TSTP Solution File: SEU262+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU262+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 : n007.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 15:25:41 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 41
% Syntax : Number of formulae : 179 ( 9 unt; 0 def)
% Number of atoms : 529 ( 25 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 611 ( 261 ~; 256 |; 46 &)
% ( 28 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 17 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-2 aty)
% Number of variables : 283 ( 246 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1127,plain,
$false,
inference(avatar_sat_refutation,[],[f143,f221,f368,f492,f544,f555,f644,f645,f677,f828,f948,f950,f966,f982,f1126]) ).
fof(f1126,plain,
( spl15_2
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f1125]) ).
fof(f1125,plain,
( $false
| spl15_2
| ~ spl15_6 ),
inference(subsumption_resolution,[],[f1124,f142]) ).
fof(f142,plain,
( ~ subset(relation_rng(sK2),sK1)
| spl15_2 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f140,plain,
( spl15_2
<=> subset(relation_rng(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f1124,plain,
( subset(relation_rng(sK2),sK1)
| ~ spl15_6 ),
inference(duplicate_literal_removal,[],[f1120]) ).
fof(f1120,plain,
( subset(relation_rng(sK2),sK1)
| subset(relation_rng(sK2),sK1)
| ~ spl15_6 ),
inference(resolution,[],[f672,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) )
=> ( ~ in(sK10(X0,X1),X1)
& in(sK10(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f73,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,[],[f72]) ).
fof(f72,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,[],[f48]) ).
fof(f48,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(f672,plain,
( ! [X0] :
( in(sK10(relation_rng(sK2),X0),sK1)
| subset(relation_rng(sK2),X0) )
| ~ spl15_6 ),
inference(resolution,[],[f668,f109]) ).
fof(f109,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f668,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK2))
| in(X0,sK1) )
| ~ spl15_6 ),
inference(subsumption_resolution,[],[f666,f234]) ).
fof(f234,plain,
relation(sK2),
inference(resolution,[],[f230,f88]) ).
fof(f88,plain,
relation_of2_as_subset(sK2,sK0,sK1),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
( ( ~ subset(relation_rng(sK2),sK1)
| ~ subset(relation_dom(sK2),sK0) )
& relation_of2_as_subset(sK2,sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f40,f56]) ).
fof(f56,plain,
( ? [X0,X1,X2] :
( ( ~ subset(relation_rng(X2),X1)
| ~ subset(relation_dom(X2),X0) )
& relation_of2_as_subset(X2,X0,X1) )
=> ( ( ~ subset(relation_rng(sK2),sK1)
| ~ subset(relation_dom(sK2),sK0) )
& relation_of2_as_subset(sK2,sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0,X1,X2] :
( ( ~ subset(relation_rng(X2),X1)
| ~ subset(relation_dom(X2),X0) )
& relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,negated_conjecture,
~ ! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
inference(negated_conjecture,[],[f29]) ).
fof(f29,conjecture,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> ( subset(relation_rng(X2),X1)
& subset(relation_dom(X2),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_relset_1) ).
fof(f230,plain,
! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| relation(X0) ),
inference(resolution,[],[f117,f118]) ).
fof(f118,plain,
! [X2,X0,X1] :
( ~ element(X2,powerset(cartesian_product2(X0,X1)))
| relation(X2) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( relation(X2)
| ~ element(X2,powerset(cartesian_product2(X0,X1))) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
=> relation(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(f117,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f666,plain,
( ! [X0] :
( in(X0,sK1)
| ~ in(X0,relation_rng(sK2))
| ~ relation(sK2) )
| ~ spl15_6 ),
inference(resolution,[],[f652,f129]) ).
fof(f129,plain,
! [X0,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,relation_rng(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X5] :
( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( in(ordered_pair(sK5(X0,X5),X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f59,f62,f61,f60]) ).
fof(f60,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(X3,sK3(X0,X1)),X0)
| ~ in(sK3(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(X4,sK3(X0,X1)),X0)
| in(sK3(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(X4,sK3(X0,X1)),X0)
=> in(ordered_pair(sK4(X0,X1),sK3(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X7,X5),X0)
=> in(ordered_pair(sK5(X0,X5),X5),X0) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X4,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X6,X5),X0) )
& ( ? [X7] : in(ordered_pair(X7,X5),X0)
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( relation_rng(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X3,X2),X0) )
& ( ? [X3] : in(ordered_pair(X3,X2),X0)
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_rng(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_relat_1) ).
fof(f652,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK2)
| in(X1,sK1) )
| ~ spl15_6 ),
inference(resolution,[],[f367,f124]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X1,X3)
| ~ in(X0,X2) )
& ( ( in(X1,X3)
& in(X0,X2) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X1,X3)
& in(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f367,plain,
( ! [X0] :
( in(X0,cartesian_product2(sK0,sK1))
| ~ in(X0,sK2) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f366,plain,
( spl15_6
<=> ! [X0] :
( ~ in(X0,sK2)
| in(X0,cartesian_product2(sK0,sK1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_6])]) ).
fof(f982,plain,
( spl15_15
| spl15_16
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f967,f136,f979,f975]) ).
fof(f975,plain,
( spl15_15
<=> empty(relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_15])]) ).
fof(f979,plain,
( spl15_16
<=> element(sK9(relation_dom(sK2)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_16])]) ).
fof(f136,plain,
( spl15_1
<=> subset(relation_dom(sK2),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f967,plain,
( element(sK9(relation_dom(sK2)),sK0)
| empty(relation_dom(sK2))
| ~ spl15_1 ),
inference(resolution,[],[f952,f150]) ).
fof(f150,plain,
! [X0] :
( in(sK9(X0),X0)
| empty(X0) ),
inference(resolution,[],[f107,f100]) ).
fof(f100,plain,
! [X0] : element(sK9(X0),X0),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] : element(sK9(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f20,f70]) ).
fof(f70,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK9(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f107,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f952,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK2))
| element(X0,sK0) )
| ~ spl15_1 ),
inference(resolution,[],[f137,f254]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ subset(X2,X1)
| ~ in(X0,X2)
| element(X0,X1) ),
inference(resolution,[],[f119,f112]) ).
fof(f112,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( element(X0,powerset(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f137,plain,
( subset(relation_dom(sK2),sK0)
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f966,plain,
( ~ spl15_13
| spl15_14
| ~ spl15_1 ),
inference(avatar_split_clause,[],[f953,f136,f964,f960]) ).
fof(f960,plain,
( spl15_13
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_13])]) ).
fof(f964,plain,
( spl15_14
<=> ! [X0] : ~ in(X0,relation_dom(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_14])]) ).
fof(f953,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK2))
| ~ empty(sK0) )
| ~ spl15_1 ),
inference(resolution,[],[f137,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ subset(X2,X0)
| ~ in(X1,X2)
| ~ empty(X0) ),
inference(resolution,[],[f122,f112]) ).
fof(f122,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f950,plain,
( ~ spl15_9
| spl15_2 ),
inference(avatar_split_clause,[],[f160,f140,f637]) ).
fof(f637,plain,
( spl15_9
<=> empty(relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_9])]) ).
fof(f160,plain,
( ~ empty(relation_rng(sK2))
| spl15_2 ),
inference(resolution,[],[f157,f142]) ).
fof(f157,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[],[f109,f114]) ).
fof(f114,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f948,plain,
( spl15_1
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f947]) ).
fof(f947,plain,
( $false
| spl15_1
| ~ spl15_6 ),
inference(subsumption_resolution,[],[f946,f138]) ).
fof(f138,plain,
( ~ subset(relation_dom(sK2),sK0)
| spl15_1 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f946,plain,
( subset(relation_dom(sK2),sK0)
| ~ spl15_6 ),
inference(duplicate_literal_removal,[],[f943]) ).
fof(f943,plain,
( subset(relation_dom(sK2),sK0)
| subset(relation_dom(sK2),sK0)
| ~ spl15_6 ),
inference(resolution,[],[f772,f110]) ).
fof(f772,plain,
( ! [X0] :
( in(sK10(relation_dom(sK2),X0),sK0)
| subset(relation_dom(sK2),X0) )
| ~ spl15_6 ),
inference(resolution,[],[f769,f109]) ).
fof(f769,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK2))
| in(X0,sK0) )
| ~ spl15_6 ),
inference(subsumption_resolution,[],[f764,f234]) ).
fof(f764,plain,
( ! [X0] :
( in(X0,sK0)
| ~ in(X0,relation_dom(sK2))
| ~ relation(sK2) )
| ~ spl15_6 ),
inference(resolution,[],[f653,f131]) ).
fof(f131,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK8(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK8(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ( ( ! [X3] : ~ in(ordered_pair(sK6(X0,X1),X3),X0)
| ~ in(sK6(X0,X1),X1) )
& ( in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0)
| in(sK6(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK8(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f65,f68,f67,f66]) ).
fof(f66,plain,
! [X0,X1] :
( ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) )
=> ( ( ! [X3] : ~ in(ordered_pair(sK6(X0,X1),X3),X0)
| ~ in(sK6(X0,X1),X1) )
& ( ? [X4] : in(ordered_pair(sK6(X0,X1),X4),X0)
| in(sK6(X0,X1),X1) ) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X4] : in(ordered_pair(sK6(X0,X1),X4),X0)
=> in(ordered_pair(sK6(X0,X1),sK7(X0,X1)),X0) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X5] :
( ? [X7] : in(ordered_pair(X5,X7),X0)
=> in(ordered_pair(X5,sK8(X0,X5)),X0) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( relation_dom(X0) = X1
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation_dom(X0) = X1
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f653,plain,
( ! [X0,X1] :
( ~ in(ordered_pair(X0,X1),sK2)
| in(X0,sK0) )
| ~ spl15_6 ),
inference(resolution,[],[f367,f123]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[],[f83]) ).
fof(f828,plain,
( ~ spl15_11
| ~ spl15_12
| ~ spl15_2
| ~ spl15_6
| ~ spl15_9 ),
inference(avatar_split_clause,[],[f712,f637,f366,f140,f825,f821]) ).
fof(f821,plain,
( spl15_11
<=> in(sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_11])]) ).
fof(f825,plain,
( spl15_12
<=> in(cartesian_product2(sK0,sK1),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_12])]) ).
fof(f712,plain,
( ~ in(cartesian_product2(sK0,sK1),empty_set)
| ~ in(sK1,sK2)
| ~ spl15_2
| ~ spl15_6
| ~ spl15_9 ),
inference(resolution,[],[f703,f649]) ).
fof(f649,plain,
( ! [X0] :
( ~ in(cartesian_product2(sK0,sK1),X0)
| ~ in(X0,sK2) )
| ~ spl15_6 ),
inference(resolution,[],[f367,f105]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,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(f703,plain,
( ! [X0] :
( in(X0,sK1)
| ~ in(X0,empty_set) )
| ~ spl15_2
| ~ spl15_9 ),
inference(resolution,[],[f693,f108]) ).
fof(f108,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f693,plain,
( subset(empty_set,sK1)
| ~ spl15_2
| ~ spl15_9 ),
inference(superposition,[],[f141,f678]) ).
fof(f678,plain,
( empty_set = relation_rng(sK2)
| ~ spl15_9 ),
inference(resolution,[],[f639,f99]) ).
fof(f99,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f639,plain,
( empty(relation_rng(sK2))
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f141,plain,
( subset(relation_rng(sK2),sK1)
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f140]) ).
fof(f677,plain,
( ~ spl15_6
| spl15_9
| spl15_10 ),
inference(avatar_contradiction_clause,[],[f676]) ).
fof(f676,plain,
( $false
| ~ spl15_6
| spl15_9
| spl15_10 ),
inference(subsumption_resolution,[],[f675,f638]) ).
fof(f638,plain,
( ~ empty(relation_rng(sK2))
| spl15_9 ),
inference(avatar_component_clause,[],[f637]) ).
fof(f675,plain,
( empty(relation_rng(sK2))
| ~ spl15_6
| spl15_10 ),
inference(subsumption_resolution,[],[f670,f642]) ).
fof(f642,plain,
( ~ in(sK9(relation_rng(sK2)),sK1)
| spl15_10 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f641,plain,
( spl15_10
<=> in(sK9(relation_rng(sK2)),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_10])]) ).
fof(f670,plain,
( in(sK9(relation_rng(sK2)),sK1)
| empty(relation_rng(sK2))
| ~ spl15_6 ),
inference(resolution,[],[f668,f150]) ).
fof(f645,plain,
( ~ spl15_9
| spl15_2 ),
inference(avatar_split_clause,[],[f160,f140,f637]) ).
fof(f644,plain,
( spl15_9
| spl15_10
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f556,f140,f641,f637]) ).
fof(f556,plain,
( in(sK9(relation_rng(sK2)),sK1)
| empty(relation_rng(sK2))
| ~ spl15_2 ),
inference(resolution,[],[f547,f150]) ).
fof(f547,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK2))
| in(X0,sK1) )
| ~ spl15_2 ),
inference(resolution,[],[f141,f108]) ).
fof(f555,plain,
( ~ spl15_7
| spl15_8
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f546,f140,f553,f549]) ).
fof(f549,plain,
( spl15_7
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_7])]) ).
fof(f553,plain,
( spl15_8
<=> ! [X0] : ~ in(X0,relation_rng(sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f546,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK2))
| ~ empty(sK1) )
| ~ spl15_2 ),
inference(resolution,[],[f141,f181]) ).
fof(f544,plain,
( spl15_1
| ~ spl15_5 ),
inference(avatar_contradiction_clause,[],[f543]) ).
fof(f543,plain,
( $false
| spl15_1
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f538,f445]) ).
fof(f445,plain,
( ~ empty(relation_dom(empty_set))
| spl15_1
| ~ spl15_5 ),
inference(superposition,[],[f159,f428]) ).
fof(f428,plain,
( empty_set = sK2
| ~ spl15_5 ),
inference(resolution,[],[f425,f99]) ).
fof(f425,plain,
( empty(sK2)
| ~ spl15_5 ),
inference(resolution,[],[f422,f150]) ).
fof(f422,plain,
( ! [X0] : ~ in(X0,sK2)
| ~ spl15_5 ),
inference(resolution,[],[f369,f88]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ relation_of2_as_subset(X0,sK0,sK1)
| ~ in(X1,X0) )
| ~ spl15_5 ),
inference(resolution,[],[f364,f231]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( ~ empty(cartesian_product2(X1,X2))
| ~ relation_of2_as_subset(X0,X1,X2)
| ~ in(X3,X0) ),
inference(resolution,[],[f117,f122]) ).
fof(f364,plain,
( empty(cartesian_product2(sK0,sK1))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f362]) ).
fof(f362,plain,
( spl15_5
<=> empty(cartesian_product2(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_5])]) ).
fof(f159,plain,
( ~ empty(relation_dom(sK2))
| spl15_1 ),
inference(resolution,[],[f157,f138]) ).
fof(f538,plain,
( empty(relation_dom(empty_set))
| ~ spl15_5 ),
inference(resolution,[],[f536,f150]) ).
fof(f536,plain,
( ! [X0] : ~ in(X0,relation_dom(empty_set))
| ~ spl15_5 ),
inference(forward_demodulation,[],[f535,f428]) ).
fof(f535,plain,
( ! [X0] : ~ in(X0,relation_dom(sK2))
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f524,f234]) ).
fof(f524,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK2))
| ~ relation(sK2) )
| ~ spl15_5 ),
inference(resolution,[],[f131,f422]) ).
fof(f492,plain,
( spl15_2
| ~ spl15_5 ),
inference(avatar_contradiction_clause,[],[f491]) ).
fof(f491,plain,
( $false
| spl15_2
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f487,f446]) ).
fof(f446,plain,
( ~ empty(relation_rng(empty_set))
| spl15_2
| ~ spl15_5 ),
inference(superposition,[],[f160,f428]) ).
fof(f487,plain,
( empty(relation_rng(empty_set))
| ~ spl15_5 ),
inference(resolution,[],[f472,f150]) ).
fof(f472,plain,
( ! [X0] : ~ in(X0,relation_rng(empty_set))
| ~ spl15_5 ),
inference(forward_demodulation,[],[f471,f428]) ).
fof(f471,plain,
( ! [X0] : ~ in(X0,relation_rng(sK2))
| ~ spl15_5 ),
inference(subsumption_resolution,[],[f462,f234]) ).
fof(f462,plain,
( ! [X0] :
( ~ in(X0,relation_rng(sK2))
| ~ relation(sK2) )
| ~ spl15_5 ),
inference(resolution,[],[f129,f422]) ).
fof(f368,plain,
( spl15_5
| spl15_6 ),
inference(avatar_split_clause,[],[f360,f366,f362]) ).
fof(f360,plain,
! [X0] :
( ~ in(X0,sK2)
| empty(cartesian_product2(sK0,sK1))
| in(X0,cartesian_product2(sK0,sK1)) ),
inference(resolution,[],[f357,f107]) ).
fof(f357,plain,
! [X0] :
( element(X0,cartesian_product2(sK0,sK1))
| ~ in(X0,sK2) ),
inference(resolution,[],[f255,f88]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X3,X1,X2)
| ~ in(X0,X3)
| element(X0,cartesian_product2(X1,X2)) ),
inference(resolution,[],[f119,f117]) ).
fof(f221,plain,
( spl15_3
| ~ spl15_4 ),
inference(avatar_split_clause,[],[f207,f218,f214]) ).
fof(f214,plain,
( spl15_3
<=> empty(powerset(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_3])]) ).
fof(f218,plain,
( spl15_4
<=> in(powerset(empty_set),empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_4])]) ).
fof(f207,plain,
( ~ in(powerset(empty_set),empty_set)
| empty(powerset(empty_set)) ),
inference(superposition,[],[f153,f197]) ).
fof(f197,plain,
empty_set = sK9(powerset(empty_set)),
inference(resolution,[],[f187,f90]) ).
fof(f90,plain,
empty(empty_set),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f187,plain,
! [X0] :
( ~ empty(X0)
| empty_set = sK9(powerset(X0)) ),
inference(resolution,[],[f183,f99]) ).
fof(f183,plain,
! [X0] :
( empty(sK9(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f180,f150]) ).
fof(f180,plain,
! [X0,X1] :
( ~ in(X1,sK9(powerset(X0)))
| ~ empty(X0) ),
inference(resolution,[],[f122,f100]) ).
fof(f153,plain,
! [X0] :
( ~ in(X0,sK9(X0))
| empty(X0) ),
inference(resolution,[],[f150,f105]) ).
fof(f143,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f89,f140,f136]) ).
fof(f89,plain,
( ~ subset(relation_rng(sK2),sK1)
| ~ subset(relation_dom(sK2),sK0) ),
inference(cnf_transformation,[],[f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU262+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36 % Computer : n007.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Mon Apr 29 20:55:47 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % (29010)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (29017)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)
% 0.13/0.38 % (29012)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (29013)WARNING: value z3 for option sas not known
% 0.13/0.38 % (29016)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)
% 0.13/0.38 % (29014)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (29013)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)
% 0.13/0.38 % (29015)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)
% 0.13/0.38 % (29011)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [1]
% 0.20/0.40 TRYING [2]
% 0.20/0.41 % (29013)First to succeed.
% 0.20/0.41 TRYING [4]
% 0.20/0.41 % (29013)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41 % (29013)------------------------------
% 0.20/0.41 % (29013)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.41 % (29013)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (29013)Memory used [KB]: 1267
% 0.20/0.41 % (29013)Time elapsed: 0.035 s
% 0.20/0.41 % (29013)Instructions burned: 63 (million)
% 0.20/0.41 % (29013)------------------------------
% 0.20/0.41 % (29013)------------------------------
% 0.20/0.41 % (29010)Success in time 0.05 s
%------------------------------------------------------------------------------