TSTP Solution File: SET647+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---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 : n015.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 : Fri Sep 1 23:37:06 EDT 2023
% Result : Theorem 0.23s 0.49s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 19
% Syntax : Number of formulae : 100 ( 20 unt; 0 def)
% Number of atoms : 377 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 455 ( 178 ~; 163 |; 59 &)
% ( 15 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 205 (; 191 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2650,plain,
$false,
inference(subsumption_resolution,[],[f2640,f2591]) ).
fof(f2591,plain,
~ member(sK24(cross_product(sK15,range_of(sK16)),sK16),cross_product(sK15,range_of(sK16))),
inference(unit_resulting_resolution,[],[f2494,f201]) ).
fof(f201,plain,
! [X0,X1] :
( ~ member(sK24(X0,X1),X0)
| sP13(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ~ member(sK24(X0,X1),X0)
& member(sK24(X0,X1),X1)
& ilf_type(sK24(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP13(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f126,f127]) ).
fof(f127,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK24(X0,X1),X0)
& member(sK24(X0,X1),X1)
& ilf_type(sK24(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f126,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP13(X0,X1) ) ),
inference(rectify,[],[f125]) ).
fof(f125,plain,
! [X1,X0] :
( ( sP13(X1,X0)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ sP13(X1,X0) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X1,X0] :
( sP13(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f2494,plain,
~ sP13(cross_product(sK15,range_of(sK16)),sK16),
inference(unit_resulting_resolution,[],[f239,f2488,f197]) ).
fof(f197,plain,
! [X0,X1] :
( ~ sP14(X0,X1)
| ~ sP13(X1,X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( ( member(X0,power_set(X1))
| ~ sP13(X1,X0) )
& ( sP13(X1,X0)
| ~ member(X0,power_set(X1)) ) )
| ~ sP14(X0,X1) ),
inference(nnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
<=> sP13(X1,X0) )
| ~ sP14(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f2488,plain,
~ member(sK16,power_set(cross_product(sK15,range_of(sK16)))),
inference(unit_resulting_resolution,[],[f221,f2480,f258]) ).
fof(f258,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f257,f143]) ).
fof(f143,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.qERMmSS7DQ/Vampire---4.8_3527',p26) ).
fof(f257,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f211,f143]) ).
fof(f211,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,[],[f132]) ).
fof(f132,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.qERMmSS7DQ/Vampire---4.8_3527',p22) ).
fof(f2480,plain,
~ ilf_type(sK16,member_type(power_set(cross_product(sK15,range_of(sK16))))),
inference(unit_resulting_resolution,[],[f2462,f241]) ).
fof(f241,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f240,f143]) ).
fof(f240,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,[],[f204,f143]) ).
fof(f204,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,[],[f129]) ).
fof(f129,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.qERMmSS7DQ/Vampire---4.8_3527',p15) ).
fof(f2462,plain,
~ ilf_type(sK16,subset_type(cross_product(sK15,range_of(sK16)))),
inference(unit_resulting_resolution,[],[f142,f233]) ).
fof(f233,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f232,f143]) ).
fof(f232,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,[],[f187,f143]) ).
fof(f187,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.qERMmSS7DQ/Vampire---4.8_3527',p4) ).
fof(f142,plain,
~ ilf_type(sK16,relation_type(sK15,range_of(sK16))),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( ~ ilf_type(sK16,relation_type(sK15,range_of(sK16)))
& subset(domain_of(sK16),sK15)
& ilf_type(sK16,binary_relation_type)
& ilf_type(sK15,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16])],[f31,f87,f86]) ).
fof(f86,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(sK15,range_of(X1)))
& subset(domain_of(X1),sK15)
& ilf_type(X1,binary_relation_type) )
& ilf_type(sK15,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ? [X1] :
( ~ ilf_type(X1,relation_type(sK15,range_of(X1)))
& subset(domain_of(X1),sK15)
& ilf_type(X1,binary_relation_type) )
=> ( ~ ilf_type(sK16,relation_type(sK15,range_of(sK16)))
& subset(domain_of(sK16),sK15)
& ilf_type(sK16,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.qERMmSS7DQ/Vampire---4.8_3527',prove_relset_1_9) ).
fof(f221,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f160,f143]) ).
fof(f160,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.qERMmSS7DQ/Vampire---4.8_3527',p21) ).
fof(f239,plain,
! [X0,X1] : sP14(X0,X1),
inference(subsumption_resolution,[],[f238,f143]) ).
fof(f238,plain,
! [X0,X1] :
( sP14(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f202,f143]) ).
fof(f202,plain,
! [X0,X1] :
( sP14(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( sP14(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f49,f84,f83]) ).
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.qERMmSS7DQ/Vampire---4.8_3527',p20) ).
fof(f2640,plain,
member(sK24(cross_product(sK15,range_of(sK16)),sK16),cross_product(sK15,range_of(sK16))),
inference(unit_resulting_resolution,[],[f1821,f2492,f234]) ).
fof(f234,plain,
! [X3,X0,X1] :
( ~ sP11(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f191,f143]) ).
fof(f191,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ~ member(sK23(X0,X1),X0)
& member(sK23(X0,X1),X1)
& ilf_type(sK23(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP11(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f121,f122]) ).
fof(f122,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK23(X0,X1),X0)
& member(sK23(X0,X1),X1)
& ilf_type(sK23(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f121,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f120]) ).
fof(f120,plain,
! [X1,X0] :
( ( sP11(X1,X0)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X1,X0] :
( sP11(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f2492,plain,
member(sK24(cross_product(sK15,range_of(sK16)),sK16),sK16),
inference(unit_resulting_resolution,[],[f2488,f1091]) ).
fof(f1091,plain,
! [X0,X1] :
( member(sK24(X1,X0),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f1078,f200]) ).
fof(f200,plain,
! [X0,X1] :
( sP13(X0,X1)
| member(sK24(X0,X1),X1) ),
inference(cnf_transformation,[],[f128]) ).
fof(f1078,plain,
! [X0,X1] :
( ~ sP13(X0,X1)
| member(X1,power_set(X0)) ),
inference(resolution,[],[f197,f239]) ).
fof(f1821,plain,
sP11(cross_product(sK15,range_of(sK16)),sK16),
inference(unit_resulting_resolution,[],[f236,f1809,f189]) ).
fof(f189,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ~ subset(X0,X1)
| sP11(X1,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| ~ subset(X0,X1) ) )
| ~ sP12(X0,X1) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( subset(X0,X1)
<=> sP11(X1,X0) )
| ~ sP12(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f1809,plain,
subset(sK16,cross_product(sK15,range_of(sK16))),
inference(unit_resulting_resolution,[],[f520,f1768,f252]) ).
fof(f252,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f251,f143]) ).
fof(f251,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f250,f143]) ).
fof(f250,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,[],[f207,f143]) ).
fof(f207,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.qERMmSS7DQ/Vampire---4.8_3527',p1) ).
fof(f1768,plain,
! [X0] : subset(cross_product(domain_of(sK16),X0),cross_product(sK15,X0)),
inference(unit_resulting_resolution,[],[f141,f249]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(subsumption_resolution,[],[f248,f143]) ).
fof(f248,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f247,f143]) ).
fof(f247,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,[],[f205,f143]) ).
fof(f205,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.qERMmSS7DQ/Vampire---4.8_3527',p3) ).
fof(f141,plain,
subset(domain_of(sK16),sK15),
inference(cnf_transformation,[],[f88]) ).
fof(f520,plain,
subset(sK16,cross_product(domain_of(sK16),range_of(sK16))),
inference(unit_resulting_resolution,[],[f140,f146]) ).
fof(f146,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.qERMmSS7DQ/Vampire---4.8_3527',p2) ).
fof(f140,plain,
ilf_type(sK16,binary_relation_type),
inference(cnf_transformation,[],[f88]) ).
fof(f236,plain,
! [X0,X1] : sP12(X0,X1),
inference(subsumption_resolution,[],[f235,f143]) ).
fof(f235,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f195,f143]) ).
fof(f195,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( sP12(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f47,f81,f80]) ).
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.qERMmSS7DQ/Vampire---4.8_3527',p12) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET647+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.36 % Computer : n015.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Wed Aug 30 15:55:57 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.16/0.42 % (3781)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.43 % (3793)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.16/0.43 % (3792)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.16/0.43 % (3795)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.16/0.43 % (3796)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 Vampire---4 for (531ds/0Mi)
% 0.16/0.43 % (3797)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 Vampire---4 for (522ds/0Mi)
% 0.16/0.43 % (3794)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 Vampire---4 for (569ds/0Mi)
% 0.16/0.43 % (3799)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 Vampire---4 for (497ds/0Mi)
% 0.23/0.43 TRYING [1]
% 0.23/0.44 TRYING [2]
% 0.23/0.44 TRYING [3]
% 0.23/0.44 TRYING [1]
% 0.23/0.45 TRYING [2]
% 0.23/0.46 TRYING [4]
% 0.23/0.48 TRYING [3]
% 0.23/0.48 % (3799)First to succeed.
% 0.23/0.49 % (3799)Refutation found. Thanks to Tanya!
% 0.23/0.49 % SZS status Theorem for Vampire---4
% 0.23/0.49 % SZS output start Proof for Vampire---4
% See solution above
% 0.23/0.49 % (3799)------------------------------
% 0.23/0.49 % (3799)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.49 % (3799)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.49 % (3799)Termination reason: Refutation
% 0.23/0.49
% 0.23/0.49 % (3799)Memory used [KB]: 2046
% 0.23/0.49 % (3799)Time elapsed: 0.056 s
% 0.23/0.49 % (3799)------------------------------
% 0.23/0.49 % (3799)------------------------------
% 0.23/0.49 % (3781)Success in time 0.115 s
% 0.23/0.49 3794 Aborted by signal SIGHUP on /export/starexec/sandbox2/tmp/tmp.qERMmSS7DQ/Vampire---4.8_3527
% 0.23/0.49 % (3794)------------------------------
% 0.23/0.49 % (3794)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.23/0.49 % (3794)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.23/0.49 % (3794)Termination reason: Unknown
% 0.23/0.49 % (3794)Termination phase: Saturation
% 0.23/0.49
% 0.23/0.49 % (3794)Memory used [KB]: 5500
% 0.23/0.49 % (3794)Time elapsed: 0.060 s
% 0.23/0.49 % (3794)------------------------------
% 0.23/0.49 % (3794)------------------------------
% 0.23/0.49 % Vampire---4.8 exiting
%------------------------------------------------------------------------------