TSTP Solution File: SEU166+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : Tue Apr 30 15:22:45 EDT 2024
% Result : Theorem 1.96s 0.69s
% Output : Refutation 1.96s
% 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(f6982,plain,
$false,
inference(avatar_sat_refutation,[],[f111,f3186,f3189,f3315,f3318,f3339,f3378,f3565,f3671,f3689,f3698,f4157,f4251,f6955,f6958,f6981]) ).
fof(f6981,plain,
( spl12_2
| ~ spl12_11
| ~ spl12_20 ),
inference(avatar_contradiction_clause,[],[f6980]) ).
fof(f6980,plain,
( $false
| spl12_2
| ~ spl12_11
| ~ spl12_20 ),
inference(subsumption_resolution,[],[f6975,f110]) ).
fof(f110,plain,
( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| spl12_2 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f108,plain,
( spl12_2
<=> subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f6975,plain,
( subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ spl12_11
| ~ spl12_20 ),
inference(resolution,[],[f6972,f44]) ).
fof(f44,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,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])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK4(X0,X1),X1)
& in(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f21,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,[],[f20]) ).
fof(f20,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,[],[f15]) ).
fof(f15,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/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f6972,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK2))
| ~ spl12_11
| ~ spl12_20 ),
inference(subsumption_resolution,[],[f6969,f3560]) ).
fof(f3560,plain,
( in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f3559]) ).
fof(f3559,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(f6969,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,[],[f6954,f112]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(sK8(X2,X1,X0),X1)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f45,f58]) ).
fof(f58,plain,
! [X0,X1] : sP0(X1,X0,cartesian_product2(X0,X1)),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( sP0(X1,X0,X2)
| cartesian_product2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,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,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( cartesian_product2(X0,X1) = X2
<=> sP0(X1,X0,X2) ),
inference(definition_folding,[],[f3,f16]) ).
fof(f16,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/sandbox/benchmark/theBenchmark.p',d2_zfmisc_1) ).
fof(f45,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK8(X0,X1,X8),X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,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])],[f25,f28,f27,f26]) ).
fof(f26,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(f27,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(f28,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(f25,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,[],[f24]) ).
fof(f24,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,[],[f16]) ).
fof(f6954,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,[],[f6953]) ).
fof(f6953,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(f6958,plain,
( ~ spl12_11
| spl12_19 ),
inference(avatar_contradiction_clause,[],[f6957]) ).
fof(f6957,plain,
( $false
| ~ spl12_11
| spl12_19 ),
inference(subsumption_resolution,[],[f6956,f3560]) ).
fof(f6956,plain,
( ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| spl12_19 ),
inference(resolution,[],[f6951,f114]) ).
fof(f114,plain,
! [X2,X0,X1] :
( in(sK9(X2,X1,X0),X2)
| ~ in(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f46,f58]) ).
fof(f46,plain,
! [X2,X0,X1,X8] :
( ~ sP0(X0,X1,X2)
| ~ in(X8,X2)
| in(sK9(X0,X1,X8),X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f6951,plain,
( ~ in(sK9(sK1,sK3,sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))),sK1)
| spl12_19 ),
inference(avatar_component_clause,[],[f6949]) ).
fof(f6949,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(f6955,plain,
( ~ spl12_19
| spl12_20
| spl12_2 ),
inference(avatar_split_clause,[],[f3556,f108,f6953,f6949]) ).
fof(f3556,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,[],[f1542,f62]) ).
fof(f62,plain,
! [X0] :
( in(X0,sK2)
| ~ in(X0,sK1) ),
inference(resolution,[],[f42,f35]) ).
fof(f35,plain,
subset(sK1,sK2),
inference(cnf_transformation,[],[f19]) ).
fof(f19,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])],[f13,f18]) ).
fof(f18,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(f13,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,[],[f11]) ).
fof(f11,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,[],[f10]) ).
fof(f10,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/sandbox/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(f42,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f1542,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,[],[f115,f1497]) ).
fof(f1497,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,[],[f304,f110]) ).
fof(f304,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,[],[f302,f43]) ).
fof(f43,plain,
! [X0,X1] :
( in(sK4(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f302,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X2))
| ordered_pair(sK8(X2,X1,X0),sK9(X2,X1,X0)) = X0 ),
inference(resolution,[],[f47,f58]) ).
fof(f47,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,[],[f29]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X2,X0),cartesian_product2(X3,X1))
| ~ in(X2,X3)
| ~ in(X0,X1) ),
inference(resolution,[],[f57,f58]) ).
fof(f57,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,[],[f48]) ).
fof(f48,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,[],[f29]) ).
fof(f4251,plain,
( spl12_1
| ~ spl12_6 ),
inference(avatar_contradiction_clause,[],[f4250]) ).
fof(f4250,plain,
( $false
| spl12_1
| ~ spl12_6 ),
inference(subsumption_resolution,[],[f4246,f106]) ).
fof(f106,plain,
( ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| spl12_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f104,plain,
( spl12_1
<=> subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f4246,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| ~ spl12_6 ),
inference(resolution,[],[f3314,f44]) ).
fof(f3314,plain,
( in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK2,sK3))
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f3312]) ).
fof(f3312,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(f4157,plain,
( spl12_17
| spl12_18
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f4143,f104,f4154,f4150]) ).
fof(f4150,plain,
( spl12_17
<=> subset(cartesian_product2(sK1,sK3),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f4154,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(f4143,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,[],[f4130]) ).
fof(f4130,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,[],[f3410,f65]) ).
fof(f65,plain,
! [X0] :
( ~ in(sK4(X0,sK2),sK1)
| subset(X0,sK2) ),
inference(resolution,[],[f62,f44]) ).
fof(f3410,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,[],[f3379,f43]) ).
fof(f3379,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,[],[f3346,f42]) ).
fof(f3346,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,[],[f3320,f43]) ).
fof(f3320,plain,
( ! [X0] :
( ~ in(X0,cartesian_product2(sK1,sK3))
| ordered_pair(sK8(sK3,sK2,X0),sK9(sK3,sK2,X0)) = X0 )
| ~ spl12_1 ),
inference(resolution,[],[f3319,f302]) ).
fof(f3319,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK2,sK3))
| ~ in(X0,cartesian_product2(sK1,sK3)) )
| ~ spl12_1 ),
inference(resolution,[],[f105,f42]) ).
fof(f105,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f3698,plain,
( ~ spl12_15
| spl12_16
| ~ spl12_1
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f3680,f3563,f104,f3695,f3691]) ).
fof(f3691,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(f3695,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(f3563,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(f3680,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,[],[f3564,f3319]) ).
fof(f3564,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,[],[f3563]) ).
fof(f3689,plain,
( ~ spl12_13
| spl12_14
| ~ spl12_12 ),
inference(avatar_split_clause,[],[f3679,f3563,f3686,f3682]) ).
fof(f3682,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(f3686,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(f3679,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,[],[f3564,f62]) ).
fof(f3671,plain,
( spl12_2
| spl12_11 ),
inference(avatar_contradiction_clause,[],[f3670]) ).
fof(f3670,plain,
( $false
| spl12_2
| spl12_11 ),
inference(subsumption_resolution,[],[f3669,f110]) ).
fof(f3669,plain,
( subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| spl12_11 ),
inference(resolution,[],[f3561,f43]) ).
fof(f3561,plain,
( ~ in(sK4(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2)),cartesian_product2(sK3,sK1))
| spl12_11 ),
inference(avatar_component_clause,[],[f3559]) ).
fof(f3565,plain,
( ~ spl12_11
| spl12_12
| spl12_2 ),
inference(avatar_split_clause,[],[f3555,f108,f3563,f3559]) ).
fof(f3555,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,[],[f1542,f114]) ).
fof(f3378,plain,
( spl12_9
| ~ spl12_10
| ~ spl12_1
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f3323,f3184,f104,f3375,f3371]) ).
fof(f3371,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(f3375,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(f3184,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(f3323,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,[],[f3319,f3185]) ).
fof(f3185,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,[],[f3184]) ).
fof(f3339,plain,
( ~ spl12_7
| ~ spl12_8
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f3322,f104,f3336,f3332]) ).
fof(f3332,plain,
( spl12_7
<=> in(cartesian_product2(sK2,sK3),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f3336,plain,
( spl12_8
<=> in(sK2,cartesian_product2(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f3322,plain,
( ~ in(sK2,cartesian_product2(sK1,sK3))
| ~ in(cartesian_product2(sK2,sK3),sK1)
| ~ spl12_1 ),
inference(resolution,[],[f3319,f64]) ).
fof(f64,plain,
! [X0] :
( ~ in(sK2,X0)
| ~ in(X0,sK1) ),
inference(resolution,[],[f62,f41]) ).
fof(f41,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f3318,plain,
( ~ spl12_3
| spl12_5 ),
inference(avatar_contradiction_clause,[],[f3317]) ).
fof(f3317,plain,
( $false
| ~ spl12_3
| spl12_5 ),
inference(subsumption_resolution,[],[f3316,f3181]) ).
fof(f3181,plain,
( in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f3180,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(f3316,plain,
( ~ in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| spl12_5 ),
inference(resolution,[],[f3310,f112]) ).
fof(f3310,plain,
( ~ in(sK8(sK3,sK1,sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))),sK1)
| spl12_5 ),
inference(avatar_component_clause,[],[f3308]) ).
fof(f3308,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(f3315,plain,
( ~ spl12_5
| spl12_6
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f3306,f3184,f3312,f3308]) ).
fof(f3306,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,[],[f3185,f62]) ).
fof(f3189,plain,
( spl12_1
| spl12_3 ),
inference(avatar_contradiction_clause,[],[f3188]) ).
fof(f3188,plain,
( $false
| spl12_1
| spl12_3 ),
inference(subsumption_resolution,[],[f3187,f106]) ).
fof(f3187,plain,
( subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3))
| spl12_3 ),
inference(resolution,[],[f3182,f43]) ).
fof(f3182,plain,
( ~ in(sK4(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)),cartesian_product2(sK1,sK3))
| spl12_3 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f3186,plain,
( ~ spl12_3
| spl12_4
| spl12_1 ),
inference(avatar_split_clause,[],[f3177,f104,f3184,f3180]) ).
fof(f3177,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,[],[f1509,f114]) ).
fof(f1509,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,[],[f115,f1496]) ).
fof(f1496,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,[],[f304,f106]) ).
fof(f111,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f36,f108,f104]) ).
fof(f36,plain,
( ~ subset(cartesian_product2(sK3,sK1),cartesian_product2(sK3,sK2))
| ~ subset(cartesian_product2(sK1,sK3),cartesian_product2(sK2,sK3)) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU166+3 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n006.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 20:42:05 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (18040)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (18043)WARNING: value z3 for option sas not known
% 0.14/0.38 % (18042)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (18044)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (18041)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (18045)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)
% 0.14/0.38 % (18046)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)
% 0.14/0.38 % (18047)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)
% 0.14/0.38 % (18043)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)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [4]
% 0.21/0.50 TRYING [4]
% 1.96/0.66 TRYING [5]
% 1.96/0.68 % (18043)First to succeed.
% 1.96/0.69 % (18043)Refutation found. Thanks to Tanya!
% 1.96/0.69 % SZS status Theorem for theBenchmark
% 1.96/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 1.96/0.69 % (18043)------------------------------
% 1.96/0.69 % (18043)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.96/0.69 % (18043)Termination reason: Refutation
% 1.96/0.69
% 1.96/0.69 % (18043)Memory used [KB]: 4448
% 1.96/0.69 % (18043)Time elapsed: 0.304 s
% 1.96/0.69 % (18043)Instructions burned: 746 (million)
% 1.96/0.69 % (18043)------------------------------
% 1.96/0.69 % (18043)------------------------------
% 1.96/0.69 % (18040)Success in time 0.323 s
%------------------------------------------------------------------------------