TSTP Solution File: SET655+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET655+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 : n009.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 15:09:34 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 109 ( 23 unt; 0 def)
% Number of atoms : 458 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 548 ( 199 ~; 179 |; 110 &)
% ( 15 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 253 ( 212 !; 41 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1413,plain,
$false,
inference(unit_resulting_resolution,[],[f108,f109,f1342,f190]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1) ),
inference(subsumption_resolution,[],[f189,f111]) ).
fof(f111,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(f189,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,[],[f188,f111]) ).
fof(f188,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,[],[f187,f111]) ).
fof(f187,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,[],[f153,f111]) ).
fof(f153,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,[],[f41]) ).
fof(f41,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,[],[f40]) ).
fof(f40,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,[],[f2]) ).
fof(f2,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',p2) ).
fof(f1342,plain,
~ subset(cross_product(sK9,sK11),cross_product(sK10,sK12)),
inference(unit_resulting_resolution,[],[f176,f1330,f136]) ).
fof(f136,plain,
! [X0,X1] :
( ~ sP6(X0,X1)
| ~ subset(X0,X1)
| sP5(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ( ( subset(X0,X1)
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| ~ subset(X0,X1) ) )
| ~ sP6(X0,X1) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( subset(X0,X1)
<=> sP5(X1,X0) )
| ~ sP6(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f1330,plain,
~ sP5(cross_product(sK10,sK12),cross_product(sK9,sK11)),
inference(unit_resulting_resolution,[],[f1072,f1106,f174]) ).
fof(f174,plain,
! [X3,X0,X1] :
( ~ sP5(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f138,f111]) ).
fof(f138,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ~ member(sK18(X0,X1),X0)
& member(sK18(X0,X1),X1)
& ilf_type(sK18(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP5(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f87,f88]) ).
fof(f88,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK18(X0,X1),X0)
& member(sK18(X0,X1),X1)
& ilf_type(sK18(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
! [X0,X1] :
( ( sP5(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) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f86,plain,
! [X1,X0] :
( ( sP5(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) )
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X1,X0] :
( sP5(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f1106,plain,
member(sK19(cross_product(sK10,sK12),sK13),cross_product(sK9,sK11)),
inference(unit_resulting_resolution,[],[f774,f991,f177]) ).
fof(f177,plain,
! [X3,X0,X1] :
( ~ sP7(X0,X1)
| ~ member(X3,X1)
| member(X3,X0) ),
inference(subsumption_resolution,[],[f145,f111]) ).
fof(f145,plain,
! [X3,X0,X1] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( ~ member(sK19(X0,X1),X0)
& member(sK19(X0,X1),X1)
& ilf_type(sK19(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X0)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type) )
| ~ sP7(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X0)
& member(X2,X1)
& ilf_type(X2,set_type) )
=> ( ~ member(sK19(X0,X1),X0)
& member(sK19(X0,X1),X1)
& ilf_type(sK19(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1] :
( ( sP7(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) )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X1,X0] :
( ( sP7(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) )
| ~ sP7(X1,X0) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X1,X0] :
( sP7(X1,X0)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f991,plain,
member(sK19(cross_product(sK10,sK12),sK13),sK13),
inference(unit_resulting_resolution,[],[f985,f465]) ).
fof(f465,plain,
! [X0,X1] :
( member(sK19(X1,X0),X0)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f461,f147]) ).
fof(f147,plain,
! [X0,X1] :
( sP7(X0,X1)
| member(sK19(X0,X1),X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f461,plain,
! [X0,X1] :
( ~ sP7(X0,X1)
| member(X1,power_set(X0)) ),
inference(resolution,[],[f144,f179]) ).
fof(f179,plain,
! [X0,X1] : sP8(X0,X1),
inference(subsumption_resolution,[],[f178,f111]) ).
fof(f178,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f149,f111]) ).
fof(f149,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( sP8(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f36,f62,f61]) ).
fof(f62,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
<=> sP7(X1,X0) )
| ~ sP8(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f36,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,[],[f35]) ).
fof(f35,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,[],[f10]) ).
fof(f10,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',p10) ).
fof(f144,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ~ sP7(X1,X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ( ( member(X0,power_set(X1))
| ~ sP7(X1,X0) )
& ( sP7(X1,X0)
| ~ member(X0,power_set(X1)) ) )
| ~ sP8(X0,X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f985,plain,
~ member(sK13,power_set(cross_product(sK10,sK12))),
inference(unit_resulting_resolution,[],[f163,f971,f196]) ).
fof(f196,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f195,f111]) ).
fof(f195,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f157,f111]) ).
fof(f157,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,[],[f98]) ).
fof(f98,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,[],[f45]) ).
fof(f45,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,[],[f44]) ).
fof(f44,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,[],[f12]) ).
fof(f12,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',p12) ).
fof(f971,plain,
~ ilf_type(sK13,member_type(power_set(cross_product(sK10,sK12)))),
inference(unit_resulting_resolution,[],[f946,f181]) ).
fof(f181,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f180,f111]) ).
fof(f180,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,[],[f151,f111]) ).
fof(f151,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,[],[f95]) ).
fof(f95,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,[],[f37]) ).
fof(f37,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,[],[f7]) ).
fof(f7,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',p7) ).
fof(f946,plain,
~ ilf_type(sK13,subset_type(cross_product(sK10,sK12))),
inference(unit_resulting_resolution,[],[f110,f173]) ).
fof(f173,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f172,f111]) ).
fof(f172,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,[],[f134,f111]) ).
fof(f134,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,[],[f32]) ).
fof(f32,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,[],[f22]) ).
fof(f22,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,[],[f3]) ).
fof(f3,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',p3) ).
fof(f110,plain,
~ ilf_type(sK13,relation_type(sK10,sK12)),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
( ~ ilf_type(sK13,relation_type(sK10,sK12))
& subset(sK11,sK12)
& subset(sK9,sK10)
& ilf_type(sK13,relation_type(sK9,sK11))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f24,f68,f67,f66,f65,f64]) ).
fof(f64,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X2,X3)
& subset(X0,X1)
& ilf_type(X4,relation_type(X0,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X2,X3)
& subset(sK9,X1)
& ilf_type(X4,relation_type(sK9,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK9,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X2,X3)
& subset(sK9,X1)
& ilf_type(X4,relation_type(sK9,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,X3))
& subset(X2,X3)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK10,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,X3))
& subset(X2,X3)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,X3))
& subset(sK11,X3)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,sK11)) )
& ilf_type(X3,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,X3))
& subset(sK11,X3)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,sK11)) )
& ilf_type(X3,set_type) )
=> ( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,sK12))
& subset(sK11,sK12)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,sK11)) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
( ? [X4] :
( ~ ilf_type(X4,relation_type(sK10,sK12))
& subset(sK11,sK12)
& subset(sK9,sK10)
& ilf_type(X4,relation_type(sK9,sK11)) )
=> ( ~ ilf_type(sK13,relation_type(sK10,sK12))
& subset(sK11,sK12)
& subset(sK9,sK10)
& ilf_type(sK13,relation_type(sK9,sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X2,X3)
& subset(X0,X1)
& ilf_type(X4,relation_type(X0,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ~ ilf_type(X4,relation_type(X1,X3))
& subset(X2,X3)
& subset(X0,X1)
& ilf_type(X4,relation_type(X0,X2)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X2))
=> ( ( subset(X2,X3)
& subset(X0,X1) )
=> ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
inference(negated_conjecture,[],[f20]) ).
fof(f20,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X2))
=> ( ( subset(X2,X3)
& subset(X0,X1) )
=> ilf_type(X4,relation_type(X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_17) ).
fof(f163,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f113,f111]) ).
fof(f113,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,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',p11) ).
fof(f774,plain,
sP7(cross_product(sK9,sK11),sK13),
inference(unit_resulting_resolution,[],[f179,f770,f143]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sP8(X0,X1)
| ~ member(X0,power_set(X1))
| sP7(X1,X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f770,plain,
member(sK13,power_set(cross_product(sK9,sK11))),
inference(unit_resulting_resolution,[],[f163,f700,f198]) ).
fof(f198,plain,
! [X0,X1] :
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f197,f111]) ).
fof(f197,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f156,f111]) ).
fof(f156,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,[],[f98]) ).
fof(f700,plain,
ilf_type(sK13,member_type(power_set(cross_product(sK9,sK11)))),
inference(unit_resulting_resolution,[],[f695,f183]) ).
fof(f183,plain,
! [X0,X1] :
( ~ ilf_type(X1,subset_type(X0))
| ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f182,f111]) ).
fof(f182,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,[],[f150,f111]) ).
fof(f150,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,[],[f95]) ).
fof(f695,plain,
ilf_type(sK13,subset_type(cross_product(sK9,sK11))),
inference(unit_resulting_resolution,[],[f107,f171]) ).
fof(f171,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f170,f111]) ).
fof(f170,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,[],[f135,f111]) ).
fof(f135,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,[],[f32]) ).
fof(f107,plain,
ilf_type(sK13,relation_type(sK9,sK11)),
inference(cnf_transformation,[],[f69]) ).
fof(f1072,plain,
~ member(sK19(cross_product(sK10,sK12),sK13),cross_product(sK10,sK12)),
inference(unit_resulting_resolution,[],[f993,f148]) ).
fof(f148,plain,
! [X0,X1] :
( ~ member(sK19(X0,X1),X0)
| sP7(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f993,plain,
~ sP7(cross_product(sK10,sK12),sK13),
inference(unit_resulting_resolution,[],[f179,f985,f144]) ).
fof(f176,plain,
! [X0,X1] : sP6(X0,X1),
inference(subsumption_resolution,[],[f175,f111]) ).
fof(f175,plain,
! [X0,X1] :
( sP6(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f142,f111]) ).
fof(f142,plain,
! [X0,X1] :
( sP6(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( sP6(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f34,f59,f58]) ).
fof(f34,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,[],[f33]) ).
fof(f33,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,[],[f5]) ).
fof(f5,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',p5) ).
fof(f109,plain,
subset(sK11,sK12),
inference(cnf_transformation,[],[f69]) ).
fof(f108,plain,
subset(sK9,sK10),
inference(cnf_transformation,[],[f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET655+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n009.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 01:12:56 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.36 % (16346)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (16354)WARNING: value z3 for option sas not known
% 0.15/0.37 % (16354)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)
% 0.15/0.37 % (16355)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.37 % (16356)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)
% 0.15/0.37 % (16353)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.37 % (16358)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)
% 0.15/0.37 % (16352)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.37 % (16357)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)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.38 TRYING [3]
% 0.22/0.39 TRYING [1]
% 0.22/0.39 TRYING [2]
% 0.22/0.40 % (16358)First to succeed.
% 0.22/0.40 TRYING [4]
% 0.22/0.41 % (16358)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (16358)------------------------------
% 0.22/0.41 % (16358)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.41 % (16358)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (16358)Memory used [KB]: 1241
% 0.22/0.41 % (16358)Time elapsed: 0.031 s
% 0.22/0.41 % (16358)Instructions burned: 50 (million)
% 0.22/0.41 % (16358)------------------------------
% 0.22/0.41 % (16358)------------------------------
% 0.22/0.41 % (16346)Success in time 0.048 s
%------------------------------------------------------------------------------