference(cnf_transformation,[],[f548]) ).
fof(f548,plain,
( relation(sK75)
& ~ empty(sK75) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK75])],[f100,f547]) ).
fof(f547,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK75)
& ~ empty(sK75) ) ),
introduced(choice_axiom,[]) ).
fof(f100,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f1080,plain,
~ spl77_7,
inference(avatar_split_clause,[],[f887,f1077]) ).
fof(f1077,plain,
( spl77_7
<=> empty(sK75) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_7])]) ).
fof(f887,plain,
~ empty(sK75),
inference(cnf_transformation,[],[f548]) ).
fof(f1075,plain,
spl77_6,
inference(avatar_split_clause,[],[f886,f1072]) ).
fof(f886,plain,
empty(sK74),
inference(cnf_transformation,[],[f546]) ).
fof(f546,plain,
empty(sK74),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74])],[f99,f545]) ).
fof(f545,plain,
( ? [X0] : empty(X0)
=> empty(sK74) ),
introduced(choice_axiom,[]) ).
fof(f99,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f1070,plain,
~ spl77_5,
inference(avatar_split_clause,[],[f885,f1067]) ).
fof(f1067,plain,
( spl77_5
<=> empty(sK73) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_5])]) ).
fof(f885,plain,
~ empty(sK73),
inference(cnf_transformation,[],[f544]) ).
fof(f544,plain,
~ empty(sK73),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73])],[f102,f543]) ).
fof(f543,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK73) ),
introduced(choice_axiom,[]) ).
fof(f102,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f1065,plain,
spl77_4,
inference(avatar_split_clause,[],[f669,f1062]) ).
fof(f1062,plain,
( spl77_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_4])]) ).
fof(f669,plain,
relation(empty_set),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f1060,plain,
spl77_3,
inference(avatar_split_clause,[],[f667,f1057]) ).
fof(f1057,plain,
( spl77_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl77_3])]) ).
fof(f667,plain,
empty(empty_set),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f1055,plain,
~ spl77_2,
inference(avatar_split_clause,[],[f552,f1052]) ).
fof(f552,plain,
~ subset(relation_rng(relation_dom_restriction(sK17,sK16)),relation_rng(sK17)),
inference(cnf_transformation,[],[f370]) ).
fof(f370,plain,
( ~ subset(relation_rng(relation_dom_restriction(sK17,sK16)),relation_rng(sK17))
& relation(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f200,f369]) ).
fof(f369,plain,
( ? [X0,X1] :
( ~ subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
& relation(X1) )
=> ( ~ subset(relation_rng(relation_dom_restriction(sK17,sK16)),relation_rng(sK17))
& relation(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f200,plain,
? [X0,X1] :
( ~ subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f185]) ).
fof(f185,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
inference(negated_conjecture,[],[f184]) ).
fof(f184,conjecture,
! [X0,X1] :
( relation(X1)
=> subset(relation_rng(relation_dom_restriction(X1,X0)),relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t99_relat_1) ).
fof(f1050,plain,
spl77_1,
inference(avatar_split_clause,[],[f551,f1047]) ).
fof(f551,plain,
relation(sK17),
inference(cnf_transformation,[],[f370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU196+2 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 11:11:59 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (6629)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33 % (6632)WARNING: value z3 for option sas not known
% 0.15/0.33 % (6631)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33 % (6633)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.33 % (6632)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.33 % (6634)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.33 % (6630)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33 % (6636)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.33 % (6635)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)
% 0.15/0.35 TRYING [1]
% 0.15/0.36 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.44 TRYING [1]
% 0.15/0.45 TRYING [2]
% 0.15/0.48 % (6634)First to succeed.
% 0.15/0.51 % (6634)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6629"
% 0.15/0.51 % (6634)Refutation found. Thanks to Tanya!
% 0.15/0.51 % SZS status Theorem for theBenchmark
% 0.15/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.53 % (6634)------------------------------
% 0.15/0.53 % (6634)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.53 % (6634)Termination reason: Refutation
% 0.15/0.53
% 0.15/0.53 % (6634)Memory used [KB]: 4248
% 0.15/0.53 % (6634)Time elapsed: 0.184 s
% 0.15/0.53 % (6634)Instructions burned: 380 (million)
% 0.15/0.53 % (6629)Success in time 0.203 s
%------------------------------------------------------------------------------