TSTP Solution File: SET951+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:14:05 EDT 2024
% Result : Theorem 0.54s 0.57s
% Output : Refutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 21
% Syntax : Number of formulae : 630 ( 297 unt; 0 def)
% Number of atoms : 1358 ( 536 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 1343 ( 615 ~; 630 |; 79 &)
% ( 10 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 1447 (1406 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f925,plain,
$false,
inference(global_subsumption,[],[f69,f70,f43,f44,f48,f72,f73,f74,f41,f75,f45,f46,f77,f76,f58,f66,f47,f86,f89,f90,f91,f59,f92,f97,f98,f95,f99,f93,f100,f104,f60,f67,f68,f85,f115,f117,f118,f88,f119,f120,f124,f125,f114,f128,f130,f131,f132,f133,f134,f42,f49,f135,f139,f136,f50,f140,f144,f141,f61,f146,f71,f145,f153,f158,f152,f164,f165,f149,f166,f163,f112,f167,f168,f169,f170,f171,f172,f173,f174,f113,f176,f177,f178,f179,f180,f181,f182,f183,f184,f175,f187,f188,f191,f192,f197,f213,f215,f200,f201,f202,f207,f216,f218,f210,f211,f212,f53,f220,f221,f223,f225,f226,f228,f123,f241,f242,f235,f236,f237,f238,f129,f258,f260,f251,f252,f253,f254,f261,f262,f54,f264,f265,f267,f269,f270,f271,f272,f87,f290,f291,f275,f276,f277,f278,f279,f280,f281,f282,f283,f284,f285,f286,f287,f288,f289,f116,f312,f314,f296,f297,f298,f299,f300,f301,f302,f303,f304,f305,f306,f307,f308,f309,f310,f121,f315,f316,f317,f318,f319,f320,f321,f322,f323,f324,f325,f326,f327,f342,f343,f334,f335,f336,f337,f338,f339,f122,f346,f347,f348,f349,f350,f351,f352,f353,f354,f355,f356,f357,f374,f376,f364,f365,f366,f367,f368,f369,f370,f138,f378,f379,f380,f381,f384,f143,f387,f388,f389,f390,f393,f62,f396,f397,f398,f399,f401,f402,f403,f404,f405,f407,f408,f409,f410,f406,f137,f412,f413,f414,f415,f418,f142,f421,f422,f423,f424,f427,f377,f431,f63,f434,f435,f436,f437,f439,f440,f441,f442,f443,f445,f446,f447,f448,f444,f383,f449,f450,f451,f452,f453,f386,f460,f392,f462,f463,f464,f465,f466,f196,f471,f472,f491,f501,f206,f505,f506,f525,f535,f51,f411,f542,f417,f544,f545,f546,f547,f548,f420,f555,f426,f557,f558,f559,f560,f561,f430,f459,f64,f580,f587,f595,f588,f608,f541,f554,f219,f224,f55,f623,f624,f625,f626,f627,f263,f268,f395,f400,f433,f438,f539,f628,f631,f632,f633,f634,f635,f636,f637,f638,f639,f640,f641,f642,f643,f644,f645,f646,f647,f648,f649,f650,f651,f629,f654,f656,f657,f658,f671,f672,f673,f675,f676,f678,f670,f667,f652,f630,f681,f683,f684,f685,f698,f699,f700,f702,f703,f705,f692,f697,f694,f695,f696,f653,f56,f711,f712,f713,f715,f714,f716,f710,f717,f720,f721,f655,f723,f724,f727,f732,f733,f680,f222,f682,f745,f746,f668,f765,f775,f669,f796,f806,f227,f665,f814,f815,f818,f816,f820,f813,f823,f824,f826,f819,f828,f855,f829,f830,f831,f832,f833,f834,f856,f857,f858,f860,f861,f863,f841,f854,f843,f844,f845,f864,f865,f852,f866,f869,f870,f266,f853,f825,f878,f905,f879,f880,f881,f882,f883,f884,f906,f907,f908,f910,f911,f913,f891,f904,f893,f894,f895,f914,f915,f902,f916,f903,f923,f924]) ).
fof(f924,plain,
in(sK10(sK4,sK3,sK2),sK3),
inference(subsumption_resolution,[],[f921,f824]) ).
fof(f921,plain,
( in(sK10(sK4,sK3,sK2),sK3)
| ~ in(sK2,cartesian_product2(sK3,sK6)) ),
inference(superposition,[],[f135,f903]) ).
fof(f923,plain,
~ in(sK3,sK10(sK4,sK3,sK2)),
inference(subsumption_resolution,[],[f920,f824]) ).
fof(f920,plain,
( ~ in(sK3,sK10(sK4,sK3,sK2))
| ~ in(sK2,cartesian_product2(sK3,sK6)) ),
inference(superposition,[],[f136,f903]) ).
fof(f903,plain,
sK10(sK4,sK3,sK2) = sK10(sK6,sK3,sK2),
inference(trivial_inequality_removal,[],[f896]) ).
fof(f896,plain,
( sK2 != sK2
| sK10(sK4,sK3,sK2) = sK10(sK6,sK3,sK2) ),
inference(superposition,[],[f653,f825]) ).
fof(f916,plain,
sK2 = ordered_pair(sK10(sK6,sK3,sK2),sK11(sK4,sK3,sK2)),
inference(superposition,[],[f825,f902]) ).
fof(f902,plain,
sK11(sK4,sK3,sK2) = sK11(sK6,sK3,sK2),
inference(trivial_inequality_removal,[],[f897]) ).
fof(f897,plain,
( sK2 != sK2
| sK11(sK4,sK3,sK2) = sK11(sK6,sK3,sK2) ),
inference(superposition,[],[f655,f825]) ).
fof(f915,plain,
sK11(sK4,sK3,sK2) = sK11(sK6,sK3,sK2),
inference(forward_demodulation,[],[f900,f727]) ).
fof(f900,plain,
sK11(sK6,sK5,sK2) = sK11(sK6,sK3,sK2),
inference(trivial_inequality_removal,[],[f899]) ).
fof(f899,plain,
( sK2 != sK2
| sK11(sK6,sK5,sK2) = sK11(sK6,sK3,sK2) ),
inference(superposition,[],[f682,f825]) ).
fof(f914,plain,
sK10(sK4,sK3,sK2) = sK10(sK6,sK3,sK2),
inference(forward_demodulation,[],[f901,f710]) ).
fof(f901,plain,
sK10(sK6,sK5,sK2) = sK10(sK6,sK3,sK2),
inference(trivial_inequality_removal,[],[f898]) ).
fof(f898,plain,
( sK2 != sK2
| sK10(sK6,sK5,sK2) = sK10(sK6,sK3,sK2) ),
inference(superposition,[],[f680,f825]) ).
fof(f895,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK6,sK3,sK2) ),
inference(superposition,[],[f206,f825]) ).
fof(f894,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK6,sK3,sK2) ),
inference(superposition,[],[f196,f825]) ).
fof(f893,plain,
! [X0,X1] :
( ~ in(cartesian_product2(X0,X1),sK2)
| ~ in(sK11(sK6,sK3,sK2),X1)
| ~ in(sK10(sK6,sK3,sK2),X0) ),
inference(superposition,[],[f166,f825]) ).
fof(f904,plain,
( ~ in(sK11(sK6,sK3,sK2),sK4)
| ~ in(sK11(sK6,sK3,sK2),sK6)
| ~ in(sK10(sK6,sK3,sK2),sK3)
| ~ in(sK10(sK6,sK3,sK2),sK5) ),
inference(trivial_inequality_removal,[],[f892]) ).
fof(f892,plain,
( sK2 != sK2
| ~ in(sK11(sK6,sK3,sK2),sK4)
| ~ in(sK11(sK6,sK3,sK2),sK6)
| ~ in(sK10(sK6,sK3,sK2),sK3)
| ~ in(sK10(sK6,sK3,sK2),sK5) ),
inference(superposition,[],[f163,f825]) ).
fof(f891,plain,
! [X0,X1] :
( in(sK2,cartesian_product2(X0,X1))
| ~ in(sK10(sK6,sK3,sK2),X0)
| ~ in(sK11(sK6,sK3,sK2),X1) ),
inference(superposition,[],[f149,f825]) ).
fof(f913,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f912,f45]) ).
fof(f912,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))) = ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2))),
inference(forward_demodulation,[],[f890,f45]) ).
fof(f890,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2))) = unordered_pair(singleton(singleton(sK10(sK6,sK3,sK2))),sK2),
inference(superposition,[],[f129,f825]) ).
fof(f911,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f889,f45]) ).
fof(f889,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))) = unordered_pair(singleton(singleton(sK10(sK6,sK3,sK2))),sK2),
inference(superposition,[],[f123,f825]) ).
fof(f910,plain,
ordered_pair(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f909,f45]) ).
fof(f909,plain,
ordered_pair(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f888,f45]) ).
fof(f888,plain,
ordered_pair(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(singleton(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2))),sK2),
inference(superposition,[],[f122,f825]) ).
fof(f908,plain,
ordered_pair(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f887,f45]) ).
fof(f887,plain,
ordered_pair(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(singleton(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))),sK2),
inference(superposition,[],[f121,f825]) ).
fof(f907,plain,
ordered_pair(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f886,f45]) ).
fof(f886,plain,
ordered_pair(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2)))),
inference(superposition,[],[f116,f825]) ).
fof(f906,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))),
inference(forward_demodulation,[],[f885,f45]) ).
fof(f885,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))) = ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK11(sK6,sK3,sK2),sK10(sK6,sK3,sK2))),
inference(superposition,[],[f113,f825]) ).
fof(f884,plain,
ordered_pair(singleton(sK10(sK6,sK3,sK2)),unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK3,sK2)))),
inference(superposition,[],[f112,f825]) ).
fof(f883,plain,
ordered_pair(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),singleton(sK10(sK6,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)))),
inference(superposition,[],[f87,f825]) ).
fof(f882,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK6,sK3,sK2) = X1 ),
inference(superposition,[],[f68,f825]) ).
fof(f881,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK6,sK3,sK2) = X1 ),
inference(superposition,[],[f68,f825]) ).
fof(f880,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK6,sK3,sK2) = X0 ),
inference(superposition,[],[f67,f825]) ).
fof(f879,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK6,sK3,sK2) = X0 ),
inference(superposition,[],[f67,f825]) ).
fof(f905,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK6,sK3,sK2),X0)
| ~ in(sK10(sK6,sK3,sK2),X1)
| ~ in(sK2,X2) ),
inference(inner_rewriting,[],[f878]) ).
fof(f878,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK6,sK3,sK2),X0)
| ~ in(sK10(sK6,sK3,sK2),X1)
| ~ in(sK7(X0,X1,X2),X2) ),
inference(superposition,[],[f56,f825]) ).
fof(f825,plain,
sK2 = ordered_pair(sK10(sK6,sK3,sK2),sK11(sK6,sK3,sK2)),
inference(resolution,[],[f824,f539]) ).
fof(f853,plain,
sK10(sK4,sK3,sK2) = sK10(sK4,sK5,sK2),
inference(trivial_inequality_removal,[],[f846]) ).
fof(f846,plain,
( sK2 != sK2
| sK10(sK4,sK3,sK2) = sK10(sK4,sK5,sK2) ),
inference(superposition,[],[f653,f819]) ).
fof(f266,plain,
! [X2,X0,X1] :
( sK2 != ordered_pair(X2,sK9(set_intersection2(sK4,sK6),X0,X1))
| sP0(set_intersection2(sK4,sK6),X0,X1)
| ~ in(X2,set_intersection2(sK3,sK5))
| in(sK7(set_intersection2(sK4,sK6),X0,X1),X1) ),
inference(resolution,[],[f54,f42]) ).
fof(f870,plain,
in(sK11(sK4,sK3,sK2),sK4),
inference(subsumption_resolution,[],[f868,f816]) ).
fof(f868,plain,
( in(sK11(sK4,sK3,sK2),sK4)
| ~ in(sK2,cartesian_product2(sK5,sK4)) ),
inference(superposition,[],[f140,f852]) ).
fof(f869,plain,
~ in(sK4,sK11(sK4,sK3,sK2)),
inference(subsumption_resolution,[],[f867,f816]) ).
fof(f867,plain,
( ~ in(sK4,sK11(sK4,sK3,sK2))
| ~ in(sK2,cartesian_product2(sK5,sK4)) ),
inference(superposition,[],[f141,f852]) ).
fof(f866,plain,
sK2 = ordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK3,sK2)),
inference(superposition,[],[f819,f852]) ).
fof(f852,plain,
sK11(sK4,sK3,sK2) = sK11(sK4,sK5,sK2),
inference(trivial_inequality_removal,[],[f847]) ).
fof(f847,plain,
( sK2 != sK2
| sK11(sK4,sK3,sK2) = sK11(sK4,sK5,sK2) ),
inference(superposition,[],[f655,f819]) ).
fof(f865,plain,
sK11(sK4,sK3,sK2) = sK11(sK4,sK5,sK2),
inference(forward_demodulation,[],[f850,f727]) ).
fof(f850,plain,
sK11(sK6,sK5,sK2) = sK11(sK4,sK5,sK2),
inference(trivial_inequality_removal,[],[f849]) ).
fof(f849,plain,
( sK2 != sK2
| sK11(sK6,sK5,sK2) = sK11(sK4,sK5,sK2) ),
inference(superposition,[],[f682,f819]) ).
fof(f864,plain,
sK10(sK4,sK3,sK2) = sK10(sK4,sK5,sK2),
inference(forward_demodulation,[],[f851,f710]) ).
fof(f851,plain,
sK10(sK6,sK5,sK2) = sK10(sK4,sK5,sK2),
inference(trivial_inequality_removal,[],[f848]) ).
fof(f848,plain,
( sK2 != sK2
| sK10(sK6,sK5,sK2) = sK10(sK4,sK5,sK2) ),
inference(superposition,[],[f680,f819]) ).
fof(f845,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK4,sK5,sK2) ),
inference(superposition,[],[f206,f819]) ).
fof(f844,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK4,sK5,sK2) ),
inference(superposition,[],[f196,f819]) ).
fof(f843,plain,
! [X0,X1] :
( ~ in(cartesian_product2(X0,X1),sK2)
| ~ in(sK11(sK4,sK5,sK2),X1)
| ~ in(sK10(sK4,sK5,sK2),X0) ),
inference(superposition,[],[f166,f819]) ).
fof(f854,plain,
( ~ in(sK11(sK4,sK5,sK2),sK4)
| ~ in(sK11(sK4,sK5,sK2),sK6)
| ~ in(sK10(sK4,sK5,sK2),sK3)
| ~ in(sK10(sK4,sK5,sK2),sK5) ),
inference(trivial_inequality_removal,[],[f842]) ).
fof(f842,plain,
( sK2 != sK2
| ~ in(sK11(sK4,sK5,sK2),sK4)
| ~ in(sK11(sK4,sK5,sK2),sK6)
| ~ in(sK10(sK4,sK5,sK2),sK3)
| ~ in(sK10(sK4,sK5,sK2),sK5) ),
inference(superposition,[],[f163,f819]) ).
fof(f841,plain,
! [X0,X1] :
( in(sK2,cartesian_product2(X0,X1))
| ~ in(sK10(sK4,sK5,sK2),X0)
| ~ in(sK11(sK4,sK5,sK2),X1) ),
inference(superposition,[],[f149,f819]) ).
fof(f863,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f862,f45]) ).
fof(f862,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))) = ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2))),
inference(forward_demodulation,[],[f840,f45]) ).
fof(f840,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2))) = unordered_pair(singleton(singleton(sK10(sK4,sK5,sK2))),sK2),
inference(superposition,[],[f129,f819]) ).
fof(f861,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f839,f45]) ).
fof(f839,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))) = unordered_pair(singleton(singleton(sK10(sK4,sK5,sK2))),sK2),
inference(superposition,[],[f123,f819]) ).
fof(f860,plain,
ordered_pair(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f859,f45]) ).
fof(f859,plain,
ordered_pair(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f838,f45]) ).
fof(f838,plain,
ordered_pair(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(singleton(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2))),sK2),
inference(superposition,[],[f122,f819]) ).
fof(f858,plain,
ordered_pair(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f837,f45]) ).
fof(f837,plain,
ordered_pair(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(singleton(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))),sK2),
inference(superposition,[],[f121,f819]) ).
fof(f857,plain,
ordered_pair(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f836,f45]) ).
fof(f836,plain,
ordered_pair(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2)))),
inference(superposition,[],[f116,f819]) ).
fof(f856,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))),
inference(forward_demodulation,[],[f835,f45]) ).
fof(f835,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))) = ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK11(sK4,sK5,sK2),sK10(sK4,sK5,sK2))),
inference(superposition,[],[f113,f819]) ).
fof(f834,plain,
ordered_pair(singleton(sK10(sK4,sK5,sK2)),unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK5,sK2)))),
inference(superposition,[],[f112,f819]) ).
fof(f833,plain,
ordered_pair(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),singleton(sK10(sK4,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)))),
inference(superposition,[],[f87,f819]) ).
fof(f832,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK4,sK5,sK2) = X1 ),
inference(superposition,[],[f68,f819]) ).
fof(f831,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK4,sK5,sK2) = X1 ),
inference(superposition,[],[f68,f819]) ).
fof(f830,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK4,sK5,sK2) = X0 ),
inference(superposition,[],[f67,f819]) ).
fof(f829,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK4,sK5,sK2) = X0 ),
inference(superposition,[],[f67,f819]) ).
fof(f855,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK4,sK5,sK2),X0)
| ~ in(sK10(sK4,sK5,sK2),X1)
| ~ in(sK2,X2) ),
inference(inner_rewriting,[],[f828]) ).
fof(f828,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK4,sK5,sK2),X0)
| ~ in(sK10(sK4,sK5,sK2),X1)
| ~ in(sK7(X0,X1,X2),X2) ),
inference(superposition,[],[f56,f819]) ).
fof(f819,plain,
sK2 = ordered_pair(sK10(sK4,sK5,sK2),sK11(sK4,sK5,sK2)),
inference(resolution,[],[f816,f539]) ).
fof(f826,plain,
~ in(cartesian_product2(sK3,sK6),sK2),
inference(resolution,[],[f824,f48]) ).
fof(f824,plain,
in(sK2,cartesian_product2(sK3,sK6)),
inference(subsumption_resolution,[],[f822,f95]) ).
fof(f822,plain,
( in(sK2,cartesian_product2(sK3,sK6))
| ~ in(sK2,cartesian_product2(sK3,sK4)) ),
inference(resolution,[],[f813,f135]) ).
fof(f823,plain,
! [X0,X1] :
( in(sK2,cartesian_product2(set_intersection2(X0,X1),sK6))
| ~ in(sK10(sK4,sK3,sK2),X0)
| ~ in(sK10(sK4,sK3,sK2),X1) ),
inference(resolution,[],[f813,f145]) ).
fof(f813,plain,
! [X0] :
( ~ in(sK10(sK4,sK3,sK2),X0)
| in(sK2,cartesian_product2(X0,sK6)) ),
inference(resolution,[],[f665,f733]) ).
fof(f820,plain,
~ in(cartesian_product2(sK5,sK4),sK2),
inference(resolution,[],[f816,f48]) ).
fof(f816,plain,
in(sK2,cartesian_product2(sK5,sK4)),
inference(resolution,[],[f815,f721]) ).
fof(f818,plain,
! [X0,X1] :
( in(sK2,cartesian_product2(set_intersection2(X0,X1),sK4))
| ~ in(sK10(sK4,sK3,sK2),X0)
| ~ in(sK10(sK4,sK3,sK2),X1) ),
inference(resolution,[],[f815,f145]) ).
fof(f815,plain,
! [X0] :
( ~ in(sK10(sK4,sK3,sK2),X0)
| in(sK2,cartesian_product2(X0,sK4)) ),
inference(subsumption_resolution,[],[f812,f95]) ).
fof(f812,plain,
! [X0] :
( ~ in(sK10(sK4,sK3,sK2),X0)
| in(sK2,cartesian_product2(X0,sK4))
| ~ in(sK2,cartesian_product2(sK3,sK4)) ),
inference(resolution,[],[f665,f140]) ).
fof(f814,plain,
! [X2,X0,X1] :
( ~ in(sK10(sK4,sK3,sK2),X0)
| in(sK2,cartesian_product2(X0,set_intersection2(X1,X2)))
| ~ in(sK11(sK4,sK3,sK2),X1)
| ~ in(sK11(sK4,sK3,sK2),X2) ),
inference(resolution,[],[f665,f145]) ).
fof(f665,plain,
! [X0,X1] :
( ~ in(sK11(sK4,sK3,sK2),X1)
| ~ in(sK10(sK4,sK3,sK2),X0)
| in(sK2,cartesian_product2(X0,X1)) ),
inference(superposition,[],[f149,f629]) ).
fof(f227,plain,
! [X2,X0,X1] :
( sK2 != ordered_pair(X2,sK7(X0,X1,set_intersection2(sK4,sK6)))
| sP0(X0,X1,set_intersection2(sK4,sK6))
| ~ in(X2,set_intersection2(sK3,sK5))
| in(sK8(X0,X1,set_intersection2(sK4,sK6)),X1) ),
inference(resolution,[],[f53,f42]) ).
fof(f806,plain,
! [X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f789,f112]) ).
fof(f789,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f669,f129]) ).
fof(f796,plain,
! [X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f783,f123]) ).
fof(f783,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f669,f113]) ).
fof(f669,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f206,f629]) ).
fof(f775,plain,
! [X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f758,f112]) ).
fof(f758,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f668,f129]) ).
fof(f765,plain,
! [X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f752,f123]) ).
fof(f752,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f668,f113]) ).
fof(f668,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f196,f629]) ).
fof(f746,plain,
! [X0,X1] :
( unordered_pair(X1,X0) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1)) ),
inference(forward_demodulation,[],[f741,f727]) ).
fof(f741,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK6,sK5,sK2) ),
inference(superposition,[],[f682,f175]) ).
fof(f745,plain,
! [X0,X1] :
( unordered_pair(X0,X1) = sK11(sK4,sK3,sK2)
| sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0)) ),
inference(forward_demodulation,[],[f740,f727]) ).
fof(f740,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK6,sK5,sK2) ),
inference(superposition,[],[f682,f175]) ).
fof(f682,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK6,sK5,sK2) = X1 ),
inference(superposition,[],[f68,f630]) ).
fof(f222,plain,
! [X2,X0,X1] :
( sK2 != ordered_pair(X2,sK8(X0,set_intersection2(sK4,sK6),X1))
| sP0(X0,set_intersection2(sK4,sK6),X1)
| ~ in(X2,set_intersection2(sK3,sK5))
| in(sK7(X0,set_intersection2(sK4,sK6),X1),X1) ),
inference(resolution,[],[f53,f42]) ).
fof(f680,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK6,sK5,sK2) = X0 ),
inference(superposition,[],[f67,f630]) ).
fof(f733,plain,
in(sK11(sK4,sK3,sK2),sK6),
inference(subsumption_resolution,[],[f730,f100]) ).
fof(f730,plain,
( in(sK11(sK4,sK3,sK2),sK6)
| ~ in(sK2,cartesian_product2(sK5,sK6)) ),
inference(superposition,[],[f140,f727]) ).
fof(f732,plain,
~ in(sK6,sK11(sK4,sK3,sK2)),
inference(subsumption_resolution,[],[f729,f100]) ).
fof(f729,plain,
( ~ in(sK6,sK11(sK4,sK3,sK2))
| ~ in(sK2,cartesian_product2(sK5,sK6)) ),
inference(superposition,[],[f141,f727]) ).
fof(f727,plain,
sK11(sK4,sK3,sK2) = sK11(sK6,sK5,sK2),
inference(trivial_inequality_removal,[],[f726]) ).
fof(f726,plain,
( sK2 != sK2
| sK11(sK4,sK3,sK2) = sK11(sK6,sK5,sK2) ),
inference(superposition,[],[f655,f630]) ).
fof(f724,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f655,f175]) ).
fof(f723,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK4,sK3,sK2) ),
inference(superposition,[],[f655,f175]) ).
fof(f655,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK4,sK3,sK2) = X1 ),
inference(superposition,[],[f68,f629]) ).
fof(f721,plain,
in(sK10(sK4,sK3,sK2),sK5),
inference(subsumption_resolution,[],[f719,f100]) ).
fof(f719,plain,
( in(sK10(sK4,sK3,sK2),sK5)
| ~ in(sK2,cartesian_product2(sK5,sK6)) ),
inference(superposition,[],[f135,f710]) ).
fof(f720,plain,
~ in(sK5,sK10(sK4,sK3,sK2)),
inference(subsumption_resolution,[],[f718,f100]) ).
fof(f718,plain,
( ~ in(sK5,sK10(sK4,sK3,sK2))
| ~ in(sK2,cartesian_product2(sK5,sK6)) ),
inference(superposition,[],[f136,f710]) ).
fof(f717,plain,
sK2 = ordered_pair(sK10(sK4,sK3,sK2),sK11(sK6,sK5,sK2)),
inference(superposition,[],[f630,f710]) ).
fof(f710,plain,
sK10(sK4,sK3,sK2) = sK10(sK6,sK5,sK2),
inference(trivial_inequality_removal,[],[f709]) ).
fof(f709,plain,
( sK2 != sK2
| sK10(sK4,sK3,sK2) = sK10(sK6,sK5,sK2) ),
inference(superposition,[],[f653,f630]) ).
fof(f716,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK6,sK5,sK2),X0)
| ~ in(sK10(sK6,sK5,sK2),X1)
| ~ in(sK2,X2) ),
inference(inner_rewriting,[],[f714]) ).
fof(f714,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK6,sK5,sK2),X0)
| ~ in(sK10(sK6,sK5,sK2),X1)
| ~ in(sK7(X0,X1,X2),X2) ),
inference(superposition,[],[f56,f630]) ).
fof(f715,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK4,sK3,sK2),X0)
| ~ in(sK10(sK4,sK3,sK2),X1)
| ~ in(sK2,X2) ),
inference(inner_rewriting,[],[f713]) ).
fof(f713,plain,
! [X2,X0,X1] :
( sK2 != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(sK11(sK4,sK3,sK2),X0)
| ~ in(sK10(sK4,sK3,sK2),X1)
| ~ in(sK7(X0,X1,X2),X2) ),
inference(superposition,[],[f56,f629]) ).
fof(f712,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) != sK7(X2,X3,X4)
| sP0(X2,X3,X4)
| ~ in(unordered_pair(X1,X0),X2)
| ~ in(singleton(X0),X3)
| ~ in(sK7(X2,X3,X4),X4) ),
inference(superposition,[],[f56,f175]) ).
fof(f711,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(singleton(X0),unordered_pair(X1,X0)) != sK7(X2,X3,X4)
| sP0(X2,X3,X4)
| ~ in(unordered_pair(X0,X1),X2)
| ~ in(singleton(X0),X3)
| ~ in(sK7(X2,X3,X4),X4) ),
inference(superposition,[],[f56,f175]) ).
fof(f56,plain,
! [X2,X0,X1,X4,X5] :
( ordered_pair(X4,X5) != sK7(X0,X1,X2)
| sP0(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1)
| ~ in(sK7(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK7(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK7(X0,X1,X2),X2) )
& ( ( sK7(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2))
& in(sK9(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X1) )
| in(sK7(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK10(X0,X1,X8),sK11(X0,X1,X8)) = X8
& in(sK11(X0,X1,X8),X0)
& in(sK10(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f25,f28,f27,f26]) ).
fof(f26,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) != sK7(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK7(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK7(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK7(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK7(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK7(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2))
& in(sK9(X0,X1,X2),X0)
& in(sK8(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK10(X0,X1,X8),sK11(X0,X1,X8)) = X8
& in(sK11(X0,X1,X8),X0)
& in(sK10(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( sP0(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) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0,X2] :
( ( sP0(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) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X1,X0,X2] :
( sP0(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,[sP0])]) ).
fof(f653,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK4,sK3,sK2) = X0 ),
inference(superposition,[],[f67,f629]) ).
fof(f696,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = sK11(sK6,sK5,sK2) ),
inference(superposition,[],[f206,f630]) ).
fof(f695,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = sK11(sK6,sK5,sK2) ),
inference(superposition,[],[f196,f630]) ).
fof(f694,plain,
! [X0,X1] :
( ~ in(cartesian_product2(X0,X1),sK2)
| ~ in(sK11(sK6,sK5,sK2),X1)
| ~ in(sK10(sK6,sK5,sK2),X0) ),
inference(superposition,[],[f166,f630]) ).
fof(f697,plain,
( ~ in(sK11(sK6,sK5,sK2),sK4)
| ~ in(sK11(sK6,sK5,sK2),sK6)
| ~ in(sK10(sK6,sK5,sK2),sK3)
| ~ in(sK10(sK6,sK5,sK2),sK5) ),
inference(trivial_inequality_removal,[],[f693]) ).
fof(f693,plain,
( sK2 != sK2
| ~ in(sK11(sK6,sK5,sK2),sK4)
| ~ in(sK11(sK6,sK5,sK2),sK6)
| ~ in(sK10(sK6,sK5,sK2),sK3)
| ~ in(sK10(sK6,sK5,sK2),sK5) ),
inference(superposition,[],[f163,f630]) ).
fof(f692,plain,
! [X0,X1] :
( in(sK2,cartesian_product2(X0,X1))
| ~ in(sK10(sK6,sK5,sK2),X0)
| ~ in(sK11(sK6,sK5,sK2),X1) ),
inference(superposition,[],[f149,f630]) ).
fof(f705,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f704,f45]) ).
fof(f704,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))) = ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2))),
inference(forward_demodulation,[],[f691,f45]) ).
fof(f691,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2))) = unordered_pair(singleton(singleton(sK10(sK6,sK5,sK2))),sK2),
inference(superposition,[],[f129,f630]) ).
fof(f703,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f690,f45]) ).
fof(f690,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))) = unordered_pair(singleton(singleton(sK10(sK6,sK5,sK2))),sK2),
inference(superposition,[],[f123,f630]) ).
fof(f702,plain,
ordered_pair(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f701,f45]) ).
fof(f701,plain,
ordered_pair(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f689,f45]) ).
fof(f689,plain,
ordered_pair(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(singleton(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2))),sK2),
inference(superposition,[],[f122,f630]) ).
fof(f700,plain,
ordered_pair(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f688,f45]) ).
fof(f688,plain,
ordered_pair(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(singleton(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))),sK2),
inference(superposition,[],[f121,f630]) ).
fof(f699,plain,
ordered_pair(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f687,f45]) ).
fof(f687,plain,
ordered_pair(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2)))),
inference(superposition,[],[f116,f630]) ).
fof(f698,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))),
inference(forward_demodulation,[],[f686,f45]) ).
fof(f686,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))) = ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK11(sK6,sK5,sK2),sK10(sK6,sK5,sK2))),
inference(superposition,[],[f113,f630]) ).
fof(f685,plain,
ordered_pair(singleton(sK10(sK6,sK5,sK2)),unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK6,sK5,sK2)))),
inference(superposition,[],[f112,f630]) ).
fof(f684,plain,
ordered_pair(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),singleton(sK10(sK6,sK5,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)))),
inference(superposition,[],[f87,f630]) ).
fof(f683,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK6,sK5,sK2) = X1 ),
inference(superposition,[],[f68,f630]) ).
fof(f681,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK6,sK5,sK2) = X0 ),
inference(superposition,[],[f67,f630]) ).
fof(f630,plain,
sK2 = ordered_pair(sK10(sK6,sK5,sK2),sK11(sK6,sK5,sK2)),
inference(resolution,[],[f539,f100]) ).
fof(f652,plain,
~ empty(sK2),
inference(superposition,[],[f43,f629]) ).
fof(f667,plain,
! [X0,X1] :
( ~ in(cartesian_product2(X0,X1),sK2)
| ~ in(sK11(sK4,sK3,sK2),X1)
| ~ in(sK10(sK4,sK3,sK2),X0) ),
inference(superposition,[],[f166,f629]) ).
fof(f670,plain,
( ~ in(sK11(sK4,sK3,sK2),sK4)
| ~ in(sK11(sK4,sK3,sK2),sK6)
| ~ in(sK10(sK4,sK3,sK2),sK3)
| ~ in(sK10(sK4,sK3,sK2),sK5) ),
inference(trivial_inequality_removal,[],[f666]) ).
fof(f666,plain,
( sK2 != sK2
| ~ in(sK11(sK4,sK3,sK2),sK4)
| ~ in(sK11(sK4,sK3,sK2),sK6)
| ~ in(sK10(sK4,sK3,sK2),sK3)
| ~ in(sK10(sK4,sK3,sK2),sK5) ),
inference(superposition,[],[f163,f629]) ).
fof(f678,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f677,f45]) ).
fof(f677,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))) = ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2))),
inference(forward_demodulation,[],[f664,f45]) ).
fof(f664,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2))) = unordered_pair(singleton(singleton(sK10(sK4,sK3,sK2))),sK2),
inference(superposition,[],[f129,f629]) ).
fof(f676,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f663,f45]) ).
fof(f663,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))) = unordered_pair(singleton(singleton(sK10(sK4,sK3,sK2))),sK2),
inference(superposition,[],[f123,f629]) ).
fof(f675,plain,
ordered_pair(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f674,f45]) ).
fof(f674,plain,
ordered_pair(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f662,f45]) ).
fof(f662,plain,
ordered_pair(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(singleton(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2))),sK2),
inference(superposition,[],[f122,f629]) ).
fof(f673,plain,
ordered_pair(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f661,f45]) ).
fof(f661,plain,
ordered_pair(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(singleton(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))),sK2),
inference(superposition,[],[f121,f629]) ).
fof(f672,plain,
ordered_pair(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f660,f45]) ).
fof(f660,plain,
ordered_pair(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2)))),
inference(superposition,[],[f116,f629]) ).
fof(f671,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))),
inference(forward_demodulation,[],[f659,f45]) ).
fof(f659,plain,
unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))) = ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK11(sK4,sK3,sK2),sK10(sK4,sK3,sK2))),
inference(superposition,[],[f113,f629]) ).
fof(f658,plain,
ordered_pair(singleton(sK10(sK4,sK3,sK2)),unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(singleton(sK10(sK4,sK3,sK2)))),
inference(superposition,[],[f112,f629]) ).
fof(f657,plain,
ordered_pair(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),singleton(sK10(sK4,sK3,sK2))) = unordered_pair(sK2,singleton(unordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)))),
inference(superposition,[],[f87,f629]) ).
fof(f656,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK11(sK4,sK3,sK2) = X1 ),
inference(superposition,[],[f68,f629]) ).
fof(f654,plain,
! [X0,X1] :
( ordered_pair(X0,X1) != sK2
| sK10(sK4,sK3,sK2) = X0 ),
inference(superposition,[],[f67,f629]) ).
fof(f629,plain,
sK2 = ordered_pair(sK10(sK4,sK3,sK2),sK11(sK4,sK3,sK2)),
inference(resolution,[],[f539,f95]) ).
fof(f651,plain,
! [X2,X0,X1] :
( sK12(cartesian_product2(X1,X0),X2,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK12(cartesian_product2(X1,X0),X2,cartesian_product2(X1,X0))),sK11(X0,X1,sK12(cartesian_product2(X1,X0),X2,cartesian_product2(X1,X0))))
| sP1(cartesian_product2(X1,X0),X2,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f443]) ).
fof(f650,plain,
! [X2,X0,X1] :
( sK12(X2,cartesian_product2(X1,X0),cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK12(X2,cartesian_product2(X1,X0),cartesian_product2(X1,X0))),sK11(X0,X1,sK12(X2,cartesian_product2(X1,X0),cartesian_product2(X1,X0))))
| sP1(X2,cartesian_product2(X1,X0),cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f405]) ).
fof(f649,plain,
! [X2,X3,X0,X1] :
( sK12(cartesian_product2(X1,X0),X2,X3) = ordered_pair(sK10(X0,X1,sK12(cartesian_product2(X1,X0),X2,X3)),sK11(X0,X1,sK12(cartesian_product2(X1,X0),X2,X3)))
| in(sK12(cartesian_product2(X1,X0),X2,X3),X3)
| sP1(cartesian_product2(X1,X0),X2,X3) ),
inference(resolution,[],[f539,f63]) ).
fof(f648,plain,
! [X2,X3,X0,X1] :
( sK12(X2,cartesian_product2(X1,X0),X3) = ordered_pair(sK10(X0,X1,sK12(X2,cartesian_product2(X1,X0),X3)),sK11(X0,X1,sK12(X2,cartesian_product2(X1,X0),X3)))
| in(sK12(X2,cartesian_product2(X1,X0),X3),X3)
| sP1(X2,cartesian_product2(X1,X0),X3) ),
inference(resolution,[],[f539,f62]) ).
fof(f647,plain,
! [X2,X3,X0,X1] :
( sK12(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK12(X2,X3,cartesian_product2(X1,X0))),sK11(X0,X1,sK12(X2,X3,cartesian_product2(X1,X0))))
| in(sK12(X2,X3,cartesian_product2(X1,X0)),X3)
| sP1(X2,X3,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f62]) ).
fof(f646,plain,
! [X2,X3,X0,X1] :
( sK12(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK12(X2,X3,cartesian_product2(X1,X0))),sK11(X0,X1,sK12(X2,X3,cartesian_product2(X1,X0))))
| in(sK12(X2,X3,cartesian_product2(X1,X0)),X2)
| sP1(X2,X3,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f63]) ).
fof(f645,plain,
! [X2,X3,X0,X1,X4] :
( sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4) = ordered_pair(sK10(X0,X1,sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4)),sK11(X0,X1,sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4)))
| ~ in(X4,cartesian_product2(X3,set_intersection2(X2,cartesian_product2(X1,X0)))) ),
inference(resolution,[],[f539,f142]) ).
fof(f644,plain,
! [X2,X3,X0,X1,X4] :
( sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4) = ordered_pair(sK10(X0,X1,sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4)),sK11(X0,X1,sK11(set_intersection2(X2,cartesian_product2(X1,X0)),X3,X4)))
| ~ in(X4,cartesian_product2(X3,set_intersection2(cartesian_product2(X1,X0),X2))) ),
inference(resolution,[],[f539,f392]) ).
fof(f643,plain,
! [X2,X3,X0,X1,X4] :
( sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4) = ordered_pair(sK10(X0,X1,sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4)),sK11(X0,X1,sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4)))
| ~ in(X4,cartesian_product2(X3,set_intersection2(cartesian_product2(X1,X0),X2))) ),
inference(resolution,[],[f539,f143]) ).
fof(f642,plain,
! [X2,X3,X0,X1,X4] :
( sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4) = ordered_pair(sK10(X0,X1,sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4)),sK11(X0,X1,sK11(set_intersection2(cartesian_product2(X1,X0),X2),X3,X4)))
| ~ in(X4,cartesian_product2(X3,set_intersection2(X2,cartesian_product2(X1,X0)))) ),
inference(resolution,[],[f539,f426]) ).
fof(f641,plain,
! [X2,X3,X0,X1] :
( sK11(cartesian_product2(X1,X0),X2,X3) = ordered_pair(sK10(X0,X1,sK11(cartesian_product2(X1,X0),X2,X3)),sK11(X0,X1,sK11(cartesian_product2(X1,X0),X2,X3)))
| ~ in(X3,cartesian_product2(X2,cartesian_product2(X1,X0))) ),
inference(resolution,[],[f539,f140]) ).
fof(f640,plain,
! [X2,X3,X0,X1,X4] :
( sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4) = ordered_pair(sK10(X0,X1,sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4)),sK11(X0,X1,sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4)))
| ~ in(X4,cartesian_product2(set_intersection2(X3,cartesian_product2(X1,X0)),X2)) ),
inference(resolution,[],[f539,f137]) ).
fof(f639,plain,
! [X2,X3,X0,X1,X4] :
( sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4) = ordered_pair(sK10(X0,X1,sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4)),sK11(X0,X1,sK10(X2,set_intersection2(X3,cartesian_product2(X1,X0)),X4)))
| ~ in(X4,cartesian_product2(set_intersection2(cartesian_product2(X1,X0),X3),X2)) ),
inference(resolution,[],[f539,f383]) ).
fof(f638,plain,
! [X2,X3,X0,X1,X4] :
( sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4) = ordered_pair(sK10(X0,X1,sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4)),sK11(X0,X1,sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4)))
| ~ in(X4,cartesian_product2(set_intersection2(cartesian_product2(X1,X0),X3),X2)) ),
inference(resolution,[],[f539,f138]) ).
fof(f637,plain,
! [X2,X3,X0,X1,X4] :
( sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4) = ordered_pair(sK10(X0,X1,sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4)),sK11(X0,X1,sK10(X2,set_intersection2(cartesian_product2(X1,X0),X3),X4)))
| ~ in(X4,cartesian_product2(set_intersection2(X3,cartesian_product2(X1,X0)),X2)) ),
inference(resolution,[],[f539,f417]) ).
fof(f636,plain,
! [X2,X3,X0,X1] :
( sK10(X2,cartesian_product2(X1,X0),X3) = ordered_pair(sK10(X0,X1,sK10(X2,cartesian_product2(X1,X0),X3)),sK11(X0,X1,sK10(X2,cartesian_product2(X1,X0),X3)))
| ~ in(X3,cartesian_product2(cartesian_product2(X1,X0),X2)) ),
inference(resolution,[],[f539,f135]) ).
fof(f635,plain,
! [X2,X3,X0,X1] :
( sK9(cartesian_product2(X1,X0),X2,X3) = ordered_pair(sK10(X0,X1,sK9(cartesian_product2(X1,X0),X2,X3)),sK11(X0,X1,sK9(cartesian_product2(X1,X0),X2,X3)))
| in(sK7(cartesian_product2(X1,X0),X2,X3),X3)
| sP0(cartesian_product2(X1,X0),X2,X3) ),
inference(resolution,[],[f539,f54]) ).
fof(f634,plain,
! [X2,X3,X0,X1] :
( sK8(X2,cartesian_product2(X1,X0),X3) = ordered_pair(sK10(X0,X1,sK8(X2,cartesian_product2(X1,X0),X3)),sK11(X0,X1,sK8(X2,cartesian_product2(X1,X0),X3)))
| in(sK7(X2,cartesian_product2(X1,X0),X3),X3)
| sP0(X2,cartesian_product2(X1,X0),X3) ),
inference(resolution,[],[f539,f53]) ).
fof(f633,plain,
! [X2,X3,X0,X1] :
( sK7(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))),sK11(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))))
| in(sK8(X2,X3,cartesian_product2(X1,X0)),X3)
| sP0(X2,X3,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f53]) ).
fof(f632,plain,
! [X2,X3,X0,X1] :
( sK7(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))),sK11(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))))
| in(sK9(X2,X3,cartesian_product2(X1,X0)),X2)
| sP0(X2,X3,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f54]) ).
fof(f631,plain,
! [X2,X3,X0,X1] :
( sK7(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK10(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))),sK11(X0,X1,sK7(X2,X3,cartesian_product2(X1,X0))))
| sK7(X2,X3,cartesian_product2(X1,X0)) = ordered_pair(sK8(X2,X3,cartesian_product2(X1,X0)),sK9(X2,X3,cartesian_product2(X1,X0)))
| sP0(X2,X3,cartesian_product2(X1,X0)) ),
inference(resolution,[],[f539,f55]) ).
fof(f628,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) = ordered_pair(sK10(X0,X1,ordered_pair(X2,X3)),sK11(X0,X1,ordered_pair(X2,X3)))
| ~ in(X2,X1)
| ~ in(X3,X0) ),
inference(resolution,[],[f539,f149]) ).
fof(f539,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| ordered_pair(sK10(X2,X1,X0),sK11(X2,X1,X0)) = X0 ),
inference(resolution,[],[f51,f72]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ in(X0,sK12(X0,X1,X2))
| sP1(X0,X1,X2)
| in(sK12(X0,X1,X2),X2) ),
inference(resolution,[],[f63,f48]) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ in(X2,sK12(X0,X1,X2))
| sP1(X0,X1,X2)
| in(sK12(X0,X1,X2),X0) ),
inference(resolution,[],[f63,f48]) ).
fof(f400,plain,
! [X2,X0,X1] :
( ~ in(X1,sK12(X0,X1,X2))
| sP1(X0,X1,X2)
| in(sK12(X0,X1,X2),X2) ),
inference(resolution,[],[f62,f48]) ).
fof(f395,plain,
! [X2,X0,X1] :
( ~ in(X2,sK12(X0,X1,X2))
| sP1(X0,X1,X2)
| in(sK12(X0,X1,X2),X1) ),
inference(resolution,[],[f62,f48]) ).
fof(f268,plain,
! [X2,X0,X1] :
( ~ in(X2,sK7(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK9(X0,X1,X2),X0) ),
inference(resolution,[],[f54,f48]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ in(X0,sK9(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK7(X0,X1,X2),X2) ),
inference(resolution,[],[f54,f48]) ).
fof(f627,plain,
! [X2,X0,X1] :
( sK7(X0,X1,set_intersection2(sK3,sK5)) = ordered_pair(sK8(X0,X1,set_intersection2(sK3,sK5)),sK9(X0,X1,set_intersection2(sK3,sK5)))
| sP0(X0,X1,set_intersection2(sK3,sK5))
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK7(X0,X1,set_intersection2(sK3,sK5)),X2) ),
inference(resolution,[],[f55,f152]) ).
fof(f626,plain,
! [X2,X0,X1] :
( sK7(X0,X1,set_intersection2(sK4,sK6)) = ordered_pair(sK8(X0,X1,set_intersection2(sK4,sK6)),sK9(X0,X1,set_intersection2(sK4,sK6)))
| sP0(X0,X1,set_intersection2(sK4,sK6))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK7(X0,X1,set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f55,f42]) ).
fof(f625,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,set_intersection2(X2,X3)) = ordered_pair(sK8(X0,X1,set_intersection2(X2,X3)),sK9(X0,X1,set_intersection2(X2,X3)))
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X2) ),
inference(resolution,[],[f55,f92]) ).
fof(f624,plain,
! [X2,X3,X0,X1] :
( sK7(X0,X1,set_intersection2(X2,X3)) = ordered_pair(sK8(X0,X1,set_intersection2(X2,X3)),sK9(X0,X1,set_intersection2(X2,X3)))
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f55,f93]) ).
fof(f623,plain,
! [X2,X0,X1] :
( sK7(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2))
| sP0(X0,X1,X2)
| ~ in(X2,sK7(X0,X1,X2)) ),
inference(resolution,[],[f55,f48]) ).
fof(f55,plain,
! [X2,X0,X1] :
( in(sK7(X0,X1,X2),X2)
| sK7(X0,X1,X2) = ordered_pair(sK8(X0,X1,X2),sK9(X0,X1,X2))
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f224,plain,
! [X2,X0,X1] :
( ~ in(X2,sK7(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK8(X0,X1,X2),X1) ),
inference(resolution,[],[f53,f48]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ~ in(X1,sK8(X0,X1,X2))
| sP0(X0,X1,X2)
| in(sK7(X0,X1,X2),X2) ),
inference(resolution,[],[f53,f48]) ).
fof(f554,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,sK11(set_intersection2(X1,X0),X2,X3))
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f420,f46]) ).
fof(f541,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,sK10(X2,set_intersection2(X1,X0),X3))
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f411,f46]) ).
fof(f608,plain,
! [X2,X0,X1] :
( sP1(X0,set_intersection2(X1,X2),X0)
| ~ in(sK12(X0,set_intersection2(X1,X2),X0),X1)
| ~ in(sK12(X0,set_intersection2(X1,X2),X0),X2) ),
inference(resolution,[],[f588,f145]) ).
fof(f588,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X0),X1)
| sP1(X0,X1,X0) ),
inference(subsumption_resolution,[],[f581,f63]) ).
fof(f581,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X0),X0)
| ~ in(sK12(X0,X1,X0),X1)
| sP1(X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f579]) ).
fof(f579,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X0),X0)
| ~ in(sK12(X0,X1,X0),X1)
| sP1(X0,X1,X0)
| sP1(X0,X1,X0) ),
inference(resolution,[],[f64,f443]) ).
fof(f595,plain,
! [X2,X0,X1] :
( sP1(set_intersection2(X0,X1),X2,X2)
| ~ in(sK12(set_intersection2(X0,X1),X2,X2),X0)
| ~ in(sK12(set_intersection2(X0,X1),X2,X2),X1) ),
inference(resolution,[],[f587,f145]) ).
fof(f587,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X1),X0)
| sP1(X0,X1,X1) ),
inference(subsumption_resolution,[],[f582,f62]) ).
fof(f582,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X1),X0)
| ~ in(sK12(X0,X1,X1),X1)
| sP1(X0,X1,X1) ),
inference(duplicate_literal_removal,[],[f578]) ).
fof(f578,plain,
! [X0,X1] :
( ~ in(sK12(X0,X1,X1),X0)
| ~ in(sK12(X0,X1,X1),X1)
| sP1(X0,X1,X1)
| sP1(X0,X1,X1) ),
inference(resolution,[],[f64,f405]) ).
fof(f580,plain,
! [X2,X3,X0,X1] :
( ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X0)
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| sP1(X0,X1,set_intersection2(X2,X3))
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X2)
| ~ in(sK12(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f64,f145]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ in(sK12(X0,X1,X2),X2)
| ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ( sP1(X0,X1,X2)
| ( ( ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) )
& ( ( in(sK12(X0,X1,X2),X0)
& in(sK12(X0,X1,X2),X1) )
| in(sK12(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f33,f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) )
=> ( ( ~ in(sK12(X0,X1,X2),X0)
| ~ in(sK12(X0,X1,X2),X1)
| ~ in(sK12(X0,X1,X2),X2) )
& ( ( in(sK12(X0,X1,X2),X0)
& in(sK12(X0,X1,X2),X1) )
| in(sK12(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( sP1(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) ) )
| ~ sP1(X0,X1,X2) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X1,X0,X2] :
( ( sP1(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) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X1,X0,X2] :
( ( sP1(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) ) )
| ~ sP1(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( sP1(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f459,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK11(set_intersection2(X1,X0),X2,X3))
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f386,f46]) ).
fof(f430,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK10(X2,set_intersection2(X1,X0),X3))
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f377,f46]) ).
fof(f561,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(sK3,sK5))))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK11(set_intersection2(set_intersection2(sK3,sK5),X2),X1,X0),X3) ),
inference(resolution,[],[f426,f152]) ).
fof(f560,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(sK4,sK6))))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK11(set_intersection2(set_intersection2(sK4,sK6),X2),X1,X0)) ),
inference(resolution,[],[f426,f42]) ).
fof(f559,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(X3,X4))))
| in(sK11(set_intersection2(set_intersection2(X3,X4),X2),X1,X0),X3) ),
inference(resolution,[],[f426,f92]) ).
fof(f558,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(X3,X4))))
| in(sK11(set_intersection2(set_intersection2(X3,X4),X2),X1,X0),X4) ),
inference(resolution,[],[f426,f93]) ).
fof(f557,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3)))
| ~ in(X3,sK11(set_intersection2(X3,X2),X1,X0)) ),
inference(resolution,[],[f426,f48]) ).
fof(f426,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X1,X0),X2,X3),X1)
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f142,f46]) ).
fof(f555,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,sK11(set_intersection2(X1,X0),X2,X3))
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f420,f46]) ).
fof(f420,plain,
! [X2,X3,X0,X1] :
( ~ in(X3,sK11(set_intersection2(X2,X3),X1,X0))
| ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3))) ),
inference(resolution,[],[f142,f48]) ).
fof(f548,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(sK3,sK5)),X2))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK10(X2,set_intersection2(set_intersection2(sK3,sK5),X1),X0),X3) ),
inference(resolution,[],[f417,f152]) ).
fof(f547,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(sK4,sK6)),X2))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK10(X2,set_intersection2(set_intersection2(sK4,sK6),X1),X0)) ),
inference(resolution,[],[f417,f42]) ).
fof(f546,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(X2,X3)),X4))
| in(sK10(X4,set_intersection2(set_intersection2(X2,X3),X1),X0),X2) ),
inference(resolution,[],[f417,f92]) ).
fof(f545,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(X2,X3)),X4))
| in(sK10(X4,set_intersection2(set_intersection2(X2,X3),X1),X0),X3) ),
inference(resolution,[],[f417,f93]) ).
fof(f544,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3))
| ~ in(X2,sK10(X3,set_intersection2(X2,X1),X0)) ),
inference(resolution,[],[f417,f48]) ).
fof(f417,plain,
! [X2,X3,X0,X1] :
( in(sK10(X2,set_intersection2(X1,X0),X3),X1)
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f137,f46]) ).
fof(f542,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,sK10(X2,set_intersection2(X1,X0),X3))
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f411,f46]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( ~ in(X2,sK10(X3,set_intersection2(X1,X2),X0))
| ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3)) ),
inference(resolution,[],[f137,f48]) ).
fof(f51,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| ordered_pair(sK10(X0,X1,X8),sK11(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f29]) ).
fof(f535,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = X3
| ordered_pair(X2,X3) != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f517,f112]) ).
fof(f517,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = X3 ),
inference(superposition,[],[f206,f129]) ).
fof(f525,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = X3
| ordered_pair(X2,X3) != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f511,f123]) ).
fof(f511,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = X3 ),
inference(superposition,[],[f206,f113]) ).
fof(f506,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) != ordered_pair(singleton(X2),unordered_pair(X2,X3))
| unordered_pair(X1,X0) = unordered_pair(X3,X2) ),
inference(superposition,[],[f206,f175]) ).
fof(f505,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X1,X0)) != ordered_pair(singleton(X2),unordered_pair(X2,X3))
| unordered_pair(X0,X1) = unordered_pair(X3,X2) ),
inference(superposition,[],[f206,f175]) ).
fof(f206,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = X3 ),
inference(superposition,[],[f68,f175]) ).
fof(f501,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = X3
| ordered_pair(X2,X3) != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f483,f112]) ).
fof(f483,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = X3 ),
inference(superposition,[],[f196,f129]) ).
fof(f491,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) = X3
| ordered_pair(X2,X3) != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
inference(forward_demodulation,[],[f477,f123]) ).
fof(f477,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = X3 ),
inference(superposition,[],[f196,f113]) ).
fof(f472,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X0,X1)) != ordered_pair(singleton(X2),unordered_pair(X3,X2))
| unordered_pair(X1,X0) = unordered_pair(X2,X3) ),
inference(superposition,[],[f196,f175]) ).
fof(f471,plain,
! [X2,X3,X0,X1] :
( ordered_pair(singleton(X0),unordered_pair(X1,X0)) != ordered_pair(singleton(X2),unordered_pair(X3,X2))
| unordered_pair(X0,X1) = unordered_pair(X2,X3) ),
inference(superposition,[],[f196,f175]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = X3 ),
inference(superposition,[],[f68,f175]) ).
fof(f466,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(sK3,sK5),X2)))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK11(set_intersection2(X2,set_intersection2(sK3,sK5)),X1,X0),X3) ),
inference(resolution,[],[f392,f152]) ).
fof(f465,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(sK4,sK6),X2)))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK11(set_intersection2(X2,set_intersection2(sK4,sK6)),X1,X0)) ),
inference(resolution,[],[f392,f42]) ).
fof(f464,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(X2,X3),X4)))
| in(sK11(set_intersection2(X4,set_intersection2(X2,X3)),X1,X0),X2) ),
inference(resolution,[],[f392,f92]) ).
fof(f463,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(X2,X3),X4)))
| in(sK11(set_intersection2(X4,set_intersection2(X2,X3)),X1,X0),X3) ),
inference(resolution,[],[f392,f93]) ).
fof(f462,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3)))
| ~ in(X2,sK11(set_intersection2(X3,X2),X1,X0)) ),
inference(resolution,[],[f392,f48]) ).
fof(f392,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f143,f46]) ).
fof(f460,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK11(set_intersection2(X1,X0),X2,X3))
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f386,f46]) ).
fof(f386,plain,
! [X2,X3,X0,X1] :
( ~ in(X2,sK11(set_intersection2(X2,X3),X1,X0))
| ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3))) ),
inference(resolution,[],[f143,f48]) ).
fof(f453,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(sK3,sK5),X1),X2))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK10(X2,set_intersection2(X1,set_intersection2(sK3,sK5)),X0),X3) ),
inference(resolution,[],[f383,f152]) ).
fof(f452,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(sK4,sK6),X1),X2))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK10(X2,set_intersection2(X1,set_intersection2(sK4,sK6)),X0)) ),
inference(resolution,[],[f383,f42]) ).
fof(f451,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(X1,X2),X3),X4))
| in(sK10(X4,set_intersection2(X3,set_intersection2(X1,X2)),X0),X1) ),
inference(resolution,[],[f383,f92]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(X1,X2),X3),X4))
| in(sK10(X4,set_intersection2(X3,set_intersection2(X1,X2)),X0),X2) ),
inference(resolution,[],[f383,f93]) ).
fof(f449,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3))
| ~ in(X1,sK10(X3,set_intersection2(X2,X1),X0)) ),
inference(resolution,[],[f383,f48]) ).
fof(f383,plain,
! [X2,X3,X0,X1] :
( in(sK10(X2,set_intersection2(X1,X0),X3),X0)
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f138,f46]) ).
fof(f444,plain,
! [X0,X1] :
( ~ in(X0,sK12(X0,X1,X0))
| sP1(X0,X1,X0) ),
inference(resolution,[],[f443,f48]) ).
fof(f448,plain,
! [X0,X1] :
( sP1(set_intersection2(sK3,sK5),X0,set_intersection2(sK3,sK5))
| ~ in(X1,sK6)
| ~ in(X1,sK4)
| sK2 != ordered_pair(sK12(set_intersection2(sK3,sK5),X0,set_intersection2(sK3,sK5)),X1) ),
inference(resolution,[],[f443,f152]) ).
fof(f447,plain,
! [X0,X1] :
( sP1(set_intersection2(sK4,sK6),X0,set_intersection2(sK4,sK6))
| ~ in(X1,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X1,sK12(set_intersection2(sK4,sK6),X0,set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f443,f42]) ).
fof(f446,plain,
! [X2,X0,X1] :
( sP1(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK12(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X0) ),
inference(resolution,[],[f443,f92]) ).
fof(f445,plain,
! [X2,X0,X1] :
( sP1(set_intersection2(X0,X1),X2,set_intersection2(X0,X1))
| in(sK12(set_intersection2(X0,X1),X2,set_intersection2(X0,X1)),X1) ),
inference(resolution,[],[f443,f93]) ).
fof(f443,plain,
! [X0,X1] :
( in(sK12(X0,X1,X0),X0)
| sP1(X0,X1,X0) ),
inference(factoring,[],[f63]) ).
fof(f442,plain,
! [X2,X0,X1] :
( in(sK12(set_intersection2(sK3,sK5),X0,X1),X1)
| sP1(set_intersection2(sK3,sK5),X0,X1)
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK12(set_intersection2(sK3,sK5),X0,X1),X2) ),
inference(resolution,[],[f63,f152]) ).
fof(f441,plain,
! [X2,X0,X1] :
( in(sK12(set_intersection2(sK4,sK6),X0,X1),X1)
| sP1(set_intersection2(sK4,sK6),X0,X1)
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK12(set_intersection2(sK4,sK6),X0,X1)) ),
inference(resolution,[],[f63,f42]) ).
fof(f440,plain,
! [X2,X3,X0,X1] :
( in(sK12(set_intersection2(X0,X1),X2,X3),X3)
| sP1(set_intersection2(X0,X1),X2,X3)
| in(sK12(set_intersection2(X0,X1),X2,X3),X0) ),
inference(resolution,[],[f63,f92]) ).
fof(f439,plain,
! [X2,X3,X0,X1] :
( in(sK12(set_intersection2(X0,X1),X2,X3),X3)
| sP1(set_intersection2(X0,X1),X2,X3)
| in(sK12(set_intersection2(X0,X1),X2,X3),X1) ),
inference(resolution,[],[f63,f93]) ).
fof(f437,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,set_intersection2(sK3,sK5)),X0)
| sP1(X0,X1,set_intersection2(sK3,sK5))
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK12(X0,X1,set_intersection2(sK3,sK5)),X2) ),
inference(resolution,[],[f63,f152]) ).
fof(f436,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,set_intersection2(sK4,sK6)),X0)
| sP1(X0,X1,set_intersection2(sK4,sK6))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK12(X0,X1,set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f63,f42]) ).
fof(f435,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X0)
| sP1(X0,X1,set_intersection2(X2,X3))
| in(sK12(X0,X1,set_intersection2(X2,X3)),X2) ),
inference(resolution,[],[f63,f92]) ).
fof(f434,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X0)
| sP1(X0,X1,set_intersection2(X2,X3))
| in(sK12(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f63,f93]) ).
fof(f63,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X0)
| sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f431,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,sK10(X2,set_intersection2(X1,X0),X3))
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f377,f46]) ).
fof(f377,plain,
! [X2,X3,X0,X1] :
( ~ in(X1,sK10(X3,set_intersection2(X1,X2),X0))
| ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3)) ),
inference(resolution,[],[f138,f48]) ).
fof(f427,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X1,X0),X2,X3),X1)
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f142,f46]) ).
fof(f424,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(sK3,sK5))))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK11(set_intersection2(X2,set_intersection2(sK3,sK5)),X1,X0),X3) ),
inference(resolution,[],[f142,f152]) ).
fof(f423,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(sK4,sK6))))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK11(set_intersection2(X2,set_intersection2(sK4,sK6)),X1,X0)) ),
inference(resolution,[],[f142,f42]) ).
fof(f422,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(X3,X4))))
| in(sK11(set_intersection2(X2,set_intersection2(X3,X4)),X1,X0),X3) ),
inference(resolution,[],[f142,f92]) ).
fof(f421,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(X2,set_intersection2(X3,X4))))
| in(sK11(set_intersection2(X2,set_intersection2(X3,X4)),X1,X0),X4) ),
inference(resolution,[],[f142,f93]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X2,X3),X1,X0),X3)
| ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3))) ),
inference(resolution,[],[f140,f93]) ).
fof(f418,plain,
! [X2,X3,X0,X1] :
( in(sK10(X2,set_intersection2(X1,X0),X3),X1)
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f137,f46]) ).
fof(f415,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(sK3,sK5)),X2))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK10(X2,set_intersection2(X1,set_intersection2(sK3,sK5)),X0),X3) ),
inference(resolution,[],[f137,f152]) ).
fof(f414,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(sK4,sK6)),X2))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK10(X2,set_intersection2(X1,set_intersection2(sK4,sK6)),X0)) ),
inference(resolution,[],[f137,f42]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(X2,X3)),X4))
| in(sK10(X4,set_intersection2(X1,set_intersection2(X2,X3)),X0),X2) ),
inference(resolution,[],[f137,f92]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(X1,set_intersection2(X2,X3)),X4))
| in(sK10(X4,set_intersection2(X1,set_intersection2(X2,X3)),X0),X3) ),
inference(resolution,[],[f137,f93]) ).
fof(f137,plain,
! [X2,X3,X0,X1] :
( in(sK10(X3,set_intersection2(X1,X2),X0),X2)
| ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3)) ),
inference(resolution,[],[f135,f93]) ).
fof(f406,plain,
! [X0,X1] :
( ~ in(X1,sK12(X0,X1,X1))
| sP1(X0,X1,X1) ),
inference(resolution,[],[f405,f48]) ).
fof(f410,plain,
! [X0,X1] :
( sP1(X0,set_intersection2(sK3,sK5),set_intersection2(sK3,sK5))
| ~ in(X1,sK6)
| ~ in(X1,sK4)
| sK2 != ordered_pair(sK12(X0,set_intersection2(sK3,sK5),set_intersection2(sK3,sK5)),X1) ),
inference(resolution,[],[f405,f152]) ).
fof(f409,plain,
! [X0,X1] :
( sP1(X0,set_intersection2(sK4,sK6),set_intersection2(sK4,sK6))
| ~ in(X1,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X1,sK12(X0,set_intersection2(sK4,sK6),set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f405,f42]) ).
fof(f408,plain,
! [X2,X0,X1] :
( sP1(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X1) ),
inference(resolution,[],[f405,f92]) ).
fof(f407,plain,
! [X2,X0,X1] :
( sP1(X0,set_intersection2(X1,X2),set_intersection2(X1,X2))
| in(sK12(X0,set_intersection2(X1,X2),set_intersection2(X1,X2)),X2) ),
inference(resolution,[],[f405,f93]) ).
fof(f405,plain,
! [X0,X1] :
( in(sK12(X0,X1,X1),X1)
| sP1(X0,X1,X1) ),
inference(factoring,[],[f62]) ).
fof(f404,plain,
! [X2,X0,X1] :
( in(sK12(X0,set_intersection2(sK3,sK5),X1),X1)
| sP1(X0,set_intersection2(sK3,sK5),X1)
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK12(X0,set_intersection2(sK3,sK5),X1),X2) ),
inference(resolution,[],[f62,f152]) ).
fof(f403,plain,
! [X2,X0,X1] :
( in(sK12(X0,set_intersection2(sK4,sK6),X1),X1)
| sP1(X0,set_intersection2(sK4,sK6),X1)
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK12(X0,set_intersection2(sK4,sK6),X1)) ),
inference(resolution,[],[f62,f42]) ).
fof(f402,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X3)
| sP1(X0,set_intersection2(X1,X2),X3)
| in(sK12(X0,set_intersection2(X1,X2),X3),X1) ),
inference(resolution,[],[f62,f92]) ).
fof(f401,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,set_intersection2(X1,X2),X3),X3)
| sP1(X0,set_intersection2(X1,X2),X3)
| in(sK12(X0,set_intersection2(X1,X2),X3),X2) ),
inference(resolution,[],[f62,f93]) ).
fof(f399,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,set_intersection2(sK3,sK5)),X1)
| sP1(X0,X1,set_intersection2(sK3,sK5))
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK12(X0,X1,set_intersection2(sK3,sK5)),X2) ),
inference(resolution,[],[f62,f152]) ).
fof(f398,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,set_intersection2(sK4,sK6)),X1)
| sP1(X0,X1,set_intersection2(sK4,sK6))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK12(X0,X1,set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f62,f42]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| sP1(X0,X1,set_intersection2(X2,X3))
| in(sK12(X0,X1,set_intersection2(X2,X3)),X2) ),
inference(resolution,[],[f62,f92]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( in(sK12(X0,X1,set_intersection2(X2,X3)),X1)
| sP1(X0,X1,set_intersection2(X2,X3))
| in(sK12(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f62,f93]) ).
fof(f62,plain,
! [X2,X0,X1] :
( in(sK12(X0,X1,X2),X2)
| in(sK12(X0,X1,X2),X1)
| sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f393,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X1,X0),X2,X3),X0)
| ~ in(X3,cartesian_product2(X2,set_intersection2(X0,X1))) ),
inference(superposition,[],[f143,f46]) ).
fof(f390,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(sK3,sK5),X2)))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK11(set_intersection2(set_intersection2(sK3,sK5),X2),X1,X0),X3) ),
inference(resolution,[],[f143,f152]) ).
fof(f389,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(sK4,sK6),X2)))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK11(set_intersection2(set_intersection2(sK4,sK6),X2),X1,X0)) ),
inference(resolution,[],[f143,f42]) ).
fof(f388,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(X2,X3),X4)))
| in(sK11(set_intersection2(set_intersection2(X2,X3),X4),X1,X0),X2) ),
inference(resolution,[],[f143,f92]) ).
fof(f387,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(set_intersection2(X2,X3),X4)))
| in(sK11(set_intersection2(set_intersection2(X2,X3),X4),X1,X0),X3) ),
inference(resolution,[],[f143,f93]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( in(sK11(set_intersection2(X2,X3),X1,X0),X2)
| ~ in(X0,cartesian_product2(X1,set_intersection2(X2,X3))) ),
inference(resolution,[],[f140,f92]) ).
fof(f384,plain,
! [X2,X3,X0,X1] :
( in(sK10(X2,set_intersection2(X1,X0),X3),X0)
| ~ in(X3,cartesian_product2(set_intersection2(X0,X1),X2)) ),
inference(superposition,[],[f138,f46]) ).
fof(f381,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(sK3,sK5),X1),X2))
| ~ in(X3,sK6)
| ~ in(X3,sK4)
| sK2 != ordered_pair(sK10(X2,set_intersection2(set_intersection2(sK3,sK5),X1),X0),X3) ),
inference(resolution,[],[f138,f152]) ).
fof(f380,plain,
! [X2,X3,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(sK4,sK6),X1),X2))
| ~ in(X3,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X3,sK10(X2,set_intersection2(set_intersection2(sK4,sK6),X1),X0)) ),
inference(resolution,[],[f138,f42]) ).
fof(f379,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(X1,X2),X3),X4))
| in(sK10(X4,set_intersection2(set_intersection2(X1,X2),X3),X0),X1) ),
inference(resolution,[],[f138,f92]) ).
fof(f378,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X0,cartesian_product2(set_intersection2(set_intersection2(X1,X2),X3),X4))
| in(sK10(X4,set_intersection2(set_intersection2(X1,X2),X3),X0),X2) ),
inference(resolution,[],[f138,f93]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( in(sK10(X3,set_intersection2(X1,X2),X0),X1)
| ~ in(X0,cartesian_product2(set_intersection2(X1,X2),X3)) ),
inference(resolution,[],[f135,f92]) ).
fof(f370,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X1))),ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0))),
inference(superposition,[],[f121,f122]) ).
fof(f369,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(ordered_pair(X1,X0))) = unordered_pair(ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X1)))),
inference(superposition,[],[f116,f122]) ).
fof(f368,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X1,X0)),ordered_pair(unordered_pair(X0,X1),singleton(X1))),
inference(superposition,[],[f114,f122]) ).
fof(f367,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)) = unordered_pair(singleton(singleton(unordered_pair(X0,X1))),ordered_pair(unordered_pair(X0,X1),singleton(X1))),
inference(superposition,[],[f88,f122]) ).
fof(f366,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X1)))),
inference(superposition,[],[f87,f122]) ).
fof(f365,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(ordered_pair(X1,X0))),
inference(superposition,[],[f85,f122]) ).
fof(f364,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f47,f122]) ).
fof(f376,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f375,f114]) ).
fof(f375,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f359,f45]) ).
fof(f359,plain,
! [X0,X1] : ordered_pair(unordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(unordered_pair(X1,X0),singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f122,f175]) ).
fof(f374,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f373,f88]) ).
fof(f373,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f358,f45]) ).
fof(f358,plain,
! [X0,X1] : ordered_pair(unordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(unordered_pair(X0,X1),singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f122,f175]) ).
fof(f357,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(ordered_pair(X1,X0))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X1))),ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f122,f122]) ).
fof(f356,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0))),ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f122,f121]) ).
fof(f355,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))),
inference(superposition,[],[f122,f123]) ).
fof(f354,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))),
inference(superposition,[],[f122,f129]) ).
fof(f353,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X1,X0),singleton(X0))),
inference(superposition,[],[f122,f114]) ).
fof(f352,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f122,f88]) ).
fof(f351,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(singleton(unordered_pair(X1,X0)))) = unordered_pair(singleton(ordered_pair(unordered_pair(X1,X0),singleton(X0))),ordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1))),
inference(superposition,[],[f122,f116]) ).
fof(f350,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0))),ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1))),
inference(superposition,[],[f122,f87]) ).
fof(f349,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))),
inference(superposition,[],[f122,f112]) ).
fof(f348,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))),
inference(superposition,[],[f122,f113]) ).
fof(f347,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))) = unordered_pair(singleton(ordered_pair(X1,X0)),ordered_pair(singleton(X1),unordered_pair(X0,X1))),
inference(superposition,[],[f122,f85]) ).
fof(f346,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f122,f47]) ).
fof(f122,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f88,f85]) ).
fof(f339,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0)))),
inference(superposition,[],[f116,f121]) ).
fof(f338,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f114,f121]) ).
fof(f337,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(unordered_pair(X0,X1))),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f88,f121]) ).
fof(f336,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0)))),
inference(superposition,[],[f87,f121]) ).
fof(f335,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f85,f121]) ).
fof(f334,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f47,f121]) ).
fof(f343,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f329,f114]) ).
fof(f329,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f121,f175]) ).
fof(f342,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f328,f88]) ).
fof(f328,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(X0))) = unordered_pair(singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f121,f175]) ).
fof(f327,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0))),ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1))),
inference(superposition,[],[f121,f121]) ).
fof(f326,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))),
inference(superposition,[],[f121,f123]) ).
fof(f325,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))),
inference(superposition,[],[f121,f129]) ).
fof(f324,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f121,f114]) ).
fof(f323,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f121,f88]) ).
fof(f322,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(unordered_pair(X1,X0),singleton(X0))),ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0)))),
inference(superposition,[],[f121,f116]) ).
fof(f321,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0))),ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f121,f87]) ).
fof(f320,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1))),ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))),
inference(superposition,[],[f121,f112]) ).
fof(f319,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0))),ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))),
inference(superposition,[],[f121,f113]) ).
fof(f318,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X1,X0)),ordered_pair(unordered_pair(X0,X1),singleton(X1))),
inference(superposition,[],[f121,f85]) ).
fof(f317,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f121,f47]) ).
fof(f316,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f121,f45]) ).
fof(f315,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f121,f45]) ).
fof(f121,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f88,f47]) ).
fof(f310,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(unordered_pair(X1,X0))),ordered_pair(unordered_pair(X1,X0),singleton(X0))),
inference(superposition,[],[f114,f116]) ).
fof(f309,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X1,X0),singleton(X0))),
inference(superposition,[],[f88,f116]) ).
fof(f308,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),singleton(ordered_pair(unordered_pair(X1,X0),singleton(X0)))),
inference(superposition,[],[f87,f116]) ).
fof(f307,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(singleton(unordered_pair(X1,X0)))),
inference(superposition,[],[f85,f116]) ).
fof(f306,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))) = unordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f47,f116]) ).
fof(f305,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(superposition,[],[f116,f123]) ).
fof(f304,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(superposition,[],[f116,f129]) ).
fof(f303,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))) = unordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f116,f114]) ).
fof(f302,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f116,f88]) ).
fof(f301,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(singleton(unordered_pair(X1,X0)))) = unordered_pair(ordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),singleton(ordered_pair(unordered_pair(X1,X0),singleton(X0)))),
inference(superposition,[],[f116,f116]) ).
fof(f300,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))) = unordered_pair(ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0)))),
inference(superposition,[],[f116,f87]) ).
fof(f299,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = unordered_pair(ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(superposition,[],[f116,f112]) ).
fof(f298,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))) = unordered_pair(ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(superposition,[],[f116,f113]) ).
fof(f297,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))) = unordered_pair(ordered_pair(singleton(X1),unordered_pair(X0,X1)),singleton(ordered_pair(X1,X0))),
inference(superposition,[],[f116,f85]) ).
fof(f296,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f116,f47]) ).
fof(f314,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(forward_demodulation,[],[f313,f114]) ).
fof(f313,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(forward_demodulation,[],[f293,f45]) ).
fof(f293,plain,
! [X0,X1] : ordered_pair(unordered_pair(unordered_pair(X1,X0),singleton(X0)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(unordered_pair(unordered_pair(X1,X0),singleton(X0)))),
inference(superposition,[],[f116,f175]) ).
fof(f312,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))),
inference(forward_demodulation,[],[f311,f88]) ).
fof(f311,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(forward_demodulation,[],[f292,f45]) ).
fof(f292,plain,
! [X0,X1] : ordered_pair(unordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(unordered_pair(unordered_pair(X0,X1),singleton(X0)))),
inference(superposition,[],[f116,f175]) ).
fof(f116,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X1)) = unordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f47,f85]) ).
fof(f289,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(unordered_pair(X0,X1))),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f114,f87]) ).
fof(f288,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f88,f87]) ).
fof(f287,plain,
! [X0,X1] : ordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(singleton(unordered_pair(X0,X1)))),
inference(superposition,[],[f85,f87]) ).
fof(f286,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f47,f87]) ).
fof(f285,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = unordered_pair(ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(superposition,[],[f87,f123]) ).
fof(f284,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))) = unordered_pair(ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(superposition,[],[f87,f129]) ).
fof(f283,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f87,f114]) ).
fof(f282,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f87,f88]) ).
fof(f281,plain,
! [X0,X1] : ordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),singleton(ordered_pair(unordered_pair(X0,X1),singleton(X0)))),
inference(superposition,[],[f87,f87]) ).
fof(f280,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),singleton(ordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(superposition,[],[f87,f112]) ).
fof(f279,plain,
! [X0,X1] : ordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))) = unordered_pair(ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),singleton(ordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(superposition,[],[f87,f113]) ).
fof(f278,plain,
! [X0,X1] : ordered_pair(ordered_pair(X1,X0),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X1)),singleton(ordered_pair(X1,X0))),
inference(superposition,[],[f87,f85]) ).
fof(f277,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))) = unordered_pair(ordered_pair(unordered_pair(X0,X1),singleton(X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f87,f47]) ).
fof(f276,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f87,f45]) ).
fof(f275,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f87,f45]) ).
fof(f291,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(forward_demodulation,[],[f274,f114]) ).
fof(f274,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(unordered_pair(singleton(X0),unordered_pair(X1,X0)))),
inference(superposition,[],[f87,f175]) ).
fof(f290,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))),
inference(forward_demodulation,[],[f273,f88]) ).
fof(f273,plain,
! [X0,X1] : ordered_pair(unordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(unordered_pair(singleton(X0),unordered_pair(X0,X1)))),
inference(superposition,[],[f87,f175]) ).
fof(f87,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f47,f47]) ).
fof(f272,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,set_intersection2(sK3,sK5)),X0)
| sP0(X0,X1,set_intersection2(sK3,sK5))
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK7(X0,X1,set_intersection2(sK3,sK5)),X2) ),
inference(resolution,[],[f54,f152]) ).
fof(f271,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,set_intersection2(sK4,sK6)),X0)
| sP0(X0,X1,set_intersection2(sK4,sK6))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK7(X0,X1,set_intersection2(sK4,sK6))) ),
inference(resolution,[],[f54,f42]) ).
fof(f270,plain,
! [X2,X3,X0,X1] :
( in(sK9(X0,X1,set_intersection2(X2,X3)),X0)
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X2) ),
inference(resolution,[],[f54,f92]) ).
fof(f269,plain,
! [X2,X3,X0,X1] :
( in(sK9(X0,X1,set_intersection2(X2,X3)),X0)
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f54,f93]) ).
fof(f267,plain,
! [X2,X0,X1] :
( in(sK7(set_intersection2(sK3,sK5),X0,X1),X1)
| sP0(set_intersection2(sK3,sK5),X0,X1)
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK9(set_intersection2(sK3,sK5),X0,X1),X2) ),
inference(resolution,[],[f54,f152]) ).
fof(f265,plain,
! [X2,X3,X0,X1] :
( in(sK7(set_intersection2(X0,X1),X2,X3),X3)
| sP0(set_intersection2(X0,X1),X2,X3)
| in(sK9(set_intersection2(X0,X1),X2,X3),X0) ),
inference(resolution,[],[f54,f92]) ).
fof(f264,plain,
! [X2,X3,X0,X1] :
( in(sK7(set_intersection2(X0,X1),X2,X3),X3)
| sP0(set_intersection2(X0,X1),X2,X3)
| in(sK9(set_intersection2(X0,X1),X2,X3),X1) ),
inference(resolution,[],[f54,f93]) ).
fof(f54,plain,
! [X2,X0,X1] :
( in(sK9(X0,X1,X2),X0)
| in(sK7(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f262,plain,
! [X0,X1] : ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))) = ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f256,f112]) ).
fof(f256,plain,
! [X0,X1] : ordered_pair(singleton(ordered_pair(X0,X1)),unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))) = ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f175,f129]) ).
fof(f261,plain,
! [X0,X1] : ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) = ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f255,f112]) ).
fof(f255,plain,
! [X0,X1] : ordered_pair(singleton(singleton(singleton(X0))),unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0)))) = ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f175,f129]) ).
fof(f254,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f114,f129]) ).
fof(f253,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f88,f129]) ).
fof(f252,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f85,f129]) ).
fof(f251,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f47,f129]) ).
fof(f260,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f259,f114]) ).
fof(f259,plain,
! [X0,X1] : unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))) = ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f244,f175]) ).
fof(f244,plain,
! [X0,X1] : unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))) = ordered_pair(singleton(singleton(X0)),unordered_pair(unordered_pair(X1,X0),singleton(X0))),
inference(superposition,[],[f129,f175]) ).
fof(f258,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f257,f88]) ).
fof(f257,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f243,f175]) ).
fof(f243,plain,
! [X0,X1] : unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))) = ordered_pair(singleton(singleton(X0)),unordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f129,f175]) ).
fof(f129,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X1)),ordered_pair(X1,X0)),
inference(superposition,[],[f114,f85]) ).
fof(f238,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f114,f123]) ).
fof(f237,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f88,f123]) ).
fof(f236,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f85,f123]) ).
fof(f235,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f47,f123]) ).
fof(f242,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(forward_demodulation,[],[f230,f114]) ).
fof(f230,plain,
! [X0,X1] : unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))) = ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f123,f175]) ).
fof(f241,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f229,f88]) ).
fof(f229,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f123,f175]) ).
fof(f123,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f88,f88]) ).
fof(f228,plain,
! [X2,X0,X1] :
( in(sK8(X0,X1,set_intersection2(sK3,sK5)),X1)
| sP0(X0,X1,set_intersection2(sK3,sK5))
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK7(X0,X1,set_intersection2(sK3,sK5)),X2) ),
inference(resolution,[],[f53,f152]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( in(sK8(X0,X1,set_intersection2(X2,X3)),X1)
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X2) ),
inference(resolution,[],[f53,f92]) ).
fof(f225,plain,
! [X2,X3,X0,X1] :
( in(sK8(X0,X1,set_intersection2(X2,X3)),X1)
| sP0(X0,X1,set_intersection2(X2,X3))
| in(sK7(X0,X1,set_intersection2(X2,X3)),X3) ),
inference(resolution,[],[f53,f93]) ).
fof(f223,plain,
! [X2,X0,X1] :
( in(sK7(X0,set_intersection2(sK3,sK5),X1),X1)
| sP0(X0,set_intersection2(sK3,sK5),X1)
| ~ in(X2,sK6)
| ~ in(X2,sK4)
| sK2 != ordered_pair(sK8(X0,set_intersection2(sK3,sK5),X1),X2) ),
inference(resolution,[],[f53,f152]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| sP0(X0,set_intersection2(X1,X2),X3)
| in(sK8(X0,set_intersection2(X1,X2),X3),X1) ),
inference(resolution,[],[f53,f92]) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( in(sK7(X0,set_intersection2(X1,X2),X3),X3)
| sP0(X0,set_intersection2(X1,X2),X3)
| in(sK8(X0,set_intersection2(X1,X2),X3),X2) ),
inference(resolution,[],[f53,f93]) ).
fof(f53,plain,
! [X2,X0,X1] :
( in(sK8(X0,X1,X2),X1)
| in(sK7(X0,X1,X2),X2)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X2,X3),ordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ in(unordered_pair(X1,X0),X3)
| ~ in(singleton(X0),X2) ),
inference(superposition,[],[f166,f175]) ).
fof(f211,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| ~ in(unordered_pair(X1,X0),sK4)
| ~ in(unordered_pair(X1,X0),sK6)
| ~ in(singleton(X0),sK3)
| ~ in(singleton(X0),sK5) ),
inference(superposition,[],[f163,f175]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,X3))
| ~ in(singleton(X0),X2)
| ~ in(unordered_pair(X1,X0),X3) ),
inference(superposition,[],[f149,f175]) ).
fof(f218,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f217,f114]) ).
fof(f217,plain,
! [X0,X1] : unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(forward_demodulation,[],[f209,f175]) ).
fof(f209,plain,
! [X0,X1] : unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = ordered_pair(singleton(singleton(X0)),unordered_pair(unordered_pair(X1,X0),singleton(X0))),
inference(superposition,[],[f113,f175]) ).
fof(f216,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f208,f114]) ).
fof(f208,plain,
! [X0,X1] : unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))) = ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f112,f175]) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(X0),unordered_pair(X0,X1))
| unordered_pair(X1,X0) = X3 ),
inference(superposition,[],[f68,f175]) ).
fof(f202,plain,
! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X2,X3),ordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ in(unordered_pair(X0,X1),X3)
| ~ in(singleton(X0),X2) ),
inference(superposition,[],[f166,f175]) ).
fof(f201,plain,
! [X0,X1] :
( sK2 != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| ~ in(unordered_pair(X0,X1),sK4)
| ~ in(unordered_pair(X0,X1),sK6)
| ~ in(singleton(X0),sK3)
| ~ in(singleton(X0),sK5) ),
inference(superposition,[],[f163,f175]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(singleton(X0),unordered_pair(X1,X0)),cartesian_product2(X2,X3))
| ~ in(singleton(X0),X2)
| ~ in(unordered_pair(X0,X1),X3) ),
inference(superposition,[],[f149,f175]) ).
fof(f215,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f214,f88]) ).
fof(f214,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f199,f175]) ).
fof(f199,plain,
! [X0,X1] : unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))) = ordered_pair(singleton(singleton(X0)),unordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(superposition,[],[f113,f175]) ).
fof(f213,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(forward_demodulation,[],[f198,f88]) ).
fof(f198,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),unordered_pair(singleton(X0),unordered_pair(X0,X1))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f112,f175]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X2,X3) != ordered_pair(singleton(X0),unordered_pair(X1,X0))
| unordered_pair(X0,X1) = X3 ),
inference(superposition,[],[f68,f175]) ).
fof(f192,plain,
! [X0,X1] : ordered_pair(singleton(singleton(singleton(X0))),unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))) = ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f175,f112]) ).
fof(f191,plain,
! [X0,X1] : ordered_pair(singleton(singleton(singleton(X0))),unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))) = ordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f175,f113]) ).
fof(f188,plain,
! [X0,X1] : ordered_pair(singleton(ordered_pair(X0,X1)),unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))) = ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f175,f112]) ).
fof(f187,plain,
! [X0,X1] : ordered_pair(singleton(ordered_pair(X0,X1)),unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1))) = ordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f175,f113]) ).
fof(f175,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f113,f112]) ).
fof(f184,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f45,f113]) ).
fof(f183,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f45,f113]) ).
fof(f182,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f47,f113]) ).
fof(f181,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X1,X0)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f85,f113]) ).
fof(f180,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f88,f113]) ).
fof(f179,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X1,X0))),
inference(superposition,[],[f114,f113]) ).
fof(f178,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f112,f113]) ).
fof(f177,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f113,f45]) ).
fof(f176,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f113,f45]) ).
fof(f113,plain,
! [X0,X1] : ordered_pair(singleton(X1),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X1,X0),singleton(singleton(X1))),
inference(superposition,[],[f85,f85]) ).
fof(f174,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f45,f112]) ).
fof(f173,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f45,f112]) ).
fof(f172,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(ordered_pair(X0,X1))),
inference(superposition,[],[f47,f112]) ).
fof(f171,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(ordered_pair(singleton(X0),unordered_pair(X0,X1)),singleton(singleton(singleton(X0)))),
inference(superposition,[],[f85,f112]) ).
fof(f170,plain,
! [X0,X1] : ordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = unordered_pair(singleton(ordered_pair(X0,X1)),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f88,f112]) ).
fof(f169,plain,
! [X0,X1] : ordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = unordered_pair(singleton(singleton(singleton(X0))),ordered_pair(singleton(X0),unordered_pair(X0,X1))),
inference(superposition,[],[f114,f112]) ).
fof(f168,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f112,f45]) ).
fof(f167,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f112,f45]) ).
fof(f112,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f85,f47]) ).
fof(f163,plain,
! [X0,X1] :
( sK2 != ordered_pair(X1,X0)
| ~ in(X0,sK4)
| ~ in(X0,sK6)
| ~ in(X1,sK3)
| ~ in(X1,sK5) ),
inference(resolution,[],[f152,f145]) ).
fof(f166,plain,
! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X1,X3),ordered_pair(X0,X2))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[],[f149,f48]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X2,X0),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[],[f71,f72]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ in(X0,sK6)
| ~ in(X0,sK4)
| sK2 != ordered_pair(sK11(set_intersection2(sK3,sK5),X1,X2),X0)
| ~ in(X2,cartesian_product2(X1,set_intersection2(sK3,sK5))) ),
inference(resolution,[],[f152,f140]) ).
fof(f164,plain,
! [X2,X0,X1] :
( ~ in(X0,sK6)
| ~ in(X0,sK4)
| sK2 != ordered_pair(sK10(X1,set_intersection2(sK3,sK5),X2),X0)
| ~ in(X2,cartesian_product2(set_intersection2(sK3,sK5),X1)) ),
inference(resolution,[],[f152,f135]) ).
fof(f152,plain,
! [X0,X1] :
( ~ in(X1,set_intersection2(sK3,sK5))
| ~ in(X0,sK6)
| ~ in(X0,sK4)
| sK2 != ordered_pair(X1,X0) ),
inference(resolution,[],[f145,f42]) ).
fof(f158,plain,
! [X2,X3,X0,X1] :
( ~ in(set_intersection2(X0,X1),X2)
| ~ in(set_intersection2(X0,X1),X3)
| ~ in(set_intersection2(X3,X2),X0)
| ~ in(set_intersection2(X3,X2),X1) ),
inference(resolution,[],[f153,f145]) ).
fof(f153,plain,
! [X2,X0,X1] :
( ~ in(set_intersection2(X1,X2),X0)
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f145,f48]) ).
fof(f145,plain,
! [X2,X0,X1] :
( in(X0,set_intersection2(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(resolution,[],[f61,f73]) ).
fof(f71,plain,
! [X2,X10,X0,X1,X9] :
( ~ sP0(X0,X1,X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| in(ordered_pair(X9,X10),X2) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
fof(f146,plain,
! [X2,X0,X1] :
( ~ in(X0,X1)
| ~ in(X0,X2)
| in(X0,set_intersection2(X1,X2)) ),
inference(resolution,[],[f61,f76]) ).
fof(f61,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f35]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(X2,sK11(X2,X1,X0))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f140,f48]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,set_intersection2(sK4,sK6)))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK11(set_intersection2(sK4,sK6),X1,X0)) ),
inference(resolution,[],[f140,f42]) ).
fof(f140,plain,
! [X2,X0,X1] :
( in(sK11(X2,X1,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f50,f72]) ).
fof(f50,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK11(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ in(X1,sK10(X2,X1,X0))
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f135,f48]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(set_intersection2(sK4,sK6),X1))
| ~ in(X2,set_intersection2(sK3,sK5))
| sK2 != ordered_pair(X2,sK10(X1,set_intersection2(sK4,sK6),X0)) ),
inference(resolution,[],[f135,f42]) ).
fof(f135,plain,
! [X2,X0,X1] :
( in(sK10(X2,X1,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f49,f72]) ).
fof(f49,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK10(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X6,X5] :
( ~ in(X6,set_intersection2(sK4,sK6))
| ~ in(X5,set_intersection2(sK3,sK5))
| ordered_pair(X5,X6) != sK2 ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ! [X5,X6] :
( ~ in(X6,set_intersection2(sK4,sK6))
| ~ in(X5,set_intersection2(sK3,sK5))
| ordered_pair(X5,X6) != sK2 )
& in(sK2,set_intersection2(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f15,f22]) ).
fof(f22,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ~ in(X6,set_intersection2(X2,X4))
| ~ in(X5,set_intersection2(X1,X3))
| ordered_pair(X5,X6) != X0 )
& in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) )
=> ( ! [X6,X5] :
( ~ in(X6,set_intersection2(sK4,sK6))
| ~ in(X5,set_intersection2(sK3,sK5))
| ordered_pair(X5,X6) != sK2 )
& in(sK2,set_intersection2(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6))) ) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
? [X0,X1,X2,X3,X4] :
( ! [X5,X6] :
( ~ in(X6,set_intersection2(X2,X4))
| ~ in(X5,set_intersection2(X1,X3))
| ordered_pair(X5,X6) != X0 )
& in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( in(X6,set_intersection2(X2,X4))
& in(X5,set_intersection2(X1,X3))
& ordered_pair(X5,X6) = X0 )
& in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1,X2,X3,X4] :
~ ( ! [X5,X6] :
~ ( in(X6,set_intersection2(X2,X4))
& in(X5,set_intersection2(X1,X3))
& ordered_pair(X5,X6) = X0 )
& in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t104_zfmisc_1) ).
fof(f134,plain,
! [X0,X1] : unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f47,f114]) ).
fof(f133,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X1,X0))),
inference(superposition,[],[f85,f114]) ).
fof(f132,plain,
! [X0,X1] : unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)) = ordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f88,f114]) ).
fof(f131,plain,
! [X0,X1] : ordered_pair(unordered_pair(X1,X0),singleton(X0)) = unordered_pair(singleton(unordered_pair(X1,X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f114,f114]) ).
fof(f130,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(singleton(unordered_pair(X0,X1)),ordered_pair(X0,X1)),
inference(superposition,[],[f114,f88]) ).
fof(f128,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(singleton(singleton(X0)),ordered_pair(X0,X1)),
inference(superposition,[],[f114,f47]) ).
fof(f114,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f85,f45]) ).
fof(f125,plain,
! [X0,X1] : ordered_pair(singleton(X0),unordered_pair(X0,X1)) = unordered_pair(ordered_pair(X0,X1),singleton(singleton(X0))),
inference(superposition,[],[f47,f88]) ).
fof(f124,plain,
! [X0,X1] : ordered_pair(unordered_pair(X0,X1),singleton(X0)) = unordered_pair(ordered_pair(X0,X1),singleton(unordered_pair(X0,X1))),
inference(superposition,[],[f85,f88]) ).
fof(f120,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f88,f45]) ).
fof(f119,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X1,X0)),
inference(superposition,[],[f88,f45]) ).
fof(f88,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f47,f45]) ).
fof(f118,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f45,f85]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f45,f85]) ).
fof(f115,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(singleton(X1),unordered_pair(X0,X1)),
inference(superposition,[],[f85,f45]) ).
fof(f85,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f47,f45]) ).
fof(f68,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( X1 = X3
& X0 = X2 )
| ordered_pair(X0,X1) != ordered_pair(X2,X3) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ordered_pair(X0,X1) = ordered_pair(X2,X3)
=> ( X1 = X3
& X0 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t33_zfmisc_1) ).
fof(f67,plain,
! [X2,X3,X0,X1] :
( ordered_pair(X0,X1) != ordered_pair(X2,X3)
| X0 = X2 ),
inference(cnf_transformation,[],[f17]) ).
fof(f60,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f104,plain,
~ in(cartesian_product2(sK5,sK6),sK2),
inference(resolution,[],[f100,f48]) ).
fof(f100,plain,
in(sK2,cartesian_product2(sK5,sK6)),
inference(resolution,[],[f93,f41]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(resolution,[],[f59,f76]) ).
fof(f99,plain,
~ in(cartesian_product2(sK3,sK4),sK2),
inference(resolution,[],[f95,f48]) ).
fof(f95,plain,
in(sK2,cartesian_product2(sK3,sK4)),
inference(resolution,[],[f92,f41]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| in(X2,X0) ),
inference(superposition,[],[f92,f46]) ).
fof(f97,plain,
! [X2,X0,X1] :
( ~ in(X2,set_intersection2(X1,X0))
| in(X2,X0) ),
inference(superposition,[],[f92,f46]) ).
fof(f92,plain,
! [X2,X0,X1] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(resolution,[],[f59,f73]) ).
fof(f59,plain,
! [X2,X0,X1,X4] :
( ~ sP1(X0,X1,X2)
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f91,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f45,f47]) ).
fof(f90,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f45,f47]) ).
fof(f89,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,X1)),
inference(superposition,[],[f47,f45]) ).
fof(f86,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X1,X0),singleton(X0)),
inference(superposition,[],[f47,f45]) ).
fof(f47,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f66,plain,
! [X2,X0,X1] :
( ~ sP1(X1,X0,X2)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) = X2
| ~ sP1(X1,X0,X2) )
& ( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> sP1(X1,X0,X2) ),
inference(definition_folding,[],[f5,f20]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( set_intersection2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f58,plain,
! [X2,X0,X1] :
( ~ sP0(X1,X0,X2)
| cartesian_product2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f4,f18]) ).
fof(f4,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f76,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X1,X0)),
inference(superposition,[],[f73,f46]) ).
fof(f77,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X1,X0)),
inference(superposition,[],[f73,f46]) ).
fof(f46,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f45,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f75,plain,
~ in(set_intersection2(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6)),sK2),
inference(resolution,[],[f41,f48]) ).
fof(f41,plain,
in(sK2,set_intersection2(cartesian_product2(sK3,sK4),cartesian_product2(sK5,sK6))),
inference(cnf_transformation,[],[f23]) ).
fof(f74,plain,
! [X0] : sP1(X0,X0,X0),
inference(superposition,[],[f73,f44]) ).
fof(f73,plain,
! [X0,X1] : sP1(X1,X0,set_intersection2(X0,X1)),
inference(equality_resolution,[],[f65]) ).
fof(f65,plain,
! [X2,X0,X1] :
( sP1(X1,X0,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f72,plain,
! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,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/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f44,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] : set_intersection2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(f43,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f70,plain,
empty(sK14),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
empty(sK14),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f9,f39]) ).
fof(f39,plain,
( ? [X0] : empty(X0)
=> empty(sK14) ),
introduced(choice_axiom,[]) ).
fof(f9,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f69,plain,
~ empty(sK13),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
~ empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f10,f37]) ).
fof(f37,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f10,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.23 % Problem : SET951+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.24 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.45 % Computer : n016.cluster.edu
% 0.10/0.45 % Model : x86_64 x86_64
% 0.10/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.45 % Memory : 8042.1875MB
% 0.10/0.45 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.45 % CPULimit : 300
% 0.10/0.45 % WCLimit : 300
% 0.10/0.45 % DateTime : Tue Apr 30 01:46:55 EDT 2024
% 0.10/0.45 % CPUTime :
% 0.10/0.45 % (6356)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.47 % (6361)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)
% 0.17/0.47 % (6363)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)
% 0.17/0.47 % (6360)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.47 TRYING [1]
% 0.17/0.47 TRYING [2]
% 0.17/0.48 TRYING [3]
% 0.17/0.48 % (6359)WARNING: value z3 for option sas not known
% 0.17/0.48 % (6358)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.48 % (6359)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)
% 0.17/0.49 % (6357)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.49 % (6362)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)
% 0.17/0.51 TRYING [4]
% 0.17/0.52 TRYING [1]
% 0.17/0.52 TRYING [2]
% 0.45/0.54 % (6359)First to succeed.
% 0.54/0.57 % (6359)Refutation found. Thanks to Tanya!
% 0.54/0.57 % SZS status Theorem for theBenchmark
% 0.54/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.58 % (6359)------------------------------
% 0.54/0.58 % (6359)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.54/0.58 % (6359)Termination reason: Refutation
% 0.54/0.58
% 0.54/0.58 % (6359)Memory used [KB]: 1291
% 0.54/0.58 % (6359)Time elapsed: 0.079 s
% 0.54/0.58 % (6359)Instructions burned: 95 (million)
% 0.54/0.58 % (6359)------------------------------
% 0.54/0.58 % (6359)------------------------------
% 0.54/0.58 % (6356)Success in time 0.12 s
%------------------------------------------------------------------------------