TSTP Solution File: SET657+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET657+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 : n017.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 : Sun May 5 09:15:10 EDT 2024
% Result : Theorem 198.11s 28.61s
% Output : Refutation 198.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 28
% Syntax : Number of formulae : 158 ( 35 unt; 0 def)
% Number of atoms : 526 ( 21 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 605 ( 237 ~; 230 |; 63 &)
% ( 19 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 5 con; 0-3 aty)
% Number of variables : 306 ( 288 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1663248,plain,
$false,
inference(subsumption_resolution,[],[f1663247,f166]) ).
fof(f166,plain,
~ subset(field_of(sK18),union(sK16,sK17)),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
( ~ subset(field_of(sK18),union(sK16,sK17))
& ilf_type(sK18,relation_type(sK16,sK17))
& ilf_type(sK17,set_type)
& ilf_type(sK16,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f41,f110,f109,f108]) ).
fof(f108,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(X0,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(sK16,X1))
& ilf_type(X2,relation_type(sK16,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK16,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(sK16,X1))
& ilf_type(X2,relation_type(sK16,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ subset(field_of(X2),union(sK16,sK17))
& ilf_type(X2,relation_type(sK16,sK17)) )
& ilf_type(sK17,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ? [X2] :
( ~ subset(field_of(X2),union(sK16,sK17))
& ilf_type(X2,relation_type(sK16,sK17)) )
=> ( ~ subset(field_of(sK18),union(sK16,sK17))
& ilf_type(sK18,relation_type(sK16,sK17)) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(X0,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> subset(field_of(X2),union(X0,X1)) ) ) ),
inference(negated_conjecture,[],[f38]) ).
fof(f38,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> subset(field_of(X2),union(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_19) ).
fof(f1663247,plain,
subset(field_of(sK18),union(sK16,sK17)),
inference(forward_demodulation,[],[f1663246,f2612]) ).
fof(f2612,plain,
field_of(sK18) = union(domain_of(sK18),range_of(sK18)),
inference(unit_resulting_resolution,[],[f2608,f172]) ).
fof(f172,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| field_of(X0) = union(domain_of(X0),range_of(X0)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( field_of(X0) = union(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)
=> field_of(X0) = union(domain_of(X0),range_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f2608,plain,
ilf_type(sK18,binary_relation_type),
inference(unit_resulting_resolution,[],[f266,f2593,f196]) ).
fof(f196,plain,
! [X0] :
( ~ sP6(X0)
| ~ sP5(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f2593,plain,
sP5(sK18),
inference(unit_resulting_resolution,[],[f2587,f265]) ).
fof(f265,plain,
! [X0] :
( ~ relation_like(X0)
| sP5(X0) ),
inference(subsumption_resolution,[],[f199,f167]) ).
fof(f167,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p37) ).
fof(f199,plain,
! [X0] :
( sP5(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ( sP5(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ sP5(X0) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ( sP5(X0)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( sP5(X0)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f2587,plain,
relation_like(sK18),
inference(unit_resulting_resolution,[],[f2583,f306]) ).
fof(f306,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| relation_like(X2) ),
inference(subsumption_resolution,[],[f305,f167]) ).
fof(f305,plain,
! [X2,X0,X1] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f246,f167]) ).
fof(f246,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,[],[f76]) ).
fof(f76,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,[],[f27]) ).
fof(f27,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',p27) ).
fof(f2583,plain,
ilf_type(sK18,subset_type(cross_product(sK16,sK17))),
inference(unit_resulting_resolution,[],[f165,f270]) ).
fof(f270,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f269,f167]) ).
fof(f269,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,[],[f206,f167]) ).
fof(f206,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,[],[f60]) ).
fof(f60,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,[],[f40]) ).
fof(f40,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,[],[f7]) ).
fof(f7,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',p7) ).
fof(f165,plain,
ilf_type(sK18,relation_type(sK16,sK17)),
inference(cnf_transformation,[],[f111]) ).
fof(f266,plain,
! [X0] : sP6(X0),
inference(subsumption_resolution,[],[f200,f167]) ).
fof(f200,plain,
! [X0] :
( sP6(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0] :
( sP6(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f55,f93,f92]) ).
fof(f55,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,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',p14) ).
fof(f1663246,plain,
subset(union(domain_of(sK18),range_of(sK18)),union(sK16,sK17)),
inference(forward_demodulation,[],[f1663245,f268]) ).
fof(f268,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(subsumption_resolution,[],[f267,f167]) ).
fof(f267,plain,
! [X0,X1] :
( union(X0,X1) = union(X1,X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f204,f167]) ).
fof(f204,plain,
! [X0,X1] :
( union(X0,X1) = union(X1,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( union(X0,X1) = union(X1,X0)
| ~ 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)
=> union(X0,X1) = union(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f1663245,plain,
subset(union(range_of(sK18),domain_of(sK18)),union(sK16,sK17)),
inference(forward_demodulation,[],[f1663233,f268]) ).
fof(f1663233,plain,
subset(union(range_of(sK18),domain_of(sK18)),union(sK17,sK16)),
inference(unit_resulting_resolution,[],[f5358,f1663190,f292]) ).
fof(f292,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| subset(union(X0,X2),union(X1,X3))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f291,f167]) ).
fof(f291,plain,
! [X2,X3,X0,X1] :
( subset(union(X0,X2),union(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f290,f167]) ).
fof(f290,plain,
! [X2,X3,X0,X1] :
( subset(union(X0,X2),union(X1,X3))
| ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f289,f167]) ).
fof(f289,plain,
! [X2,X3,X0,X1] :
( subset(union(X0,X2),union(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,[],[f239,f167]) ).
fof(f239,plain,
! [X2,X3,X0,X1] :
( subset(union(X0,X2),union(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,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(union(X0,X2),union(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,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(union(X0,X2),union(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,[],[f1]) ).
fof(f1,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(union(X0,X2),union(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f1663190,plain,
subset(domain_of(sK18),sK16),
inference(unit_resulting_resolution,[],[f278,f1663131,f218]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| ~ sP10(X1,X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
| ~ sP10(X1,X0) )
& ( sP10(X1,X0)
| ~ subset(X0,X1) ) )
| ~ sP11(X0,X1) ),
inference(nnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( subset(X0,X1)
<=> sP10(X1,X0) )
| ~ sP11(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f1663131,plain,
sP10(sK16,domain_of(sK18)),
inference(subsumption_resolution,[],[f1663121,f394]) ).
fof(f394,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| sP10(X1,X0) ),
inference(resolution,[],[f217,f278]) ).
fof(f217,plain,
! [X0,X1] :
( ~ sP11(X0,X1)
| ~ subset(X0,X1)
| sP10(X1,X0) ),
inference(cnf_transformation,[],[f138]) ).
fof(f1663121,plain,
( subset(domain_of(sK18),sK16)
| sP10(sK16,domain_of(sK18)) ),
inference(resolution,[],[f4421,f222]) ).
fof(f222,plain,
! [X0,X1] :
( ~ member(sK24(X0,X1),X0)
| sP10(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ( sP10(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) )
| ~ sP10(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f140,f141]) ).
fof(f141,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(f140,plain,
! [X0,X1] :
( ( sP10(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) )
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f139]) ).
fof(f139,plain,
! [X1,X0] :
( ( sP10(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) )
| ~ sP10(X1,X0) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X1,X0] :
( sP10(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f4421,plain,
! [X0] :
( member(sK24(X0,domain_of(sK18)),sK16)
| subset(domain_of(sK18),X0) ),
inference(resolution,[],[f4408,f407]) ).
fof(f407,plain,
! [X0,X1] :
( member(sK24(X1,X0),X0)
| subset(X0,X1) ),
inference(resolution,[],[f399,f221]) ).
fof(f221,plain,
! [X0,X1] :
( sP10(X0,X1)
| member(sK24(X0,X1),X1) ),
inference(cnf_transformation,[],[f142]) ).
fof(f399,plain,
! [X0,X1] :
( ~ sP10(X0,X1)
| subset(X1,X0) ),
inference(resolution,[],[f218,f278]) ).
fof(f4408,plain,
! [X0] :
( ~ member(X0,domain_of(sK18))
| member(X0,sK16) ),
inference(resolution,[],[f4383,f279]) ).
fof(f279,plain,
! [X3,X0,X1] :
( ~ sP12(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f226,f167]) ).
fof(f226,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ member(sK25(X0,X1),X0)
& member(sK25(X0,X1),X1)
& ilf_type(sK25(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP12(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f145,f146]) ).
fof(f146,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK25(X0,X1),X0)
& member(sK25(X0,X1),X1)
& ilf_type(sK25(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f145,plain,
! [X0,X1] :
( ( sP12(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) )
| ~ sP12(X0,X1) ) ),
inference(rectify,[],[f144]) ).
fof(f144,plain,
! [X1,X0] :
( ( sP12(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) )
| ~ sP12(X1,X0) ) ),
inference(nnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X1,X0] :
( sP12(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f4383,plain,
sP12(sK16,domain_of(sK18)),
inference(unit_resulting_resolution,[],[f281,f4379,f224]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sP13(X0,X1)
| ~ member(X0,power_set(X1))
| sP12(X1,X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0,X1] :
( ( ( member(X0,power_set(X1))
| ~ sP12(X1,X0) )
& ( sP12(X1,X0)
| ~ member(X0,power_set(X1)) ) )
| ~ sP13(X0,X1) ),
inference(nnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
<=> sP12(X1,X0) )
| ~ sP13(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f4379,plain,
member(domain_of(sK18),power_set(sK16)),
inference(unit_resulting_resolution,[],[f258,f4376,f312]) ).
fof(f312,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f311,f167]) ).
fof(f311,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f248,f167]) ).
fof(f248,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,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,[],[f79]) ).
fof(f79,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,[],[f78]) ).
fof(f78,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,[],[f23]) ).
fof(f23,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/benchmark/theBenchmark.p',p23) ).
fof(f4376,plain,
ilf_type(domain_of(sK18),member_type(power_set(sK16))),
inference(unit_resulting_resolution,[],[f4368,f285]) ).
fof(f285,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f284,f167]) ).
fof(f284,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f231,f167]) ).
fof(f231,plain,
! [X0,X1] :
( 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(cnf_transformation,[],[f148]) ).
fof(f148,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,[],[f66]) ).
fof(f66,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,[],[f16]) ).
fof(f16,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/benchmark/theBenchmark.p',p16) ).
fof(f4368,plain,
ilf_type(domain_of(sK18),subset_type(sK16)),
inference(forward_demodulation,[],[f4346,f3156]) ).
fof(f3156,plain,
domain_of(sK18) = domain(sK16,sK17,sK18),
inference(unit_resulting_resolution,[],[f165,f294]) ).
fof(f294,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| domain(X0,X1,X2) = domain_of(X2) ),
inference(subsumption_resolution,[],[f293,f167]) ).
fof(f293,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f240,f167]) ).
fof(f240,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f4346,plain,
ilf_type(domain(sK16,sK17,sK18),subset_type(sK16)),
inference(unit_resulting_resolution,[],[f165,f300]) ).
fof(f300,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(domain(X0,X1,X2),subset_type(X0)) ),
inference(subsumption_resolution,[],[f299,f167]) ).
fof(f299,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f243,f167]) ).
fof(f243,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f258,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f176,f167]) ).
fof(f176,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f281,plain,
! [X0,X1] : sP13(X0,X1),
inference(subsumption_resolution,[],[f280,f167]) ).
fof(f280,plain,
! [X0,X1] :
( sP13(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f230,f167]) ).
fof(f230,plain,
! [X0,X1] :
( sP13(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( sP13(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f65,f103,f102]) ).
fof(f65,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,[],[f64]) ).
fof(f64,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,[],[f21]) ).
fof(f21,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/benchmark/theBenchmark.p',p21) ).
fof(f278,plain,
! [X0,X1] : sP11(X0,X1),
inference(subsumption_resolution,[],[f277,f167]) ).
fof(f277,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f223,f167]) ).
fof(f223,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ! [X1] :
( sP11(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f63,f100,f99]) ).
fof(f63,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,[],[f62]) ).
fof(f62,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/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f5358,plain,
subset(range_of(sK18),sK17),
inference(unit_resulting_resolution,[],[f278,f5356,f218]) ).
fof(f5356,plain,
sP10(sK17,range_of(sK18)),
inference(subsumption_resolution,[],[f5348,f394]) ).
fof(f5348,plain,
( subset(range_of(sK18),sK17)
| sP10(sK17,range_of(sK18)) ),
inference(resolution,[],[f3963,f222]) ).
fof(f3963,plain,
! [X0] :
( member(sK24(X0,range_of(sK18)),sK17)
| subset(range_of(sK18),X0) ),
inference(resolution,[],[f3950,f407]) ).
fof(f3950,plain,
! [X0] :
( ~ member(X0,range_of(sK18))
| member(X0,sK17) ),
inference(resolution,[],[f3925,f279]) ).
fof(f3925,plain,
sP12(sK17,range_of(sK18)),
inference(unit_resulting_resolution,[],[f281,f3921,f224]) ).
fof(f3921,plain,
member(range_of(sK18),power_set(sK17)),
inference(unit_resulting_resolution,[],[f258,f3918,f312]) ).
fof(f3918,plain,
ilf_type(range_of(sK18),member_type(power_set(sK17))),
inference(unit_resulting_resolution,[],[f3910,f285]) ).
fof(f3910,plain,
ilf_type(range_of(sK18),subset_type(sK17)),
inference(forward_demodulation,[],[f3888,f3560]) ).
fof(f3560,plain,
range_of(sK18) = range(sK16,sK17,sK18),
inference(unit_resulting_resolution,[],[f165,f296]) ).
fof(f296,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(subsumption_resolution,[],[f295,f167]) ).
fof(f295,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f241,f167]) ).
fof(f241,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(f3888,plain,
ilf_type(range(sK16,sK17,sK18),subset_type(sK17)),
inference(unit_resulting_resolution,[],[f165,f298]) ).
fof(f298,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(subsumption_resolution,[],[f297,f167]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f242,f167]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p36) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET657+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri May 3 16:36:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (4334)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (4337)WARNING: value z3 for option sas not known
% 0.13/0.36 % (4341)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.36 % (4339)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36 % (4337)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (4338)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (4336)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (4340)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37 % (4335)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.38 TRYING [3]
% 0.13/0.39 TRYING [1]
% 0.19/0.40 TRYING [2]
% 0.19/0.40 TRYING [4]
% 0.19/0.45 TRYING [3]
% 0.19/0.58 TRYING [5]
% 2.12/0.70 TRYING [4]
% 7.77/1.47 TRYING [1]
% 7.77/1.47 TRYING [2]
% 7.77/1.48 TRYING [3]
% 7.77/1.51 TRYING [4]
% 8.64/1.58 TRYING [6]
% 9.86/1.76 TRYING [5]
% 18.12/3.03 TRYING [6]
% 58.86/8.80 TRYING [7]
% 72.37/10.72 TRYING [7]
% 94.30/13.87 TRYING [5]
% 197.78/28.54 % (4341)First to succeed.
% 197.78/28.55 % (4341)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4334"
% 198.11/28.61 % (4341)Refutation found. Thanks to Tanya!
% 198.11/28.61 % SZS status Theorem for theBenchmark
% 198.11/28.61 % SZS output start Proof for theBenchmark
% See solution above
% 198.11/28.61 % (4341)------------------------------
% 198.11/28.61 % (4341)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 198.11/28.61 % (4341)Termination reason: Refutation
% 198.11/28.61
% 198.11/28.61 % (4341)Memory used [KB]: 595105
% 198.11/28.61 % (4341)Time elapsed: 28.192 s
% 198.11/28.61 % (4341)Instructions burned: 83693 (million)
% 198.11/28.61 % (4334)Success in time 27.882 s
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