TSTP Solution File: SET652+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.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 15:09:33 EDT 2024
% Result : Theorem 0.22s 0.47s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 138 ( 29 unt; 0 def)
% Number of atoms : 522 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 623 ( 239 ~; 219 |; 91 &)
% ( 19 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 289 ( 259 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3826,plain,
$false,
inference(subsumption_resolution,[],[f3819,f2074]) ).
fof(f2074,plain,
~ member(sK23(cross_product(sK15,sK14),sK16),cross_product(sK15,sK14)),
inference(unit_resulting_resolution,[],[f2053,f190]) ).
fof(f190,plain,
! [X0,X1] :
( ~ member(sK23(X0,X1),X0)
| sP11(X0,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,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])],[f119,f120]) ).
fof(f120,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(f119,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,[],[f118]) ).
fof(f118,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(f2053,plain,
~ sP11(cross_product(sK15,sK14),sK16),
inference(unit_resulting_resolution,[],[f228,f2051,f186]) ).
fof(f186,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ~ sP11(X1,X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( ( member(X0,power_set(X1))
| ~ sP11(X1,X0) )
& ( sP11(X1,X0)
| ~ member(X0,power_set(X1)) ) )
| ~ sP12(X0,X1) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
<=> sP11(X1,X0) )
| ~ sP12(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f2051,plain,
~ member(sK16,power_set(cross_product(sK15,sK14))),
inference(unit_resulting_resolution,[],[f210,f2049,f249]) ).
fof(f249,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f248,f138]) ).
fof(f138,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f248,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f201,f138]) ).
fof(f201,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,[],[f125]) ).
fof(f125,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,[],[f20]) ).
fof(f20,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/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f2049,plain,
~ ilf_type(sK16,member_type(power_set(cross_product(sK15,sK14)))),
inference(unit_resulting_resolution,[],[f2038,f230]) ).
fof(f230,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f229,f138]) ).
fof(f229,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,[],[f193,f138]) ).
fof(f193,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,[],[f122]) ).
fof(f122,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,[],[f49]) ).
fof(f49,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/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f2038,plain,
~ ilf_type(sK16,subset_type(cross_product(sK15,sK14))),
inference(unit_resulting_resolution,[],[f137,f222]) ).
fof(f222,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f221,f138]) ).
fof(f221,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,[],[f176,f138]) ).
fof(f176,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,[],[f44]) ).
fof(f44,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/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f137,plain,
~ ilf_type(sK16,relation_type(sK15,sK14)),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( ~ ilf_type(sK16,relation_type(sK15,sK14))
& subset(range_of(sK16),sK14)
& ilf_type(sK16,relation_type(sK15,sK13))
& ilf_type(sK15,set_type)
& ilf_type(sK14,set_type)
& ilf_type(sK13,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f31,f86,f85,f84,f83]) ).
fof(f83,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK13)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK13)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK14))
& subset(range_of(X3),sK14)
& ilf_type(X3,relation_type(X2,sK13)) )
& ilf_type(X2,set_type) )
& ilf_type(sK14,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK14))
& subset(range_of(X3),sK14)
& ilf_type(X3,relation_type(X2,sK13)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(X3,relation_type(sK15,sK14))
& subset(range_of(X3),sK14)
& ilf_type(X3,relation_type(sK15,sK13)) )
& ilf_type(sK15,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK15,sK14))
& subset(range_of(X3),sK14)
& ilf_type(X3,relation_type(sK15,sK13)) )
=> ( ~ ilf_type(sK16,relation_type(sK15,sK14))
& subset(range_of(sK16),sK14)
& ilf_type(sK16,relation_type(sK15,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(f210,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f149,f138]) ).
fof(f149,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f228,plain,
! [X0,X1] : sP12(X0,X1),
inference(subsumption_resolution,[],[f227,f138]) ).
fof(f227,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f191,f138]) ).
fof(f191,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,[],[f48,f81,f80]) ).
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(flattening,[],[f47]) ).
fof(f47,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,[],[f18]) ).
fof(f18,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/sandbox/benchmark/theBenchmark.p',p18) ).
fof(f3819,plain,
member(sK23(cross_product(sK15,sK14),sK16),cross_product(sK15,sK14)),
inference(unit_resulting_resolution,[],[f2075,f3815,f223]) ).
fof(f223,plain,
! [X3,X0,X1] :
( ~ sP9(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f180,f138]) ).
fof(f180,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ~ member(sK22(X0,X1),X0)
& member(sK22(X0,X1),X1)
& ilf_type(sK22(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP9(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f114,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK22(X0,X1),X0)
& member(sK22(X0,X1),X1)
& ilf_type(sK22(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f114,plain,
! [X0,X1] :
( ( sP9(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) )
| ~ sP9(X0,X1) ) ),
inference(rectify,[],[f113]) ).
fof(f113,plain,
! [X1,X0] :
( ( sP9(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) )
| ~ sP9(X1,X0) ) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X1,X0] :
( sP9(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f3815,plain,
sP9(cross_product(sK15,sK14),sK16),
inference(unit_resulting_resolution,[],[f225,f3730,f178]) ).
fof(f178,plain,
! [X0,X1] :
( ~ sP10(X0,X1)
| ~ subset(X0,X1)
| sP9(X1,X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
| ~ sP9(X1,X0) )
& ( sP9(X1,X0)
| ~ subset(X0,X1) ) )
| ~ sP10(X0,X1) ),
inference(nnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( subset(X0,X1)
<=> sP9(X1,X0) )
| ~ sP10(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f3730,plain,
subset(sK16,cross_product(sK15,sK14)),
inference(unit_resulting_resolution,[],[f3539,f2450,f235]) ).
fof(f235,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f234,f138]) ).
fof(f234,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f233,f138]) ).
fof(f233,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,[],[f194,f138]) ).
fof(f194,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,[],[f51]) ).
fof(f51,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,[],[f50]) ).
fof(f50,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/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2450,plain,
! [X0] : subset(cross_product(domain_of(sK16),X0),cross_product(sK15,X0)),
inference(unit_resulting_resolution,[],[f454,f209,f239]) ).
fof(f239,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f238,f138]) ).
fof(f238,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f237,f138]) ).
fof(f237,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f236,f138]) ).
fof(f236,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f195,f138]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X2,X3)
| ~ subset(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)
=> ( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cross_product(X0,X2),cross_product(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f209,plain,
! [X0] : subset(X0,X0),
inference(subsumption_resolution,[],[f148,f138]) ).
fof(f148,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,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/sandbox/benchmark/theBenchmark.p',p17) ).
fof(f454,plain,
subset(domain_of(sK16),sK15),
inference(unit_resulting_resolution,[],[f135,f243]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| subset(domain_of(X2),X0) ),
inference(subsumption_resolution,[],[f242,f138]) ).
fof(f242,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f196,f138]) ).
fof(f196,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [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/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f135,plain,
ilf_type(sK16,relation_type(sK15,sK13)),
inference(cnf_transformation,[],[f87]) ).
fof(f3539,plain,
subset(sK16,cross_product(domain_of(sK16),sK14)),
inference(unit_resulting_resolution,[],[f1765,f2860,f235]) ).
fof(f2860,plain,
! [X0] : subset(cross_product(X0,range_of(sK16)),cross_product(X0,sK14)),
inference(unit_resulting_resolution,[],[f209,f136,f239]) ).
fof(f136,plain,
subset(range_of(sK16),sK14),
inference(cnf_transformation,[],[f87]) ).
fof(f1765,plain,
subset(sK16,cross_product(domain_of(sK16),range_of(sK16))),
inference(unit_resulting_resolution,[],[f1761,f141]) ).
fof(f141,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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f1761,plain,
ilf_type(sK16,binary_relation_type),
inference(unit_resulting_resolution,[],[f218,f1749,f169]) ).
fof(f169,plain,
! [X0] :
( ~ sP8(X0)
| ~ sP7(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f1749,plain,
sP7(sK16),
inference(unit_resulting_resolution,[],[f1743,f217]) ).
fof(f217,plain,
! [X0] :
( ~ relation_like(X0)
| sP7(X0) ),
inference(subsumption_resolution,[],[f172,f138]) ).
fof(f172,plain,
! [X0] :
( sP7(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( ( sP7(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ sP7(X0) ) ),
inference(flattening,[],[f110]) ).
fof(f110,plain,
! [X0] :
( ( sP7(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( sP7(X0)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f1743,plain,
relation_like(sK16),
inference(unit_resulting_resolution,[],[f1739,f245]) ).
fof(f245,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(subsumption_resolution,[],[f244,f138]) ).
fof(f244,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f198,f138]) ).
fof(f198,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) )
| ~ ilf_type(X1,set_type) )
| ~ 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/sandbox/benchmark/theBenchmark.p',p23) ).
fof(f1739,plain,
ilf_type(sK16,subset_type(cross_product(sK15,sK13))),
inference(unit_resulting_resolution,[],[f135,f220]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f219,f138]) ).
fof(f219,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f177,f138]) ).
fof(f177,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f218,plain,
! [X0] : sP8(X0),
inference(subsumption_resolution,[],[f173,f138]) ).
fof(f173,plain,
! [X0] :
( sP8(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( sP8(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f41,f75,f74]) ).
fof(f41,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
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/sandbox/benchmark/theBenchmark.p',p13) ).
fof(f225,plain,
! [X0,X1] : sP10(X0,X1),
inference(subsumption_resolution,[],[f224,f138]) ).
fof(f224,plain,
! [X0,X1] :
( sP10(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f184,f138]) ).
fof(f184,plain,
! [X0,X1] :
( sP10(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( sP10(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f46,f78,f77]) ).
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(flattening,[],[f45]) ).
fof(f45,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,[],[f9]) ).
fof(f9,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/sandbox/benchmark/theBenchmark.p',p9) ).
fof(f2075,plain,
member(sK23(cross_product(sK15,sK14),sK16),sK16),
inference(unit_resulting_resolution,[],[f2053,f189]) ).
fof(f189,plain,
! [X0,X1] :
( sP11(X0,X1)
| member(sK23(X0,X1),X1) ),
inference(cnf_transformation,[],[f121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n018.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 : Tue Apr 30 01:37:13 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (21254)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (21258)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.38 % (21255)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.38 % (21260)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)
% 0.22/0.38 % (21256)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.38 % (21261)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)
% 0.22/0.38 % (21259)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)
% 0.22/0.38 % (21257)WARNING: value z3 for option sas not known
% 0.22/0.38 % (21257)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)
% 0.22/0.38 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.39 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.42 TRYING [4]
% 0.22/0.42 TRYING [3]
% 0.22/0.46 % (21261)First to succeed.
% 0.22/0.47 % (21261)Refutation found. Thanks to Tanya!
% 0.22/0.47 % SZS status Theorem for theBenchmark
% 0.22/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.47 % (21261)------------------------------
% 0.22/0.47 % (21261)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.47 % (21261)Termination reason: Refutation
% 0.22/0.47
% 0.22/0.47 % (21261)Memory used [KB]: 2221
% 0.22/0.47 % (21261)Time elapsed: 0.088 s
% 0.22/0.47 % (21261)Instructions burned: 163 (million)
% 0.22/0.47 % (21261)------------------------------
% 0.22/0.47 % (21261)------------------------------
% 0.22/0.47 % (21254)Success in time 0.106 s
%------------------------------------------------------------------------------