TSTP Solution File: SET650+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET650+3 : TPTP v8.1.0. Released v2.2.0.
% 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 : n024.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 18:25:13 EDT 2022
% Result : Theorem 0.21s 0.58s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 15
% Syntax : Number of formulae : 99 ( 10 unt; 0 def)
% Number of atoms : 440 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 520 ( 179 ~; 234 |; 64 &)
% ( 9 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 249 ( 224 !; 25 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f586,plain,
$false,
inference(resolution,[],[f578,f185]) ).
fof(f185,plain,
~ ilf_type(sK5,relation_type(sK3,sK4)),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f123,plain,
ilf_type(sK5,relation_type(sK3,sK4)),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ilf_type(sK3,set_type)
& ilf_type(sK4,set_type)
& ( ~ subset(range_of(sK5),sK4)
| ~ subset(domain_of(sK5),sK3) )
& ilf_type(sK5,relation_type(sK3,sK4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f34,f71,f70,f69]) ).
fof(f69,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),X0) )
& ilf_type(X2,relation_type(X0,X1)) ) ) )
=> ( ilf_type(sK3,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),sK3) )
& ilf_type(X2,relation_type(sK3,X1)) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
( ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),sK3) )
& ilf_type(X2,relation_type(sK3,X1)) ) )
=> ( ilf_type(sK4,set_type)
& ? [X2] :
( ( ~ subset(range_of(X2),sK4)
| ~ subset(domain_of(X2),sK3) )
& ilf_type(X2,relation_type(sK3,sK4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
( ? [X2] :
( ( ~ subset(range_of(X2),sK4)
| ~ subset(domain_of(X2),sK3) )
& ilf_type(X2,relation_type(sK3,sK4)) )
=> ( ( ~ subset(range_of(sK5),sK4)
| ~ subset(domain_of(sK5),sK3) )
& ilf_type(sK5,relation_type(sK3,sK4)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),X0) )
& ilf_type(X2,relation_type(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(f578,plain,
! [X0,X1] : ilf_type(sK5,relation_type(X0,X1)),
inference(resolution,[],[f519,f252]) ).
fof(f252,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f251,f207]) ).
fof(f207,plain,
! [X0] : ~ ilf_type(X0,set_type),
inference(consistent_polarity_flipping,[],[f158]) ).
fof(f158,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f251,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f225,f207]) ).
fof(f225,plain,
! [X3,X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X0,set_type)
| ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(consistent_polarity_flipping,[],[f156]) ).
fof(f156,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8) ).
fof(f519,plain,
! [X0,X1] : ilf_type(sK5,subset_type(cross_product(X0,X1))),
inference(resolution,[],[f518,f237]) ).
fof(f237,plain,
! [X2,X0,X1] :
( ~ relation_like(X2)
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f236,f207]) ).
fof(f236,plain,
! [X2,X0,X1] :
( ilf_type(X0,set_type)
| ~ relation_like(X2)
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f183,f207]) ).
fof(f183,plain,
! [X2,X0,X1] :
( ~ relation_like(X2)
| ilf_type(X1,set_type)
| ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X0,set_type) ),
inference(consistent_polarity_flipping,[],[f115]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> relation_like(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f518,plain,
relation_like(sK5),
inference(resolution,[],[f504,f238]) ).
fof(f238,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(subsumption_resolution,[],[f227,f207]) ).
fof(f227,plain,
! [X0] :
( ilf_type(X0,set_type)
| relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(duplicate_literal_removal,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ilf_type(X0,set_type)
| ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(consistent_polarity_flipping,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f504,plain,
ilf_type(sK5,binary_relation_type),
inference(resolution,[],[f490,f185]) ).
fof(f490,plain,
! [X0] :
( ilf_type(sK5,relation_type(sK3,X0))
| ilf_type(sK5,binary_relation_type) ),
inference(subsumption_resolution,[],[f482,f396]) ).
fof(f396,plain,
( subset(domain_of(sK5),sK3)
| ilf_type(sK5,binary_relation_type) ),
inference(resolution,[],[f387,f185]) ).
fof(f387,plain,
! [X0] :
( ilf_type(sK5,relation_type(X0,sK4))
| ilf_type(sK5,binary_relation_type)
| subset(domain_of(sK5),sK3) ),
inference(subsumption_resolution,[],[f380,f224]) ).
fof(f224,plain,
( subset(range_of(sK5),sK4)
| subset(domain_of(sK5),sK3) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f124,plain,
( ~ subset(domain_of(sK5),sK3)
| ~ subset(range_of(sK5),sK4) ),
inference(cnf_transformation,[],[f72]) ).
fof(f380,plain,
! [X0] :
( subset(domain_of(sK5),sK3)
| ilf_type(sK5,binary_relation_type)
| ~ subset(range_of(sK5),sK4)
| ilf_type(sK5,relation_type(X0,sK4)) ),
inference(resolution,[],[f329,f270]) ).
fof(f270,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f269,f207]) ).
fof(f269,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| ~ subset(X0,X1)
| ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f170,f207]) ).
fof(f170,plain,
! [X0,X1] :
( ilf_type(X0,set_type)
| ~ member(sK7(X0,X1),X1)
| ilf_type(X1,set_type)
| ~ subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ilf_type(sK7(X0,X1),set_type)
& ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f80,f81]) ).
fof(f81,plain,
! [X0,X1] :
( ? [X3] :
( ilf_type(X3,set_type)
& ~ member(X3,X1)
& member(X3,X0) )
=> ( ilf_type(sK7(X0,X1),set_type)
& ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ilf_type(X3,set_type)
& ~ member(X3,X1)
& member(X3,X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ilf_type(X2,set_type)
& ~ member(X2,X1)
& member(X2,X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
<=> subset(X0,X1) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f329,plain,
! [X2,X1] :
( ilf_type(sK5,relation_type(X1,X2))
| member(sK7(range_of(sK5),sK4),X2)
| ilf_type(sK5,binary_relation_type)
| subset(domain_of(sK5),sK3) ),
inference(resolution,[],[f325,f256]) ).
fof(f256,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ilf_type(X4,relation_type(X0,X1))
| member(X3,X1) ),
inference(subsumption_resolution,[],[f255,f207]) ).
fof(f255,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X2,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f254,f207]) ).
fof(f254,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ilf_type(X0,set_type)
| member(X3,X1)
| ilf_type(X2,set_type) ),
inference(subsumption_resolution,[],[f253,f207]) ).
fof(f253,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X1,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ilf_type(X0,set_type)
| ilf_type(X2,set_type)
| member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(subsumption_resolution,[],[f203,f207]) ).
fof(f203,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X3,set_type)
| ilf_type(X0,set_type)
| ilf_type(X2,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ilf_type(X1,set_type)
| member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(consistent_polarity_flipping,[],[f121]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X4,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X3,set_type)
| member(X3,X1) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1))
| ( member(X3,X1)
& member(X2,X0) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f325,plain,
( member(ordered_pair(sK16(sK7(range_of(sK5),sK4),sK5),sK7(range_of(sK5),sK4)),sK5)
| ilf_type(sK5,binary_relation_type)
| subset(domain_of(sK5),sK3) ),
inference(resolution,[],[f299,f224]) ).
fof(f299,plain,
! [X0,X1] :
( ~ subset(range_of(X0),X1)
| ilf_type(X0,binary_relation_type)
| member(ordered_pair(sK16(sK7(range_of(X0),X1),X0),sK7(range_of(X0),X1)),X0) ),
inference(resolution,[],[f282,f284]) ).
fof(f284,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f283,f207]) ).
fof(f283,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| ~ subset(X0,X1)
| ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f216,f207]) ).
fof(f216,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| ~ subset(X0,X1)
| ilf_type(X0,set_type)
| ilf_type(X1,set_type) ),
inference(consistent_polarity_flipping,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(sK7(X0,X1),X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f282,plain,
! [X0,X1] :
( ~ member(X0,range_of(X1))
| ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK16(X0,X1),X0),X1) ),
inference(subsumption_resolution,[],[f222,f207]) ).
fof(f222,plain,
! [X0,X1] :
( ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1))
| ilf_type(X0,set_type)
| member(ordered_pair(sK16(X0,X1),X0),X1) ),
inference(consistent_polarity_flipping,[],[f163]) ).
fof(f163,plain,
! [X0,X1] :
( ~ ilf_type(X1,binary_relation_type)
| ~ member(X0,range_of(X1))
| member(ordered_pair(sK16(X0,X1),X0),X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ( ilf_type(sK16(X0,X1),set_type)
& member(ordered_pair(sK16(X0,X1),X0),X1) )
| ~ member(X0,range_of(X1)) )
& ( member(X0,range_of(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X0),X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f107,f108]) ).
fof(f108,plain,
! [X0,X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
=> ( ilf_type(sK16(X0,X1),set_type)
& member(ordered_pair(sK16(X0,X1),X0),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f107,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
| ~ member(X0,range_of(X1)) )
& ( member(X0,range_of(X1))
| ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(ordered_pair(X3,X0),X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f106]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
| ~ member(X0,range_of(X1)) )
& ( member(X0,range_of(X1))
| ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(ordered_pair(X2,X0),X1) ) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,binary_relation_type)
| ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
<=> member(X0,range_of(X1)) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( ? [X2] :
( ilf_type(X2,set_type)
& member(ordered_pair(X2,X0),X1) )
<=> member(X0,range_of(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f482,plain,
! [X0] :
( ~ subset(domain_of(sK5),sK3)
| ilf_type(sK5,relation_type(sK3,X0))
| ilf_type(sK5,binary_relation_type) ),
inference(resolution,[],[f426,f270]) ).
fof(f426,plain,
! [X3,X4] :
( ilf_type(sK5,relation_type(X3,X4))
| member(sK7(domain_of(sK5),sK3),X3)
| ilf_type(sK5,binary_relation_type) ),
inference(resolution,[],[f419,f245]) ).
fof(f245,plain,
! [X2,X3,X0,X1,X4] :
( ~ member(ordered_pair(X2,X3),X4)
| member(X2,X0)
| ilf_type(X4,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f244,f207]) ).
fof(f244,plain,
! [X2,X3,X0,X1,X4] :
( ilf_type(X4,relation_type(X0,X1))
| member(X2,X0)
| ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(subsumption_resolution,[],[f243,f207]) ).
fof(f243,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ilf_type(X2,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ilf_type(X3,set_type)
| ~ member(ordered_pair(X2,X3),X4) ),
inference(subsumption_resolution,[],[f242,f207]) ).
fof(f242,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ilf_type(X1,set_type)
| ilf_type(X3,set_type)
| ilf_type(X4,relation_type(X0,X1))
| ~ member(ordered_pair(X2,X3),X4)
| ilf_type(X2,set_type) ),
inference(subsumption_resolution,[],[f186,f207]) ).
fof(f186,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ilf_type(X4,relation_type(X0,X1))
| ilf_type(X0,set_type)
| ~ member(ordered_pair(X2,X3),X4)
| ilf_type(X2,set_type)
| ilf_type(X3,set_type)
| ilf_type(X1,set_type) ),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f120,plain,
! [X2,X3,X0,X1,X4] :
( ~ ilf_type(X3,set_type)
| member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f419,plain,
( member(ordered_pair(sK7(domain_of(sK5),sK3),sK1(sK5,sK7(domain_of(sK5),sK3))),sK5)
| ilf_type(sK5,binary_relation_type) ),
inference(duplicate_literal_removal,[],[f418]) ).
fof(f418,plain,
( member(ordered_pair(sK7(domain_of(sK5),sK3),sK1(sK5,sK7(domain_of(sK5),sK3))),sK5)
| ilf_type(sK5,binary_relation_type)
| ilf_type(sK5,binary_relation_type) ),
inference(resolution,[],[f396,f295]) ).
fof(f295,plain,
! [X0,X1] :
( ~ subset(domain_of(X0),X1)
| member(ordered_pair(sK7(domain_of(X0),X1),sK1(X0,sK7(domain_of(X0),X1))),X0)
| ilf_type(X0,binary_relation_type) ),
inference(resolution,[],[f231,f284]) ).
fof(f231,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| ilf_type(X0,binary_relation_type)
| member(ordered_pair(X1,sK1(X0,X1)),X0) ),
inference(subsumption_resolution,[],[f177,f207]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(X1,set_type)
| ilf_type(X0,binary_relation_type)
| ~ member(X1,domain_of(X0))
| member(ordered_pair(X1,sK1(X0,X1)),X0) ),
inference(consistent_polarity_flipping,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ~ member(X1,domain_of(X0))
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X1,set_type)
| member(ordered_pair(X1,sK1(X0,X1)),X0) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ( member(ordered_pair(X1,sK1(X0,X1)),X0)
& ilf_type(sK1(X0,X1),set_type) )
| ~ member(X1,domain_of(X0)) )
& ( member(X1,domain_of(X0))
| ! [X3] :
( ~ member(ordered_pair(X1,X3),X0)
| ~ ilf_type(X3,set_type) ) ) ) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f64,f65]) ).
fof(f65,plain,
! [X0,X1] :
( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
=> ( member(ordered_pair(X1,sK1(X0,X1)),X0)
& ilf_type(sK1(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
| ~ member(X1,domain_of(X0)) )
& ( member(X1,domain_of(X0))
| ! [X3] :
( ~ member(ordered_pair(X1,X3),X0)
| ~ ilf_type(X3,set_type) ) ) ) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
| ~ member(X1,domain_of(X0)) )
& ( member(X1,domain_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) ) ) ) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
<=> member(X1,domain_of(X0)) ) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
<=> member(X1,domain_of(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET650+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % 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 : n024.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 14:12:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.21/0.51 % (29341)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)
% 0.21/0.52 % (29348)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)
% 0.21/0.52 % (29343)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)
% 0.21/0.52 TRYING [1]
% 0.21/0.52 % (29364)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)
% 0.21/0.52 TRYING [1]
% 0.21/0.52 % (29349)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.53 % (29363)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.21/0.53 % (29359)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.21/0.53 TRYING [2]
% 0.21/0.53 TRYING [2]
% 0.21/0.53 % (29370)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 % (29368)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)
% 0.21/0.54 % (29347)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)
% 0.21/0.54 % (29352)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.21/0.54 % (29369)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)
% 0.21/0.54 % (29345)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)
% 0.21/0.54 TRYING [3]
% 0.21/0.54 % (29349)Instruction limit reached!
% 0.21/0.54 % (29349)------------------------------
% 0.21/0.54 % (29349)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (29349)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (29349)Termination reason: Unknown
% 0.21/0.54 % (29349)Termination phase: Saturation
% 0.21/0.54
% 0.21/0.54 % (29349)Memory used [KB]: 5500
% 0.21/0.54 % (29349)Time elapsed: 0.125 s
% 0.21/0.54 % (29349)Instructions burned: 7 (million)
% 0.21/0.54 % (29349)------------------------------
% 0.21/0.54 % (29349)------------------------------
% 0.21/0.54 % (29346)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.21/0.54 % (29358)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)
% 0.21/0.54 % (29350)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.54 % (29356)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)
% 0.21/0.54 % (29350)Instruction limit reached!
% 0.21/0.54 % (29350)------------------------------
% 0.21/0.54 % (29350)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.54 % (29350)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.54 % (29350)Termination reason: Unknown
% 0.21/0.54 % (29350)Termination phase: shuffling
% 0.21/0.54
% 0.21/0.54 % (29350)Memory used [KB]: 895
% 0.21/0.54 % (29350)Time elapsed: 0.002 s
% 0.21/0.54 % (29350)Instructions burned: 2 (million)
% 0.21/0.54 % (29350)------------------------------
% 0.21/0.54 % (29350)------------------------------
% 0.21/0.54 % (29365)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)
% 0.21/0.55 % (29362)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)
% 0.21/0.55 % (29360)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.21/0.55 TRYING [3]
% 0.21/0.55 % (29351)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)
% 0.21/0.55 % (29361)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)
% 0.21/0.55 % (29354)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.21/0.55 % (29342)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)
% 0.21/0.55 % (29355)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.21/0.55 % (29366)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.21/0.55 % (29353)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)
% 0.21/0.55 % (29342)Refutation not found, incomplete strategy% (29342)------------------------------
% 0.21/0.55 % (29342)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.55 % (29342)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.55 % (29342)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.55
% 0.21/0.55 % (29342)Memory used [KB]: 5500
% 0.21/0.55 % (29342)Time elapsed: 0.141 s
% 0.21/0.55 % (29342)Instructions burned: 6 (million)
% 0.21/0.55 % (29342)------------------------------
% 0.21/0.55 % (29342)------------------------------
% 0.21/0.56 % (29371)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)
% 0.21/0.56 % (29367)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.21/0.56 % (29357)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)
% 0.21/0.56 TRYING [1]
% 0.21/0.56 TRYING [2]
% 0.21/0.56 % (29348)Instruction limit reached!
% 0.21/0.56 % (29348)------------------------------
% 0.21/0.56 % (29348)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.56 TRYING [3]
% 0.21/0.57 % (29348)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.57 % (29348)Termination reason: Unknown
% 0.21/0.57 % (29348)Termination phase: Finite model building SAT solving
% 0.21/0.57
% 0.21/0.57 % (29348)Memory used [KB]: 7036
% 0.21/0.57 % (29348)Time elapsed: 0.134 s
% 0.21/0.57 % (29348)Instructions burned: 51 (million)
% 0.21/0.57 % (29348)------------------------------
% 0.21/0.57 % (29348)------------------------------
% 0.21/0.58 % (29361)First to succeed.
% 0.21/0.58 % (29361)Refutation found. Thanks to Tanya!
% 0.21/0.58 % SZS status Theorem for theBenchmark
% 0.21/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.59 % (29361)------------------------------
% 0.21/0.59 % (29361)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.59 % (29361)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.59 % (29361)Termination reason: Refutation
% 0.21/0.59
% 0.21/0.59 % (29361)Memory used [KB]: 1279
% 0.21/0.59 % (29361)Time elapsed: 0.185 s
% 0.21/0.59 % (29361)Instructions burned: 20 (million)
% 0.21/0.59 % (29361)------------------------------
% 0.21/0.59 % (29361)------------------------------
% 0.21/0.59 % (29338)Success in time 0.228 s
%------------------------------------------------------------------------------