TSTP Solution File: SET647+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET647+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n004.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 : Thu Aug 31 15:45:00 EDT 2023
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 20
% Syntax : Number of formulae : 111 ( 20 unt; 0 def)
% Number of atoms : 429 ( 3 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 527 ( 209 ~; 199 |; 63 &)
% ( 13 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 7 con; 0-2 aty)
% Number of variables : 214 (; 197 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f363,plain,
$false,
inference(subsumption_resolution,[],[f362,f168]) ).
fof(f168,plain,
~ ilf_type(sK3,sF17),
inference(definition_folding,[],[f112,f167,f166]) ).
fof(f166,plain,
range_of(sK3) = sF16,
introduced(function_definition,[]) ).
fof(f167,plain,
relation_type(sK2,sF16) = sF17,
introduced(function_definition,[]) ).
fof(f112,plain,
~ ilf_type(sK3,relation_type(sK2,range_of(sK3))),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ~ ilf_type(sK3,relation_type(sK2,range_of(sK3)))
& subset(domain_of(sK3),sK2)
& ilf_type(sK3,binary_relation_type)
& ilf_type(sK2,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f68,f67]) ).
fof(f67,plain,
( ? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ~ ilf_type(X1,relation_type(sK2,range_of(X1)))
& subset(domain_of(X1),sK2)
& ilf_type(X1,binary_relation_type) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X1] :
( ~ ilf_type(X1,relation_type(sK2,range_of(X1)))
& subset(domain_of(X1),sK2)
& ilf_type(X1,binary_relation_type) )
=> ( ~ ilf_type(sK3,relation_type(sK2,range_of(sK3)))
& subset(domain_of(sK3),sK2)
& ilf_type(sK3,binary_relation_type) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(X1))) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(X1))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',prove_relset_1_9) ).
fof(f362,plain,
ilf_type(sK3,sF17),
inference(forward_demodulation,[],[f361,f167]) ).
fof(f361,plain,
ilf_type(sK3,relation_type(sK2,sF16)),
inference(forward_literal_rewriting,[],[f360,f194]) ).
fof(f194,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f193,f113]) ).
fof(f113,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p26) ).
fof(f193,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,[],[f143,f113]) ).
fof(f143,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [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) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(X2,subset_type(cross_product(X0,X1))) )
& ! [X3] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
=> ilf_type(X3,relation_type(X0,X1)) ) ) ) ),
inference(rectify,[],[f4]) ).
fof(f4,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/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p4) ).
fof(f360,plain,
ilf_type(sK3,subset_type(cross_product(sK2,sF16))),
inference(forward_literal_rewriting,[],[f359,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f210,f229]) ).
fof(f229,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f228,f188]) ).
fof(f188,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f187,f113]) ).
fof(f187,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f135,f113]) ).
fof(f135,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f86,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK9(X0),X0)
& ilf_type(sK9(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p24) ).
fof(f228,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f227,f113]) ).
fof(f227,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f161,f113]) ).
fof(f161,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p22) ).
fof(f210,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f209,f113]) ).
fof(f209,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f154,f113]) ).
fof(f154,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p15) ).
fof(f359,plain,
member(sK3,power_set(cross_product(sK2,sF16))),
inference(subsumption_resolution,[],[f358,f168]) ).
fof(f358,plain,
( ilf_type(sK3,sF17)
| member(sK3,power_set(cross_product(sK2,sF16))) ),
inference(resolution,[],[f357,f205]) ).
fof(f205,plain,
! [X0,X1] :
( member(sK11(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f204,f113]) ).
fof(f204,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f151,f113]) ).
fof(f151,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f96,f97]) ).
fof(f97,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(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,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p20) ).
fof(f357,plain,
! [X1] :
( ~ member(sK11(X1,cross_product(sK2,sF16)),sK3)
| ilf_type(X1,sF17) ),
inference(forward_demodulation,[],[f356,f167]) ).
fof(f356,plain,
! [X1] :
( ilf_type(X1,relation_type(sK2,sF16))
| ~ member(sK11(X1,cross_product(sK2,sF16)),sK3) ),
inference(forward_literal_rewriting,[],[f355,f194]) ).
fof(f355,plain,
! [X1] :
( ilf_type(X1,subset_type(cross_product(sK2,sF16)))
| ~ member(sK11(X1,cross_product(sK2,sF16)),sK3) ),
inference(forward_literal_rewriting,[],[f354,f258]) ).
fof(f354,plain,
! [X1] :
( ~ member(sK11(X1,cross_product(sK2,sF16)),sK3)
| member(X1,power_set(cross_product(sK2,sF16))) ),
inference(resolution,[],[f350,f203]) ).
fof(f203,plain,
! [X0,X1] :
( ~ member(sK11(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f202,f113]) ).
fof(f202,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f152,f113]) ).
fof(f152,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f98]) ).
fof(f350,plain,
! [X1] :
( member(X1,cross_product(sK2,sF16))
| ~ member(X1,sK3) ),
inference(resolution,[],[f348,f201]) ).
fof(f201,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f200,f113]) ).
fof(f200,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f199,f113]) ).
fof(f199,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f145,f113]) ).
fof(f145,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK10(X0,X1),X1)
& member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,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(flattening,[],[f46]) ).
fof(f46,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,[],[f12]) ).
fof(f12,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/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p12) ).
fof(f348,plain,
subset(sK3,cross_product(sK2,sF16)),
inference(resolution,[],[f344,f178]) ).
fof(f178,plain,
! [X0] : subset(X0,X0),
inference(subsumption_resolution,[],[f123,f113]) ).
fof(f123,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p17) ).
fof(f344,plain,
! [X0] :
( ~ subset(cross_product(sK2,sF16),X0)
| subset(sK3,X0) ),
inference(resolution,[],[f342,f170]) ).
fof(f170,plain,
subset(sF18,sK2),
inference(definition_folding,[],[f111,f169]) ).
fof(f169,plain,
domain_of(sK3) = sF18,
introduced(function_definition,[]) ).
fof(f111,plain,
subset(domain_of(sK3),sK2),
inference(cnf_transformation,[],[f69]) ).
fof(f342,plain,
! [X0,X1] :
( ~ subset(sF18,X0)
| ~ subset(cross_product(X0,sF16),X1)
| subset(sK3,X1) ),
inference(resolution,[],[f339,f221]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(subsumption_resolution,[],[f220,f113]) ).
fof(f220,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f219,f113]) ).
fof(f219,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f157,f113]) ).
fof(f157,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p1) ).
fof(f339,plain,
! [X0] :
( subset(sK3,cross_product(X0,sF16))
| ~ subset(sF18,X0) ),
inference(resolution,[],[f218,f288]) ).
fof(f288,plain,
! [X0] :
( ~ subset(cross_product(sF18,sF16),X0)
| subset(sK3,X0) ),
inference(resolution,[],[f287,f221]) ).
fof(f287,plain,
subset(sK3,cross_product(sF18,sF16)),
inference(forward_demodulation,[],[f286,f169]) ).
fof(f286,plain,
subset(sK3,cross_product(domain_of(sK3),sF16)),
inference(forward_demodulation,[],[f285,f166]) ).
fof(f285,plain,
subset(sK3,cross_product(domain_of(sK3),range_of(sK3))),
inference(resolution,[],[f116,f110]) ).
fof(f110,plain,
ilf_type(sK3,binary_relation_type),
inference(cnf_transformation,[],[f69]) ).
fof(f116,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p2) ).
fof(f218,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f217,f113]) ).
fof(f217,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f216,f113]) ).
fof(f216,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f155,f113]) ).
fof(f155,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) )
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) )
| ~ subset(X0,X1)
| ~ 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)
=> ( subset(X0,X1)
=> ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202',p3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET647+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.35 % Computer : n004.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Sat Aug 26 09:48:08 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.15/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.35 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/tmp/tmp.heUlWAQC1U/Vampire---4.8_13202
% 0.15/0.36 % (13316)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.39 % (13322)dis+1011_4_add=large:amm=off:sims=off:sac=on:sp=frequency:tgt=ground_413 on Vampire---4 for (413ds/0Mi)
% 0.21/0.42 % (13319)dis-11_4:1_aac=none:add=off:afr=on:anc=none:bd=preordered:bs=on:bsr=on:drc=off:fsr=off:fde=none:gsp=on:irw=on:lcm=reverse:lma=on:nm=0:nwc=1.7:nicw=on:sas=z3:sims=off:sos=all:sac=on:sp=weighted_frequency:tgt=full_602 on Vampire---4 for (602ds/0Mi)
% 0.21/0.42 % (13321)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_424 on Vampire---4 for (424ds/0Mi)
% 0.21/0.42 % (13320)lrs-3_8_anc=none:bce=on:cond=on:drc=off:flr=on:fsd=off:fsr=off:fde=unused:gsp=on:gs=on:gsaa=full_model:lcm=predicate:lma=on:nm=16:sos=all:sp=weighted_frequency:tgt=ground:urr=ec_only:stl=188_482 on Vampire---4 for (482ds/0Mi)
% 0.21/0.42 % (13318)dis+1010_4:1_anc=none:bd=off:drc=off:flr=on:fsr=off:nm=4:nwc=1.1:nicw=on:sas=z3_680 on Vampire---4 for (680ds/0Mi)
% 0.21/0.42 % (13317)lrs+10_11_cond=on:drc=off:flr=on:fsr=off:gsp=on:gs=on:gsem=off:lma=on:msp=off:nm=4:nwc=1.5:nicw=on:sas=z3:sims=off:sp=scramble:stl=188_730 on Vampire---4 for (730ds/0Mi)
% 0.21/0.42 % (13323)ott+11_14_av=off:bs=on:bsr=on:cond=on:flr=on:fsd=off:fde=unused:gsp=on:nm=4:nwc=1.5:tgt=full_386 on Vampire---4 for (386ds/0Mi)
% 0.21/0.43 % (13323)First to succeed.
% 0.21/0.43 % (13323)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for Vampire---4
% 0.21/0.43 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.43 % (13323)------------------------------
% 0.21/0.43 % (13323)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.43 % (13323)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.43 % (13323)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (13323)Memory used [KB]: 1279
% 0.21/0.43 % (13323)Time elapsed: 0.013 s
% 0.21/0.43 % (13323)------------------------------
% 0.21/0.43 % (13323)------------------------------
% 0.21/0.43 % (13316)Success in time 0.074 s
% 0.21/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------