TSTP Solution File: SET955+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n013.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 : Wed Aug 31 18:26:11 EDT 2022
% Result : Theorem 0.20s 0.59s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 80 ( 11 unt; 0 def)
% Number of atoms : 276 ( 72 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 311 ( 115 ~; 119 |; 54 &)
% ( 13 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 180 ( 138 !; 42 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f675,plain,
$false,
inference(avatar_sat_refutation,[],[f339,f469,f478,f481,f484,f659]) ).
fof(f659,plain,
( ~ spl14_1
| spl14_7
| ~ spl14_9 ),
inference(avatar_contradiction_clause,[],[f658]) ).
fof(f658,plain,
( $false
| ~ spl14_1
| spl14_7
| ~ spl14_9 ),
inference(subsumption_resolution,[],[f657,f328]) ).
fof(f328,plain,
( ~ in(sK6(sF13,sF12),sF13)
| spl14_7 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f327,plain,
( spl14_7
<=> in(sK6(sF13,sF12),sF13) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_7])]) ).
fof(f657,plain,
( in(sK6(sF13,sF12),sF13)
| ~ spl14_1
| ~ spl14_9 ),
inference(subsumption_resolution,[],[f494,f338]) ).
fof(f338,plain,
( in(sK6(sF13,sF12),sF12)
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f336,plain,
( spl14_9
<=> in(sK6(sF13,sF12),sF12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_9])]) ).
fof(f494,plain,
( ~ in(sK6(sF13,sF12),sF12)
| in(sK6(sF13,sF12),sF13)
| ~ spl14_1 ),
inference(superposition,[],[f78,f257]) ).
fof(f257,plain,
( unordered_pair(singleton(sK7(sK2,sK1,sK6(sF13,sF12))),unordered_pair(sK7(sK2,sK1,sK6(sF13,sF12)),sK8(sK2,sK1,sK6(sF13,sF12)))) = sK6(sF13,sF12)
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f255,plain,
( spl14_1
<=> unordered_pair(singleton(sK7(sK2,sK1,sK6(sF13,sF12))),unordered_pair(sK7(sK2,sK1,sK6(sF13,sF12)),sK8(sK2,sK1,sK6(sF13,sF12)))) = sK6(sF13,sF12) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_1])]) ).
fof(f78,plain,
! [X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF12)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF13) ),
inference(forward_demodulation,[],[f77,f45]) ).
fof(f45,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X1,X0] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f77,plain,
! [X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF12)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF13) ),
inference(forward_demodulation,[],[f71,f45]) ).
fof(f71,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF12)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF13) ),
inference(definition_folding,[],[f58,f68,f69]) ).
fof(f69,plain,
cartesian_product2(sK3,sK4) = sF13,
introduced(function_definition,[]) ).
fof(f68,plain,
cartesian_product2(sK2,sK1) = sF12,
introduced(function_definition,[]) ).
fof(f58,plain,
! [X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),cartesian_product2(sK3,sK4))
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),cartesian_product2(sK2,sK1)) ),
inference(definition_unfolding,[],[f41,f39,f39]) ).
fof(f39,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(cnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1] : ordered_pair(X1,X0) = unordered_pair(unordered_pair(X1,X0),singleton(X1)),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X0] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f41,plain,
! [X4,X5] :
( in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
( ! [X4,X5] :
( ( in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4)) )
& ( in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1)) ) )
& cartesian_product2(sK3,sK4) != cartesian_product2(sK2,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4])],[f22,f23]) ).
fof(f23,plain,
( ? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ( in(ordered_pair(X5,X4),cartesian_product2(X1,X0))
| ~ in(ordered_pair(X5,X4),cartesian_product2(X2,X3)) )
& ( in(ordered_pair(X5,X4),cartesian_product2(X2,X3))
| ~ in(ordered_pair(X5,X4),cartesian_product2(X1,X0)) ) )
& cartesian_product2(X2,X3) != cartesian_product2(X1,X0) )
=> ( ! [X5,X4] :
( ( in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4)) )
& ( in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1)) ) )
& cartesian_product2(sK3,sK4) != cartesian_product2(sK2,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
? [X0,X1,X2,X3] :
( ! [X4,X5] :
( ( in(ordered_pair(X5,X4),cartesian_product2(X1,X0))
| ~ in(ordered_pair(X5,X4),cartesian_product2(X2,X3)) )
& ( in(ordered_pair(X5,X4),cartesian_product2(X2,X3))
| ~ in(ordered_pair(X5,X4),cartesian_product2(X1,X0)) ) )
& cartesian_product2(X2,X3) != cartesian_product2(X1,X0) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
? [X0,X3,X1,X2] :
( ! [X5,X4] :
( ( in(ordered_pair(X4,X5),cartesian_product2(X3,X0))
| ~ in(ordered_pair(X4,X5),cartesian_product2(X1,X2)) )
& ( in(ordered_pair(X4,X5),cartesian_product2(X1,X2))
| ~ in(ordered_pair(X4,X5),cartesian_product2(X3,X0)) ) )
& cartesian_product2(X3,X0) != cartesian_product2(X1,X2) ),
inference(nnf_transformation,[],[f18]) ).
fof(f18,plain,
? [X0,X3,X1,X2] :
( ! [X5,X4] :
( in(ordered_pair(X4,X5),cartesian_product2(X3,X0))
<=> in(ordered_pair(X4,X5),cartesian_product2(X1,X2)) )
& cartesian_product2(X3,X0) != cartesian_product2(X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X3,X2,X0,X1] :
( ! [X5,X4] :
( in(ordered_pair(X4,X5),cartesian_product2(X3,X0))
<=> in(ordered_pair(X4,X5),cartesian_product2(X1,X2)) )
=> cartesian_product2(X3,X0) = cartesian_product2(X1,X2) ),
inference(rectify,[],[f9]) ).
fof(f9,negated_conjecture,
~ ! [X3,X0,X1,X2] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
<=> in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
inference(negated_conjecture,[],[f8]) ).
fof(f8,conjecture,
! [X3,X0,X1,X2] :
( ! [X4,X5] :
( in(ordered_pair(X4,X5),cartesian_product2(X2,X3))
<=> in(ordered_pair(X4,X5),cartesian_product2(X0,X1)) )
=> cartesian_product2(X0,X1) = cartesian_product2(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t108_zfmisc_1) ).
fof(f484,plain,
( spl14_2
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f483,plain,
( $false
| spl14_2
| ~ spl14_7 ),
inference(subsumption_resolution,[],[f472,f260]) ).
fof(f260,plain,
( sK6(sF13,sF12) != unordered_pair(singleton(sK7(sK3,sK4,sK6(sF13,sF12))),unordered_pair(sK7(sK3,sK4,sK6(sF13,sF12)),sK8(sK3,sK4,sK6(sF13,sF12))))
| spl14_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f259,plain,
( spl14_2
<=> sK6(sF13,sF12) = unordered_pair(singleton(sK7(sK3,sK4,sK6(sF13,sF12))),unordered_pair(sK7(sK3,sK4,sK6(sF13,sF12)),sK8(sK3,sK4,sK6(sF13,sF12)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl14_2])]) ).
fof(f472,plain,
( sK6(sF13,sF12) = unordered_pair(singleton(sK7(sK3,sK4,sK6(sF13,sF12))),unordered_pair(sK7(sK3,sK4,sK6(sF13,sF12)),sK8(sK3,sK4,sK6(sF13,sF12))))
| ~ spl14_7 ),
inference(resolution,[],[f329,f202]) ).
fof(f202,plain,
! [X1] :
( ~ in(X1,sF13)
| unordered_pair(singleton(sK7(sK3,sK4,X1)),unordered_pair(sK7(sK3,sK4,X1),sK8(sK3,sK4,X1))) = X1 ),
inference(superposition,[],[f76,f69]) ).
fof(f76,plain,
! [X3,X0,X1] :
( ~ in(X3,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK7(X0,X1,X3)),unordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3))) = X3 ),
inference(forward_demodulation,[],[f65,f45]) ).
fof(f65,plain,
! [X3,X0,X1] :
( unordered_pair(unordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3)),singleton(sK7(X0,X1,X3))) = X3
| ~ in(X3,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3)),singleton(sK7(X0,X1,X3))) = X3
| ~ in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f53,f39]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3)) = X3
| ~ in(X3,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ( in(sK8(X0,X1,X3),X1)
& in(sK7(X0,X1,X3),X0)
& ordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3)) = X3 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X6,X7] :
( ~ in(X7,X1)
| ~ in(X6,X0)
| ordered_pair(X6,X7) != X3 ) ) )
| cartesian_product2(X0,X1) != X2 )
& ( cartesian_product2(X0,X1) = X2
| ( ( ~ in(sK9(X0,X1,X2),X2)
| ! [X9,X10] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| sK9(X0,X1,X2) != ordered_pair(X9,X10) ) )
& ( in(sK9(X0,X1,X2),X2)
| ( in(sK11(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0)
& sK9(X0,X1,X2) = ordered_pair(sK10(X0,X1,X2),sK11(X0,X1,X2)) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f32,f35,f34,f33]) ).
fof(f33,plain,
! [X0,X1,X3] :
( ? [X4,X5] :
( in(X5,X1)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
=> ( in(sK8(X0,X1,X3),X1)
& in(sK7(X0,X1,X3),X0)
& ordered_pair(sK7(X0,X1,X3),sK8(X0,X1,X3)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ? [X8] :
( ( ~ in(X8,X2)
| ! [X9,X10] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| ordered_pair(X9,X10) != X8 ) )
& ( in(X8,X2)
| ? [X11,X12] :
( in(X12,X1)
& in(X11,X0)
& ordered_pair(X11,X12) = X8 ) ) )
=> ( ( ~ in(sK9(X0,X1,X2),X2)
| ! [X10,X9] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| sK9(X0,X1,X2) != ordered_pair(X9,X10) ) )
& ( in(sK9(X0,X1,X2),X2)
| ? [X12,X11] :
( in(X12,X1)
& in(X11,X0)
& ordered_pair(X11,X12) = sK9(X0,X1,X2) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ? [X12,X11] :
( in(X12,X1)
& in(X11,X0)
& ordered_pair(X11,X12) = sK9(X0,X1,X2) )
=> ( in(sK11(X0,X1,X2),X1)
& in(sK10(X0,X1,X2),X0)
& sK9(X0,X1,X2) = ordered_pair(sK10(X0,X1,X2),sK11(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( ? [X4,X5] :
( in(X5,X1)
& in(X4,X0)
& ordered_pair(X4,X5) = X3 )
| ~ in(X3,X2) )
& ( in(X3,X2)
| ! [X6,X7] :
( ~ in(X7,X1)
| ~ in(X6,X0)
| ordered_pair(X6,X7) != X3 ) ) )
| cartesian_product2(X0,X1) != X2 )
& ( cartesian_product2(X0,X1) = X2
| ? [X8] :
( ( ~ in(X8,X2)
| ! [X9,X10] :
( ~ in(X10,X1)
| ~ in(X9,X0)
| ordered_pair(X9,X10) != X8 ) )
& ( in(X8,X2)
| ? [X11,X12] :
( in(X12,X1)
& in(X11,X0)
& ordered_pair(X11,X12) = X8 ) ) ) ) ),
inference(rectify,[],[f31]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( ? [X5,X4] :
( in(X4,X0)
& in(X5,X2)
& ordered_pair(X5,X4) = X3 )
| ~ in(X3,X1) )
& ( in(X3,X1)
| ! [X5,X4] :
( ~ in(X4,X0)
| ~ in(X5,X2)
| ordered_pair(X5,X4) != X3 ) ) )
| cartesian_product2(X2,X0) != X1 )
& ( cartesian_product2(X2,X0) = X1
| ? [X3] :
( ( ~ in(X3,X1)
| ! [X5,X4] :
( ~ in(X4,X0)
| ~ in(X5,X2)
| ordered_pair(X5,X4) != X3 ) )
& ( in(X3,X1)
| ? [X5,X4] :
( in(X4,X0)
& in(X5,X2)
& ordered_pair(X5,X4) = X3 ) ) ) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X2,X0,X1] :
( ! [X3] :
( ? [X5,X4] :
( in(X4,X0)
& in(X5,X2)
& ordered_pair(X5,X4) = X3 )
<=> in(X3,X1) )
<=> cartesian_product2(X2,X0) = X1 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X1,X2,X0] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X4,X0)
& in(X5,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f329,plain,
( in(sK6(sF13,sF12),sF13)
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f481,plain,
( ~ spl14_7
| ~ spl14_9 ),
inference(avatar_contradiction_clause,[],[f480]) ).
fof(f480,plain,
( $false
| ~ spl14_7
| ~ spl14_9 ),
inference(subsumption_resolution,[],[f479,f329]) ).
fof(f479,plain,
( ~ in(sK6(sF13,sF12),sF13)
| ~ spl14_9 ),
inference(subsumption_resolution,[],[f475,f72]) ).
fof(f72,plain,
sF12 != sF13,
inference(definition_folding,[],[f40,f68,f69]) ).
fof(f40,plain,
cartesian_product2(sK3,sK4) != cartesian_product2(sK2,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f475,plain,
( sF12 = sF13
| ~ in(sK6(sF13,sF12),sF13)
| ~ spl14_9 ),
inference(resolution,[],[f338,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(sK6(X0,X1),X1)
| X0 = X1
| ~ in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( ( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) )
& ( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
=> ( ( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1) )
& ( in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X0)
| ~ in(X2,X1) )
& ( in(X2,X0)
| in(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X1)
<~> in(X2,X0) )
| X0 = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X1,X0] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
fof(f478,plain,
( spl14_1
| ~ spl14_9 ),
inference(avatar_split_clause,[],[f476,f336,f255]) ).
fof(f476,plain,
( unordered_pair(singleton(sK7(sK2,sK1,sK6(sF13,sF12))),unordered_pair(sK7(sK2,sK1,sK6(sF13,sF12)),sK8(sK2,sK1,sK6(sF13,sF12)))) = sK6(sF13,sF12)
| ~ spl14_9 ),
inference(resolution,[],[f338,f201]) ).
fof(f201,plain,
! [X0] :
( ~ in(X0,sF12)
| unordered_pair(singleton(sK7(sK2,sK1,X0)),unordered_pair(sK7(sK2,sK1,X0),sK8(sK2,sK1,X0))) = X0 ),
inference(superposition,[],[f76,f68]) ).
fof(f469,plain,
( spl14_7
| spl14_9 ),
inference(avatar_contradiction_clause,[],[f468]) ).
fof(f468,plain,
( $false
| spl14_7
| spl14_9 ),
inference(subsumption_resolution,[],[f467,f337]) ).
fof(f337,plain,
( ~ in(sK6(sF13,sF12),sF12)
| spl14_9 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f467,plain,
( in(sK6(sF13,sF12),sF12)
| spl14_7 ),
inference(subsumption_resolution,[],[f466,f72]) ).
fof(f466,plain,
( sF12 = sF13
| in(sK6(sF13,sF12),sF12)
| spl14_7 ),
inference(resolution,[],[f328,f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| in(sK6(X0,X1),X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f339,plain,
( ~ spl14_7
| spl14_9
| ~ spl14_2 ),
inference(avatar_split_clause,[],[f263,f259,f336,f327]) ).
fof(f263,plain,
( in(sK6(sF13,sF12),sF12)
| ~ in(sK6(sF13,sF12),sF13)
| ~ spl14_2 ),
inference(superposition,[],[f74,f261]) ).
fof(f261,plain,
( sK6(sF13,sF12) = unordered_pair(singleton(sK7(sK3,sK4,sK6(sF13,sF12))),unordered_pair(sK7(sK3,sK4,sK6(sF13,sF12)),sK8(sK3,sK4,sK6(sF13,sF12))))
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f74,plain,
! [X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF13)
| in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF12) ),
inference(forward_demodulation,[],[f73,f45]) ).
fof(f73,plain,
! [X4,X5] :
( ~ in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),sF13)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF12) ),
inference(forward_demodulation,[],[f70,f45]) ).
fof(f70,plain,
! [X4,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF13)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),sF12) ),
inference(definition_folding,[],[f57,f69,f68]) ).
fof(f57,plain,
! [X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),cartesian_product2(sK2,sK1))
| ~ in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),cartesian_product2(sK3,sK4)) ),
inference(definition_unfolding,[],[f42,f39,f39]) ).
fof(f42,plain,
! [X4,X5] :
( in(ordered_pair(X5,X4),cartesian_product2(sK2,sK1))
| ~ in(ordered_pair(X5,X4),cartesian_product2(sK3,sK4)) ),
inference(cnf_transformation,[],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET955+1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 14:28:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 % (27928)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.51 % (27935)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51 % (27936)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (27932)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51 % (27925)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.52 % (27946)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.52 % (27923)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.52 % (27929)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (27934)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.52 TRYING [1]
% 0.20/0.52 TRYING [2]
% 0.20/0.52 % (27948)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.52 % (27938)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.52 % (27947)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.53 % (27942)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (27924)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (27953)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.53 % (27924)Refutation not found, incomplete strategy% (27924)------------------------------
% 0.20/0.53 % (27924)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.53 % (27924)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.53 % (27924)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.53
% 0.20/0.53 % (27924)Memory used [KB]: 5500
% 0.20/0.53 % (27924)Time elapsed: 0.116 s
% 0.20/0.53 % (27924)Instructions burned: 4 (million)
% 0.20/0.53 % (27924)------------------------------
% 0.20/0.53 % (27924)------------------------------
% 0.20/0.53 % (27927)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (27930)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.53 % (27949)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.53 % (27950)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.53 % (27945)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.53 % (27933)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (27926)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.54 % (27943)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.54 % (27937)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (27931)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.54 % (27931)Instruction limit reached!
% 0.20/0.54 % (27931)------------------------------
% 0.20/0.54 % (27931)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (27931)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (27931)Termination reason: Unknown
% 0.20/0.54 % (27931)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (27931)Memory used [KB]: 5373
% 0.20/0.54 % (27931)Time elapsed: 0.003 s
% 0.20/0.54 % (27931)Instructions burned: 3 (million)
% 0.20/0.54 % (27931)------------------------------
% 0.20/0.54 % (27931)------------------------------
% 0.20/0.54 % (27940)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.54 TRYING [1]
% 0.20/0.54 TRYING [1]
% 0.20/0.54 % (27939)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.54 % (27944)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.54 % (27930)Instruction limit reached!
% 0.20/0.54 % (27930)------------------------------
% 0.20/0.54 % (27930)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (27930)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (27930)Termination reason: Unknown
% 0.20/0.54 % (27930)Termination phase: Saturation
% 0.20/0.54
% 0.20/0.54 % (27930)Memory used [KB]: 5500
% 0.20/0.54 % (27930)Time elapsed: 0.095 s
% 0.20/0.54 % (27930)Instructions burned: 8 (million)
% 0.20/0.54 % (27930)------------------------------
% 0.20/0.54 % (27930)------------------------------
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (27951)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.54 % (27941)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 TRYING [3]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 TRYING [3]
% 0.20/0.56 TRYING [3]
% 0.20/0.56 % (27935)First to succeed.
% 0.20/0.58 % (27928)Instruction limit reached!
% 0.20/0.58 % (27928)------------------------------
% 0.20/0.58 % (27928)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (27929)Instruction limit reached!
% 0.20/0.58 % (27929)------------------------------
% 0.20/0.58 % (27929)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (27929)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (27929)Termination reason: Unknown
% 0.20/0.58 % (27929)Termination phase: Finite model building SAT solving
% 0.20/0.58
% 0.20/0.58 % (27929)Memory used [KB]: 7547
% 0.20/0.58 % (27929)Time elapsed: 0.135 s
% 0.20/0.58 % (27929)Instructions burned: 51 (million)
% 0.20/0.58 % (27929)------------------------------
% 0.20/0.58 % (27929)------------------------------
% 0.20/0.58 % (27928)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (27928)Termination reason: Unknown
% 0.20/0.58 % (27928)Termination phase: Saturation
% 0.20/0.58
% 0.20/0.58 % (27928)Memory used [KB]: 6012
% 0.20/0.58 % (27928)Time elapsed: 0.165 s
% 0.20/0.58 % (27928)Instructions burned: 49 (million)
% 0.20/0.58 % (27928)------------------------------
% 0.20/0.58 % (27928)------------------------------
% 0.20/0.58 % (27927)Instruction limit reached!
% 0.20/0.58 % (27927)------------------------------
% 0.20/0.58 % (27927)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59 % (27935)Refutation found. Thanks to Tanya!
% 0.20/0.59 % SZS status Theorem for theBenchmark
% 0.20/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.59 % (27935)------------------------------
% 0.20/0.59 % (27935)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.59 % (27935)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.59 % (27935)Termination reason: Refutation
% 0.20/0.59
% 0.20/0.59 % (27935)Memory used [KB]: 5884
% 0.20/0.59 % (27935)Time elapsed: 0.154 s
% 0.20/0.59 % (27935)Instructions burned: 29 (million)
% 0.20/0.59 % (27935)------------------------------
% 0.20/0.59 % (27935)------------------------------
% 0.20/0.59 % (27919)Success in time 0.227 s
%------------------------------------------------------------------------------