TSTP Solution File: SET649+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET649+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 May 21 03:20:14 EDT 2024
% Result : Theorem 0.17s 0.37s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 20
% Syntax : Number of formulae : 100 ( 20 unt; 0 def)
% Number of atoms : 413 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 509 ( 196 ~; 175 |; 79 &)
% ( 15 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 220 ( 199 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2117,plain,
$false,
inference(unit_resulting_resolution,[],[f143,f144,f1940,f253]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f252,f146]) ).
fof(f146,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f252,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,[],[f251,f146]) ).
fof(f251,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,[],[f250,f146]) ).
fof(f250,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,[],[f209,f146]) ).
fof(f209,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,[],[f54]) ).
fof(f54,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,[],[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(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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f1940,plain,
~ subset(cross_product(domain_of(sK17),range_of(sK17)),cross_product(sK15,sK16)),
inference(unit_resulting_resolution,[],[f525,f1930,f249]) ).
fof(f249,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| subset(X0,X2)
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f248,f146]) ).
fof(f248,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f247,f146]) ).
fof(f247,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,[],[f208,f146]) ).
fof(f208,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,[],[f52]) ).
fof(f52,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,[],[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(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/benchmark/theBenchmark.p',p1) ).
fof(f1930,plain,
~ subset(sK17,cross_product(sK15,sK16)),
inference(unit_resulting_resolution,[],[f239,f1917,f192]) ).
fof(f192,plain,
! [X0,X1] :
( ~ sP12(X0,X1)
| ~ subset(X0,X1)
| sP11(X1,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,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(f1917,plain,
~ sP11(cross_product(sK15,sK16),sK17),
inference(unit_resulting_resolution,[],[f1727,f1726,f237]) ).
fof(f237,plain,
! [X3,X0,X1] :
( ~ sP11(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f194,f146]) ).
fof(f194,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( sP11(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) )
| ~ sP11(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f122,f123]) ).
fof(f123,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(f122,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,[],[f121]) ).
fof(f121,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(f1726,plain,
~ member(sK25(cross_product(sK15,sK16),sK17),cross_product(sK15,sK16)),
inference(unit_resulting_resolution,[],[f1715,f204]) ).
fof(f204,plain,
! [X0,X1] :
( ~ member(sK25(X0,X1),X0)
| sP13(X0,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1] :
( ( sP13(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) )
| ~ sP13(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f127,f128]) ).
fof(f128,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(f127,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,[],[f126]) ).
fof(f126,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(f1715,plain,
~ sP13(cross_product(sK15,sK16),sK17),
inference(unit_resulting_resolution,[],[f242,f1713,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ~ sP14(X0,X1)
| ~ sP13(X1,X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,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(f1713,plain,
~ member(sK17,power_set(cross_product(sK15,sK16))),
inference(unit_resulting_resolution,[],[f224,f1711,f259]) ).
fof(f259,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f258,f146]) ).
fof(f258,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f213,f146]) ).
fof(f213,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,[],[f133]) ).
fof(f133,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/benchmark/theBenchmark.p',p22) ).
fof(f1711,plain,
~ ilf_type(sK17,member_type(power_set(cross_product(sK15,sK16)))),
inference(unit_resulting_resolution,[],[f1700,f244]) ).
fof(f244,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f243,f146]) ).
fof(f243,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,[],[f207,f146]) ).
fof(f207,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,[],[f130]) ).
fof(f130,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/benchmark/theBenchmark.p',p15) ).
fof(f1700,plain,
~ ilf_type(sK17,subset_type(cross_product(sK15,sK16))),
inference(unit_resulting_resolution,[],[f145,f236]) ).
fof(f236,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f235,f146]) ).
fof(f235,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,[],[f190,f146]) ).
fof(f190,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/benchmark/theBenchmark.p',p4) ).
fof(f145,plain,
~ ilf_type(sK17,relation_type(sK15,sK16)),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
( ~ ilf_type(sK17,relation_type(sK15,sK16))
& subset(range_of(sK17),sK16)
& subset(domain_of(sK17),sK15)
& ilf_type(sK17,binary_relation_type)
& ilf_type(sK16,set_type)
& ilf_type(sK15,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f31,f88,f87,f86]) ).
fof(f86,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),X0)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(sK15,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),sK15)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK15,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(sK15,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),sK15)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ ilf_type(X2,relation_type(sK15,sK16))
& subset(range_of(X2),sK16)
& subset(domain_of(X2),sK15)
& ilf_type(X2,binary_relation_type) )
& ilf_type(sK16,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
( ? [X2] :
( ~ ilf_type(X2,relation_type(sK15,sK16))
& subset(range_of(X2),sK16)
& subset(domain_of(X2),sK15)
& ilf_type(X2,binary_relation_type) )
=> ( ~ ilf_type(sK17,relation_type(sK15,sK16))
& subset(range_of(sK17),sK16)
& subset(domain_of(sK17),sK15)
& ilf_type(sK17,binary_relation_type) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),X0)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),X0)
& ilf_type(X2,binary_relation_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,binary_relation_type)
=> ( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) )
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_11) ).
fof(f224,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f163,f146]) ).
fof(f163,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/benchmark/theBenchmark.p',p21) ).
fof(f242,plain,
! [X0,X1] : sP14(X0,X1),
inference(subsumption_resolution,[],[f241,f146]) ).
fof(f241,plain,
! [X0,X1] :
( sP14(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f205,f146]) ).
fof(f205,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/benchmark/theBenchmark.p',p20) ).
fof(f1727,plain,
member(sK25(cross_product(sK15,sK16),sK17),sK17),
inference(unit_resulting_resolution,[],[f1715,f203]) ).
fof(f203,plain,
! [X0,X1] :
( sP13(X0,X1)
| member(sK25(X0,X1),X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f239,plain,
! [X0,X1] : sP12(X0,X1),
inference(subsumption_resolution,[],[f238,f146]) ).
fof(f238,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f198,f146]) ).
fof(f198,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/benchmark/theBenchmark.p',p12) ).
fof(f525,plain,
subset(sK17,cross_product(domain_of(sK17),range_of(sK17))),
inference(unit_resulting_resolution,[],[f142,f149]) ).
fof(f149,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/benchmark/theBenchmark.p',p2) ).
fof(f142,plain,
ilf_type(sK17,binary_relation_type),
inference(cnf_transformation,[],[f89]) ).
fof(f144,plain,
subset(range_of(sK17),sK16),
inference(cnf_transformation,[],[f89]) ).
fof(f143,plain,
subset(domain_of(sK17),sK15),
inference(cnf_transformation,[],[f89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SET649+3 : TPTP v8.2.0. Released v2.2.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n025.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon May 20 12:44:08 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (16990)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (16993)WARNING: value z3 for option sas not known
% 0.11/0.34 % (16997)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)
% 0.11/0.34 % (16996)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)
% 0.11/0.34 % (16992)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (16993)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)
% 0.11/0.34 % (16995)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)
% 0.11/0.34 % (16994)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (16991)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.11/0.35 TRYING [3]
% 0.11/0.35 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.17/0.37 TRYING [4]
% 0.17/0.37 % (16997)First to succeed.
% 0.17/0.37 % (16997)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16990"
% 0.17/0.37 % (16997)Refutation found. Thanks to Tanya!
% 0.17/0.37 % SZS status Theorem for theBenchmark
% 0.17/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.37 % (16997)------------------------------
% 0.17/0.37 % (16997)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.17/0.37 % (16997)Termination reason: Refutation
% 0.17/0.37
% 0.17/0.37 % (16997)Memory used [KB]: 1495
% 0.17/0.37 % (16997)Time elapsed: 0.036 s
% 0.17/0.37 % (16997)Instructions burned: 71 (million)
% 0.17/0.37 % (16990)Success in time 0.049 s
%------------------------------------------------------------------------------