TSTP Solution File: SET641+3 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET641+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 : n010.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 15:09:00 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f280,plain,
$false,
inference(subsumption_resolution,[],[f279,f94]) ).
fof(f94,plain,
~ ilf_type(sK4,relation_type(sK5,sK6)),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
( ~ ilf_type(sK4,relation_type(sK5,sK6))
& subset(sK4,cross_product(sK5,sK6))
& ilf_type(sK6,set_type)
& ilf_type(sK5,set_type)
& ilf_type(sK4,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f23,f55,f54,f53]) ).
fof(f53,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,cross_product(X1,X2))
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ~ ilf_type(sK4,relation_type(X1,X2))
& subset(sK4,cross_product(X1,X2))
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK4,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
( ? [X1] :
( ? [X2] :
( ~ ilf_type(sK4,relation_type(X1,X2))
& subset(sK4,cross_product(X1,X2))
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ ilf_type(sK4,relation_type(sK5,X2))
& subset(sK4,cross_product(sK5,X2))
& ilf_type(X2,set_type) )
& ilf_type(sK5,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f55,plain,
( ? [X2] :
( ~ ilf_type(sK4,relation_type(sK5,X2))
& subset(sK4,cross_product(sK5,X2))
& ilf_type(X2,set_type) )
=> ( ~ ilf_type(sK4,relation_type(sK5,sK6))
& subset(sK4,cross_product(sK5,sK6))
& ilf_type(sK6,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,cross_product(X1,X2))
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X0,relation_type(X1,X2))
& subset(X0,cross_product(X1,X2))
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X0,cross_product(X1,X2))
=> ilf_type(X0,relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_3) ).
fof(f279,plain,
ilf_type(sK4,relation_type(sK5,sK6)),
inference(resolution,[],[f268,f155]) ).
fof(f155,plain,
! [X3,X0,X1] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154]) ).
fof(f154,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) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113]) ).
fof(f113,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,[],[f31]) ).
fof(f31,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,[],[f21]) ).
fof(f21,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,[],[f1]) ).
fof(f1,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',p1) ).
fof(f153,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152]) ).
fof(f152,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) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114]) ).
fof(f114,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,[],[f31]) ).
fof(f151,plain,
! [X0,X1] : ilf_type(cross_product(X0,X1),set_type),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150]) ).
fof(f150,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0] :
( ! [X1] :
( ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ilf_type(cross_product(X0,X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f149,plain,
! [X0,X1] : ilf_type(ordered_pair(X0,X1),set_type),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148]) ).
fof(f148,plain,
! [X0,X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ilf_type(ordered_pair(X0,X1),set_type)
| ~ 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)
=> ilf_type(ordered_pair(X0,X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f147,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108]) ).
fof(f108,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f65,f66]) ).
fof(f66,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(f146,plain,
! [X0] :
( empty(X0)
| ilf_type(sK10(X0),set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109]) ).
fof(f109,plain,
! [X0] :
( empty(X0)
| ilf_type(sK10(X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f145,plain,
! [X0] :
( member(sK10(X0),X0)
| empty(X0) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110]) ).
fof(f110,plain,
! [X0] :
( empty(X0)
| member(sK10(X0),X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f67]) ).
fof(f144,plain,
! [X0] : sP1(X0),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107]) ).
fof(f107,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( sP1(X0)
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f27,f48,f47]) ).
fof(f47,plain,
! [X0] :
( sP0(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f48,plain,
! [X0] :
( ( relation_like(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f27,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ( relation_like(X0)
<=> ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( relation_like(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,X0)
=> ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f101,plain,
! [X0,X4] :
( ilf_type(sK8(X4),set_type)
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK7(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK7(X0),X0)
& ilf_type(sK7(X0),set_type) ) )
& ( ! [X4] :
( ( ordered_pair(sK8(X4),sK9(X4)) = X4
& ilf_type(sK9(X4),set_type)
& ilf_type(sK8(X4),set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f59,f62,f61,f60]) ).
fof(f60,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) )
=> ( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != sK7(X0)
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(sK7(X0),X0)
& ilf_type(sK7(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK8(X4),X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(sK8(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
! [X4] :
( ? [X6] :
( ordered_pair(sK8(X4),X6) = X4
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK8(X4),sK9(X4)) = X4
& ilf_type(sK9(X4),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X4] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X4
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( sP0(X0)
| ? [X1] :
( ! [X2] :
( ! [X3] :
( ordered_pair(X2,X3) != X1
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
& member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ? [X2] :
( ? [X3] :
( ordered_pair(X2,X3) = X1
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
| ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f102,plain,
! [X0,X4] :
( ilf_type(sK9(X4),set_type)
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f103,plain,
! [X0,X4] :
( ordered_pair(sK8(X4),sK9(X4)) = X4
| ~ member(X4,X0)
| ~ ilf_type(X4,set_type)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f104,plain,
! [X0] :
( sP0(X0)
| ilf_type(sK7(X0),set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f105,plain,
! [X0] :
( member(sK7(X0),X0)
| sP0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X2,X3,X0] :
( sP0(X0)
| ordered_pair(X2,X3) != sK7(X0)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f63]) ).
fof(f99,plain,
! [X0] :
( sP0(X0)
| ~ relation_like(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ( ( relation_like(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ relation_like(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f143,plain,
! [X0] : ~ empty(power_set(X0)),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97]) ).
fof(f97,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',p11) ).
fof(f142,plain,
! [X0] : ilf_type(power_set(X0),set_type),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98]) ).
fof(f98,plain,
! [X0] :
( ilf_type(power_set(X0),set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f25]) ).
fof(f95,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f90,plain,
ilf_type(sK4,set_type),
inference(cnf_transformation,[],[f56]) ).
fof(f91,plain,
ilf_type(sK5,set_type),
inference(cnf_transformation,[],[f56]) ).
fof(f92,plain,
ilf_type(sK6,set_type),
inference(cnf_transformation,[],[f56]) ).
fof(f93,plain,
subset(sK4,cross_product(sK5,sK6)),
inference(cnf_transformation,[],[f56]) ).
fof(f268,plain,
ilf_type(sK4,subset_type(cross_product(sK5,sK6))),
inference(resolution,[],[f265,f241]) ).
fof(f241,plain,
member(sK4,power_set(cross_product(sK5,sK6))),
inference(duplicate_literal_removal,[],[f240]) ).
fof(f240,plain,
( member(sK4,power_set(cross_product(sK5,sK6)))
| member(sK4,power_set(cross_product(sK5,sK6))) ),
inference(resolution,[],[f210,f168]) ).
fof(f168,plain,
! [X0,X1] :
( member(sK12(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167]) ).
fof(f167,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK12(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121]) ).
fof(f121,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK12(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f73,f74]) ).
fof(f74,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK12(X0,X1),X1)
& member(sK12(X0,X1),X0)
& ilf_type(sK12(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[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(flattening,[],[f34]) ).
fof(f34,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/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(f166,plain,
! [X0,X1] :
( ~ member(sK12(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165]) ).
fof(f165,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK12(X0,X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122]) ).
fof(f122,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK12(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f164,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163]) ).
fof(f163,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162]) ).
fof(f162,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115]) ).
fof(f115,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f69,f70]) ).
fof(f70,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK11(X0,X1),X1)
& member(sK11(X0,X1),X0)
& ilf_type(sK11(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[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(flattening,[],[f32]) ).
fof(f32,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/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f161,plain,
! [X0,X1] :
( subset(X0,X1)
| ilf_type(sK11(X0,X1),set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160]) ).
fof(f160,plain,
! [X0,X1] :
( subset(X0,X1)
| ilf_type(sK11(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116]) ).
fof(f116,plain,
! [X0,X1] :
( subset(X0,X1)
| ilf_type(sK11(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f159,plain,
! [X0,X1] :
( member(sK11(X0,X1),X0)
| subset(X0,X1) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158]) ).
fof(f158,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117]) ).
fof(f117,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK11(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f157,plain,
! [X0,X1] :
( ~ member(sK11(X0,X1),X1)
| subset(X0,X1) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156]) ).
fof(f156,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118]) ).
fof(f118,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK11(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f210,plain,
! [X0] :
( ~ member(sK12(X0,cross_product(sK5,sK6)),sK4)
| member(X0,power_set(cross_product(sK5,sK6))) ),
inference(resolution,[],[f166,f197]) ).
fof(f197,plain,
! [X0] :
( member(X0,cross_product(sK5,sK6))
| ~ member(X0,sK4) ),
inference(resolution,[],[f164,f93]) ).
fof(f265,plain,
! [X0,X1] :
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(resolution,[],[f264,f175]) ).
fof(f175,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174]) ).
fof(f174,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124]) ).
fof(f124,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,[],[f76]) ).
fof(f76,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,[],[f36]) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(f173,plain,
! [X3,X0,X1] :
( ~ member(X0,power_set(X1))
| ~ member(X3,X0)
| member(X3,X1) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172]) ).
fof(f172,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171]) ).
fof(f171,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119]) ).
fof(f119,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f170,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ilf_type(sK12(X0,X1),set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169]) ).
fof(f169,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ilf_type(sK12(X0,X1),set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120]) ).
fof(f120,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ilf_type(sK12(X0,X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f264,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f263,f191]) ).
fof(f191,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0) ),
inference(subsumption_resolution,[],[f147,f95]) ).
fof(f263,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f185,f95]) ).
fof(f185,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133,f180,f181,f182,f134,f135,f183,f184,f137]) ).
fof(f137,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,[],[f85]) ).
fof(f85,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,[],[f41]) ).
fof(f41,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,[],[f40]) ).
fof(f40,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/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(f184,plain,
! [X0,X1] : ilf_type(sK15(X0,X1),relation_type(X1,X0)),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133,f180,f181,f182,f134,f135,f183]) ).
fof(f183,plain,
! [X0,X1] :
( ilf_type(sK15(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133,f180,f181,f182,f134,f135]) ).
fof(f135,plain,
! [X0,X1] :
( ilf_type(sK15(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ilf_type(sK15(X0,X1),relation_type(X1,X0))
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f39,f83]) ).
fof(f83,plain,
! [X0,X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
=> ilf_type(sK15(X0,X1),relation_type(X1,X0)) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ? [X2] : ilf_type(X2,relation_type(X1,X0))
| ~ 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,relation_type(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f134,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,[],[f38]) ).
fof(f38,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,[],[f17]) ).
fof(f17,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',p17) ).
fof(f182,plain,
! [X2,X0,X1] : sP3(X0,X1,X2),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133,f180,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ ilf_type(X2,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133,f180]) ).
fof(f180,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178,f179,f131,f130,f129,f128,f127,f133]) ).
fof(f133,plain,
! [X2,X0,X1] :
( sP3(X0,X1,X2)
| ~ 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] :
( sP3(X0,X1,X2)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(definition_folding,[],[f37,f51,f50]) ).
fof(f50,plain,
! [X2,X1,X0] :
( sP2(X2,X1,X0)
<=> ? [X3] :
( ? [X4] :
( ordered_pair(X3,X4) = X2
& member(X4,X1)
& member(X3,X0)
& ilf_type(X4,set_type) )
& ilf_type(X3,set_type) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( member(X2,cross_product(X0,X1))
<=> sP2(X2,X1,X0) )
| ~ sP3(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X2,cross_product(X0,X1))
<=> ? [X3] :
( ? [X4] :
( ordered_pair(X3,X4) = X2
& member(X4,X1)
& member(X3,X0)
& ilf_type(X4,set_type) )
& 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)
=> ( member(X2,cross_product(X0,X1))
<=> ? [X3] :
( ? [X4] :
( ordered_pair(X3,X4) = X2
& member(X4,X1)
& member(X3,X0)
& ilf_type(X4,set_type) )
& ilf_type(X3,set_type) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f127,plain,
! [X2,X0,X1] :
( ilf_type(sK13(X0,X1,X2),set_type)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( ordered_pair(X3,X4) != X0
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ ilf_type(X4,set_type) )
| ~ ilf_type(X3,set_type) ) )
& ( ( ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)) = X0
& member(sK14(X0,X1,X2),X1)
& member(sK13(X0,X1,X2),X2)
& ilf_type(sK14(X0,X1,X2),set_type)
& ilf_type(sK13(X0,X1,X2),set_type) )
| ~ sP2(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f79,f81,f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X0
& member(X6,X1)
& member(X5,X2)
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
=> ( ? [X6] :
( ordered_pair(sK13(X0,X1,X2),X6) = X0
& member(X6,X1)
& member(sK13(X0,X1,X2),X2)
& ilf_type(X6,set_type) )
& ilf_type(sK13(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ? [X6] :
( ordered_pair(sK13(X0,X1,X2),X6) = X0
& member(X6,X1)
& member(sK13(X0,X1,X2),X2)
& ilf_type(X6,set_type) )
=> ( ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)) = X0
& member(sK14(X0,X1,X2),X1)
& member(sK13(X0,X1,X2),X2)
& ilf_type(sK14(X0,X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( sP2(X0,X1,X2)
| ! [X3] :
( ! [X4] :
( ordered_pair(X3,X4) != X0
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ ilf_type(X4,set_type) )
| ~ ilf_type(X3,set_type) ) )
& ( ? [X5] :
( ? [X6] :
( ordered_pair(X5,X6) = X0
& member(X6,X1)
& member(X5,X2)
& ilf_type(X6,set_type) )
& ilf_type(X5,set_type) )
| ~ sP2(X0,X1,X2) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X2,X1,X0] :
( ( sP2(X2,X1,X0)
| ! [X3] :
( ! [X4] :
( ordered_pair(X3,X4) != X2
| ~ member(X4,X1)
| ~ member(X3,X0)
| ~ ilf_type(X4,set_type) )
| ~ ilf_type(X3,set_type) ) )
& ( ? [X3] :
( ? [X4] :
( ordered_pair(X3,X4) = X2
& member(X4,X1)
& member(X3,X0)
& ilf_type(X4,set_type) )
& ilf_type(X3,set_type) )
| ~ sP2(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ilf_type(sK14(X0,X1,X2),set_type)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f129,plain,
! [X2,X0,X1] :
( member(sK13(X0,X1,X2),X2)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f130,plain,
! [X2,X0,X1] :
( member(sK14(X0,X1,X2),X1)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ordered_pair(sK13(X0,X1,X2),sK14(X0,X1,X2)) = X0
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f179,plain,
! [X2,X3,X1,X4] :
( sP2(ordered_pair(X3,X4),X1,X2)
| ~ member(X4,X1)
| ~ member(X3,X2) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141,f178]) ).
fof(f178,plain,
! [X2,X3,X1,X4] :
( sP2(ordered_pair(X3,X4),X1,X2)
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ ilf_type(X4,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176,f177,f126,f125,f141]) ).
fof(f141,plain,
! [X2,X3,X1,X4] :
( sP2(ordered_pair(X3,X4),X1,X2)
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ),
inference(equality_resolution,[],[f132]) ).
fof(f132,plain,
! [X2,X3,X0,X1,X4] :
( sP2(X0,X1,X2)
| ordered_pair(X3,X4) != X0
| ~ member(X4,X1)
| ~ member(X3,X2)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f125,plain,
! [X2,X0,X1] :
( sP2(X2,X1,X0)
| ~ member(X2,cross_product(X0,X1))
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ( ( member(X2,cross_product(X0,X1))
| ~ sP2(X2,X1,X0) )
& ( sP2(X2,X1,X0)
| ~ member(X2,cross_product(X0,X1)) ) )
| ~ sP3(X0,X1,X2) ),
inference(nnf_transformation,[],[f51]) ).
fof(f126,plain,
! [X2,X0,X1] :
( member(X2,cross_product(X0,X1))
| ~ sP2(X2,X1,X0)
| ~ sP3(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f177,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123,f176]) ).
fof(f176,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type) ),
inference(global_subsumption,[],[f94,f93,f92,f91,f90,f95,f98,f142,f97,f143,f99,f106,f105,f104,f103,f102,f101,f107,f144,f110,f145,f109,f146,f108,f147,f111,f148,f149,f112,f150,f151,f114,f152,f153,f113,f154,f155,f118,f156,f157,f117,f158,f159,f116,f160,f161,f115,f162,f163,f164,f122,f165,f166,f121,f167,f168,f120,f169,f170,f119,f171,f172,f173,f124,f174,f175,f123]) ).
fof(f123,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,[],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Apr 30 01:06:50 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % (1370)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (1371)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 % (1374)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (1373)WARNING: value z3 for option sas not known
% 0.13/0.39 % (1375)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)
% 0.13/0.39 % (1372)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.39 % (1373)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)
% 0.13/0.39 % (1376)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)
% 0.13/0.39 % (1377)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)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [1]
% 0.13/0.40 TRYING [2]
% 0.13/0.40 TRYING [2]
% 0.20/0.40 % (1373)First to succeed.
% 0.20/0.40 TRYING [3]
% 0.20/0.41 % (1373)Refutation found. Thanks to Tanya!
% 0.20/0.41 % SZS status Theorem for theBenchmark
% 0.20/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.41 % (1373)------------------------------
% 0.20/0.41 % (1373)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.41 % (1373)Termination reason: Refutation
% 0.20/0.41
% 0.20/0.41 % (1373)Memory used [KB]: 989
% 0.20/0.41 % (1373)Time elapsed: 0.025 s
% 0.20/0.41 % (1373)Instructions burned: 21 (million)
% 0.20/0.41 % (1373)------------------------------
% 0.20/0.41 % (1373)------------------------------
% 0.20/0.41 % (1370)Success in time 0.053 s
%------------------------------------------------------------------------------