TSTP Solution File: SEU277+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU277+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:31:06 EDT 2024
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 103
% Syntax : Number of formulae : 494 ( 26 unt; 0 def)
% Number of atoms : 1752 ( 516 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 1937 ( 679 ~; 932 |; 220 &)
% ( 78 <=>; 26 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 85 ( 83 usr; 71 prp; 0-4 aty)
% Number of functors : 27 ( 27 usr; 10 con; 0-4 aty)
% Number of variables : 903 ( 749 !; 154 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f938,plain,
$false,
inference(avatar_sat_refutation,[],[f233,f244,f254,f265,f274,f286,f297,f308,f329,f340,f355,f366,f377,f389,f406,f418,f429,f440,f463,f474,f493,f504,f517,f528,f539,f555,f572,f583,f598,f609,f620,f631,f642,f748,f774,f786,f792,f801,f806,f809,f814,f839,f858,f863,f866,f869,f874,f896,f900,f903,f906,f908,f910,f927,f937]) ).
fof(f937,plain,
( ~ spl30_65
| ~ spl30_67
| spl30_69 ),
inference(avatar_contradiction_clause,[],[f936]) ).
fof(f936,plain,
( $false
| ~ spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f935,f780]) ).
fof(f780,plain,
( sP4(sK5,sK7,sK6)
| ~ spl30_67 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f779,plain,
( spl30_67
<=> sP4(sK5,sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_67])]) ).
fof(f935,plain,
( ~ sP4(sK5,sK7,sK6)
| ~ spl30_65
| spl30_69 ),
inference(subsumption_resolution,[],[f934,f768]) ).
fof(f768,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_65 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f767,plain,
( spl30_65
<=> sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_65])]) ).
fof(f934,plain,
( ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ sP4(sK5,sK7,sK6)
| spl30_69 ),
inference(resolution,[],[f834,f107]) ).
fof(f107,plain,
! [X2,X0,X1,X4] :
( in(X4,sK11(X0,X1,X2))
| ~ sP2(X2,X1,X4,X0)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK11(X0,X1,X2))
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,sK11(X0,X1,X2)) ) )
| ~ sP4(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f52,f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,X3) ) )
=> ! [X4] :
( ( in(X4,sK11(X0,X1,X2))
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,sK11(X0,X1,X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ~ sP2(X2,X1,X4,X0) )
& ( sP2(X2,X1,X4,X0)
| ~ in(X4,X3) ) )
| ~ sP4(X0,X1,X2) ),
inference(rectify,[],[f51]) ).
fof(f51,plain,
! [X0,X2,X1] :
( ? [X10] :
! [X11] :
( ( in(X11,X10)
| ~ sP2(X1,X2,X11,X0) )
& ( sP2(X1,X2,X11,X0)
| ~ in(X11,X10) ) )
| ~ sP4(X0,X2,X1) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X2,X1] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> sP2(X1,X2,X11,X0) )
| ~ sP4(X0,X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f834,plain,
( ~ in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| spl30_69 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f833,plain,
( spl30_69
<=> in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_69])]) ).
fof(f927,plain,
( ~ spl30_65
| spl30_68 ),
inference(avatar_contradiction_clause,[],[f926]) ).
fof(f926,plain,
( $false
| ~ spl30_65
| spl30_68 ),
inference(subsumption_resolution,[],[f925,f768]) ).
fof(f925,plain,
( ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_65
| spl30_68 ),
inference(subsumption_resolution,[],[f924,f784]) ).
fof(f784,plain,
( ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| spl30_68 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f783,plain,
( spl30_68
<=> in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_68])]) ).
fof(f924,plain,
( in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_65 ),
inference(superposition,[],[f113,f878]) ).
fof(f878,plain,
( sK8(sK11(sK5,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_65 ),
inference(resolution,[],[f768,f114]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| sK15(X0,X1,X2,X3) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2,X3] :
( ( sP2(X0,X1,X2,X3)
| ! [X4] :
( ! [X5,X6] :
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ordered_pair(X5,X6) != X2 )
| X2 != X4
| ~ in(X4,cartesian_product2(X3,X3)) ) )
& ( ( in(ordered_pair(apply(X1,sK16(X0,X1,X2)),apply(X1,sK17(X0,X1,X2))),X0)
& ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2)) = X2
& sK15(X0,X1,X2,X3) = X2
& in(sK15(X0,X1,X2,X3),cartesian_product2(X3,X3)) )
| ~ sP2(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f60,f62,f61]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( ? [X7] :
( ? [X8,X9] :
( in(ordered_pair(apply(X1,X8),apply(X1,X9)),X0)
& ordered_pair(X8,X9) = X2 )
& X2 = X7
& in(X7,cartesian_product2(X3,X3)) )
=> ( ? [X8,X9] :
( in(ordered_pair(apply(X1,X8),apply(X1,X9)),X0)
& ordered_pair(X8,X9) = X2 )
& sK15(X0,X1,X2,X3) = X2
& in(sK15(X0,X1,X2,X3),cartesian_product2(X3,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ? [X8,X9] :
( in(ordered_pair(apply(X1,X8),apply(X1,X9)),X0)
& ordered_pair(X8,X9) = X2 )
=> ( in(ordered_pair(apply(X1,sK16(X0,X1,X2)),apply(X1,sK17(X0,X1,X2))),X0)
& ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ( sP2(X0,X1,X2,X3)
| ! [X4] :
( ! [X5,X6] :
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ordered_pair(X5,X6) != X2 )
| X2 != X4
| ~ in(X4,cartesian_product2(X3,X3)) ) )
& ( ? [X7] :
( ? [X8,X9] :
( in(ordered_pair(apply(X1,X8),apply(X1,X9)),X0)
& ordered_pair(X8,X9) = X2 )
& X2 = X7
& in(X7,cartesian_product2(X3,X3)) )
| ~ sP2(X0,X1,X2,X3) ) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X1,X2,X11,X0] :
( ( sP2(X1,X2,X11,X0)
| ! [X12] :
( ! [X13,X14] :
( ~ in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
| ordered_pair(X13,X14) != X11 )
| X11 != X12
| ~ in(X12,cartesian_product2(X0,X0)) ) )
& ( ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) )
| ~ sP2(X1,X2,X11,X0) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X1,X2,X11,X0] :
( sP2(X1,X2,X11,X0)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( in(sK15(X0,X1,X2,X3),cartesian_product2(X3,X3))
| ~ sP2(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f63]) ).
fof(f910,plain,
( ~ spl30_64
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f909,plain,
( $false
| ~ spl30_64
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(global_subsumption,[],[f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f747,f754,f755,f756,f757,f761,f245,f762,f763,f760,f765,f764,f275,f812,f813,f780,f312,f849,f846,f847,f848,f835,f875,f821,f871,f347,f895,f892,f893,f894,f784]) ).
fof(f894,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))) = sK15(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))),X2) ),
inference(resolution,[],[f347,f114]) ).
fof(f893,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))) = ordered_pair(sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))))),sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))))) ),
inference(resolution,[],[f347,f115]) ).
fof(f892,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| in(ordered_pair(apply(X3,sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))))),apply(X3,sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))))))),X4) ),
inference(resolution,[],[f347,f116]) ).
fof(f895,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ~ in(ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),cartesian_product2(X7,X7))
| sP2(sK11(X2,X3,X4),X1,ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),X7) ),
inference(duplicate_literal_removal,[],[f891]) ).
fof(f891,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ~ in(ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),cartesian_product2(X7,X7))
| sP2(sK11(X2,X3,X4),X1,ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),X7)
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f347,f180]) ).
fof(f347,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP2(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK20(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK21(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))),X2)
| ~ sP0(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f205,f106]) ).
fof(f871,plain,
( ~ in(sK11(sK5,sK7,sK6),sK8(sK11(sK5,sK7,sK6)))
| ~ spl30_69 ),
inference(resolution,[],[f835,f105]) ).
fof(f821,plain,
( sK8(sK11(sK5,sK7,sK6)) = ordered_pair(sK9(sK11(sK5,sK7,sK6)),sK10(sK11(sK5,sK7,sK6)))
| sK8(sK11(sK5,sK7,sK6)) = ordered_pair(sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6))))
| ~ spl30_67 ),
inference(resolution,[],[f780,f182]) ).
fof(f875,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_67
| ~ spl30_69 ),
inference(subsumption_resolution,[],[f870,f780]) ).
fof(f870,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ sP4(sK5,sK7,sK6)
| ~ spl30_69 ),
inference(resolution,[],[f835,f106]) ).
fof(f835,plain,
( in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| ~ spl30_69 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f848,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))) = sK15(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))),X2) ),
inference(resolution,[],[f312,f114]) ).
fof(f847,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))) = ordered_pair(sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))))),sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))))) ),
inference(resolution,[],[f312,f115]) ).
fof(f846,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| in(ordered_pair(apply(X3,sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))))),apply(X3,sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))))))),X4) ),
inference(resolution,[],[f312,f116]) ).
fof(f849,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ~ in(ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),cartesian_product2(X7,X7))
| sP2(sK11(X2,X3,X4),X1,ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),X7) ),
inference(duplicate_literal_removal,[],[f845]) ).
fof(f845,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4)
| ~ in(ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),cartesian_product2(X7,X7))
| sP2(sK11(X2,X3,X4),X1,ordered_pair(sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))),sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),X7)
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f312,f180]) ).
fof(f312,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP2(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6))))),apply(X1,sK17(sK11(X2,X3,X4),X1,ordered_pair(apply(X5,sK18(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)),apply(X5,sK19(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)))))),X2)
| ~ sP1(sK11(X0,X1,sK11(X2,X3,X4)),X5,X6)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f195,f106]) ).
fof(f813,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(apply(X0,sK20(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3)))),apply(X0,sK21(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3))))) = sK15(X3,X2,ordered_pair(apply(X0,sK20(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3)))),apply(X0,sK21(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3))))),X1)
| ~ sP4(X1,X2,X3)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = sK15(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3))),X4)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK9(sK11(X4,X0,sK11(X1,X2,X3))),sK10(sK11(X4,X0,sK11(X1,X2,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK11(X1,X2,X3)) ),
inference(resolution,[],[f275,f189]) ).
fof(f812,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(apply(X0,sK20(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3)))),apply(X0,sK21(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3))))) = sK15(X3,X2,ordered_pair(apply(X0,sK20(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3)))),apply(X0,sK21(sK11(X1,X2,X3),X0,sK13(X0,sK11(X1,X2,X3))))),X1)
| ~ sP4(X1,X2,X3)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK16(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3)))),sK17(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3)))))
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK9(sK11(X4,X0,sK11(X1,X2,X3))),sK10(sK11(X4,X0,sK11(X1,X2,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK11(X1,X2,X3)) ),
inference(resolution,[],[f275,f203]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( ~ sP3(X3,sK11(X0,X1,X2))
| ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))),apply(X3,sK21(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2))))) = sK15(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))),apply(X3,sK21(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2))))),X0)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f207,f109]) ).
fof(f764,plain,
( ~ in(cartesian_product2(sK5,sK5),sK8(sK11(sK5,sK7,sK6)))
| ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(superposition,[],[f156,f760]) ).
fof(f765,plain,
( in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(superposition,[],[f113,f760]) ).
fof(f760,plain,
( sK8(sK11(sK5,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(trivial_inequality_removal,[],[f759]) ).
fof(f759,plain,
( sK8(sK11(sK5,sK7,sK6)) != sK8(sK11(sK5,sK7,sK6))
| sK8(sK11(sK5,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(equality_factoring,[],[f747]) ).
fof(f763,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(apply(X0,sK18(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3)))),apply(X0,sK19(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3))))) = sK15(X3,X2,ordered_pair(apply(X0,sK18(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3)))),apply(X0,sK19(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3))))),X1)
| ~ sP4(X1,X2,X3)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = sK15(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3))),X4)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK9(sK11(X4,X0,sK11(X1,X2,X3))),sK10(sK11(X4,X0,sK11(X1,X2,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK11(X1,X2,X3)) ),
inference(resolution,[],[f245,f189]) ).
fof(f762,plain,
! [X2,X3,X0,X1,X4] :
( ordered_pair(apply(X0,sK18(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3)))),apply(X0,sK19(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3))))) = sK15(X3,X2,ordered_pair(apply(X0,sK18(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3)))),apply(X0,sK19(sK11(X1,X2,X3),X0,sK14(X0,sK11(X1,X2,X3))))),X1)
| ~ sP4(X1,X2,X3)
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK16(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3)))),sK17(sK11(X1,X2,X3),X0,sK8(sK11(X4,X0,sK11(X1,X2,X3)))))
| sK8(sK11(X4,X0,sK11(X1,X2,X3))) = ordered_pair(sK9(sK11(X4,X0,sK11(X1,X2,X3))),sK10(sK11(X4,X0,sK11(X1,X2,X3))))
| ~ function(X0)
| ~ relation(X0)
| ~ relation(sK11(X1,X2,X3)) ),
inference(resolution,[],[f245,f203]) ).
fof(f245,plain,
! [X2,X3,X0,X1] :
( ~ sP3(X3,sK11(X0,X1,X2))
| ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))),apply(X3,sK19(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2))))) = sK15(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))),apply(X3,sK19(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2))))),X0)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f197,f111]) ).
fof(f761,plain,
( sK8(sK11(sK5,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(trivial_inequality_removal,[],[f758]) ).
fof(f758,plain,
( sK8(sK11(sK5,sK7,sK6)) != sK8(sK11(sK5,sK7,sK6))
| sK8(sK11(sK5,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ spl30_64 ),
inference(equality_factoring,[],[f747]) ).
fof(f757,plain,
( ! [X0] :
( in(sK8(sK11(X0,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_64 ),
inference(superposition,[],[f113,f747]) ).
fof(f756,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK5,sK5),sK8(sK11(X0,sK7,sK6)))
| ~ sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_64 ),
inference(superposition,[],[f156,f747]) ).
fof(f755,plain,
( ! [X0] :
( in(sK8(sK11(X0,sK7,sK6)),cartesian_product2(X0,X0))
| ~ sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5) )
| ~ spl30_64 ),
inference(superposition,[],[f113,f747]) ).
fof(f754,plain,
( ! [X0] :
( ~ in(cartesian_product2(X0,X0),sK8(sK11(X0,sK7,sK6)))
| ~ sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5) )
| ~ spl30_64 ),
inference(superposition,[],[f156,f747]) ).
fof(f747,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5) )
| ~ spl30_64 ),
inference(avatar_component_clause,[],[f746]) ).
fof(f746,plain,
( spl30_64
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_64])]) ).
fof(f688,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK29,X1)) = sK15(X1,sK29,sK8(sK11(X0,sK29,X1)),X0)
| sK8(sK11(X0,sK29,X1)) = ordered_pair(sK9(sK11(X0,sK29,X1)),sK10(sK11(X0,sK29,X1)))
| sK12(sK29,X1) = sK13(sK29,X1) ),
inference(subsumption_resolution,[],[f683,f139]) ).
fof(f683,plain,
! [X0,X1] :
( sK8(sK11(X0,sK29,X1)) = ordered_pair(sK9(sK11(X0,sK29,X1)),sK10(sK11(X0,sK29,X1)))
| sK8(sK11(X0,sK29,X1)) = sK15(X1,sK29,sK8(sK11(X0,sK29,X1)),X0)
| ~ relation(sK29)
| ~ relation(X1)
| sK12(sK29,X1) = sK13(sK29,X1) ),
inference(resolution,[],[f193,f140]) ).
fof(f687,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK28,X1)) = sK15(X1,sK28,sK8(sK11(X0,sK28,X1)),X0)
| sK8(sK11(X0,sK28,X1)) = ordered_pair(sK9(sK11(X0,sK28,X1)),sK10(sK11(X0,sK28,X1)))
| sK12(sK28,X1) = sK13(sK28,X1) ),
inference(subsumption_resolution,[],[f682,f137]) ).
fof(f682,plain,
! [X0,X1] :
( sK8(sK11(X0,sK28,X1)) = ordered_pair(sK9(sK11(X0,sK28,X1)),sK10(sK11(X0,sK28,X1)))
| sK8(sK11(X0,sK28,X1)) = sK15(X1,sK28,sK8(sK11(X0,sK28,X1)),X0)
| ~ relation(sK28)
| ~ relation(X1)
| sK12(sK28,X1) = sK13(sK28,X1) ),
inference(resolution,[],[f193,f138]) ).
fof(f346,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X2,ordered_pair(apply(X1,sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))))),apply(X1,sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4)))))))
| ~ sP0(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f205,f105]) ).
fof(f686,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK27,X1)) = sK15(X1,sK27,sK8(sK11(X0,sK27,X1)),X0)
| sK8(sK11(X0,sK27,X1)) = ordered_pair(sK9(sK11(X0,sK27,X1)),sK10(sK11(X0,sK27,X1)))
| sK12(sK27,X1) = sK13(sK27,X1) ),
inference(subsumption_resolution,[],[f681,f135]) ).
fof(f681,plain,
! [X0,X1] :
( sK8(sK11(X0,sK27,X1)) = ordered_pair(sK9(sK11(X0,sK27,X1)),sK10(sK11(X0,sK27,X1)))
| sK8(sK11(X0,sK27,X1)) = sK15(X1,sK27,sK8(sK11(X0,sK27,X1)),X0)
| ~ relation(sK27)
| ~ relation(X1)
| sK12(sK27,X1) = sK13(sK27,X1) ),
inference(resolution,[],[f193,f136]) ).
fof(f685,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK26,X1)) = sK15(X1,sK26,sK8(sK11(X0,sK26,X1)),X0)
| sK8(sK11(X0,sK26,X1)) = ordered_pair(sK9(sK11(X0,sK26,X1)),sK10(sK11(X0,sK26,X1)))
| sK12(sK26,X1) = sK13(sK26,X1) ),
inference(subsumption_resolution,[],[f680,f132]) ).
fof(f680,plain,
! [X0,X1] :
( sK8(sK11(X0,sK26,X1)) = ordered_pair(sK9(sK11(X0,sK26,X1)),sK10(sK11(X0,sK26,X1)))
| sK8(sK11(X0,sK26,X1)) = sK15(X1,sK26,sK8(sK11(X0,sK26,X1)),X0)
| ~ relation(sK26)
| ~ relation(X1)
| sK12(sK26,X1) = sK13(sK26,X1) ),
inference(resolution,[],[f193,f134]) ).
fof(f684,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK7,X1)) = sK15(X1,sK7,sK8(sK11(X0,sK7,X1)),X0)
| sK8(sK11(X0,sK7,X1)) = ordered_pair(sK9(sK11(X0,sK7,X1)),sK10(sK11(X0,sK7,X1)))
| sK12(sK7,X1) = sK13(sK7,X1) ),
inference(subsumption_resolution,[],[f678,f89]) ).
fof(f678,plain,
! [X0,X1] :
( sK8(sK11(X0,sK7,X1)) = ordered_pair(sK9(sK11(X0,sK7,X1)),sK10(sK11(X0,sK7,X1)))
| sK8(sK11(X0,sK7,X1)) = sK15(X1,sK7,sK8(sK11(X0,sK7,X1)),X0)
| ~ relation(sK7)
| ~ relation(X1)
| sK12(sK7,X1) = sK13(sK7,X1) ),
inference(resolution,[],[f193,f90]) ).
fof(f193,plain,
! [X2,X0,X1] :
( ~ function(X1)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| ~ relation(X1)
| ~ relation(X2)
| sK13(X1,X2) = sK12(X1,X2) ),
inference(resolution,[],[f189,f108]) ).
fof(f311,plain,
! [X2,X3,X0,X1,X4] :
( ~ in(X2,ordered_pair(apply(X1,sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))))),apply(X1,sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4)))))))
| ~ sP1(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f195,f105]) ).
fof(f658,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| sK8(sK11(X0,X1,sK11(X2,X3,X4))) = ordered_pair(sK9(sK11(X0,X1,sK11(X2,X3,X4))),sK10(sK11(X0,X1,sK11(X2,X3,X4))))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))) = sK15(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))),X2) ),
inference(resolution,[],[f202,f114]) ).
fof(f657,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| sK8(sK11(X0,X1,sK11(X2,X3,X4))) = ordered_pair(sK9(sK11(X0,X1,sK11(X2,X3,X4))),sK10(sK11(X0,X1,sK11(X2,X3,X4))))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))) = ordered_pair(sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))))),sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))))) ),
inference(resolution,[],[f202,f115]) ).
fof(f656,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| sK8(sK11(X0,X1,sK11(X2,X3,X4))) = ordered_pair(sK9(sK11(X0,X1,sK11(X2,X3,X4))),sK10(sK11(X0,X1,sK11(X2,X3,X4))))
| ~ sP4(X2,X3,X4)
| in(ordered_pair(apply(X3,sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))))),apply(X3,sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))))))),X4) ),
inference(resolution,[],[f202,f116]) ).
fof(f202,plain,
! [X2,X3,X0,X1,X4] :
( sP2(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))),X2)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| sK8(sK11(X0,X1,sK11(X2,X3,X4))) = ordered_pair(sK9(sK11(X0,X1,sK11(X2,X3,X4))),sK10(sK11(X0,X1,sK11(X2,X3,X4))))
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f181,f106]) ).
fof(f344,plain,
! [X2,X3,X0,X1] :
( sK8(X3) != ordered_pair(sK16(sK6,sK7,ordered_pair(apply(X1,sK20(sK11(X0,sK7,sK6),X1,X2)),apply(X1,sK21(sK11(X0,sK7,sK6),X1,X2)))),sK17(sK6,sK7,ordered_pair(apply(X1,sK20(sK11(X0,sK7,sK6),X1,X2)),apply(X1,sK21(sK11(X0,sK7,sK6),X1,X2)))))
| ~ sP0(sK11(X0,sK7,sK6),X1,X2)
| ~ sP4(X0,sK7,sK6)
| ~ in(sK8(X3),cartesian_product2(sK5,sK5))
| ~ in(sK8(X3),X3) ),
inference(resolution,[],[f205,f94]) ).
fof(f210,plain,
! [X0,X1] :
( sK8(sK11(X0,sK23,X1)) = ordered_pair(sK9(sK11(X0,sK23,X1)),sK10(sK11(X0,sK23,X1)))
| sK8(sK11(X0,sK23,X1)) = sK15(X1,sK23,sK8(sK11(X0,sK23,X1)),X0)
| ~ relation(sK23)
| ~ relation(X1)
| sK14(sK23,X1) = sK12(sK23,X1) ),
inference(resolution,[],[f192,f147]) ).
fof(f564,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK29)) = sK15(sK29,sK29,sK8(sK11(X0,sK29,sK29)),X0)
| sK8(sK11(X0,sK29,sK29)) = ordered_pair(sK9(sK11(X0,sK29,sK29)),sK10(sK11(X0,sK29,sK29)))
| sK14(sK29,sK29) = sK12(sK29,sK29) ),
inference(resolution,[],[f219,f139]) ).
fof(f563,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK28)) = sK15(sK28,sK29,sK8(sK11(X0,sK29,sK28)),X0)
| sK8(sK11(X0,sK29,sK28)) = ordered_pair(sK9(sK11(X0,sK29,sK28)),sK10(sK11(X0,sK29,sK28)))
| sK14(sK29,sK28) = sK12(sK29,sK28) ),
inference(resolution,[],[f219,f137]) ).
fof(f309,plain,
! [X2,X3,X0,X1] :
( sK8(X3) != ordered_pair(sK16(sK6,sK7,ordered_pair(apply(X1,sK18(sK11(X0,sK7,sK6),X1,X2)),apply(X1,sK19(sK11(X0,sK7,sK6),X1,X2)))),sK17(sK6,sK7,ordered_pair(apply(X1,sK18(sK11(X0,sK7,sK6),X1,X2)),apply(X1,sK19(sK11(X0,sK7,sK6),X1,X2)))))
| ~ sP1(sK11(X0,sK7,sK6),X1,X2)
| ~ sP4(X0,sK7,sK6)
| ~ in(sK8(X3),cartesian_product2(sK5,sK5))
| ~ in(sK8(X3),X3) ),
inference(resolution,[],[f195,f94]) ).
fof(f562,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK27)) = sK15(sK27,sK29,sK8(sK11(X0,sK29,sK27)),X0)
| sK8(sK11(X0,sK29,sK27)) = ordered_pair(sK9(sK11(X0,sK29,sK27)),sK10(sK11(X0,sK29,sK27)))
| sK14(sK29,sK27) = sK12(sK29,sK27) ),
inference(resolution,[],[f219,f135]) ).
fof(f561,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK26)) = sK15(sK26,sK29,sK8(sK11(X0,sK29,sK26)),X0)
| sK8(sK11(X0,sK29,sK26)) = ordered_pair(sK9(sK11(X0,sK29,sK26)),sK10(sK11(X0,sK29,sK26)))
| sK14(sK29,sK26) = sK12(sK29,sK26) ),
inference(resolution,[],[f219,f132]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))),cartesian_product2(X3,X3))
| ~ sP4(X0,X1,X2)
| sP2(X2,X1,ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))),X3)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2))) ),
inference(resolution,[],[f181,f146]) ).
fof(f560,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK7)) = sK15(sK7,sK29,sK8(sK11(X0,sK29,sK7)),X0)
| sK8(sK11(X0,sK29,sK7)) = ordered_pair(sK9(sK11(X0,sK29,sK7)),sK10(sK11(X0,sK29,sK7)))
| sK14(sK29,sK7) = sK12(sK29,sK7) ),
inference(resolution,[],[f219,f89]) ).
fof(f559,plain,
! [X0] :
( sK8(sK11(X0,sK29,sK6)) = sK15(sK6,sK29,sK8(sK11(X0,sK29,sK6)),X0)
| sK8(sK11(X0,sK29,sK6)) = ordered_pair(sK9(sK11(X0,sK29,sK6)),sK10(sK11(X0,sK29,sK6)))
| sK14(sK29,sK6) = sK12(sK29,sK6) ),
inference(resolution,[],[f219,f88]) ).
fof(f219,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK29,X1)) = sK15(X1,sK29,sK8(sK11(X0,sK29,X1)),X0)
| sK8(sK11(X0,sK29,X1)) = ordered_pair(sK9(sK11(X0,sK29,X1)),sK10(sK11(X0,sK29,X1)))
| sK14(sK29,X1) = sK12(sK29,X1) ),
inference(subsumption_resolution,[],[f214,f139]) ).
fof(f214,plain,
! [X0,X1] :
( sK8(sK11(X0,sK29,X1)) = ordered_pair(sK9(sK11(X0,sK29,X1)),sK10(sK11(X0,sK29,X1)))
| sK8(sK11(X0,sK29,X1)) = sK15(X1,sK29,sK8(sK11(X0,sK29,X1)),X0)
| ~ relation(sK29)
| ~ relation(X1)
| sK14(sK29,X1) = sK12(sK29,X1) ),
inference(resolution,[],[f192,f140]) ).
fof(f485,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK29)) = sK15(sK29,sK28,sK8(sK11(X0,sK28,sK29)),X0)
| sK8(sK11(X0,sK28,sK29)) = ordered_pair(sK9(sK11(X0,sK28,sK29)),sK10(sK11(X0,sK28,sK29)))
| sK14(sK28,sK29) = sK12(sK28,sK29) ),
inference(resolution,[],[f218,f139]) ).
fof(f546,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| in(sK8(sK11(X0,X1,sK11(X2,X3,X4))),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))) = sK15(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))),X2) ),
inference(resolution,[],[f188,f114]) ).
fof(f545,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| in(sK8(sK11(X0,X1,sK11(X2,X3,X4))),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X3,X4)
| ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))) = ordered_pair(sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))))),sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))))) ),
inference(resolution,[],[f188,f115]) ).
fof(f544,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP4(X0,X1,sK11(X2,X3,X4))
| in(sK8(sK11(X0,X1,sK11(X2,X3,X4))),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X3,X4)
| in(ordered_pair(apply(X3,sK16(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))))),apply(X3,sK17(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))))))),X4) ),
inference(resolution,[],[f188,f116]) ).
fof(f188,plain,
! [X2,X3,X0,X1,X4] :
( sP2(X4,X3,ordered_pair(apply(X1,sK16(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4))))),apply(X1,sK17(sK11(X2,X3,X4),X1,sK8(sK11(X0,X1,sK11(X2,X3,X4)))))),X2)
| ~ sP4(X0,X1,sK11(X2,X3,X4))
| in(sK8(sK11(X0,X1,sK11(X2,X3,X4))),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X3,X4) ),
inference(resolution,[],[f175,f106]) ).
fof(f484,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK28)) = sK15(sK28,sK28,sK8(sK11(X0,sK28,sK28)),X0)
| sK8(sK11(X0,sK28,sK28)) = ordered_pair(sK9(sK11(X0,sK28,sK28)),sK10(sK11(X0,sK28,sK28)))
| sK14(sK28,sK28) = sK12(sK28,sK28) ),
inference(resolution,[],[f218,f137]) ).
fof(f483,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK27)) = sK15(sK27,sK28,sK8(sK11(X0,sK28,sK27)),X0)
| sK8(sK11(X0,sK28,sK27)) = ordered_pair(sK9(sK11(X0,sK28,sK27)),sK10(sK11(X0,sK28,sK27)))
| sK14(sK28,sK27) = sK12(sK28,sK27) ),
inference(resolution,[],[f218,f135]) ).
fof(f482,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK26)) = sK15(sK26,sK28,sK8(sK11(X0,sK28,sK26)),X0)
| sK8(sK11(X0,sK28,sK26)) = ordered_pair(sK9(sK11(X0,sK28,sK26)),sK10(sK11(X0,sK28,sK26)))
| sK14(sK28,sK26) = sK12(sK28,sK26) ),
inference(resolution,[],[f218,f132]) ).
fof(f186,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))),cartesian_product2(X3,X3))
| ~ sP4(X0,X1,X2)
| sP2(X2,X1,ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))),X3)
| in(sK8(sK11(X0,X1,X2)),cartesian_product2(sK5,sK5)) ),
inference(resolution,[],[f175,f146]) ).
fof(f481,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK7)) = sK15(sK7,sK28,sK8(sK11(X0,sK28,sK7)),X0)
| sK8(sK11(X0,sK28,sK7)) = ordered_pair(sK9(sK11(X0,sK28,sK7)),sK10(sK11(X0,sK28,sK7)))
| sK14(sK28,sK7) = sK12(sK28,sK7) ),
inference(resolution,[],[f218,f89]) ).
fof(f480,plain,
! [X0] :
( sK8(sK11(X0,sK28,sK6)) = sK15(sK6,sK28,sK8(sK11(X0,sK28,sK6)),X0)
| sK8(sK11(X0,sK28,sK6)) = ordered_pair(sK9(sK11(X0,sK28,sK6)),sK10(sK11(X0,sK28,sK6)))
| sK14(sK28,sK6) = sK12(sK28,sK6) ),
inference(resolution,[],[f218,f88]) ).
fof(f218,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK28,X1)) = sK15(X1,sK28,sK8(sK11(X0,sK28,X1)),X0)
| sK8(sK11(X0,sK28,X1)) = ordered_pair(sK9(sK11(X0,sK28,X1)),sK10(sK11(X0,sK28,X1)))
| sK14(sK28,X1) = sK12(sK28,X1) ),
inference(subsumption_resolution,[],[f213,f137]) ).
fof(f213,plain,
! [X0,X1] :
( sK8(sK11(X0,sK28,X1)) = ordered_pair(sK9(sK11(X0,sK28,X1)),sK10(sK11(X0,sK28,X1)))
| sK8(sK11(X0,sK28,X1)) = sK15(X1,sK28,sK8(sK11(X0,sK28,X1)),X0)
| ~ relation(sK28)
| ~ relation(X1)
| sK14(sK28,X1) = sK12(sK28,X1) ),
inference(resolution,[],[f192,f138]) ).
fof(f199,plain,
! [X0,X1] :
( sK8(X1) != ordered_pair(sK16(sK6,sK7,sK8(sK11(X0,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(X0,sK7,sK6))))
| ~ sP4(X0,sK7,sK6)
| sK8(sK11(X0,sK7,sK6)) = ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6)))
| ~ in(sK8(X1),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),X1) ),
inference(resolution,[],[f181,f94]) ).
fof(f398,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK29)) = sK15(sK29,sK27,sK8(sK11(X0,sK27,sK29)),X0)
| sK8(sK11(X0,sK27,sK29)) = ordered_pair(sK9(sK11(X0,sK27,sK29)),sK10(sK11(X0,sK27,sK29)))
| sK14(sK27,sK29) = sK12(sK27,sK29) ),
inference(resolution,[],[f217,f139]) ).
fof(f397,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK28)) = sK15(sK28,sK27,sK8(sK11(X0,sK27,sK28)),X0)
| sK8(sK11(X0,sK27,sK28)) = ordered_pair(sK9(sK11(X0,sK27,sK28)),sK10(sK11(X0,sK27,sK28)))
| sK14(sK27,sK28) = sK12(sK27,sK28) ),
inference(resolution,[],[f217,f137]) ).
fof(f447,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK13(X1,X2) = sK12(X1,X2) ),
inference(resolution,[],[f203,f108]) ).
fof(f446,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK14(X1,X2) = sK12(X1,X2) ),
inference(resolution,[],[f203,f110]) ).
fof(f445,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK14(X1,X2) = ordered_pair(sK18(X2,X1,sK14(X1,X2)),sK19(X2,X1,sK14(X1,X2))) ),
inference(resolution,[],[f203,f162]) ).
fof(f444,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK13(X1,X2) = ordered_pair(sK20(X2,X1,sK13(X1,X2)),sK21(X2,X1,sK13(X1,X2))) ),
inference(resolution,[],[f203,f163]) ).
fof(f203,plain,
! [X2,X0,X1] :
( sP3(X1,X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(resolution,[],[f182,f122]) ).
fof(f396,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK27)) = sK15(sK27,sK27,sK8(sK11(X0,sK27,sK27)),X0)
| sK8(sK11(X0,sK27,sK27)) = ordered_pair(sK9(sK11(X0,sK27,sK27)),sK10(sK11(X0,sK27,sK27)))
| sK14(sK27,sK27) = sK12(sK27,sK27) ),
inference(resolution,[],[f217,f135]) ).
fof(f395,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK26)) = sK15(sK26,sK27,sK8(sK11(X0,sK27,sK26)),X0)
| sK8(sK11(X0,sK27,sK26)) = ordered_pair(sK9(sK11(X0,sK27,sK26)),sK10(sK11(X0,sK27,sK26)))
| sK14(sK27,sK26) = sK12(sK27,sK26) ),
inference(resolution,[],[f217,f132]) ).
fof(f394,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK7)) = sK15(sK7,sK27,sK8(sK11(X0,sK27,sK7)),X0)
| sK8(sK11(X0,sK27,sK7)) = ordered_pair(sK9(sK11(X0,sK27,sK7)),sK10(sK11(X0,sK27,sK7)))
| sK14(sK27,sK7) = sK12(sK27,sK7) ),
inference(resolution,[],[f217,f89]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))),apply(X3,sK21(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2))))) = ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))),apply(X3,sK21(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))))),sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))),apply(X3,sK21(sK11(X0,X1,X2),X3,sK13(X3,sK11(X0,X1,X2)))))))
| ~ sP3(X3,sK11(X0,X1,X2)) ),
inference(resolution,[],[f206,f109]) ).
fof(f206,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))) = ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))))) ),
inference(resolution,[],[f171,f115]) ).
fof(f393,plain,
! [X0] :
( sK8(sK11(X0,sK27,sK6)) = sK15(sK6,sK27,sK8(sK11(X0,sK27,sK6)),X0)
| sK8(sK11(X0,sK27,sK6)) = ordered_pair(sK9(sK11(X0,sK27,sK6)),sK10(sK11(X0,sK27,sK6)))
| sK14(sK27,sK6) = sK12(sK27,sK6) ),
inference(resolution,[],[f217,f88]) ).
fof(f217,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK27,X1)) = sK15(X1,sK27,sK8(sK11(X0,sK27,X1)),X0)
| sK8(sK11(X0,sK27,X1)) = ordered_pair(sK9(sK11(X0,sK27,X1)),sK10(sK11(X0,sK27,X1)))
| sK14(sK27,X1) = sK12(sK27,X1) ),
inference(subsumption_resolution,[],[f212,f135]) ).
fof(f212,plain,
! [X0,X1] :
( sK8(sK11(X0,sK27,X1)) = ordered_pair(sK9(sK11(X0,sK27,X1)),sK10(sK11(X0,sK27,X1)))
| sK8(sK11(X0,sK27,X1)) = sK15(X1,sK27,sK8(sK11(X0,sK27,X1)),X0)
| ~ relation(sK27)
| ~ relation(X1)
| sK14(sK27,X1) = sK12(sK27,X1) ),
inference(resolution,[],[f192,f136]) ).
fof(f321,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK29)) = sK15(sK29,sK26,sK8(sK11(X0,sK26,sK29)),X0)
| sK8(sK11(X0,sK26,sK29)) = ordered_pair(sK9(sK11(X0,sK26,sK29)),sK10(sK11(X0,sK26,sK29)))
| sK14(sK26,sK29) = sK12(sK26,sK29) ),
inference(resolution,[],[f216,f139]) ).
fof(f378,plain,
! [X2,X3,X0,X1] :
( ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))),apply(X3,sK19(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2))))) = ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))),apply(X3,sK19(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))))),sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))),apply(X3,sK19(sK11(X0,X1,X2),X3,sK14(X3,sK11(X0,X1,X2)))))))
| ~ sP3(X3,sK11(X0,X1,X2)) ),
inference(resolution,[],[f196,f111]) ).
fof(f196,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))) = ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))))) ),
inference(resolution,[],[f169,f115]) ).
fof(f320,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK28)) = sK15(sK28,sK26,sK8(sK11(X0,sK26,sK28)),X0)
| sK8(sK11(X0,sK26,sK28)) = ordered_pair(sK9(sK11(X0,sK26,sK28)),sK10(sK11(X0,sK26,sK28)))
| sK14(sK26,sK28) = sK12(sK26,sK28) ),
inference(resolution,[],[f216,f137]) ).
fof(f319,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK27)) = sK15(sK27,sK26,sK8(sK11(X0,sK26,sK27)),X0)
| sK8(sK11(X0,sK26,sK27)) = ordered_pair(sK9(sK11(X0,sK26,sK27)),sK10(sK11(X0,sK26,sK27)))
| sK14(sK26,sK27) = sK12(sK26,sK27) ),
inference(resolution,[],[f216,f135]) ).
fof(f318,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK26)) = sK15(sK26,sK26,sK8(sK11(X0,sK26,sK26)),X0)
| sK8(sK11(X0,sK26,sK26)) = ordered_pair(sK9(sK11(X0,sK26,sK26)),sK10(sK11(X0,sK26,sK26)))
| sK14(sK26,sK26) = sK12(sK26,sK26) ),
inference(resolution,[],[f216,f132]) ).
fof(f345,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP4(X0,X1,X2)
| ~ sP0(sK11(X0,X1,X2),X3,X4)
| sP2(X2,X1,ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))))),X5)
| ~ in(ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))))),cartesian_product2(X5,X5)) ),
inference(resolution,[],[f205,f146]) ).
fof(f205,plain,
! [X2,X3,X0,X1,X4] :
( in(ordered_pair(apply(X1,sK16(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))))),apply(X1,sK17(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4)))))),X2)
| ~ sP4(X0,X1,X2)
| ~ sP0(sK11(X0,X1,X2),X3,X4) ),
inference(resolution,[],[f171,f116]) ).
fof(f317,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK7)) = sK15(sK7,sK26,sK8(sK11(X0,sK26,sK7)),X0)
| sK8(sK11(X0,sK26,sK7)) = ordered_pair(sK9(sK11(X0,sK26,sK7)),sK10(sK11(X0,sK26,sK7)))
| sK14(sK26,sK7) = sK12(sK26,sK7) ),
inference(resolution,[],[f216,f89]) ).
fof(f316,plain,
! [X0] :
( sK8(sK11(X0,sK26,sK6)) = sK15(sK6,sK26,sK8(sK11(X0,sK26,sK6)),X0)
| sK8(sK11(X0,sK26,sK6)) = ordered_pair(sK9(sK11(X0,sK26,sK6)),sK10(sK11(X0,sK26,sK6)))
| sK14(sK26,sK6) = sK12(sK26,sK6) ),
inference(resolution,[],[f216,f88]) ).
fof(f216,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK26,X1)) = sK15(X1,sK26,sK8(sK11(X0,sK26,X1)),X0)
| sK8(sK11(X0,sK26,X1)) = ordered_pair(sK9(sK11(X0,sK26,X1)),sK10(sK11(X0,sK26,X1)))
| sK14(sK26,X1) = sK12(sK26,X1) ),
inference(subsumption_resolution,[],[f211,f132]) ).
fof(f211,plain,
! [X0,X1] :
( sK8(sK11(X0,sK26,X1)) = ordered_pair(sK9(sK11(X0,sK26,X1)),sK10(sK11(X0,sK26,X1)))
| sK8(sK11(X0,sK26,X1)) = sK15(X1,sK26,sK8(sK11(X0,sK26,X1)),X0)
| ~ relation(sK26)
| ~ relation(X1)
| sK14(sK26,X1) = sK12(sK26,X1) ),
inference(resolution,[],[f192,f134]) ).
fof(f310,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP4(X0,X1,X2)
| ~ sP1(sK11(X0,X1,X2),X3,X4)
| sP2(X2,X1,ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))))),X5)
| ~ in(ordered_pair(sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4)))),sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))))),cartesian_product2(X5,X5)) ),
inference(resolution,[],[f195,f146]) ).
fof(f195,plain,
! [X2,X3,X0,X1,X4] :
( in(ordered_pair(apply(X1,sK16(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))))),apply(X1,sK17(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4)))))),X2)
| ~ sP4(X0,X1,X2)
| ~ sP1(sK11(X0,X1,X2),X3,X4) ),
inference(resolution,[],[f169,f116]) ).
fof(f225,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK29)) = sK15(sK29,sK7,sK8(sK11(X0,sK7,sK29)),X0)
| sK8(sK11(X0,sK7,sK29)) = ordered_pair(sK9(sK11(X0,sK7,sK29)),sK10(sK11(X0,sK7,sK29)))
| sK14(sK7,sK29) = sK12(sK7,sK29) ),
inference(resolution,[],[f215,f139]) ).
fof(f224,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK28)) = sK15(sK28,sK7,sK8(sK11(X0,sK7,sK28)),X0)
| sK8(sK11(X0,sK7,sK28)) = ordered_pair(sK9(sK11(X0,sK7,sK28)),sK10(sK11(X0,sK7,sK28)))
| sK14(sK7,sK28) = sK12(sK7,sK28) ),
inference(resolution,[],[f215,f137]) ).
fof(f223,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK27)) = sK15(sK27,sK7,sK8(sK11(X0,sK7,sK27)),X0)
| sK8(sK11(X0,sK7,sK27)) = ordered_pair(sK9(sK11(X0,sK7,sK27)),sK10(sK11(X0,sK7,sK27)))
| sK14(sK7,sK27) = sK12(sK7,sK27) ),
inference(resolution,[],[f215,f135]) ).
fof(f207,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))) = sK15(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))),X0) ),
inference(resolution,[],[f171,f114]) ).
fof(f222,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26)))
| sK14(sK7,sK26) = sK12(sK7,sK26) ),
inference(resolution,[],[f215,f132]) ).
fof(f197,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP1(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2)
| ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))) = sK15(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))),X0) ),
inference(resolution,[],[f169,f114]) ).
fof(f221,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7)))
| sK14(sK7,sK7) = sK12(sK7,sK7) ),
inference(resolution,[],[f215,f89]) ).
fof(f220,plain,
! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6)))
| sK14(sK7,sK6) = sK12(sK7,sK6) ),
inference(resolution,[],[f215,f88]) ).
fof(f215,plain,
! [X0,X1] :
( ~ relation(X1)
| sK8(sK11(X0,sK7,X1)) = sK15(X1,sK7,sK8(sK11(X0,sK7,X1)),X0)
| sK8(sK11(X0,sK7,X1)) = ordered_pair(sK9(sK11(X0,sK7,X1)),sK10(sK11(X0,sK7,X1)))
| sK14(sK7,X1) = sK12(sK7,X1) ),
inference(subsumption_resolution,[],[f209,f89]) ).
fof(f209,plain,
! [X0,X1] :
( sK8(sK11(X0,sK7,X1)) = ordered_pair(sK9(sK11(X0,sK7,X1)),sK10(sK11(X0,sK7,X1)))
| sK8(sK11(X0,sK7,X1)) = sK15(X1,sK7,sK8(sK11(X0,sK7,X1)),X0)
| ~ relation(sK7)
| ~ relation(X1)
| sK14(sK7,X1) = sK12(sK7,X1) ),
inference(resolution,[],[f192,f90]) ).
fof(f192,plain,
! [X2,X0,X1] :
( ~ function(X1)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| ~ relation(X1)
| ~ relation(X2)
| sK14(X1,X2) = sK12(X1,X2) ),
inference(resolution,[],[f189,f110]) ).
fof(f171,plain,
! [X2,X3,X0,X1,X4] :
( sP2(X2,X1,ordered_pair(apply(X3,sK20(sK11(X0,X1,X2),X3,X4)),apply(X3,sK21(sK11(X0,X1,X2),X3,X4))),X0)
| ~ sP0(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f121,f106]) ).
fof(f201,plain,
! [X2,X0,X1] :
( ~ in(X2,ordered_pair(apply(X1,sK16(X2,X1,sK8(sK11(X0,X1,X2)))),apply(X1,sK17(X2,X1,sK8(sK11(X0,X1,X2))))))
| ~ sP4(X0,X1,X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2))) ),
inference(resolution,[],[f181,f105]) ).
fof(f182,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))) ),
inference(resolution,[],[f157,f115]) ).
fof(f181,plain,
! [X2,X0,X1] :
( in(ordered_pair(apply(X1,sK16(X2,X1,sK8(sK11(X0,X1,X2)))),apply(X1,sK17(X2,X1,sK8(sK11(X0,X1,X2))))),X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f157,f116]) ).
fof(f169,plain,
! [X2,X3,X0,X1,X4] :
( sP2(X2,X1,ordered_pair(apply(X3,sK18(sK11(X0,X1,X2),X3,X4)),apply(X3,sK19(sK11(X0,X1,X2),X3,X4))),X0)
| ~ sP1(sK11(X0,X1,X2),X3,X4)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f119,f106]) ).
fof(f185,plain,
! [X0,X1] :
( sK8(X1) != ordered_pair(sK16(sK6,sK7,sK8(sK11(X0,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(X0,sK7,sK6))))
| ~ sP4(X0,sK7,sK6)
| in(sK8(sK11(X0,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),X1) ),
inference(resolution,[],[f175,f94]) ).
fof(f180,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ sP2(X2,X1,ordered_pair(apply(X3,X4),apply(X3,X5)),X0)
| ~ in(ordered_pair(X4,X5),cartesian_product2(X6,X6))
| sP2(sK11(X0,X1,X2),X3,ordered_pair(X4,X5),X6)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f146,f107]) ).
fof(f191,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK14(X1,X2) = ordered_pair(sK18(X2,X1,sK14(X1,X2)),sK19(X2,X1,sK14(X1,X2))) ),
inference(resolution,[],[f189,f162]) ).
fof(f190,plain,
! [X2,X0,X1] :
( sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2)
| sK13(X1,X2) = ordered_pair(sK20(X2,X1,sK13(X1,X2)),sK21(X2,X1,sK13(X1,X2))) ),
inference(resolution,[],[f189,f163]) ).
fof(f189,plain,
! [X2,X0,X1] :
( sP3(X1,X2)
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| ~ function(X1)
| ~ relation(X1)
| ~ relation(X2) ),
inference(resolution,[],[f183,f122]) ).
fof(f179,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK20(X0,X1,X2),sK21(X0,X1,X2)),cartesian_product2(X3,X3))
| sP2(X0,X1,ordered_pair(sK20(X0,X1,X2),sK21(X0,X1,X2)),X3)
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f146,f121]) ).
fof(f178,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(sK18(X0,X1,X2),sK19(X0,X1,X2)),cartesian_product2(X3,X3))
| sP2(X0,X1,ordered_pair(sK18(X0,X1,X2),sK19(X0,X1,X2)),X3)
| ~ sP1(X0,X1,X2) ),
inference(resolution,[],[f146,f119]) ).
fof(f187,plain,
! [X2,X0,X1] :
( ~ in(X2,ordered_pair(apply(X1,sK16(X2,X1,sK8(sK11(X0,X1,X2)))),apply(X1,sK17(X2,X1,sK8(sK11(X0,X1,X2))))))
| ~ sP4(X0,X1,X2)
| in(sK8(sK11(X0,X1,X2)),cartesian_product2(sK5,sK5)) ),
inference(resolution,[],[f175,f105]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ~ in(cartesian_product2(sK5,sK5),sK8(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2))))
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f165,f105]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK9(sK11(X0,X1,X2)),sK10(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0) ),
inference(resolution,[],[f157,f114]) ).
fof(f175,plain,
! [X2,X0,X1] :
( in(ordered_pair(apply(X0,sK16(X1,X0,sK8(sK11(X2,X0,X1)))),apply(X0,sK17(X1,X0,sK8(sK11(X2,X0,X1))))),X1)
| in(sK8(sK11(X2,X0,X1)),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X0,X1) ),
inference(resolution,[],[f116,f158]) ).
fof(f165,plain,
! [X2,X0,X1] :
( in(sK8(sK11(X0,X1,X2)),cartesian_product2(sK5,sK5))
| ~ sP4(X0,X1,X2)
| sK8(sK11(X0,X1,X2)) = ordered_pair(sK16(X2,X1,sK8(sK11(X0,X1,X2))),sK17(X2,X1,sK8(sK11(X0,X1,X2)))) ),
inference(resolution,[],[f158,f115]) ).
fof(f164,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ sP2(X5,X4,sK11(X0,X1,X2),X3)
| ~ sP2(X2,X1,sK11(X3,X4,X5),X0)
| ~ sP4(X0,X1,X2)
| ~ sP4(X3,X4,X5) ),
inference(resolution,[],[f160,f107]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sP2(X0,X1,sK8(sK11(X2,X1,X0)),X2)
| ~ sP4(X2,X1,X0)
| sK8(sK11(X2,X1,X0)) = ordered_pair(sK9(sK11(X2,X1,X0)),sK10(sK11(X2,X1,X0))) ),
inference(resolution,[],[f106,f92]) ).
fof(f177,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK9(X0),sK10(X0)),cartesian_product2(X1,X1))
| sP2(sK6,sK7,ordered_pair(sK9(X0),sK10(X0)),X1)
| in(sK8(X0),X0) ),
inference(resolution,[],[f146,f93]) ).
fof(f146,plain,
! [X3,X0,X1,X6,X5] :
( ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| sP2(X0,X1,ordered_pair(X5,X6),X3)
| ~ in(ordered_pair(X5,X6),cartesian_product2(X3,X3)) ),
inference(equality_resolution,[],[f145]) ).
fof(f145,plain,
! [X3,X0,X1,X6,X4,X5] :
( sP2(X0,X1,ordered_pair(X5,X6),X3)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ordered_pair(X5,X6) != X4
| ~ in(X4,cartesian_product2(X3,X3)) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( sP2(X0,X1,X2,X3)
| ~ in(ordered_pair(apply(X1,X5),apply(X1,X6)),X0)
| ordered_pair(X5,X6) != X2
| X2 != X4
| ~ in(X4,cartesian_product2(X3,X3)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ in(cartesian_product2(sK5,sK5),sK8(sK11(X0,X1,X2)))
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0)
| ~ sP4(X0,X1,X2) ),
inference(resolution,[],[f166,f105]) ).
fof(f166,plain,
! [X2,X0,X1] :
( in(sK8(sK11(X0,X1,X2)),cartesian_product2(sK5,sK5))
| ~ sP4(X0,X1,X2)
| sK8(sK11(X0,X1,X2)) = sK15(X2,X1,sK8(sK11(X0,X1,X2)),X0) ),
inference(resolution,[],[f158,f114]) ).
fof(f163,plain,
! [X0,X1] :
( ~ sP3(X1,X0)
| sK13(X1,X0) = ordered_pair(sK20(X0,X1,sK13(X1,X0)),sK21(X0,X1,sK13(X1,X0))) ),
inference(resolution,[],[f120,f109]) ).
fof(f162,plain,
! [X0,X1] :
( ~ sP3(X1,X0)
| sK14(X1,X0) = ordered_pair(sK18(X0,X1,sK14(X1,X0)),sK19(X0,X1,sK14(X1,X0))) ),
inference(resolution,[],[f118,f111]) ).
fof(f174,plain,
! [X0,X1] :
( sK8(X1) != ordered_pair(sK20(sK6,sK7,X0),sK21(sK6,sK7,X0))
| ~ in(sK8(X1),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),X1)
| ~ sP0(sK6,sK7,X0) ),
inference(resolution,[],[f94,f121]) ).
fof(f173,plain,
! [X0,X1] :
( sK8(X1) != ordered_pair(sK18(sK6,sK7,X0),sK19(sK6,sK7,X0))
| ~ in(sK8(X1),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),X1)
| ~ sP1(sK6,sK7,X0) ),
inference(resolution,[],[f94,f119]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| in(ordered_pair(apply(X1,sK16(X0,X1,X2)),apply(X1,sK17(X0,X1,X2))),X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f170,plain,
! [X2,X0,X1] :
( ~ in(X0,ordered_pair(apply(X1,sK20(X0,X1,X2)),apply(X1,sK21(X0,X1,X2))))
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f121,f105]) ).
fof(f172,plain,
! [X0,X1] :
( ordered_pair(sK9(X0),sK10(X0)) != sK8(X1)
| ~ in(sK8(X1),cartesian_product2(sK5,sK5))
| ~ in(sK8(X1),X1)
| in(sK8(X0),X0) ),
inference(resolution,[],[f94,f93]) ).
fof(f94,plain,
! [X3,X6,X5] :
( ~ in(ordered_pair(apply(sK7,X5),apply(sK7,X6)),sK6)
| ordered_pair(X5,X6) != sK8(X3)
| ~ in(sK8(X3),cartesian_product2(sK5,sK5))
| ~ in(sK8(X3),X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
( ! [X3] :
( ( ! [X5,X6] :
( ~ in(ordered_pair(apply(sK7,X5),apply(sK7,X6)),sK6)
| ordered_pair(X5,X6) != sK8(X3) )
| ~ in(sK8(X3),cartesian_product2(sK5,sK5))
| ~ in(sK8(X3),X3) )
& ( ( in(ordered_pair(apply(sK7,sK9(X3)),apply(sK7,sK10(X3))),sK6)
& sK8(X3) = ordered_pair(sK9(X3),sK10(X3))
& in(sK8(X3),cartesian_product2(sK5,sK5)) )
| in(sK8(X3),X3) ) )
& function(sK7)
& relation(sK7)
& relation(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9,sK10])],[f46,f49,f48,f47]) ).
fof(f47,plain,
( ? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| ~ in(X4,X3) )
& ( ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3] :
? [X4] :
( ( ! [X6,X5] :
( ~ in(ordered_pair(apply(sK7,X5),apply(sK7,X6)),sK6)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK5,sK5))
| ~ in(X4,X3) )
& ( ( ? [X8,X7] :
( in(ordered_pair(apply(sK7,X7),apply(sK7,X8)),sK6)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(sK5,sK5)) )
| in(X4,X3) ) )
& function(sK7)
& relation(sK7)
& relation(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f48,plain,
! [X3] :
( ? [X4] :
( ( ! [X6,X5] :
( ~ in(ordered_pair(apply(sK7,X5),apply(sK7,X6)),sK6)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(sK5,sK5))
| ~ in(X4,X3) )
& ( ( ? [X8,X7] :
( in(ordered_pair(apply(sK7,X7),apply(sK7,X8)),sK6)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(sK5,sK5)) )
| in(X4,X3) ) )
=> ( ( ! [X6,X5] :
( ~ in(ordered_pair(apply(sK7,X5),apply(sK7,X6)),sK6)
| ordered_pair(X5,X6) != sK8(X3) )
| ~ in(sK8(X3),cartesian_product2(sK5,sK5))
| ~ in(sK8(X3),X3) )
& ( ( ? [X8,X7] :
( in(ordered_pair(apply(sK7,X7),apply(sK7,X8)),sK6)
& ordered_pair(X7,X8) = sK8(X3) )
& in(sK8(X3),cartesian_product2(sK5,sK5)) )
| in(sK8(X3),X3) ) ) ),
introduced(choice_axiom,[]) ).
fof(f49,plain,
! [X3] :
( ? [X8,X7] :
( in(ordered_pair(apply(sK7,X7),apply(sK7,X8)),sK6)
& ordered_pair(X7,X8) = sK8(X3) )
=> ( in(ordered_pair(apply(sK7,sK9(X3)),apply(sK7,sK10(X3))),sK6)
& sK8(X3) = ordered_pair(sK9(X3),sK10(X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| ~ in(X4,X3) )
& ( ( ? [X7,X8] :
( in(ordered_pair(apply(X2,X7),apply(X2,X8)),X1)
& ordered_pair(X7,X8) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& relation(X1) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& relation(X1) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ! [X5,X6] :
( ~ in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
| ordered_pair(X5,X6) != X4 )
| ~ in(X4,cartesian_product2(X0,X0))
| ~ in(X4,X3) )
& ( ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) )
| in(X4,X3) ) )
& function(X2)
& relation(X2)
& relation(X1) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
& function(X2)
& relation(X2)
& relation(X1) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) )
& function(X2)
& relation(X2)
& relation(X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
inference(negated_conjecture,[],[f1]) ).
fof(f1,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( ? [X5,X6] :
( in(ordered_pair(apply(X2,X5),apply(X2,X6)),X1)
& ordered_pair(X5,X6) = X4 )
& in(X4,cartesian_product2(X0,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_21__wellord2__1) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ in(X0,ordered_pair(apply(X1,sK18(X0,X1,X2)),apply(X1,sK19(X0,X1,X2))))
| ~ sP1(X0,X1,X2) ),
inference(resolution,[],[f119,f105]) ).
fof(f121,plain,
! [X2,X0,X1] :
( in(ordered_pair(apply(X1,sK20(X0,X1,X2)),apply(X1,sK21(X0,X1,X2))),X0)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(apply(X1,sK20(X0,X1,X2)),apply(X1,sK21(X0,X1,X2))),X0)
& ordered_pair(sK20(X0,X1,X2),sK21(X0,X1,X2)) = X2 )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f69,f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& ordered_pair(X3,X4) = X2 )
=> ( in(ordered_pair(apply(X1,sK20(X0,X1,X2)),apply(X1,sK21(X0,X1,X2))),X0)
& ordered_pair(sK20(X0,X1,X2),sK21(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& ordered_pair(X3,X4) = X2 )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X1,X2,X4] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
| ~ sP0(X1,X2,X4) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X1,X2,X4] :
( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
| ~ sP0(X1,X2,X4) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f119,plain,
! [X2,X0,X1] :
( in(ordered_pair(apply(X1,sK18(X0,X1,X2)),apply(X1,sK19(X0,X1,X2))),X0)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(apply(X1,sK18(X0,X1,X2)),apply(X1,sK19(X0,X1,X2))),X0)
& ordered_pair(sK18(X0,X1,X2),sK19(X0,X1,X2)) = X2 )
| ~ sP1(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f65,f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& ordered_pair(X3,X4) = X2 )
=> ( in(ordered_pair(apply(X1,sK18(X0,X1,X2)),apply(X1,sK19(X0,X1,X2))),X0)
& ordered_pair(sK18(X0,X1,X2),sK19(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( in(ordered_pair(apply(X1,X3),apply(X1,X4)),X0)
& ordered_pair(X3,X4) = X2 )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X1,X2,X5] :
( ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
| ~ sP1(X1,X2,X5) ),
inference(nnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X1,X2,X5] :
( ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
| ~ sP1(X1,X2,X5) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ in(cartesian_product2(sK5,sK5),sK8(sK11(X2,X1,X0)))
| ~ sP4(X2,X1,X0)
| sP2(X0,X1,sK8(sK11(X2,X1,X0)),X2) ),
inference(resolution,[],[f158,f105]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sP2(X0,X1,sK8(sK11(X2,X1,X0)),X2)
| in(sK8(sK11(X2,X1,X0)),cartesian_product2(sK5,sK5))
| ~ sP4(X2,X1,X0) ),
inference(resolution,[],[f106,f91]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ sP2(X0,X1,X2,X3)
| ordered_pair(sK16(X0,X1,X2),sK17(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f63]) ).
fof(f160,plain,
! [X2,X3,X0,X1] :
( ~ in(sK11(X3,X1,X0),X2)
| ~ sP4(X3,X1,X0)
| ~ sP2(X0,X1,X2,X3) ),
inference(resolution,[],[f107,f105]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ordered_pair(sK20(X0,X1,X2),sK21(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ordered_pair(sK18(X0,X1,X2),sK19(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f67]) ).
fof(f156,plain,
! [X2,X3,X0,X1] :
( ~ in(cartesian_product2(X3,X3),sK15(X0,X1,X2,X3))
| ~ sP2(X0,X1,X2,X3) ),
inference(resolution,[],[f113,f105]) ).
fof(f106,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK11(X0,X1,X2))
| sP2(X2,X1,X4,X0)
| ~ sP4(X0,X1,X2) ),
inference(cnf_transformation,[],[f54]) ).
fof(f122,plain,
! [X2,X0,X1] :
( sP4(X0,X2,X1)
| sP3(X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( sP4(X0,X2,X1)
| sP3(X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(definition_folding,[],[f37,f42,f41,f40,f39,f38]) ).
fof(f41,plain,
! [X2,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& sP1(X1,X2,X5)
& X3 = X5
& sP0(X1,X2,X4)
& X3 = X4 )
| ~ sP3(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) )
| ? [X3,X4,X5] :
( X4 != X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
| ~ function(X2)
| ~ relation(X2)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X5 )
& X3 = X5
& ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X10] :
! [X11] :
( in(X11,X10)
<=> ? [X12] :
( ? [X13,X14] :
( in(ordered_pair(apply(X2,X13),apply(X2,X14)),X1)
& ordered_pair(X13,X14) = X11 )
& X11 = X12
& in(X12,cartesian_product2(X0,X0)) ) ) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2)
& relation(X1) )
=> ( ! [X3,X4,X5] :
( ( ? [X8,X9] :
( in(ordered_pair(apply(X2,X8),apply(X2,X9)),X1)
& ordered_pair(X8,X9) = X5 )
& X3 = X5
& ? [X6,X7] :
( in(ordered_pair(apply(X2,X6),apply(X2,X7)),X1)
& ordered_pair(X6,X7) = X4 )
& X3 = X4 )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( ? [X10,X11] :
( in(ordered_pair(apply(X2,X10),apply(X2,X11)),X1)
& ordered_pair(X10,X11) = X4 )
& X4 = X5
& in(X5,cartesian_product2(X0,X0)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_21__wellord2__1) ).
fof(f155,plain,
! [X0] :
( ~ in(sK6,ordered_pair(apply(sK7,sK9(X0)),apply(sK7,sK10(X0))))
| in(sK8(X0),X0) ),
inference(resolution,[],[f93,f105]) ).
fof(f93,plain,
! [X3] :
( in(ordered_pair(apply(sK7,sK9(X3)),apply(sK7,sK10(X3))),sK6)
| in(sK8(X3),X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f112,plain,
! [X0,X1] :
( sK13(X0,X1) != sK14(X0,X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( ( sK13(X0,X1) != sK14(X0,X1)
& sP1(X1,X0,sK14(X0,X1))
& sK12(X0,X1) = sK14(X0,X1)
& sP0(X1,X0,sK13(X0,X1))
& sK12(X0,X1) = sK13(X0,X1) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f56,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP1(X1,X0,X4)
& X2 = X4
& sP0(X1,X0,X3)
& X2 = X3 )
=> ( sK13(X0,X1) != sK14(X0,X1)
& sP1(X1,X0,sK14(X0,X1))
& sK12(X0,X1) = sK14(X0,X1)
& sP0(X1,X0,sK13(X0,X1))
& sK12(X0,X1) = sK13(X0,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& sP1(X1,X0,X4)
& X2 = X4
& sP0(X1,X0,X3)
& X2 = X3 )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f55]) ).
fof(f55,plain,
! [X2,X1] :
( ? [X3,X4,X5] :
( X4 != X5
& sP1(X1,X2,X5)
& X3 = X5
& sP0(X1,X2,X4)
& X3 = X4 )
| ~ sP3(X2,X1) ),
inference(nnf_transformation,[],[f41]) ).
fof(f110,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sK12(X0,X1) = sK14(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| sK12(X0,X1) = sK13(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f154,plain,
! [X0] :
( ~ in(X0,sK8(X0))
| sK8(X0) = ordered_pair(sK9(X0),sK10(X0)) ),
inference(resolution,[],[f92,f105]) ).
fof(f92,plain,
! [X3] :
( in(sK8(X3),X3)
| sK8(X3) = ordered_pair(sK9(X3),sK10(X3)) ),
inference(cnf_transformation,[],[f50]) ).
fof(f111,plain,
! [X0,X1] :
( sP1(X1,X0,sK14(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f109,plain,
! [X0,X1] :
( sP0(X1,X0,sK13(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f151,plain,
! [X0] :
( ~ in(X0,sK8(X0))
| in(sK8(X0),cartesian_product2(sK5,sK5)) ),
inference(resolution,[],[f91,f105]) ).
fof(f150,plain,
! [X0] :
( ~ in(cartesian_product2(sK5,sK5),sK8(X0))
| in(sK8(X0),X0) ),
inference(resolution,[],[f91,f105]) ).
fof(f153,plain,
~ in(cartesian_product2(sK5,sK5),sK8(cartesian_product2(sK5,sK5))),
inference(resolution,[],[f152,f105]) ).
fof(f152,plain,
in(sK8(cartesian_product2(sK5,sK5)),cartesian_product2(sK5,sK5)),
inference(factoring,[],[f91]) ).
fof(f91,plain,
! [X3] :
( in(sK8(X3),cartesian_product2(sK5,sK5))
| in(sK8(X3),X3) ),
inference(cnf_transformation,[],[f50]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f104,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f147,plain,
function(sK23),
inference(resolution,[],[f95,f124]) ).
fof(f95,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f141,plain,
empty(sK29),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( ordinal(sK29)
& epsilon_connected(sK29)
& epsilon_transitive(sK29)
& empty(sK29)
& function(sK29)
& relation(sK29) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f25,f86]) ).
fof(f86,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) )
=> ( ordinal(sK29)
& epsilon_connected(sK29)
& epsilon_transitive(sK29)
& empty(sK29)
& function(sK29)
& relation(sK29) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f7]) ).
fof(f7,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& empty(X0)
& one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(f140,plain,
function(sK29),
inference(cnf_transformation,[],[f87]) ).
fof(f139,plain,
relation(sK29),
inference(cnf_transformation,[],[f87]) ).
fof(f138,plain,
function(sK28),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( function(sK28)
& relation(sK28) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f23,f84]) ).
fof(f84,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK28)
& relation(sK28) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f3]) ).
fof(f3,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f137,plain,
relation(sK28),
inference(cnf_transformation,[],[f85]) ).
fof(f136,plain,
function(sK27),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
( function(sK27)
& relation(sK27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f19,f82]) ).
fof(f82,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK27)
& relation(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f135,plain,
relation(sK27),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
function(sK26),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
( function(sK26)
& empty(sK26)
& relation(sK26) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f10,f80]) ).
fof(f80,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK26)
& empty(sK26)
& relation(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f10,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f133,plain,
empty(sK26),
inference(cnf_transformation,[],[f81]) ).
fof(f132,plain,
relation(sK26),
inference(cnf_transformation,[],[f81]) ).
fof(f125,plain,
~ empty(sK24),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& ~ empty(sK24) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f8,f76]) ).
fof(f76,plain,
( ? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) )
=> ( ordinal(sK24)
& epsilon_connected(sK24)
& epsilon_transitive(sK24)
& ~ empty(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f8,axiom,
? [X0] :
( ordinal(X0)
& epsilon_connected(X0)
& epsilon_transitive(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(f124,plain,
empty(sK23),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
empty(sK23),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f13,f74]) ).
fof(f74,plain,
( ? [X0] : empty(X0)
=> empty(sK23) ),
introduced(choice_axiom,[]) ).
fof(f13,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f123,plain,
~ empty(sK22),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
~ empty(sK22),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f14,f72]) ).
fof(f72,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK22) ),
introduced(choice_axiom,[]) ).
fof(f14,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f90,plain,
function(sK7),
inference(cnf_transformation,[],[f50]) ).
fof(f89,plain,
relation(sK7),
inference(cnf_transformation,[],[f50]) ).
fof(f88,plain,
relation(sK6),
inference(cnf_transformation,[],[f50]) ).
fof(f908,plain,
( ~ spl30_64
| ~ spl30_67
| spl30_68
| ~ spl30_69
| ~ spl30_70 ),
inference(avatar_contradiction_clause,[],[f907]) ).
fof(f907,plain,
( $false
| ~ spl30_64
| ~ spl30_67
| spl30_68
| ~ spl30_69
| ~ spl30_70 ),
inference(global_subsumption,[],[f838,f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f747,f754,f755,f756,f757,f761,f245,f762,f763,f760,f765,f764,f784,f275,f812,f813,f780,f312,f849,f846,f847,f848,f835,f875,f821,f871,f347,f895,f892,f893,f894]) ).
fof(f838,plain,
( ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| ~ in(sK8(X0),X0)
| ~ in(sK8(X0),cartesian_product2(sK5,sK5)) )
| ~ spl30_70 ),
inference(avatar_component_clause,[],[f837]) ).
fof(f837,plain,
( spl30_70
<=> ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| ~ in(sK8(X0),X0)
| ~ in(sK8(X0),cartesian_product2(sK5,sK5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_70])]) ).
fof(f906,plain,
( ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(avatar_contradiction_clause,[],[f905]) ).
fof(f905,plain,
( $false
| ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(global_subsumption,[],[f904,f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f747,f754,f755,f756,f757,f761,f245,f762,f763,f760,f765,f764,f784,f275,f812,f813,f780,f312,f849,f846,f847,f848,f835,f875,f821,f871,f347,f895,f892,f893,f894]) ).
fof(f904,plain,
( in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ spl30_64
| ~ spl30_65 ),
inference(subsumption_resolution,[],[f765,f768]) ).
fof(f903,plain,
( ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(avatar_contradiction_clause,[],[f902]) ).
fof(f902,plain,
( $false
| ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(global_subsumption,[],[f901,f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f747,f754,f755,f756,f757,f761,f245,f762,f763,f760,f765,f764,f784,f275,f812,f813,f780,f312,f849,f846,f847,f848,f835,f875,f821,f871,f347,f895,f892,f893,f894]) ).
fof(f901,plain,
( ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),X0) )
| ~ spl30_65
| ~ spl30_67 ),
inference(subsumption_resolution,[],[f883,f780]) ).
fof(f883,plain,
( ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| ~ sP4(sK5,sK7,sK6)
| in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),X0) )
| ~ spl30_65 ),
inference(superposition,[],[f185,f877]) ).
fof(f877,plain,
( sK8(sK11(sK5,sK7,sK6)) = ordered_pair(sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6))))
| ~ spl30_65 ),
inference(resolution,[],[f768,f115]) ).
fof(f900,plain,
( ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(avatar_contradiction_clause,[],[f899]) ).
fof(f899,plain,
( $false
| ~ spl30_64
| ~ spl30_65
| ~ spl30_67
| spl30_68
| ~ spl30_69 ),
inference(global_subsumption,[],[f898,f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f747,f754,f755,f756,f757,f761,f245,f762,f763,f760,f765,f764,f784,f275,f812,f813,f780,f312,f849,f846,f847,f848,f835,f875,f821,f871,f347,f895,f892,f893,f894]) ).
fof(f898,plain,
( ! [X0] :
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),X0)
| ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5)) )
| ~ spl30_65
| ~ spl30_67 ),
inference(forward_demodulation,[],[f897,f877]) ).
fof(f897,plain,
( ! [X0] :
( ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| sP2(sK6,sK7,ordered_pair(sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6)))),X0)
| in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5)) )
| ~ spl30_65
| ~ spl30_67 ),
inference(subsumption_resolution,[],[f885,f780]) ).
fof(f885,plain,
( ! [X0] :
( ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| ~ sP4(sK5,sK7,sK6)
| sP2(sK6,sK7,ordered_pair(sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6)))),X0)
| in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5)) )
| ~ spl30_65 ),
inference(superposition,[],[f186,f877]) ).
fof(f896,plain,
( spl30_70
| ~ spl30_65 ),
inference(avatar_split_clause,[],[f890,f767,f837]) ).
fof(f890,plain,
( ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| ~ in(sK8(X0),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),X0) )
| ~ spl30_65 ),
inference(forward_demodulation,[],[f879,f877]) ).
fof(f879,plain,
( ! [X0] :
( sK8(X0) != ordered_pair(sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6))),sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6))))
| ~ in(sK8(X0),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),X0) )
| ~ spl30_65 ),
inference(resolution,[],[f876,f94]) ).
fof(f876,plain,
( in(ordered_pair(apply(sK7,sK16(sK6,sK7,sK8(sK11(sK5,sK7,sK6)))),apply(sK7,sK17(sK6,sK7,sK8(sK11(sK5,sK7,sK6))))),sK6)
| ~ spl30_65 ),
inference(resolution,[],[f768,f116]) ).
fof(f874,plain,
( spl30_65
| ~ spl30_67
| ~ spl30_69 ),
inference(avatar_contradiction_clause,[],[f873]) ).
fof(f873,plain,
( $false
| spl30_65
| ~ spl30_67
| ~ spl30_69 ),
inference(subsumption_resolution,[],[f872,f780]) ).
fof(f872,plain,
( ~ sP4(sK5,sK7,sK6)
| spl30_65
| ~ spl30_69 ),
inference(subsumption_resolution,[],[f870,f769]) ).
fof(f769,plain,
( ~ sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| spl30_65 ),
inference(avatar_component_clause,[],[f767]) ).
fof(f869,plain,
( ~ spl30_68
| ~ spl30_69
| ~ spl30_70 ),
inference(avatar_contradiction_clause,[],[f868]) ).
fof(f868,plain,
( $false
| ~ spl30_68
| ~ spl30_69
| ~ spl30_70 ),
inference(global_subsumption,[],[f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f216,f316,f317,f205,f345,f347,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f245,f762,f763,f275,f812,f813,f785,f838,f312,f849,f846,f847,f848,f867,f835]) ).
fof(f867,plain,
( ~ in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| ~ spl30_68
| ~ spl30_70 ),
inference(subsumption_resolution,[],[f844,f785]) ).
fof(f844,plain,
( ~ in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ spl30_70 ),
inference(equality_resolution,[],[f838]) ).
fof(f785,plain,
( in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ spl30_68 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f866,plain,
( spl30_65
| ~ spl30_67
| spl30_69 ),
inference(avatar_contradiction_clause,[],[f865]) ).
fof(f865,plain,
( $false
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f864,f834]) ).
fof(f864,plain,
( in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f855,f769]) ).
fof(f855,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6))
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(resolution,[],[f850,f91]) ).
fof(f850,plain,
( ! [X0] :
( ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),X0) )
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f831,f834]) ).
fof(f831,plain,
( ! [X0] :
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),X0)
| ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6)) )
| spl30_65
| ~ spl30_67 ),
inference(forward_demodulation,[],[f828,f824]) ).
fof(f824,plain,
( sK8(sK11(sK5,sK7,sK6)) = ordered_pair(sK9(sK11(sK5,sK7,sK6)),sK10(sK11(sK5,sK7,sK6)))
| spl30_65
| ~ spl30_67 ),
inference(global_subsumption,[],[f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f223,f224,f225,f195,f310,f312,f216,f316,f317,f205,f345,f347,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f245,f762,f763,f769,f776,f777,f275,f812,f813,f780,f821]) ).
fof(f777,plain,
( in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(sK5,sK5))
| ~ sP4(sK5,sK7,sK6)
| spl30_65 ),
inference(resolution,[],[f769,f158]) ).
fof(f776,plain,
( ~ sP4(sK5,sK7,sK6)
| sK8(sK11(sK5,sK7,sK6)) = ordered_pair(sK9(sK11(sK5,sK7,sK6)),sK10(sK11(sK5,sK7,sK6)))
| spl30_65 ),
inference(resolution,[],[f769,f157]) ).
fof(f828,plain,
( ! [X0] :
( ~ in(sK8(sK11(sK5,sK7,sK6)),cartesian_product2(X0,X0))
| sP2(sK6,sK7,ordered_pair(sK9(sK11(sK5,sK7,sK6)),sK10(sK11(sK5,sK7,sK6))),X0)
| in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6)) )
| spl30_65
| ~ spl30_67 ),
inference(superposition,[],[f177,f824]) ).
fof(f863,plain,
( spl30_65
| ~ spl30_67
| spl30_69 ),
inference(avatar_contradiction_clause,[],[f862]) ).
fof(f862,plain,
( $false
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f861,f780]) ).
fof(f861,plain,
( ~ sP4(sK5,sK7,sK6)
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(subsumption_resolution,[],[f856,f769]) ).
fof(f856,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ sP4(sK5,sK7,sK6)
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(duplicate_literal_removal,[],[f854]) ).
fof(f854,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| ~ sP4(sK5,sK7,sK6)
| spl30_65
| ~ spl30_67
| spl30_69 ),
inference(resolution,[],[f850,f158]) ).
fof(f858,plain,
( spl30_65
| ~ spl30_67
| ~ spl30_68
| spl30_69 ),
inference(avatar_contradiction_clause,[],[f857]) ).
fof(f857,plain,
( $false
| spl30_65
| ~ spl30_67
| ~ spl30_68
| spl30_69 ),
inference(subsumption_resolution,[],[f851,f769]) ).
fof(f851,plain,
( sP2(sK6,sK7,sK8(sK11(sK5,sK7,sK6)),sK5)
| spl30_65
| ~ spl30_67
| ~ spl30_68
| spl30_69 ),
inference(resolution,[],[f850,f785]) ).
fof(f839,plain,
( spl30_69
| spl30_70
| spl30_65
| ~ spl30_67 ),
inference(avatar_split_clause,[],[f829,f779,f767,f837,f833]) ).
fof(f829,plain,
( ! [X0] :
( sK8(X0) != sK8(sK11(sK5,sK7,sK6))
| ~ in(sK8(X0),cartesian_product2(sK5,sK5))
| ~ in(sK8(X0),X0)
| in(sK8(sK11(sK5,sK7,sK6)),sK11(sK5,sK7,sK6)) )
| spl30_65
| ~ spl30_67 ),
inference(superposition,[],[f172,f824]) ).
fof(f814,plain,
( ~ spl30_63
| ~ spl30_1 ),
inference(avatar_split_clause,[],[f811,f227,f742]) ).
fof(f742,plain,
( spl30_63
<=> sP3(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_63])]) ).
fof(f227,plain,
( spl30_1
<=> sK14(sK7,sK6) = sK12(sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_1])]) ).
fof(f811,plain,
( ~ sP3(sK7,sK6)
| ~ spl30_1 ),
inference(subsumption_resolution,[],[f802,f108]) ).
fof(f802,plain,
( sK12(sK7,sK6) != sK13(sK7,sK6)
| ~ sP3(sK7,sK6)
| ~ spl30_1 ),
inference(superposition,[],[f112,f229]) ).
fof(f229,plain,
( sK14(sK7,sK6) = sK12(sK7,sK6)
| ~ spl30_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f809,plain,
( ~ spl30_1
| ~ spl30_63 ),
inference(avatar_contradiction_clause,[],[f808]) ).
fof(f808,plain,
( $false
| ~ spl30_1
| ~ spl30_63 ),
inference(global_subsumption,[],[f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f275,f223,f224,f225,f195,f310,f312,f216,f316,f317,f205,f345,f347,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f245,f762,f763,f744,f796,f797,f799,f798,f229,f804,f807]) ).
fof(f807,plain,
( sP1(sK6,sK7,sK12(sK7,sK6))
| ~ spl30_1
| ~ spl30_63 ),
inference(subsumption_resolution,[],[f803,f744]) ).
fof(f803,plain,
( sP1(sK6,sK7,sK12(sK7,sK6))
| ~ sP3(sK7,sK6)
| ~ spl30_1 ),
inference(superposition,[],[f111,f229]) ).
fof(f804,plain,
( sK12(sK7,sK6) != sK13(sK7,sK6)
| ~ spl30_1
| ~ spl30_63 ),
inference(subsumption_resolution,[],[f802,f744]) ).
fof(f798,plain,
( sK14(sK7,sK6) = sK12(sK7,sK6)
| ~ spl30_63 ),
inference(resolution,[],[f744,f110]) ).
fof(f799,plain,
( sK12(sK7,sK6) = sK13(sK7,sK6)
| ~ spl30_63 ),
inference(resolution,[],[f744,f108]) ).
fof(f797,plain,
( sK14(sK7,sK6) = ordered_pair(sK18(sK6,sK7,sK14(sK7,sK6)),sK19(sK6,sK7,sK14(sK7,sK6)))
| ~ spl30_63 ),
inference(resolution,[],[f744,f162]) ).
fof(f796,plain,
( sK13(sK7,sK6) = ordered_pair(sK20(sK6,sK7,sK13(sK7,sK6)),sK21(sK6,sK7,sK13(sK7,sK6)))
| ~ spl30_63 ),
inference(resolution,[],[f744,f163]) ).
fof(f744,plain,
( sP3(sK7,sK6)
| ~ spl30_63 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f806,plain,
( ~ spl30_1
| ~ spl30_63 ),
inference(avatar_contradiction_clause,[],[f805]) ).
fof(f805,plain,
( $false
| ~ spl30_1
| ~ spl30_63 ),
inference(global_subsumption,[],[f88,f89,f90,f123,f124,f125,f132,f133,f134,f135,f136,f137,f138,f139,f140,f141,f95,f147,f104,f105,f91,f152,f153,f150,f151,f109,f111,f92,f154,f108,f110,f112,f93,f155,f114,f122,f113,f106,f156,f107,f118,f120,f160,f115,f158,f167,f119,f121,f168,f94,f172,f170,f116,f173,f174,f162,f163,f166,f176,f146,f177,f157,f164,f165,f175,f183,f184,f187,f178,f179,f189,f190,f191,f180,f185,f169,f181,f182,f201,f171,f192,f215,f220,f221,f197,f222,f207,f275,f223,f224,f225,f195,f310,f312,f216,f316,f317,f205,f345,f347,f318,f319,f320,f196,f378,f321,f217,f393,f206,f410,f394,f395,f396,f203,f444,f445,f446,f447,f397,f398,f199,f218,f480,f481,f186,f482,f483,f484,f188,f544,f545,f546,f485,f219,f559,f560,f200,f561,f562,f309,f563,f564,f210,f344,f202,f656,f657,f658,f311,f193,f684,f685,f686,f346,f687,f688,f245,f762,f763,f744,f796,f797,f799,f798,f229,f804]) ).
fof(f801,plain,
( spl30_1
| ~ spl30_63 ),
inference(avatar_contradiction_clause,[],[f800]) ).
fof(f800,plain,
( $false
| spl30_1
| ~ spl30_63 ),
inference(subsumption_resolution,[],[f798,f228]) ).
fof(f228,plain,
( sK14(sK7,sK6) != sK12(sK7,sK6)
| spl30_1 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f792,plain,
( spl30_63
| spl30_67 ),
inference(avatar_contradiction_clause,[],[f791]) ).
fof(f791,plain,
( $false
| spl30_63
| spl30_67 ),
inference(subsumption_resolution,[],[f790,f88]) ).
fof(f790,plain,
( ~ relation(sK6)
| spl30_63
| spl30_67 ),
inference(subsumption_resolution,[],[f789,f89]) ).
fof(f789,plain,
( ~ relation(sK7)
| ~ relation(sK6)
| spl30_63
| spl30_67 ),
inference(subsumption_resolution,[],[f788,f90]) ).
fof(f788,plain,
( ~ function(sK7)
| ~ relation(sK7)
| ~ relation(sK6)
| spl30_63
| spl30_67 ),
inference(subsumption_resolution,[],[f787,f743]) ).
fof(f743,plain,
( ~ sP3(sK7,sK6)
| spl30_63 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f787,plain,
( sP3(sK7,sK6)
| ~ function(sK7)
| ~ relation(sK7)
| ~ relation(sK6)
| spl30_67 ),
inference(resolution,[],[f781,f122]) ).
fof(f781,plain,
( ~ sP4(sK5,sK7,sK6)
| spl30_67 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f786,plain,
( ~ spl30_67
| spl30_68
| spl30_65 ),
inference(avatar_split_clause,[],[f777,f767,f783,f779]) ).
fof(f774,plain,
( ~ spl30_65
| ~ spl30_66
| ~ spl30_64 ),
inference(avatar_split_clause,[],[f764,f746,f771,f767]) ).
fof(f771,plain,
( spl30_66
<=> in(cartesian_product2(sK5,sK5),sK8(sK11(sK5,sK7,sK6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_66])]) ).
fof(f748,plain,
( spl30_63
| spl30_64
| ~ spl30_2 ),
inference(avatar_split_clause,[],[f740,f231,f746,f742]) ).
fof(f231,plain,
( spl30_2
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_2])]) ).
fof(f740,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sP3(sK7,sK6) )
| ~ spl30_2 ),
inference(subsumption_resolution,[],[f739,f88]) ).
fof(f739,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sP3(sK7,sK6)
| ~ relation(sK6) )
| ~ spl30_2 ),
inference(subsumption_resolution,[],[f738,f89]) ).
fof(f738,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sP3(sK7,sK6)
| ~ relation(sK7)
| ~ relation(sK6) )
| ~ spl30_2 ),
inference(subsumption_resolution,[],[f737,f90]) ).
fof(f737,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sP3(sK7,sK6)
| ~ function(sK7)
| ~ relation(sK7)
| ~ relation(sK6) )
| ~ spl30_2 ),
inference(resolution,[],[f736,f122]) ).
fof(f736,plain,
( ! [X0] :
( ~ sP4(X0,sK7,sK6)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5) )
| ~ spl30_2 ),
inference(resolution,[],[f733,f114]) ).
fof(f733,plain,
( ! [X0] :
( sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| ~ sP4(X0,sK7,sK6) )
| ~ spl30_2 ),
inference(subsumption_resolution,[],[f731,f114]) ).
fof(f731,plain,
( ! [X0] :
( sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| ~ sP4(X0,sK7,sK6) )
| ~ spl30_2 ),
inference(resolution,[],[f730,f106]) ).
fof(f730,plain,
( ! [X0] :
( in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6))
| sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_2 ),
inference(duplicate_literal_removal,[],[f729]) ).
fof(f729,plain,
( ! [X0] :
( sP2(sK6,sK7,sK8(sK11(X0,sK7,sK6)),sK5)
| in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6))
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_2 ),
inference(superposition,[],[f723,f232]) ).
fof(f232,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK6)) = ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6)))
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_2 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f723,plain,
( ! [X0] :
( sP2(sK6,sK7,ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6))),sK5)
| in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6))
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_2 ),
inference(duplicate_literal_removal,[],[f722]) ).
fof(f722,plain,
( ! [X0] :
( sP2(sK6,sK7,ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6))),sK5)
| in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6))
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0)
| in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6)) )
| ~ spl30_2 ),
inference(resolution,[],[f234,f91]) ).
fof(f234,plain,
( ! [X0,X1] :
( ~ in(sK8(sK11(X0,sK7,sK6)),cartesian_product2(X1,X1))
| sP2(sK6,sK7,ordered_pair(sK9(sK11(X0,sK7,sK6)),sK10(sK11(X0,sK7,sK6))),X1)
| in(sK8(sK11(X0,sK7,sK6)),sK11(X0,sK7,sK6))
| sK8(sK11(X0,sK7,sK6)) = sK15(sK6,sK7,sK8(sK11(X0,sK7,sK6)),X0) )
| ~ spl30_2 ),
inference(superposition,[],[f177,f232]) ).
fof(f642,plain,
( ~ spl30_61
| spl30_62 ),
inference(avatar_split_clause,[],[f210,f640,f636]) ).
fof(f636,plain,
( spl30_61
<=> relation(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_61])]) ).
fof(f640,plain,
( spl30_62
<=> ! [X0,X1] :
( sK8(sK11(X0,sK23,X1)) = ordered_pair(sK9(sK11(X0,sK23,X1)),sK10(sK11(X0,sK23,X1)))
| sK14(sK23,X1) = sK12(sK23,X1)
| ~ relation(X1)
| sK8(sK11(X0,sK23,X1)) = sK15(X1,sK23,sK8(sK11(X0,sK23,X1)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_62])]) ).
fof(f631,plain,
( spl30_59
| spl30_60 ),
inference(avatar_split_clause,[],[f564,f629,f625]) ).
fof(f625,plain,
( spl30_59
<=> sK14(sK29,sK29) = sK12(sK29,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_59])]) ).
fof(f629,plain,
( spl30_60
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK29)) = sK15(sK29,sK29,sK8(sK11(X0,sK29,sK29)),X0)
| sK8(sK11(X0,sK29,sK29)) = ordered_pair(sK9(sK11(X0,sK29,sK29)),sK10(sK11(X0,sK29,sK29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_60])]) ).
fof(f620,plain,
( spl30_57
| spl30_58 ),
inference(avatar_split_clause,[],[f563,f618,f614]) ).
fof(f614,plain,
( spl30_57
<=> sK14(sK29,sK28) = sK12(sK29,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_57])]) ).
fof(f618,plain,
( spl30_58
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK28)) = sK15(sK28,sK29,sK8(sK11(X0,sK29,sK28)),X0)
| sK8(sK11(X0,sK29,sK28)) = ordered_pair(sK9(sK11(X0,sK29,sK28)),sK10(sK11(X0,sK29,sK28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_58])]) ).
fof(f609,plain,
( spl30_55
| spl30_56 ),
inference(avatar_split_clause,[],[f562,f607,f603]) ).
fof(f603,plain,
( spl30_55
<=> sK14(sK29,sK27) = sK12(sK29,sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_55])]) ).
fof(f607,plain,
( spl30_56
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK27)) = sK15(sK27,sK29,sK8(sK11(X0,sK29,sK27)),X0)
| sK8(sK11(X0,sK29,sK27)) = ordered_pair(sK9(sK11(X0,sK29,sK27)),sK10(sK11(X0,sK29,sK27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_56])]) ).
fof(f598,plain,
( spl30_53
| spl30_54 ),
inference(avatar_split_clause,[],[f561,f596,f592]) ).
fof(f592,plain,
( spl30_53
<=> sK14(sK29,sK26) = sK12(sK29,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_53])]) ).
fof(f596,plain,
( spl30_54
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK26)) = sK15(sK26,sK29,sK8(sK11(X0,sK29,sK26)),X0)
| sK8(sK11(X0,sK29,sK26)) = ordered_pair(sK9(sK11(X0,sK29,sK26)),sK10(sK11(X0,sK29,sK26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_54])]) ).
fof(f583,plain,
( spl30_51
| spl30_52 ),
inference(avatar_split_clause,[],[f560,f581,f577]) ).
fof(f577,plain,
( spl30_51
<=> sK14(sK29,sK7) = sK12(sK29,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_51])]) ).
fof(f581,plain,
( spl30_52
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK7)) = sK15(sK7,sK29,sK8(sK11(X0,sK29,sK7)),X0)
| sK8(sK11(X0,sK29,sK7)) = ordered_pair(sK9(sK11(X0,sK29,sK7)),sK10(sK11(X0,sK29,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_52])]) ).
fof(f572,plain,
( spl30_49
| spl30_50 ),
inference(avatar_split_clause,[],[f559,f570,f566]) ).
fof(f566,plain,
( spl30_49
<=> sK14(sK29,sK6) = sK12(sK29,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_49])]) ).
fof(f570,plain,
( spl30_50
<=> ! [X0] :
( sK8(sK11(X0,sK29,sK6)) = sK15(sK6,sK29,sK8(sK11(X0,sK29,sK6)),X0)
| sK8(sK11(X0,sK29,sK6)) = ordered_pair(sK9(sK11(X0,sK29,sK6)),sK10(sK11(X0,sK29,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_50])]) ).
fof(f555,plain,
( spl30_47
| spl30_48 ),
inference(avatar_split_clause,[],[f485,f553,f549]) ).
fof(f549,plain,
( spl30_47
<=> sK14(sK28,sK29) = sK12(sK28,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_47])]) ).
fof(f553,plain,
( spl30_48
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK29)) = sK15(sK29,sK28,sK8(sK11(X0,sK28,sK29)),X0)
| sK8(sK11(X0,sK28,sK29)) = ordered_pair(sK9(sK11(X0,sK28,sK29)),sK10(sK11(X0,sK28,sK29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_48])]) ).
fof(f539,plain,
( spl30_45
| spl30_46 ),
inference(avatar_split_clause,[],[f484,f537,f533]) ).
fof(f533,plain,
( spl30_45
<=> sK14(sK28,sK28) = sK12(sK28,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_45])]) ).
fof(f537,plain,
( spl30_46
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK28)) = sK15(sK28,sK28,sK8(sK11(X0,sK28,sK28)),X0)
| sK8(sK11(X0,sK28,sK28)) = ordered_pair(sK9(sK11(X0,sK28,sK28)),sK10(sK11(X0,sK28,sK28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_46])]) ).
fof(f528,plain,
( spl30_43
| spl30_44 ),
inference(avatar_split_clause,[],[f483,f526,f522]) ).
fof(f522,plain,
( spl30_43
<=> sK14(sK28,sK27) = sK12(sK28,sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_43])]) ).
fof(f526,plain,
( spl30_44
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK27)) = sK15(sK27,sK28,sK8(sK11(X0,sK28,sK27)),X0)
| sK8(sK11(X0,sK28,sK27)) = ordered_pair(sK9(sK11(X0,sK28,sK27)),sK10(sK11(X0,sK28,sK27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_44])]) ).
fof(f517,plain,
( spl30_41
| spl30_42 ),
inference(avatar_split_clause,[],[f482,f515,f511]) ).
fof(f511,plain,
( spl30_41
<=> sK14(sK28,sK26) = sK12(sK28,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_41])]) ).
fof(f515,plain,
( spl30_42
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK26)) = sK15(sK26,sK28,sK8(sK11(X0,sK28,sK26)),X0)
| sK8(sK11(X0,sK28,sK26)) = ordered_pair(sK9(sK11(X0,sK28,sK26)),sK10(sK11(X0,sK28,sK26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_42])]) ).
fof(f504,plain,
( spl30_39
| spl30_40 ),
inference(avatar_split_clause,[],[f481,f502,f498]) ).
fof(f498,plain,
( spl30_39
<=> sK14(sK28,sK7) = sK12(sK28,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_39])]) ).
fof(f502,plain,
( spl30_40
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK7)) = sK15(sK7,sK28,sK8(sK11(X0,sK28,sK7)),X0)
| sK8(sK11(X0,sK28,sK7)) = ordered_pair(sK9(sK11(X0,sK28,sK7)),sK10(sK11(X0,sK28,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_40])]) ).
fof(f493,plain,
( spl30_37
| spl30_38 ),
inference(avatar_split_clause,[],[f480,f491,f487]) ).
fof(f487,plain,
( spl30_37
<=> sK14(sK28,sK6) = sK12(sK28,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_37])]) ).
fof(f491,plain,
( spl30_38
<=> ! [X0] :
( sK8(sK11(X0,sK28,sK6)) = sK15(sK6,sK28,sK8(sK11(X0,sK28,sK6)),X0)
| sK8(sK11(X0,sK28,sK6)) = ordered_pair(sK9(sK11(X0,sK28,sK6)),sK10(sK11(X0,sK28,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_38])]) ).
fof(f474,plain,
( spl30_35
| spl30_36 ),
inference(avatar_split_clause,[],[f398,f472,f468]) ).
fof(f468,plain,
( spl30_35
<=> sK14(sK27,sK29) = sK12(sK27,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_35])]) ).
fof(f472,plain,
( spl30_36
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK29)) = sK15(sK29,sK27,sK8(sK11(X0,sK27,sK29)),X0)
| sK8(sK11(X0,sK27,sK29)) = ordered_pair(sK9(sK11(X0,sK27,sK29)),sK10(sK11(X0,sK27,sK29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_36])]) ).
fof(f463,plain,
( spl30_33
| spl30_34 ),
inference(avatar_split_clause,[],[f397,f461,f457]) ).
fof(f457,plain,
( spl30_33
<=> sK14(sK27,sK28) = sK12(sK27,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_33])]) ).
fof(f461,plain,
( spl30_34
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK28)) = sK15(sK28,sK27,sK8(sK11(X0,sK27,sK28)),X0)
| sK8(sK11(X0,sK27,sK28)) = ordered_pair(sK9(sK11(X0,sK27,sK28)),sK10(sK11(X0,sK27,sK28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_34])]) ).
fof(f440,plain,
( spl30_31
| spl30_32 ),
inference(avatar_split_clause,[],[f396,f438,f434]) ).
fof(f434,plain,
( spl30_31
<=> sK14(sK27,sK27) = sK12(sK27,sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_31])]) ).
fof(f438,plain,
( spl30_32
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK27)) = sK15(sK27,sK27,sK8(sK11(X0,sK27,sK27)),X0)
| sK8(sK11(X0,sK27,sK27)) = ordered_pair(sK9(sK11(X0,sK27,sK27)),sK10(sK11(X0,sK27,sK27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_32])]) ).
fof(f429,plain,
( spl30_29
| spl30_30 ),
inference(avatar_split_clause,[],[f395,f427,f423]) ).
fof(f423,plain,
( spl30_29
<=> sK14(sK27,sK26) = sK12(sK27,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_29])]) ).
fof(f427,plain,
( spl30_30
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK26)) = sK15(sK26,sK27,sK8(sK11(X0,sK27,sK26)),X0)
| sK8(sK11(X0,sK27,sK26)) = ordered_pair(sK9(sK11(X0,sK27,sK26)),sK10(sK11(X0,sK27,sK26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_30])]) ).
fof(f418,plain,
( spl30_27
| spl30_28 ),
inference(avatar_split_clause,[],[f394,f416,f412]) ).
fof(f412,plain,
( spl30_27
<=> sK14(sK27,sK7) = sK12(sK27,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_27])]) ).
fof(f416,plain,
( spl30_28
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK7)) = sK15(sK7,sK27,sK8(sK11(X0,sK27,sK7)),X0)
| sK8(sK11(X0,sK27,sK7)) = ordered_pair(sK9(sK11(X0,sK27,sK7)),sK10(sK11(X0,sK27,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_28])]) ).
fof(f406,plain,
( spl30_25
| spl30_26 ),
inference(avatar_split_clause,[],[f393,f404,f400]) ).
fof(f400,plain,
( spl30_25
<=> sK14(sK27,sK6) = sK12(sK27,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_25])]) ).
fof(f404,plain,
( spl30_26
<=> ! [X0] :
( sK8(sK11(X0,sK27,sK6)) = sK15(sK6,sK27,sK8(sK11(X0,sK27,sK6)),X0)
| sK8(sK11(X0,sK27,sK6)) = ordered_pair(sK9(sK11(X0,sK27,sK6)),sK10(sK11(X0,sK27,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_26])]) ).
fof(f389,plain,
( spl30_23
| spl30_24 ),
inference(avatar_split_clause,[],[f321,f387,f383]) ).
fof(f383,plain,
( spl30_23
<=> sK14(sK26,sK29) = sK12(sK26,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_23])]) ).
fof(f387,plain,
( spl30_24
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK29)) = sK15(sK29,sK26,sK8(sK11(X0,sK26,sK29)),X0)
| sK8(sK11(X0,sK26,sK29)) = ordered_pair(sK9(sK11(X0,sK26,sK29)),sK10(sK11(X0,sK26,sK29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_24])]) ).
fof(f377,plain,
( spl30_21
| spl30_22 ),
inference(avatar_split_clause,[],[f320,f375,f371]) ).
fof(f371,plain,
( spl30_21
<=> sK14(sK26,sK28) = sK12(sK26,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_21])]) ).
fof(f375,plain,
( spl30_22
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK28)) = sK15(sK28,sK26,sK8(sK11(X0,sK26,sK28)),X0)
| sK8(sK11(X0,sK26,sK28)) = ordered_pair(sK9(sK11(X0,sK26,sK28)),sK10(sK11(X0,sK26,sK28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_22])]) ).
fof(f366,plain,
( spl30_19
| spl30_20 ),
inference(avatar_split_clause,[],[f319,f364,f360]) ).
fof(f360,plain,
( spl30_19
<=> sK14(sK26,sK27) = sK12(sK26,sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_19])]) ).
fof(f364,plain,
( spl30_20
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK27)) = sK15(sK27,sK26,sK8(sK11(X0,sK26,sK27)),X0)
| sK8(sK11(X0,sK26,sK27)) = ordered_pair(sK9(sK11(X0,sK26,sK27)),sK10(sK11(X0,sK26,sK27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_20])]) ).
fof(f355,plain,
( spl30_17
| spl30_18 ),
inference(avatar_split_clause,[],[f318,f353,f349]) ).
fof(f349,plain,
( spl30_17
<=> sK14(sK26,sK26) = sK12(sK26,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_17])]) ).
fof(f353,plain,
( spl30_18
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK26)) = sK15(sK26,sK26,sK8(sK11(X0,sK26,sK26)),X0)
| sK8(sK11(X0,sK26,sK26)) = ordered_pair(sK9(sK11(X0,sK26,sK26)),sK10(sK11(X0,sK26,sK26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_18])]) ).
fof(f340,plain,
( spl30_15
| spl30_16 ),
inference(avatar_split_clause,[],[f317,f338,f334]) ).
fof(f334,plain,
( spl30_15
<=> sK14(sK26,sK7) = sK12(sK26,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_15])]) ).
fof(f338,plain,
( spl30_16
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK7)) = sK15(sK7,sK26,sK8(sK11(X0,sK26,sK7)),X0)
| sK8(sK11(X0,sK26,sK7)) = ordered_pair(sK9(sK11(X0,sK26,sK7)),sK10(sK11(X0,sK26,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_16])]) ).
fof(f329,plain,
( spl30_13
| spl30_14 ),
inference(avatar_split_clause,[],[f316,f327,f323]) ).
fof(f323,plain,
( spl30_13
<=> sK14(sK26,sK6) = sK12(sK26,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_13])]) ).
fof(f327,plain,
( spl30_14
<=> ! [X0] :
( sK8(sK11(X0,sK26,sK6)) = sK15(sK6,sK26,sK8(sK11(X0,sK26,sK6)),X0)
| sK8(sK11(X0,sK26,sK6)) = ordered_pair(sK9(sK11(X0,sK26,sK6)),sK10(sK11(X0,sK26,sK6))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_14])]) ).
fof(f308,plain,
( spl30_11
| spl30_12 ),
inference(avatar_split_clause,[],[f225,f306,f302]) ).
fof(f302,plain,
( spl30_11
<=> sK14(sK7,sK29) = sK12(sK7,sK29) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_11])]) ).
fof(f306,plain,
( spl30_12
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK29)) = sK15(sK29,sK7,sK8(sK11(X0,sK7,sK29)),X0)
| sK8(sK11(X0,sK7,sK29)) = ordered_pair(sK9(sK11(X0,sK7,sK29)),sK10(sK11(X0,sK7,sK29))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_12])]) ).
fof(f297,plain,
( spl30_9
| spl30_10 ),
inference(avatar_split_clause,[],[f224,f295,f291]) ).
fof(f291,plain,
( spl30_9
<=> sK14(sK7,sK28) = sK12(sK7,sK28) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_9])]) ).
fof(f295,plain,
( spl30_10
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK28)) = sK15(sK28,sK7,sK8(sK11(X0,sK7,sK28)),X0)
| sK8(sK11(X0,sK7,sK28)) = ordered_pair(sK9(sK11(X0,sK7,sK28)),sK10(sK11(X0,sK7,sK28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_10])]) ).
fof(f286,plain,
( spl30_7
| spl30_8 ),
inference(avatar_split_clause,[],[f223,f284,f280]) ).
fof(f280,plain,
( spl30_7
<=> sK14(sK7,sK27) = sK12(sK7,sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_7])]) ).
fof(f284,plain,
( spl30_8
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK27)) = sK15(sK27,sK7,sK8(sK11(X0,sK7,sK27)),X0)
| sK8(sK11(X0,sK7,sK27)) = ordered_pair(sK9(sK11(X0,sK7,sK27)),sK10(sK11(X0,sK7,sK27))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_8])]) ).
fof(f274,plain,
( spl30_6
| ~ spl30_5 ),
inference(avatar_split_clause,[],[f273,f259,f263]) ).
fof(f263,plain,
( spl30_6
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_6])]) ).
fof(f259,plain,
( spl30_5
<=> sK14(sK7,sK26) = sK12(sK7,sK26) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_5])]) ).
fof(f273,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26))) )
| ~ spl30_5 ),
inference(subsumption_resolution,[],[f272,f132]) ).
fof(f272,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26)))
| ~ relation(sK26) )
| ~ spl30_5 ),
inference(subsumption_resolution,[],[f271,f89]) ).
fof(f271,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26)))
| ~ relation(sK7)
| ~ relation(sK26) )
| ~ spl30_5 ),
inference(subsumption_resolution,[],[f270,f90]) ).
fof(f270,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK26)) = sK15(sK26,sK7,sK8(sK11(X0,sK7,sK26)),X0)
| sK8(sK11(X0,sK7,sK26)) = ordered_pair(sK9(sK11(X0,sK7,sK26)),sK10(sK11(X0,sK7,sK26)))
| ~ function(sK7)
| ~ relation(sK7)
| ~ relation(sK26) )
| ~ spl30_5 ),
inference(resolution,[],[f268,f189]) ).
fof(f268,plain,
( ~ sP3(sK7,sK26)
| ~ spl30_5 ),
inference(subsumption_resolution,[],[f266,f108]) ).
fof(f266,plain,
( sK12(sK7,sK26) != sK13(sK7,sK26)
| ~ sP3(sK7,sK26)
| ~ spl30_5 ),
inference(superposition,[],[f112,f261]) ).
fof(f261,plain,
( sK14(sK7,sK26) = sK12(sK7,sK26)
| ~ spl30_5 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f265,plain,
( spl30_5
| spl30_6 ),
inference(avatar_split_clause,[],[f222,f263,f259]) ).
fof(f254,plain,
( spl30_4
| ~ spl30_3 ),
inference(avatar_split_clause,[],[f253,f238,f242]) ).
fof(f242,plain,
( spl30_4
<=> ! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_4])]) ).
fof(f238,plain,
( spl30_3
<=> sK14(sK7,sK7) = sK12(sK7,sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl30_3])]) ).
fof(f253,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7))) )
| ~ spl30_3 ),
inference(subsumption_resolution,[],[f252,f89]) ).
fof(f252,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7)))
| ~ relation(sK7) )
| ~ spl30_3 ),
inference(subsumption_resolution,[],[f251,f90]) ).
fof(f251,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7)))
| ~ function(sK7)
| ~ relation(sK7) )
| ~ spl30_3 ),
inference(duplicate_literal_removal,[],[f250]) ).
fof(f250,plain,
( ! [X0] :
( sK8(sK11(X0,sK7,sK7)) = sK15(sK7,sK7,sK8(sK11(X0,sK7,sK7)),X0)
| sK8(sK11(X0,sK7,sK7)) = ordered_pair(sK9(sK11(X0,sK7,sK7)),sK10(sK11(X0,sK7,sK7)))
| ~ function(sK7)
| ~ relation(sK7)
| ~ relation(sK7) )
| ~ spl30_3 ),
inference(resolution,[],[f248,f189]) ).
fof(f248,plain,
( ~ sP3(sK7,sK7)
| ~ spl30_3 ),
inference(subsumption_resolution,[],[f246,f108]) ).
fof(f246,plain,
( sK12(sK7,sK7) != sK13(sK7,sK7)
| ~ sP3(sK7,sK7)
| ~ spl30_3 ),
inference(superposition,[],[f112,f240]) ).
fof(f240,plain,
( sK14(sK7,sK7) = sK12(sK7,sK7)
| ~ spl30_3 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f244,plain,
( spl30_3
| spl30_4 ),
inference(avatar_split_clause,[],[f221,f242,f238]) ).
fof(f233,plain,
( spl30_1
| spl30_2 ),
inference(avatar_split_clause,[],[f220,f231,f227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU277+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:24:12 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (20866)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (20871)WARNING: value z3 for option sas not known
% 0.20/0.38 % (20873)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)
% 0.20/0.38 % (20875)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)
% 0.20/0.38 % (20872)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.38 % (20871)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)
% 0.20/0.38 % (20869)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.38 % (20870)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.38 % (20876)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)
% 0.20/0.38 TRYING [1]
% 0.20/0.38 TRYING [2]
% 0.20/0.39 TRYING [3]
% 0.20/0.45 % (20871)First to succeed.
% 0.20/0.47 % (20871)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20866"
% 0.20/0.48 % (20871)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (20871)------------------------------
% 0.20/0.48 % (20871)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.48 % (20871)Termination reason: Refutation
% 0.20/0.48
% 0.20/0.48 % (20871)Memory used [KB]: 1488
% 0.20/0.48 % (20871)Time elapsed: 0.098 s
% 0.20/0.48 % (20871)Instructions burned: 129 (million)
% 0.20/0.48 % (20866)Success in time 0.113 s
%------------------------------------------------------------------------------