TSTP Solution File: SEU166+3 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% 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 : n018.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 18:32:17 EDT 2022
% Result : Theorem 1.50s 0.59s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 25
% Syntax : Number of formulae : 125 ( 11 unt; 0 def)
% Number of atoms : 376 ( 61 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 408 ( 157 ~; 170 |; 55 &)
% ( 17 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-3 aty)
% Number of variables : 192 ( 157 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f969,plain,
$false,
inference(avatar_sat_refutation,[],[f81,f546,f563,f566,f574,f578,f605,f771,f953,f956,f963,f968]) ).
fof(f968,plain,
( spl15_2
| ~ spl15_43 ),
inference(avatar_contradiction_clause,[],[f967]) ).
fof(f967,plain,
( $false
| spl15_2
| ~ spl15_43 ),
inference(subsumption_resolution,[],[f964,f80]) ).
fof(f80,plain,
( ~ subset(sF13,sF14)
| spl15_2 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f78,plain,
( spl15_2
<=> subset(sF13,sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f964,plain,
( subset(sF13,sF14)
| ~ spl15_43 ),
inference(resolution,[],[f770,f43]) ).
fof(f43,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X0)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ( in(sK2(X0,X1),X1)
& ~ in(sK2(X0,X1),X0) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| in(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) )
=> ( in(sK2(X0,X1),X1)
& ~ in(sK2(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X1,X0)
| ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) )
& ( ! [X3] :
( ~ in(X3,X1)
| in(X3,X0) )
| ~ subset(X1,X0) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X1,X0] :
( ( subset(X0,X1)
| ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) ) )
& ( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X1,X0] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f770,plain,
( in(sK2(sF14,sF13),sF14)
| ~ spl15_43 ),
inference(avatar_component_clause,[],[f768]) ).
fof(f768,plain,
( spl15_43
<=> in(sK2(sF14,sF13),sF14) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_43])]) ).
fof(f963,plain,
( spl15_42
| ~ spl15_74 ),
inference(avatar_contradiction_clause,[],[f962]) ).
fof(f962,plain,
( $false
| spl15_42
| ~ spl15_74 ),
inference(subsumption_resolution,[],[f961,f949]) ).
fof(f949,plain,
( in(sK2(sF14,sF13),sF13)
| ~ spl15_74 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f947,plain,
( spl15_74
<=> in(sK2(sF14,sF13),sF13) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_74])]) ).
fof(f961,plain,
( ~ in(sK2(sF14,sF13),sF13)
| spl15_42 ),
inference(forward_demodulation,[],[f960,f70]) ).
fof(f70,plain,
sF13 = cartesian_product2(sK4,sK3),
introduced(function_definition,[]) ).
fof(f960,plain,
( ~ in(sK2(sF14,sF13),cartesian_product2(sK4,sK3))
| spl15_42 ),
inference(resolution,[],[f766,f102]) ).
fof(f102,plain,
! [X3,X4] :
( in(sK7(X4,sK4,X3),sK5)
| ~ in(X3,cartesian_product2(sK4,X4)) ),
inference(resolution,[],[f66,f95]) ).
fof(f95,plain,
! [X0] :
( ~ in(X0,sK4)
| in(X0,sK5) ),
inference(resolution,[],[f42,f47]) ).
fof(f47,plain,
subset(sK4,sK5),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
( ( ~ subset(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5))
| ~ subset(cartesian_product2(sK4,sK3),cartesian_product2(sK5,sK3)) )
& subset(sK4,sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f29,f30]) ).
fof(f30,plain,
( ? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| ~ subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& subset(X1,X2) )
=> ( ( ~ subset(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5))
| ~ subset(cartesian_product2(sK4,sK3),cartesian_product2(sK5,sK3)) )
& subset(sK4,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X0,X1),cartesian_product2(X0,X2))
| ~ subset(cartesian_product2(X1,X0),cartesian_product2(X2,X0)) )
& subset(X1,X2) ),
inference(rectify,[],[f18]) ).
fof(f18,plain,
? [X2,X1,X0] :
( ( ~ subset(cartesian_product2(X2,X1),cartesian_product2(X2,X0))
| ~ subset(cartesian_product2(X1,X2),cartesian_product2(X0,X2)) )
& subset(X1,X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,plain,
~ ! [X1,X2,X0] :
( subset(X1,X0)
=> ( subset(cartesian_product2(X1,X2),cartesian_product2(X0,X2))
& subset(cartesian_product2(X2,X1),cartesian_product2(X2,X0)) ) ),
inference(rectify,[],[f11]) ).
fof(f11,negated_conjecture,
~ ! [X1,X0,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
inference(negated_conjecture,[],[f10]) ).
fof(f10,conjecture,
! [X1,X0,X2] :
( subset(X0,X1)
=> ( subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
& subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ subset(X1,X0)
| in(X3,X0)
| ~ in(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f66,plain,
! [X2,X3,X0] :
( in(sK7(X0,X2,X3),X2)
| ~ in(X3,cartesian_product2(X2,X0)) ),
inference(equality_resolution,[],[f54]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( in(sK7(X0,X2,X3),X2)
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X5,X2)
| ~ in(X4,X0) ) )
& ( ( ordered_pair(sK7(X0,X2,X3),sK6(X0,X2,X3)) = X3
& in(sK7(X0,X2,X3),X2)
& in(sK6(X0,X2,X3),X0) )
| ~ in(X3,X1) ) )
| cartesian_product2(X2,X0) != X1 )
& ( cartesian_product2(X2,X0) = X1
| ( ( ! [X9,X10] :
( ordered_pair(X10,X9) != sK8(X0,X1,X2)
| ~ in(X10,X2)
| ~ in(X9,X0) )
| ~ in(sK8(X0,X1,X2),X1) )
& ( ( ordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)) = sK8(X0,X1,X2)
& in(sK10(X0,X1,X2),X2)
& in(sK9(X0,X1,X2),X0) )
| in(sK8(X0,X1,X2),X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10])],[f33,f36,f35,f34]) ).
fof(f34,plain,
! [X0,X2,X3] :
( ? [X6,X7] :
( ordered_pair(X7,X6) = X3
& in(X7,X2)
& in(X6,X0) )
=> ( ordered_pair(sK7(X0,X2,X3),sK6(X0,X2,X3)) = X3
& in(sK7(X0,X2,X3),X2)
& in(sK6(X0,X2,X3),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ? [X8] :
( ( ! [X9,X10] :
( ordered_pair(X10,X9) != X8
| ~ in(X10,X2)
| ~ in(X9,X0) )
| ~ in(X8,X1) )
& ( ? [X11,X12] :
( ordered_pair(X12,X11) = X8
& in(X12,X2)
& in(X11,X0) )
| in(X8,X1) ) )
=> ( ( ! [X10,X9] :
( ordered_pair(X10,X9) != sK8(X0,X1,X2)
| ~ in(X10,X2)
| ~ in(X9,X0) )
| ~ in(sK8(X0,X1,X2),X1) )
& ( ? [X12,X11] :
( ordered_pair(X12,X11) = sK8(X0,X1,X2)
& in(X12,X2)
& in(X11,X0) )
| in(sK8(X0,X1,X2),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ? [X12,X11] :
( ordered_pair(X12,X11) = sK8(X0,X1,X2)
& in(X12,X2)
& in(X11,X0) )
=> ( ordered_pair(sK10(X0,X1,X2),sK9(X0,X1,X2)) = sK8(X0,X1,X2)
& in(sK10(X0,X1,X2),X2)
& in(sK9(X0,X1,X2),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( in(X3,X1)
| ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X5,X2)
| ~ in(X4,X0) ) )
& ( ? [X6,X7] :
( ordered_pair(X7,X6) = X3
& in(X7,X2)
& in(X6,X0) )
| ~ in(X3,X1) ) )
| cartesian_product2(X2,X0) != X1 )
& ( cartesian_product2(X2,X0) = X1
| ? [X8] :
( ( ! [X9,X10] :
( ordered_pair(X10,X9) != X8
| ~ in(X10,X2)
| ~ in(X9,X0) )
| ~ in(X8,X1) )
& ( ? [X11,X12] :
( ordered_pair(X12,X11) = X8
& in(X12,X2)
& in(X11,X0) )
| in(X8,X1) ) ) ) ),
inference(rectify,[],[f32]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ( ! [X3] :
( ( in(X3,X0)
| ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X5,X1)
| ~ in(X4,X2) ) )
& ( ? [X4,X5] :
( ordered_pair(X5,X4) = X3
& in(X5,X1)
& in(X4,X2) )
| ~ in(X3,X0) ) )
| cartesian_product2(X1,X2) != X0 )
& ( cartesian_product2(X1,X2) = X0
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X5,X4) != X3
| ~ in(X5,X1)
| ~ in(X4,X2) )
| ~ in(X3,X0) )
& ( ? [X4,X5] :
( ordered_pair(X5,X4) = X3
& in(X5,X1)
& in(X4,X2) )
| in(X3,X0) ) ) ) ),
inference(nnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X2,X0,X1] :
( ! [X3] :
( in(X3,X0)
<=> ? [X4,X5] :
( ordered_pair(X5,X4) = X3
& in(X5,X1)
& in(X4,X2) ) )
<=> cartesian_product2(X1,X2) = X0 ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ! [X3] :
( ? [X5,X4] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
<=> in(X3,X2) )
<=> cartesian_product2(X0,X1) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f766,plain,
( ~ in(sK7(sK3,sK4,sK2(sF14,sF13)),sK5)
| spl15_42 ),
inference(avatar_component_clause,[],[f764]) ).
fof(f764,plain,
( spl15_42
<=> in(sK7(sK3,sK4,sK2(sF14,sF13)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_42])]) ).
fof(f956,plain,
( spl15_2
| spl15_74 ),
inference(avatar_contradiction_clause,[],[f955]) ).
fof(f955,plain,
( $false
| spl15_2
| spl15_74 ),
inference(subsumption_resolution,[],[f954,f80]) ).
fof(f954,plain,
( subset(sF13,sF14)
| spl15_74 ),
inference(resolution,[],[f948,f44]) ).
fof(f44,plain,
! [X0,X1] :
( in(sK2(X0,X1),X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f948,plain,
( ~ in(sK2(sF14,sF13),sF13)
| spl15_74 ),
inference(avatar_component_clause,[],[f947]) ).
fof(f953,plain,
( ~ spl15_74
| spl15_40 ),
inference(avatar_split_clause,[],[f952,f755,f947]) ).
fof(f755,plain,
( spl15_40
<=> in(sK6(sK3,sK4,sK2(sF14,sF13)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_40])]) ).
fof(f952,plain,
( ~ in(sK2(sF14,sF13),sF13)
| spl15_40 ),
inference(forward_demodulation,[],[f951,f70]) ).
fof(f951,plain,
( ~ in(sK2(sF14,sF13),cartesian_product2(sK4,sK3))
| spl15_40 ),
inference(resolution,[],[f757,f67]) ).
fof(f67,plain,
! [X2,X3,X0] :
( in(sK6(X0,X2,X3),X0)
| ~ in(X3,cartesian_product2(X2,X0)) ),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X3,X0,X1] :
( in(sK6(X0,X2,X3),X0)
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f757,plain,
( ~ in(sK6(sK3,sK4,sK2(sF14,sF13)),sK3)
| spl15_40 ),
inference(avatar_component_clause,[],[f755]) ).
fof(f771,plain,
( ~ spl15_42
| ~ spl15_40
| spl15_43
| spl15_2 ),
inference(avatar_split_clause,[],[f708,f78,f768,f755,f764]) ).
fof(f708,plain,
( in(sK2(sF14,sF13),sF14)
| ~ in(sK6(sK3,sK4,sK2(sF14,sF13)),sK3)
| ~ in(sK7(sK3,sK4,sK2(sF14,sF13)),sK5)
| spl15_2 ),
inference(superposition,[],[f131,f607]) ).
fof(f607,plain,
( unordered_pair(singleton(sK7(sK3,sK4,sK2(sF14,sF13))),unordered_pair(sK6(sK3,sK4,sK2(sF14,sF13)),sK7(sK3,sK4,sK2(sF14,sF13)))) = sK2(sF14,sF13)
| spl15_2 ),
inference(resolution,[],[f80,f279]) ).
fof(f279,plain,
! [X4] :
( subset(sF13,X4)
| sK2(X4,sF13) = unordered_pair(singleton(sK7(sK3,sK4,sK2(X4,sF13))),unordered_pair(sK6(sK3,sK4,sK2(X4,sF13)),sK7(sK3,sK4,sK2(X4,sF13)))) ),
inference(resolution,[],[f257,f44]) ).
fof(f257,plain,
! [X2] :
( ~ in(X2,sF13)
| unordered_pair(singleton(sK7(sK3,sK4,X2)),unordered_pair(sK6(sK3,sK4,X2),sK7(sK3,sK4,X2))) = X2 ),
inference(forward_demodulation,[],[f256,f46]) ).
fof(f46,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f12]) ).
fof(f12,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(f256,plain,
! [X2] :
( ~ in(X2,sF13)
| unordered_pair(singleton(sK7(sK3,sK4,X2)),unordered_pair(sK7(sK3,sK4,X2),sK6(sK3,sK4,X2))) = X2 ),
inference(forward_demodulation,[],[f225,f46]) ).
fof(f225,plain,
! [X2] :
( unordered_pair(unordered_pair(sK7(sK3,sK4,X2),sK6(sK3,sK4,X2)),singleton(sK7(sK3,sK4,X2))) = X2
| ~ in(X2,sF13) ),
inference(superposition,[],[f65,f70]) ).
fof(f65,plain,
! [X2,X3,X0] :
( ~ in(X3,cartesian_product2(X2,X0))
| unordered_pair(unordered_pair(sK7(X0,X2,X3),sK6(X0,X2,X3)),singleton(sK7(X0,X2,X3))) = X3 ),
inference(equality_resolution,[],[f60]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( unordered_pair(unordered_pair(sK7(X0,X2,X3),sK6(X0,X2,X3)),singleton(sK7(X0,X2,X3))) = X3
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(definition_unfolding,[],[f55,f38]) ).
fof(f38,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/benchmark/theBenchmark.p',d5_tarski) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ordered_pair(sK7(X0,X2,X3),sK6(X0,X2,X3)) = X3
| ~ in(X3,X1)
| cartesian_product2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f131,plain,
! [X2,X3] :
( in(unordered_pair(singleton(X2),unordered_pair(X3,X2)),sF14)
| ~ in(X2,sK5)
| ~ in(X3,sK3) ),
inference(superposition,[],[f120,f46]) ).
fof(f120,plain,
! [X6,X7] :
( in(unordered_pair(singleton(X6),unordered_pair(X6,X7)),sF14)
| ~ in(X7,sK3)
| ~ in(X6,sK5) ),
inference(forward_demodulation,[],[f115,f46]) ).
fof(f115,plain,
! [X6,X7] :
( ~ in(X7,sK3)
| in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),sF14)
| ~ in(X6,sK5) ),
inference(superposition,[],[f64,f71]) ).
fof(f71,plain,
cartesian_product2(sK5,sK3) = sF14,
introduced(function_definition,[]) ).
fof(f64,plain,
! [X2,X0,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),cartesian_product2(X2,X0))
| ~ in(X4,X0)
| ~ in(X5,X2) ),
inference(equality_resolution,[],[f63]) ).
fof(f63,plain,
! [X2,X0,X1,X4,X5] :
( in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X1)
| ~ in(X5,X2)
| ~ in(X4,X0)
| cartesian_product2(X2,X0) != X1 ),
inference(equality_resolution,[],[f59]) ).
fof(f59,plain,
! [X2,X3,X0,X1,X4,X5] :
( in(X3,X1)
| unordered_pair(unordered_pair(X5,X4),singleton(X5)) != X3
| ~ in(X5,X2)
| ~ in(X4,X0)
| cartesian_product2(X2,X0) != X1 ),
inference(definition_unfolding,[],[f56,f38]) ).
fof(f56,plain,
! [X2,X3,X0,X1,X4,X5] :
( in(X3,X1)
| ordered_pair(X5,X4) != X3
| ~ in(X5,X2)
| ~ in(X4,X0)
| cartesian_product2(X2,X0) != X1 ),
inference(cnf_transformation,[],[f37]) ).
fof(f605,plain,
( spl15_1
| ~ spl15_36 ),
inference(avatar_contradiction_clause,[],[f604]) ).
fof(f604,plain,
( $false
| spl15_1
| ~ spl15_36 ),
inference(subsumption_resolution,[],[f601,f76]) ).
fof(f76,plain,
( ~ subset(sF11,sF12)
| spl15_1 ),
inference(avatar_component_clause,[],[f74]) ).
fof(f74,plain,
( spl15_1
<=> subset(sF11,sF12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f601,plain,
( subset(sF11,sF12)
| ~ spl15_36 ),
inference(resolution,[],[f545,f43]) ).
fof(f545,plain,
( in(sK2(sF12,sF11),sF12)
| ~ spl15_36 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f543,plain,
( spl15_36
<=> in(sK2(sF12,sF11),sF12) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_36])]) ).
fof(f578,plain,
( ~ spl15_10
| spl15_21 ),
inference(avatar_contradiction_clause,[],[f577]) ).
fof(f577,plain,
( $false
| ~ spl15_10
| spl15_21 ),
inference(subsumption_resolution,[],[f575,f462]) ).
fof(f462,plain,
( ~ in(sK6(sK4,sK3,sK2(sF12,sF11)),sK5)
| spl15_21 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f460,plain,
( spl15_21
<=> in(sK6(sK4,sK3,sK2(sF12,sF11)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_21])]) ).
fof(f575,plain,
( in(sK6(sK4,sK3,sK2(sF12,sF11)),sK5)
| ~ spl15_10 ),
inference(resolution,[],[f404,f95]) ).
fof(f404,plain,
( in(sK6(sK4,sK3,sK2(sF12,sF11)),sK4)
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f403,plain,
( spl15_10
<=> in(sK6(sK4,sK3,sK2(sF12,sF11)),sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f574,plain,
( spl15_10
| ~ spl15_31 ),
inference(avatar_contradiction_clause,[],[f573]) ).
fof(f573,plain,
( $false
| spl15_10
| ~ spl15_31 ),
inference(subsumption_resolution,[],[f572,f517]) ).
fof(f517,plain,
( in(sK2(sF12,sF11),sF11)
| ~ spl15_31 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f515,plain,
( spl15_31
<=> in(sK2(sF12,sF11),sF11) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_31])]) ).
fof(f572,plain,
( ~ in(sK2(sF12,sF11),sF11)
| spl15_10 ),
inference(forward_demodulation,[],[f571,f68]) ).
fof(f68,plain,
sF11 = cartesian_product2(sK3,sK4),
introduced(function_definition,[]) ).
fof(f571,plain,
( ~ in(sK2(sF12,sF11),cartesian_product2(sK3,sK4))
| spl15_10 ),
inference(resolution,[],[f405,f67]) ).
fof(f405,plain,
( ~ in(sK6(sK4,sK3,sK2(sF12,sF11)),sK4)
| spl15_10 ),
inference(avatar_component_clause,[],[f403]) ).
fof(f566,plain,
( spl15_1
| spl15_31 ),
inference(avatar_contradiction_clause,[],[f565]) ).
fof(f565,plain,
( $false
| spl15_1
| spl15_31 ),
inference(subsumption_resolution,[],[f564,f76]) ).
fof(f564,plain,
( subset(sF11,sF12)
| spl15_31 ),
inference(resolution,[],[f516,f44]) ).
fof(f516,plain,
( ~ in(sK2(sF12,sF11),sF11)
| spl15_31 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f563,plain,
( ~ spl15_31
| spl15_9 ),
inference(avatar_split_clause,[],[f562,f399,f515]) ).
fof(f399,plain,
( spl15_9
<=> in(sK7(sK4,sK3,sK2(sF12,sF11)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f562,plain,
( ~ in(sK2(sF12,sF11),sF11)
| spl15_9 ),
inference(forward_demodulation,[],[f561,f68]) ).
fof(f561,plain,
( ~ in(sK2(sF12,sF11),cartesian_product2(sK3,sK4))
| spl15_9 ),
inference(resolution,[],[f401,f66]) ).
fof(f401,plain,
( ~ in(sK7(sK4,sK3,sK2(sF12,sF11)),sK3)
| spl15_9 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f546,plain,
( ~ spl15_21
| ~ spl15_9
| spl15_36
| spl15_1 ),
inference(avatar_split_clause,[],[f333,f74,f543,f399,f460]) ).
fof(f333,plain,
( in(sK2(sF12,sF11),sF12)
| ~ in(sK7(sK4,sK3,sK2(sF12,sF11)),sK3)
| ~ in(sK6(sK4,sK3,sK2(sF12,sF11)),sK5)
| spl15_1 ),
inference(superposition,[],[f127,f328]) ).
fof(f328,plain,
( sK2(sF12,sF11) = unordered_pair(singleton(sK7(sK4,sK3,sK2(sF12,sF11))),unordered_pair(sK6(sK4,sK3,sK2(sF12,sF11)),sK7(sK4,sK3,sK2(sF12,sF11))))
| spl15_1 ),
inference(resolution,[],[f292,f76]) ).
fof(f292,plain,
! [X4] :
( subset(sF11,X4)
| sK2(X4,sF11) = unordered_pair(singleton(sK7(sK4,sK3,sK2(X4,sF11))),unordered_pair(sK6(sK4,sK3,sK2(X4,sF11)),sK7(sK4,sK3,sK2(X4,sF11)))) ),
inference(resolution,[],[f259,f44]) ).
fof(f259,plain,
! [X0] :
( ~ in(X0,sF11)
| unordered_pair(singleton(sK7(sK4,sK3,X0)),unordered_pair(sK6(sK4,sK3,X0),sK7(sK4,sK3,X0))) = X0 ),
inference(forward_demodulation,[],[f258,f46]) ).
fof(f258,plain,
! [X0] :
( unordered_pair(singleton(sK7(sK4,sK3,X0)),unordered_pair(sK7(sK4,sK3,X0),sK6(sK4,sK3,X0))) = X0
| ~ in(X0,sF11) ),
inference(forward_demodulation,[],[f223,f46]) ).
fof(f223,plain,
! [X0] :
( unordered_pair(unordered_pair(sK7(sK4,sK3,X0),sK6(sK4,sK3,X0)),singleton(sK7(sK4,sK3,X0))) = X0
| ~ in(X0,sF11) ),
inference(superposition,[],[f65,f68]) ).
fof(f127,plain,
! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X1,X0)),sF12)
| ~ in(X0,sK3)
| ~ in(X1,sK5) ),
inference(superposition,[],[f118,f46]) ).
fof(f118,plain,
! [X2,X3] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),sF12)
| ~ in(X2,sK3)
| ~ in(X3,sK5) ),
inference(forward_demodulation,[],[f113,f46]) ).
fof(f113,plain,
! [X2,X3] :
( ~ in(X2,sK3)
| in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),sF12)
| ~ in(X3,sK5) ),
inference(superposition,[],[f64,f69]) ).
fof(f69,plain,
cartesian_product2(sK3,sK5) = sF12,
introduced(function_definition,[]) ).
fof(f81,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f72,f78,f74]) ).
fof(f72,plain,
( ~ subset(sF13,sF14)
| ~ subset(sF11,sF12) ),
inference(definition_folding,[],[f48,f71,f70,f69,f68]) ).
fof(f48,plain,
( ~ subset(cartesian_product2(sK3,sK4),cartesian_product2(sK3,sK5))
| ~ subset(cartesian_product2(sK4,sK3),cartesian_product2(sK5,sK3)) ),
inference(cnf_transformation,[],[f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU166+3 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n018.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 : Tue Aug 30 14:48:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.51 % (10442)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.51 % (10459)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)
% 0.21/0.51 % (10451)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.52 % (10450)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)
% 0.21/0.52 % (10458)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)
% 0.21/0.53 % (10461)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)
% 0.21/0.53 % (10467)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.21/0.53 % (10444)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)
% 1.37/0.53 % (10468)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)
% 1.37/0.53 % (10466)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)
% 1.37/0.53 % (10438)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)
% 1.37/0.53 % (10441)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)
% 1.37/0.53 TRYING [1]
% 1.37/0.54 % (10460)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.37/0.54 TRYING [2]
% 1.37/0.54 % (10446)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.37/0.54 % (10446)Instruction limit reached!
% 1.37/0.54 % (10446)------------------------------
% 1.37/0.54 % (10446)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.37/0.54 % (10462)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)
% 1.37/0.54 % (10454)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)
% 1.37/0.54 % (10443)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)
% 1.37/0.54 % (10440)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)
% 1.37/0.54 % (10453)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)
% 1.37/0.54 % (10447)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)
% 1.37/0.54 % (10448)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.37/0.54 % (10446)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.37/0.54 % (10446)Termination reason: Unknown
% 1.37/0.54 % (10446)Termination phase: Saturation
% 1.37/0.54
% 1.37/0.54 % (10446)Memory used [KB]: 5373
% 1.37/0.54 % (10446)Time elapsed: 0.120 s
% 1.37/0.54 % (10446)Instructions burned: 3 (million)
% 1.37/0.54 % (10446)------------------------------
% 1.37/0.54 % (10446)------------------------------
% 1.37/0.54 % (10439)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)
% 1.50/0.55 TRYING [1]
% 1.50/0.55 TRYING [3]
% 1.50/0.55 TRYING [2]
% 1.50/0.55 % (10452)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.50/0.55 % (10455)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)
% 1.50/0.55 % (10457)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.50/0.55 % (10464)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.50/0.56 % (10465)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)
% 1.50/0.56 TRYING [3]
% 1.50/0.56 % (10439)Refutation not found, incomplete strategy% (10439)------------------------------
% 1.50/0.56 % (10439)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.50/0.56 % (10463)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 1.50/0.56 % (10445)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.50/0.56 % (10456)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.50/0.56 % (10439)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.50/0.56 % (10439)Termination reason: Refutation not found, incomplete strategy
% 1.50/0.56
% 1.50/0.56 % (10439)Memory used [KB]: 5500
% 1.50/0.56 % (10439)Time elapsed: 0.144 s
% 1.50/0.56 % (10439)Instructions burned: 3 (million)
% 1.50/0.56 % (10439)------------------------------
% 1.50/0.56 % (10439)------------------------------
% 1.50/0.56 % (10445)Instruction limit reached!
% 1.50/0.56 % (10445)------------------------------
% 1.50/0.56 % (10445)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.50/0.56 % (10445)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.50/0.56 % (10445)Termination reason: Unknown
% 1.50/0.56 % (10445)Termination phase: Saturation
% 1.50/0.56
% 1.50/0.56 % (10445)Memory used [KB]: 5500
% 1.50/0.56 % (10445)Time elapsed: 0.110 s
% 1.50/0.56 % (10445)Instructions burned: 8 (million)
% 1.50/0.56 % (10445)------------------------------
% 1.50/0.56 % (10445)------------------------------
% 1.50/0.57 TRYING [1]
% 1.50/0.57 TRYING [2]
% 1.50/0.58 % (10451)First to succeed.
% 1.50/0.58 TRYING [3]
% 1.50/0.58 % (10442)Instruction limit reached!
% 1.50/0.58 % (10442)------------------------------
% 1.50/0.58 % (10442)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.50/0.59 % (10444)Instruction limit reached!
% 1.50/0.59 % (10444)------------------------------
% 1.50/0.59 % (10444)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.50/0.59 % (10444)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.50/0.59 % (10444)Termination reason: Unknown
% 1.50/0.59 % (10444)Termination phase: Finite model building SAT solving
% 1.50/0.59
% 1.50/0.59 % (10444)Memory used [KB]: 7803
% 1.50/0.59 % (10444)Time elapsed: 0.140 s
% 1.50/0.59 % (10444)Instructions burned: 53 (million)
% 1.50/0.59 % (10444)------------------------------
% 1.50/0.59 % (10444)------------------------------
% 1.50/0.59 % (10442)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.50/0.59 % (10442)Termination reason: Unknown
% 1.50/0.59 % (10442)Termination phase: Saturation
% 1.50/0.59
% 1.50/0.59 % (10442)Memory used [KB]: 6524
% 1.50/0.59 % (10442)Time elapsed: 0.156 s
% 1.50/0.59 % (10442)Instructions burned: 52 (million)
% 1.50/0.59 % (10442)------------------------------
% 1.50/0.59 % (10442)------------------------------
% 1.50/0.59 % (10451)Refutation found. Thanks to Tanya!
% 1.50/0.59 % SZS status Theorem for theBenchmark
% 1.50/0.59 % SZS output start Proof for theBenchmark
% See solution above
% 1.50/0.59 % (10451)------------------------------
% 1.50/0.59 % (10451)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.50/0.59 % (10451)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.50/0.59 % (10451)Termination reason: Refutation
% 1.50/0.59
% 1.50/0.59 % (10451)Memory used [KB]: 6524
% 1.50/0.59 % (10451)Time elapsed: 0.181 s
% 1.50/0.59 % (10451)Instructions burned: 51 (million)
% 1.50/0.59 % (10451)------------------------------
% 1.50/0.59 % (10451)------------------------------
% 1.50/0.59 % (10435)Success in time 0.233 s
%------------------------------------------------------------------------------