TSTP Solution File: SET894+1 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n011.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 09:08:58 EDT 2024
% Result : Theorem 0.60s 0.79s
% Output : Refutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of formulae : 76 ( 16 unt; 0 def)
% Number of atoms : 273 ( 96 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 330 ( 133 ~; 130 |; 52 &)
% ( 7 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 182 ( 151 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f347,plain,
$false,
inference(avatar_sat_refutation,[],[f108,f225,f340]) ).
fof(f340,plain,
~ spl11_1,
inference(avatar_contradiction_clause,[],[f339]) ).
fof(f339,plain,
( $false
| ~ spl11_1 ),
inference(subsumption_resolution,[],[f331,f76]) ).
fof(f76,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f75]) ).
fof(f75,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f50]) ).
fof(f50,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ( ( sK8(X0,X1) != X0
| ~ in(sK8(X0,X1),X1) )
& ( sK8(X0,X1) = X0
| in(sK8(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f28,f29]) ).
fof(f29,plain,
! [X0,X1] :
( ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) )
=> ( ( sK8(X0,X1) != X0
| ~ in(sK8(X0,X1),X1) )
& ( sK8(X0,X1) = X0
| in(sK8(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f28,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( singleton(X0) = X1
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X0 = X2
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X0 = X2
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( singleton(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> X0 = X2 ) ),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d1_tarski) ).
fof(f331,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ spl11_1 ),
inference(backward_demodulation,[],[f243,f328]) ).
fof(f328,plain,
( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) = sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ spl11_1 ),
inference(backward_demodulation,[],[f298,f321]) ).
fof(f321,plain,
( sK1 = sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))
| ~ spl11_1 ),
inference(resolution,[],[f251,f77]) ).
fof(f77,plain,
! [X3,X0] :
( ~ in(X3,singleton(X0))
| X0 = X3 ),
inference(equality_resolution,[],[f49]) ).
fof(f49,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f30]) ).
fof(f251,plain,
( in(sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),singleton(sK1))
| ~ spl11_1 ),
inference(resolution,[],[f104,f73]) ).
fof(f73,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK7(X0,X1,X8),X1) ),
inference(equality_resolution,[],[f42]) ).
fof(f42,plain,
! [X2,X0,X1,X8] :
( in(sK7(X0,X1,X8),X1)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK3(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2))
& in(sK5(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
& in(sK7(X0,X1,X8),X1)
& in(sK6(X0,X1,X8),X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7])],[f22,f25,f24,f23]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK3(X0,X1,X2)
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK3(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
| in(sK3(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK3(X0,X1,X2)
& in(X7,X1)
& in(X6,X0) )
=> ( sK3(X0,X1,X2) = ordered_pair(sK4(X0,X1,X2),sK5(X0,X1,X2))
& in(sK5(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
=> ( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
& in(sK7(X0,X1,X8),X1)
& in(sK6(X0,X1,X8),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X1)
& in(X6,X0) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X1)
& in(X11,X0) )
| ~ in(X8,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d2_zfmisc_1) ).
fof(f104,plain,
( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f103,plain,
( spl11_1
<=> in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_1])]) ).
fof(f298,plain,
( sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) = unordered_pair(singleton(sK0),unordered_pair(sK0,sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))))
| ~ spl11_1 ),
inference(backward_demodulation,[],[f249,f290]) ).
fof(f290,plain,
( sK0 = sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))
| ~ spl11_1 ),
inference(resolution,[],[f250,f77]) ).
fof(f250,plain,
( in(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),singleton(sK0))
| ~ spl11_1 ),
inference(resolution,[],[f104,f74]) ).
fof(f74,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| in(sK6(X0,X1,X8),X0) ),
inference(equality_resolution,[],[f41]) ).
fof(f41,plain,
! [X2,X0,X1,X8] :
( in(sK6(X0,X1,X8),X0)
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f249,plain,
( sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) = unordered_pair(singleton(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))),unordered_pair(sK6(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))),sK7(singleton(sK0),singleton(sK1),sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))))))
| ~ spl11_1 ),
inference(resolution,[],[f104,f82]) ).
fof(f82,plain,
! [X0,X1,X8] :
( ~ in(X8,cartesian_product2(X0,X1))
| unordered_pair(singleton(sK6(X0,X1,X8)),unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8))) = X8 ),
inference(backward_demodulation,[],[f72,f53]) ).
fof(f53,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',commutativity_k2_tarski) ).
fof(f72,plain,
! [X0,X1,X8] :
( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
| ~ in(X8,cartesian_product2(X0,X1)) ),
inference(equality_resolution,[],[f65]) ).
fof(f65,plain,
! [X2,X0,X1,X8] :
( unordered_pair(unordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)),singleton(sK6(X0,X1,X8))) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f43,f40]) ).
fof(f40,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',d5_tarski) ).
fof(f43,plain,
! [X2,X0,X1,X8] :
( ordered_pair(sK6(X0,X1,X8),sK7(X0,X1,X8)) = X8
| ~ in(X8,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f243,plain,
( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ spl11_1 ),
inference(subsumption_resolution,[],[f120,f104]) ).
fof(f120,plain,
( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(extensionality_resolution,[],[f39,f80]) ).
fof(f80,plain,
cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))),
inference(backward_demodulation,[],[f61,f53]) ).
fof(f61,plain,
cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(unordered_pair(unordered_pair(sK0,sK1),singleton(sK0))),
inference(definition_unfolding,[],[f37,f40]) ).
fof(f37,plain,
cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f13,f16]) ).
fof(f16,plain,
( ? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1))
=> cartesian_product2(singleton(sK0),singleton(sK1)) != singleton(ordered_pair(sK0,sK1)) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) != singleton(ordered_pair(X0,X1)),
inference(ennf_transformation,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X1] : cartesian_product2(singleton(X0),singleton(X1)) = singleton(ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',t35_zfmisc_1) ).
fof(f39,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| X0 = X1
| ~ in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( X0 = X1
| ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f18,f19]) ).
fof(f19,plain,
! [X0,X1] :
( ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) )
=> ( ( ~ in(sK2(X0,X1),X1)
| ~ in(sK2(X0,X1),X0) )
& ( in(sK2(X0,X1),X1)
| in(sK2(X0,X1),X0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( ( ~ in(X2,X1)
| ~ in(X2,X0) )
& ( in(X2,X1)
| in(X2,X0) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( in(X2,X0)
<~> in(X2,X1) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
<=> in(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789',t2_tarski) ).
fof(f225,plain,
~ spl11_2,
inference(avatar_contradiction_clause,[],[f210]) ).
fof(f210,plain,
( $false
| ~ spl11_2 ),
inference(resolution,[],[f188,f127]) ).
fof(f127,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),cartesian_product2(singleton(sK0),singleton(sK1)))
| ~ spl11_2 ),
inference(forward_demodulation,[],[f126,f116]) ).
fof(f116,plain,
( unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)) = sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ spl11_2 ),
inference(resolution,[],[f107,f77]) ).
fof(f107,plain,
( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f106]) ).
fof(f106,plain,
( spl11_2
<=> in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl11_2])]) ).
fof(f126,plain,
( ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
| ~ spl11_2 ),
inference(subsumption_resolution,[],[f125,f76]) ).
fof(f125,plain,
( ~ in(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| ~ in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1)))
| ~ spl11_2 ),
inference(forward_demodulation,[],[f120,f116]) ).
fof(f188,plain,
! [X0,X1] : in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(singleton(X0),singleton(X1))),
inference(resolution,[],[f155,f76]) ).
fof(f155,plain,
! [X2,X0,X1] :
( ~ in(X0,X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),cartesian_product2(X2,singleton(X1))) ),
inference(resolution,[],[f78,f76]) ).
fof(f78,plain,
! [X10,X0,X1,X9] :
( ~ in(X10,X1)
| in(unordered_pair(singleton(X9),unordered_pair(X9,X10)),cartesian_product2(X0,X1))
| ~ in(X9,X0) ),
inference(backward_demodulation,[],[f71,f53]) ).
fof(f71,plain,
! [X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),cartesian_product2(X0,X1))
| ~ in(X10,X1)
| ~ in(X9,X0) ),
inference(equality_resolution,[],[f70]) ).
fof(f70,plain,
! [X2,X10,X0,X1,X9] :
( in(unordered_pair(unordered_pair(X9,X10),singleton(X9)),X2)
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(equality_resolution,[],[f64]) ).
fof(f64,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| unordered_pair(unordered_pair(X9,X10),singleton(X9)) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(definition_unfolding,[],[f44,f40]) ).
fof(f44,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X1)
| ~ in(X9,X0)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f26]) ).
fof(f108,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f96,f106,f103]) ).
fof(f96,plain,
( in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1))))
| in(sK2(cartesian_product2(singleton(sK0),singleton(sK1)),singleton(unordered_pair(singleton(sK0),unordered_pair(sK0,sK1)))),cartesian_product2(singleton(sK0),singleton(sK1))) ),
inference(extensionality_resolution,[],[f38,f80]) ).
fof(f38,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| X0 = X1
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SET894+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.08/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37 % Computer : n011.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 3 16:45:38 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.37 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.9ilGNSTdPj/Vampire---4.8_2789
% 0.60/0.76 % (3077)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.76 % (3083)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.60/0.77 % (3079)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.77 % (3078)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.60/0.77 % (3080)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.77 % (3082)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.77 % (3081)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.77 % (3077)Refutation not found, incomplete strategy% (3077)------------------------------
% 0.60/0.77 % (3077)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (3077)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77
% 0.60/0.77 % (3077)Memory used [KB]: 1065
% 0.60/0.77 % (3077)Time elapsed: 0.003 s
% 0.60/0.77 % (3077)Instructions burned: 6 (million)
% 0.60/0.77 % (3077)------------------------------
% 0.60/0.77 % (3077)------------------------------
% 0.60/0.77 % (3082)Refutation not found, incomplete strategy% (3082)------------------------------
% 0.60/0.77 % (3082)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (3082)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77
% 0.60/0.77 % (3082)Memory used [KB]: 1024
% 0.60/0.77 % (3082)Time elapsed: 0.003 s
% 0.60/0.77 % (3082)Instructions burned: 3 (million)
% 0.60/0.77 % (3082)------------------------------
% 0.60/0.77 % (3082)------------------------------
% 0.60/0.77 % (3081)Refutation not found, incomplete strategy% (3081)------------------------------
% 0.60/0.77 % (3081)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (3081)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77
% 0.60/0.77 % (3081)Memory used [KB]: 1051
% 0.60/0.77 % (3081)Time elapsed: 0.004 s
% 0.60/0.77 % (3081)Instructions burned: 4 (million)
% 0.60/0.77 % (3081)------------------------------
% 0.60/0.77 % (3081)------------------------------
% 0.60/0.77 % (3084)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.60/0.77 % (3084)Refutation not found, incomplete strategy% (3084)------------------------------
% 0.60/0.77 % (3084)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (3084)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77
% 0.60/0.77 % (3084)Memory used [KB]: 1047
% 0.60/0.77 % (3084)Time elapsed: 0.002 s
% 0.60/0.77 % (3084)Instructions burned: 3 (million)
% 0.60/0.77 % (3084)------------------------------
% 0.60/0.77 % (3084)------------------------------
% 0.60/0.77 % (3086)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.60/0.77 % (3087)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.60/0.77 % (3088)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.60/0.77 % (3085)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.60/0.77 % (3086)Refutation not found, incomplete strategy% (3086)------------------------------
% 0.60/0.77 % (3086)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.77 % (3086)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.77
% 0.60/0.77 % (3086)Memory used [KB]: 1034
% 0.60/0.77 % (3086)Time elapsed: 0.003 s
% 0.60/0.77 % (3086)Instructions burned: 3 (million)
% 0.60/0.77 % (3086)------------------------------
% 0.60/0.77 % (3086)------------------------------
% 0.60/0.78 % (3089)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.60/0.78 % (3089)Refutation not found, incomplete strategy% (3089)------------------------------
% 0.60/0.78 % (3089)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78 % (3089)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.78
% 0.60/0.78 % (3089)Memory used [KB]: 1033
% 0.60/0.78 % (3089)Time elapsed: 0.004 s
% 0.60/0.78 % (3089)Instructions burned: 4 (million)
% 0.60/0.78 % (3089)------------------------------
% 0.60/0.78 % (3089)------------------------------
% 0.60/0.78 % (3080)Instruction limit reached!
% 0.60/0.78 % (3080)------------------------------
% 0.60/0.78 % (3080)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78 % (3080)Termination reason: Unknown
% 0.60/0.78 % (3080)Termination phase: Saturation
% 0.60/0.78
% 0.60/0.78 % (3080)Memory used [KB]: 1363
% 0.60/0.78 % (3080)Time elapsed: 0.020 s
% 0.60/0.78 % (3080)Instructions burned: 33 (million)
% 0.60/0.78 % (3080)------------------------------
% 0.60/0.78 % (3080)------------------------------
% 0.60/0.78 % (3088)First to succeed.
% 0.60/0.78 % (3088)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3003"
% 0.60/0.79 % (3088)Refutation found. Thanks to Tanya!
% 0.60/0.79 % SZS status Theorem for Vampire---4
% 0.60/0.79 % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.79 % (3088)------------------------------
% 0.60/0.79 % (3088)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79 % (3088)Termination reason: Refutation
% 0.60/0.79
% 0.60/0.79 % (3088)Memory used [KB]: 1243
% 0.60/0.79 % (3088)Time elapsed: 0.012 s
% 0.60/0.79 % (3088)Instructions burned: 32 (million)
% 0.60/0.79 % (3003)Success in time 0.401 s
% 0.60/0.79 % Vampire---4.8 exiting
%------------------------------------------------------------------------------