TSTP Solution File: SEU166+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU166+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 : n032.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 09:27:32 EDT 2024
% Result : Theorem 1.98s 0.62s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 127 ( 3 unt; 0 def)
% Number of atoms : 418 ( 40 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 472 ( 181 ~; 201 |; 54 &)
% ( 27 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 21 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 186 ( 154 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6986,plain,
$false,
inference(avatar_sat_refutation,[],[f115,f3190,f3193,f3319,f3322,f3343,f3382,f3569,f3675,f3693,f3702,f4161,f4255,f6959,f6962,f6985]) ).
fof(f6985,plain,
( spl12_2
| ~ spl12_11
| ~ spl12_20 ),
inference(avatar_contradiction_clause,[],[f6984]) ).
fof(f6984,plain,
( $false
| spl12_2
| ~ spl12_11
| ~ spl12_20 ),
inference(subsumption_resolution,[],[f6979,f114]) ).
fof(f114,plain,
( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| spl12_2 ),
inference(avatar_component_clause,[],[f112]) ).
fof(f112,plain,
( spl12_2
<=> subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f6979,plain,
( subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ spl12_11
| ~ spl12_20 ),
inference(resolution,[],[f6976,f48]) ).
fof(f48,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f25,f26]) ).
fof(f26,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6976,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK2))
| ~ spl12_11
| ~ spl12_20 ),
inference(subsumption_resolution,[],[f6973,f3564]) ).
fof(f3564,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f3563]) ).
fof(f3563,plain,
( spl12_11
<=> in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f6973,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK2))
| ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| ~ spl12_20 ),
inference(resolution,[],[f6958,f116]) ).
fof(f116,plain,
! [X2,X0,X1] :
( in(sK8(X2,X1,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f49,f62]) ).
fof(f62,plain,
! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ( cartesian_product2(X0,X1) = X2
| ~ sP0(X1,X0,X2) )
& ( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f20]) ).
fof(f20,plain,
! [X1,X0,X2] :
( sP0(X1,X0,X2)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f3,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/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f49,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK8(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ! [X4,X5] :
( ordered_pair(X4,X5) != sK5(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1) )
| in(sK5(X0,X1,X2),X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
& in(sK9(X0,X1,X8),X0)
& in(sK8(X0,X1,X8),X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8,sK9])],[f29,f32,f31,f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) )
=> ( ( ! [X5,X4] :
( ordered_pair(X4,X5) != sK5(X0,X1,X2)
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(sK5(X0,X1,X2),X2) )
& ( ? [X7,X6] :
( ordered_pair(X6,X7) = sK5(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
| in(sK5(X0,X1,X2),X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ? [X7,X6] :
( ordered_pair(X6,X7) = sK5(X0,X1,X2)
& in(X7,X0)
& in(X6,X1) )
=> ( sK5(X0,X1,X2) = ordered_pair(sK6(X0,X1,X2),sK7(X0,X1,X2))
& in(sK7(X0,X1,X2),X0)
& in(sK6(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f32,plain,
! [X0,X1,X8] :
( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
=> ( ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8
& in(sK9(X0,X1,X8),X0)
& in(sK8(X0,X1,X8),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X6,X7] :
( ordered_pair(X6,X7) = X3
& in(X7,X0)
& in(X6,X1) )
| in(X3,X2) ) ) )
& ( ! [X8] :
( ( in(X8,X2)
| ! [X9,X10] :
( ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1) ) )
& ( ? [X11,X12] :
( ordered_pair(X11,X12) = X8
& in(X12,X0)
& in(X11,X1) )
| ~ in(X8,X2) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f28]) ).
fof(f28,plain,
! [X1,X0,X2] :
( ( sP0(X1,X0,X2)
| ? [X3] :
( ( ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) )
| ~ in(X3,X2) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4,X5] :
( ordered_pair(X4,X5) != X3
| ~ in(X5,X1)
| ~ in(X4,X0) ) )
& ( ? [X4,X5] :
( ordered_pair(X4,X5) = X3
& in(X5,X1)
& in(X4,X0) )
| ~ in(X3,X2) ) )
| ~ sP0(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f6958,plain,
( ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK2)) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f6957]) ).
fof(f6957,plain,
( spl12_20
<=> ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).
fof(f6962,plain,
( ~ spl12_11
| spl12_19 ),
inference(avatar_contradiction_clause,[],[f6961]) ).
fof(f6961,plain,
( $false
| ~ spl12_11
| spl12_19 ),
inference(subsumption_resolution,[],[f6960,f3564]) ).
fof(f6960,plain,
( ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| spl12_19 ),
inference(resolution,[],[f6955,f118]) ).
fof(f118,plain,
! [X2,X0,X1] :
( in(sK9(X2,X1,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f50,f62]) ).
fof(f50,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK9(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f6955,plain,
( ~ in(sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1)
| spl12_19 ),
inference(avatar_component_clause,[],[f6953]) ).
fof(f6953,plain,
( spl12_19
<=> in(sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).
fof(f6959,plain,
( ~ spl12_19
| spl12_20
| spl12_2 ),
inference(avatar_split_clause,[],[f3560,f112,f6957,f6953]) ).
fof(f3560,plain,
( ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK2))
| ~ in(sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1) )
| spl12_2 ),
inference(resolution,[],[f1546,f66]) ).
fof(f66,plain,
! [X0] :
( in(X0,sK2)
| ~ in(X0,sK1) ),
inference(resolution,[],[f46,f39]) ).
fof(f39,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) )
& subset(sK1,sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f17,f22]) ).
fof(f22,plain,
( ? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
& subset(X0,X1) )
=> ( ( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) )
& subset(sK1,sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
? [X0,X1,X2] :
( ( ~ subset(cartesian_product2(X2,X0),cartesian_product2(X2,X1))
| ~ subset(cartesian_product2(X0,X2),cartesian_product2(X1,X2)) )
& subset(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,negated_conjecture,
~ ! [X0,X1,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,[],[f14]) ).
fof(f14,conjecture,
! [X0,X1,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(f46,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f1546,plain,
( ! [X0,X1] :
( ~ in(sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X1)
| ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,X1)) )
| spl12_2 ),
inference(superposition,[],[f119,f1501]) ).
fof(f1501,plain,
( sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)) = ordered_pair(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))))
| spl12_2 ),
inference(resolution,[],[f308,f114]) ).
fof(f308,plain,
! [X2,X0,X1] :
( subset(cartesian_product2(X1,X0),X2)
| sK4(cartesian_product2(X1,X0),X2) = ordered_pair(sK8(X0,X1,sK4(cartesian_product2(X1,X0),X2)),sK9(X0,X1,sK4(cartesian_product2(X1,X0),X2))) ),
inference(resolution,[],[f306,f47]) ).
fof(f47,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| ordered_pair(sK8(X2,X1,X0),sK9(X2,X1,X0)) = X0 ),
inference(resolution,[],[f51,f62]) ).
fof(f51,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| ordered_pair(sK8(X0,X1,X8),sK9(X0,X1,X8)) = X8 ),
inference(cnf_transformation,[],[f33]) ).
fof(f119,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X2,X0),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[],[f61,f62]) ).
fof(f61,plain,
! [X2,X10,X0,X1,X9] :
( ~ sP0(X0,X1,X2)
| ~ in(X10,X0)
| ~ in(X9,X1)
| in(ordered_pair(X9,X10),X2) ),
inference(equality_resolution,[],[f52]) ).
fof(f52,plain,
! [X2,X10,X0,X1,X8,X9] :
( in(X8,X2)
| ordered_pair(X9,X10) != X8
| ~ in(X10,X0)
| ~ in(X9,X1)
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f33]) ).
fof(f4255,plain,
( spl12_1
| ~ spl12_6 ),
inference(avatar_contradiction_clause,[],[f4254]) ).
fof(f4254,plain,
( $false
| spl12_1
| ~ spl12_6 ),
inference(subsumption_resolution,[],[f4250,f110]) ).
fof(f110,plain,
( ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| spl12_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl12_1
<=> subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f4250,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| ~ spl12_6 ),
inference(resolution,[],[f3318,f48]) ).
fof(f3318,plain,
( in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f3316]) ).
fof(f3316,plain,
( spl12_6
<=> in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f4161,plain,
( spl12_17
| spl12_18
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f4147,f108,f4158,f4154]) ).
fof(f4154,plain,
( spl12_17
<=> subset(cartesian_product2(sK1,sK3),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f4158,plain,
( spl12_18
<=> sK4(cartesian_product2(sK1,sK3),sK1) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f4147,plain,
( sK4(cartesian_product2(sK1,sK3),sK1) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1)))
| subset(cartesian_product2(sK1,sK3),sK2)
| ~ spl12_1 ),
inference(duplicate_literal_removal,[],[f4134]) ).
fof(f4134,plain,
( sK4(cartesian_product2(sK1,sK3),sK1) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),sK1)))
| subset(cartesian_product2(sK1,sK3),sK2)
| subset(cartesian_product2(sK1,sK3),sK2)
| ~ spl12_1 ),
inference(resolution,[],[f3414,f69]) ).
fof(f69,plain,
! [X0] :
( ~ in(sK4(X0,sK2),sK1)
| subset(X0,sK2) ),
inference(resolution,[],[f66,f48]) ).
fof(f3414,plain,
( ! [X0,X1] :
( in(sK4(cartesian_product2(sK1,sK3),X1),X0)
| sK4(cartesian_product2(sK1,sK3),X0) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0)))
| subset(cartesian_product2(sK1,sK3),X1) )
| ~ spl12_1 ),
inference(resolution,[],[f3383,f47]) ).
fof(f3383,plain,
( ! [X0,X1] :
( ~ in(X1,cartesian_product2(sK1,sK3))
| sK4(cartesian_product2(sK1,sK3),X0) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0)))
| in(X1,X0) )
| ~ spl12_1 ),
inference(resolution,[],[f3350,f46]) ).
fof(f3350,plain,
( ! [X0] :
( subset(cartesian_product2(sK1,sK3),X0)
| sK4(cartesian_product2(sK1,sK3),X0) = ordered_pair(sK8(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0)),sK9(sK3,sK2,sK4(cartesian_product2(sK1,sK3),X0))) )
| ~ spl12_1 ),
inference(resolution,[],[f3324,f47]) ).
fof(f3324,plain,
( ! [X0] :
( ~ in(X0,cartesian_product2(sK1,sK3))
| ordered_pair(sK8(sK3,sK2,X0),sK9(sK3,sK2,X0)) = X0 )
| ~ spl12_1 ),
inference(resolution,[],[f3323,f306]) ).
fof(f3323,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK2,sK3))
| ~ in(X0,cartesian_product2(sK1,sK3)) )
| ~ spl12_1 ),
inference(resolution,[],[f109,f46]) ).
fof(f109,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f3702,plain,
( ~ spl12_15
| spl12_16
| ~ spl12_1
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f3684,f3567,f108,f3699,f3695]) ).
fof(f3695,plain,
( spl12_15
<=> in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f3699,plain,
( spl12_16
<=> in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(cartesian_product2(sK2,sK3),sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).
fof(f3567,plain,
( spl12_12
<=> ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f3684,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(cartesian_product2(sK2,sK3),sK1))
| ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),cartesian_product2(sK1,sK3))
| ~ spl12_1
| ~ spl12_12 ),
inference(resolution,[],[f3568,f3323]) ).
fof(f3568,plain,
( ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK1)) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f3693,plain,
( ~ spl12_13
| spl12_14
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f3683,f3567,f3690,f3686]) ).
fof(f3686,plain,
( spl12_13
<=> in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f3690,plain,
( spl12_14
<=> in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK2,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f3683,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK2,sK1))
| ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1)
| ~ spl12_12 ),
inference(resolution,[],[f3568,f66]) ).
fof(f3675,plain,
( spl12_2
| spl12_11 ),
inference(avatar_contradiction_clause,[],[f3674]) ).
fof(f3674,plain,
( $false
| spl12_2
| spl12_11 ),
inference(subsumption_resolution,[],[f3673,f114]) ).
fof(f3673,plain,
( subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| spl12_11 ),
inference(resolution,[],[f3565,f47]) ).
fof(f3565,plain,
( ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| spl12_11 ),
inference(avatar_component_clause,[],[f3563]) ).
fof(f3569,plain,
( ~ spl12_11
| spl12_12
| spl12_2 ),
inference(avatar_split_clause,[],[f3559,f112,f3567,f3563]) ).
fof(f3559,plain,
( ! [X0] :
( ~ in(sK8(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),X0)
| in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(X0,sK1))
| ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1)) )
| spl12_2 ),
inference(resolution,[],[f1546,f118]) ).
fof(f3382,plain,
( spl12_9
| ~ spl12_10
| ~ spl12_1
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f3327,f3188,f108,f3379,f3375]) ).
fof(f3375,plain,
( spl12_9
<=> in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(cartesian_product2(sK2,sK3),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f3379,plain,
( spl12_10
<=> in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f3188,plain,
( spl12_4
<=> ! [X0] :
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),X0)
| in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(X0,sK3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f3327,plain,
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),cartesian_product2(sK1,sK3))
| in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(cartesian_product2(sK2,sK3),sK3))
| ~ spl12_1
| ~ spl12_4 ),
inference(resolution,[],[f3323,f3189]) ).
fof(f3189,plain,
( ! [X0] :
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),X0)
| in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(X0,sK3)) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f3343,plain,
( ~ spl12_7
| ~ spl12_8
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f3326,f108,f3340,f3336]) ).
fof(f3336,plain,
( spl12_7
<=> in(cartesian_product2(sK2,sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f3340,plain,
( spl12_8
<=> in(sK2,cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f3326,plain,
( ~ in(sK2,cartesian_product2(sK1,sK3))
| ~ in(cartesian_product2(sK2,sK3),sK1)
| ~ spl12_1 ),
inference(resolution,[],[f3323,f68]) ).
fof(f68,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(X0,sK1) ),
inference(resolution,[],[f66,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f3322,plain,
( ~ spl12_3
| spl12_5 ),
inference(avatar_contradiction_clause,[],[f3321]) ).
fof(f3321,plain,
( $false
| ~ spl12_3
| spl12_5 ),
inference(subsumption_resolution,[],[f3320,f3185]) ).
fof(f3185,plain,
( in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f3184,plain,
( spl12_3
<=> in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f3320,plain,
( ~ in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| spl12_5 ),
inference(resolution,[],[f3314,f116]) ).
fof(f3314,plain,
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),sK1)
| spl12_5 ),
inference(avatar_component_clause,[],[f3312]) ).
fof(f3312,plain,
( spl12_5
<=> in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f3319,plain,
( ~ spl12_5
| spl12_6
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f3310,f3188,f3316,f3312]) ).
fof(f3310,plain,
( in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),sK1)
| ~ spl12_4 ),
inference(resolution,[],[f3189,f66]) ).
fof(f3193,plain,
( spl12_1
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f3192]) ).
fof(f3192,plain,
( $false
| spl12_1
| spl12_3 ),
inference(subsumption_resolution,[],[f3191,f110]) ).
fof(f3191,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| spl12_3 ),
inference(resolution,[],[f3186,f47]) ).
fof(f3186,plain,
( ~ in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| spl12_3 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f3190,plain,
( ~ spl12_3
| spl12_4
| spl12_1 ),
inference(avatar_split_clause,[],[f3181,f108,f3188,f3184]) ).
fof(f3181,plain,
( ! [X0] :
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),X0)
| in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(X0,sK3))
| ~ in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3)) )
| spl12_1 ),
inference(resolution,[],[f1513,f118]) ).
fof(f1513,plain,
( ! [X0,X1] :
( ~ in(sK9(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),X1)
| ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),X0)
| in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(X0,X1)) )
| spl12_1 ),
inference(superposition,[],[f119,f1500]) ).
fof(f1500,plain,
( sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) = ordered_pair(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),sK9(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))))
| spl12_1 ),
inference(resolution,[],[f308,f110]) ).
fof(f115,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f40,f112,f108]) ).
fof(f40,plain,
( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU166+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri May 3 11:14:39 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.32 % (4589)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.33 % (4593)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.33 % (4591)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.33 % (4592)WARNING: value z3 for option sas not known
% 0.11/0.33 % (4595)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)
% 0.11/0.33 % (4590)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.33 % (4594)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)
% 0.11/0.33 % (4596)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)
% 0.11/0.33 % (4592)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)
% 0.11/0.33 TRYING [1]
% 0.11/0.33 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.35 TRYING [3]
% 0.16/0.36 TRYING [4]
% 0.16/0.42 TRYING [4]
% 1.98/0.61 % (4592)First to succeed.
% 1.98/0.61 % (4592)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4589"
% 1.98/0.62 % (4592)Refutation found. Thanks to Tanya!
% 1.98/0.62 % SZS status Theorem for theBenchmark
% 1.98/0.62 % SZS output start Proof for theBenchmark
% See solution above
% 1.98/0.62 % (4592)------------------------------
% 1.98/0.62 % (4592)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.98/0.62 % (4592)Termination reason: Refutation
% 1.98/0.62
% 1.98/0.62 % (4592)Memory used [KB]: 4449
% 1.98/0.62 % (4592)Time elapsed: 0.284 s
% 1.98/0.62 % (4592)Instructions burned: 746 (million)
% 1.98/0.62 % (4589)Success in time 0.288 s
%------------------------------------------------------------------------------