TSTP Solution File: SET649+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET649+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 : Fri May 3 03:01:07 EDT 2024
% Result : Theorem 7.46s 1.67s
% Output : CNFRefutation 7.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f3,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X2,X3)
& subset(X0,X1) )
=> subset(cross_product(X0,X2),cross_product(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ilf_type(X3,subset_type(cross_product(X0,X1))) )
& ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f10,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
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/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
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/sandbox/benchmark/theBenchmark.p',p20) ).
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/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f24,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
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/sandbox/benchmark/theBenchmark.p',prove_relset_1_11) ).
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(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(f30,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(f31,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,[],[f30]) ).
fof(f32,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f33,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(f34,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,[],[f33]) ).
fof(f35,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(f41,plain,
! [X0] :
( ( ilf_type(X0,binary_relation_type)
<=> ( ilf_type(X0,set_type)
& relation_like(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f10]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f46,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(f48,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f17]) ).
fof(f52,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(f53,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,[],[f52]) ).
fof(f55,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(f56,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,[],[f55]) ).
fof(f59,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f24]) ).
fof(f62,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(f63,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,[],[f62]) ).
fof(f74,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f41]) ).
fof(f75,plain,
! [X0] :
( ( ( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) )
& ( ( ilf_type(X0,set_type)
& relation_like(X0) )
| ~ ilf_type(X0,binary_relation_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f74]) ).
fof(f78,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,[],[f43]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0)
& ilf_type(sK4(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0)
& ilf_type(sK4(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,[sK4])],[f79,f80]) ).
fof(f82,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,[],[f46]) ).
fof(f91,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,[],[f53]) ).
fof(f92,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,[],[f91]) ).
fof(f93,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK9(X0,X1),X1)
& member(sK9(X0,X1),X0)
& ilf_type(sK9(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK9(X0,X1),X1)
& member(sK9(X0,X1),X0)
& ilf_type(sK9(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,[sK9])],[f92,f93]) ).
fof(f95,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,[],[f56]) ).
fof(f98,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,[],[f59]) ).
fof(f99,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,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK11(X0),X0)
& ilf_type(sK11(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK11(X0),X0)
& ilf_type(sK11(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,[sK11])],[f99,f100]) ).
fof(f102,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(sK12,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),sK12)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(sK12,X1))
& subset(range_of(X2),X1)
& subset(domain_of(X2),sK12)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ ilf_type(X2,relation_type(sK12,sK13))
& subset(range_of(X2),sK13)
& subset(domain_of(X2),sK12)
& ilf_type(X2,binary_relation_type) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( ? [X2] :
( ~ ilf_type(X2,relation_type(sK12,sK13))
& subset(range_of(X2),sK13)
& subset(domain_of(X2),sK12)
& ilf_type(X2,binary_relation_type) )
=> ( ~ ilf_type(sK14,relation_type(sK12,sK13))
& subset(range_of(sK14),sK13)
& subset(domain_of(sK14),sK12)
& ilf_type(sK14,binary_relation_type) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
( ~ ilf_type(sK14,relation_type(sK12,sK13))
& subset(range_of(sK14),sK13)
& subset(domain_of(sK14),sK12)
& ilf_type(sK14,binary_relation_type)
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f63,f104,f103,f102]) ).
fof(f106,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,[],[f31]) ).
fof(f107,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f32]) ).
fof(f108,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,[],[f34]) ).
fof(f109,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,[],[f35]) ).
fof(f120,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f75]) ).
fof(f124,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,[],[f81]) ).
fof(f131,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,[],[f82]) ).
fof(f133,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f48]) ).
fof(f143,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f144,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f148,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,[],[f95]) ).
fof(f150,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f101]) ).
fof(f154,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f157,plain,
ilf_type(sK14,binary_relation_type),
inference(cnf_transformation,[],[f105]) ).
fof(f158,plain,
subset(domain_of(sK14),sK12),
inference(cnf_transformation,[],[f105]) ).
fof(f159,plain,
subset(range_of(sK14),sK13),
inference(cnf_transformation,[],[f105]) ).
fof(f160,plain,
~ ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f105]) ).
cnf(c_49,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_50,plain,
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_51,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_53,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_63,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_64,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_69,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_72,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,subset_type(X1)) ),
inference(cnf_transformation,[],[f131]) ).
cnf(c_75,plain,
( ~ ilf_type(X0,set_type)
| subset(X0,X0) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_83,plain,
( ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f144]) ).
cnf(c_84,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f143]) ).
cnf(c_89,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf_transformation,[],[f148]) ).
cnf(c_94,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_96,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f154]) ).
cnf(c_97,negated_conjecture,
~ ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f160]) ).
cnf(c_98,negated_conjecture,
subset(range_of(sK14),sK13),
inference(cnf_transformation,[],[f159]) ).
cnf(c_99,negated_conjecture,
subset(domain_of(sK14),sK12),
inference(cnf_transformation,[],[f158]) ).
cnf(c_100,negated_conjecture,
ilf_type(sK14,binary_relation_type),
inference(cnf_transformation,[],[f157]) ).
cnf(c_144,plain,
subset(X0,X0),
inference(global_subsumption_just,[status(thm)],[c_75,c_96,c_75]) ).
cnf(c_171,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_96,c_64]) ).
cnf(c_174,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_63,c_96,c_63]) ).
cnf(c_210,plain,
( ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_96,c_84]) ).
cnf(c_211,plain,
( ~ ilf_type(X0,set_type)
| member(sK9(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(renaming,[status(thm)],[c_210]) ).
cnf(c_212,plain,
( member(sK9(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_211,c_96,c_211]) ).
cnf(c_213,plain,
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_212]) ).
cnf(c_219,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_89,c_96,c_94,c_89]) ).
cnf(c_220,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_219]) ).
cnf(c_222,plain,
( ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_96,c_83]) ).
cnf(c_226,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,subset_type(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_96,c_72]) ).
cnf(c_252,plain,
( ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_96,c_69]) ).
cnf(c_253,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(renaming,[status(thm)],[c_252]) ).
cnf(c_254,plain,
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_96,c_49]) ).
cnf(c_255,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ),
inference(renaming,[status(thm)],[c_254]) ).
cnf(c_258,plain,
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_51,c_96,c_51]) ).
cnf(c_259,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(renaming,[status(thm)],[c_258]) ).
cnf(c_268,plain,
( ~ relation_like(X0)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(prop_impl_just,[status(thm)],[c_50,c_174]) ).
cnf(c_404,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_259,c_96]) ).
cnf(c_405,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_96]) ).
cnf(c_407,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_255,c_96]) ).
cnf(c_411,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,relation_type(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_53,c_96]) ).
cnf(c_416,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_220,c_96]) ).
cnf(c_418,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_226,c_96]) ).
cnf(c_420,plain,
( ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_222,c_96]) ).
cnf(c_568,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_411,c_96]) ).
cnf(c_591,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_405,c_96]) ).
cnf(c_605,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_407,c_96]) ).
cnf(c_634,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_404,c_96,c_96]) ).
cnf(c_1053,plain,
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_171]) ).
cnf(c_1054,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(renaming,[status(thm)],[c_1053]) ).
cnf(c_1057,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_568]) ).
cnf(c_1058,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_1057]) ).
cnf(c_1061,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_418]) ).
cnf(c_1062,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_1061]) ).
cnf(c_1071,plain,
( ~ relation_like(X0)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(prop_impl_just,[status(thm)],[c_268]) ).
cnf(c_1083,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_416]) ).
cnf(c_1087,plain,
( ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_420]) ).
cnf(c_1091,plain,
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_213]) ).
cnf(c_1092,plain,
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_1091]) ).
cnf(c_1732,plain,
domain_of(sK14) = sP0_iProver_def,
definition ).
cnf(c_1733,plain,
range_of(sK14) = sP1_iProver_def,
definition ).
cnf(c_1734,plain,
relation_type(sK12,sK13) = sP2_iProver_def,
definition ).
cnf(c_1735,negated_conjecture,
ilf_type(sK14,binary_relation_type),
inference(demodulation,[status(thm)],[c_100]) ).
cnf(c_1736,negated_conjecture,
subset(sP0_iProver_def,sK12),
inference(demodulation,[status(thm)],[c_99,c_1732]) ).
cnf(c_1737,negated_conjecture,
subset(sP1_iProver_def,sK13),
inference(demodulation,[status(thm)],[c_98,c_1733]) ).
cnf(c_1738,negated_conjecture,
~ ilf_type(sK14,sP2_iProver_def),
inference(demodulation,[status(thm)],[c_97,c_1734]) ).
cnf(c_2593,plain,
relation_like(sK14),
inference(superposition,[status(thm)],[c_1735,c_1054]) ).
cnf(c_2625,plain,
( ~ subset(cross_product(X0,X1),X2)
| ~ subset(X3,X0)
| ~ subset(X4,X1)
| subset(cross_product(X3,X4),X2) ),
inference(superposition,[status(thm)],[c_634,c_605]) ).
cnf(c_2739,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ subset(X4,X0)
| ~ subset(X5,X2)
| subset(cross_product(X4,X5),cross_product(X1,X3)) ),
inference(superposition,[status(thm)],[c_634,c_2625]) ).
cnf(c_2756,plain,
( ~ relation_like(sK14)
| subset(sK14,cross_product(domain_of(sK14),sP1_iProver_def)) ),
inference(superposition,[status(thm)],[c_1733,c_1071]) ).
cnf(c_2761,plain,
( ~ relation_like(sK14)
| subset(sK14,cross_product(sP0_iProver_def,sP1_iProver_def)) ),
inference(light_normalisation,[status(thm)],[c_2756,c_1732]) ).
cnf(c_2762,plain,
subset(sK14,cross_product(sP0_iProver_def,sP1_iProver_def)),
inference(forward_subsumption_resolution,[status(thm)],[c_2761,c_2593]) ).
cnf(c_2792,plain,
( ~ subset(cross_product(sP0_iProver_def,sP1_iProver_def),X0)
| subset(sK14,X0) ),
inference(superposition,[status(thm)],[c_2762,c_605]) ).
cnf(c_2934,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X0)
| ~ subset(X3,sP0_iProver_def)
| subset(cross_product(X3,X2),cross_product(sK12,X1)) ),
inference(superposition,[status(thm)],[c_1736,c_2739]) ).
cnf(c_3123,plain,
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_1083,c_1062]) ).
cnf(c_3154,plain,
( ~ subset(X0,sP1_iProver_def)
| ~ subset(X1,sP0_iProver_def)
| subset(cross_product(X1,X0),cross_product(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_1737,c_2934]) ).
cnf(c_3304,plain,
( ~ subset(sP0_iProver_def,sP0_iProver_def)
| ~ subset(sP1_iProver_def,sP1_iProver_def)
| subset(sK14,cross_product(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_3154,c_2792]) ).
cnf(c_3307,plain,
subset(sK14,cross_product(sK12,sK13)),
inference(forward_subsumption_resolution,[status(thm)],[c_3304,c_144,c_144]) ).
cnf(c_4098,plain,
( ~ member(X0,sK14)
| member(X0,cross_product(sK12,sK13)) ),
inference(superposition,[status(thm)],[c_3307,c_591]) ).
cnf(c_20935,plain,
( ~ member(sK9(X0,cross_product(sK12,sK13)),sK14)
| member(X0,power_set(cross_product(sK12,sK13))) ),
inference(superposition,[status(thm)],[c_4098,c_1087]) ).
cnf(c_24243,plain,
member(sK14,power_set(cross_product(sK12,sK13))),
inference(superposition,[status(thm)],[c_1092,c_20935]) ).
cnf(c_24253,plain,
ilf_type(sK14,subset_type(cross_product(sK12,sK13))),
inference(superposition,[status(thm)],[c_24243,c_3123]) ).
cnf(c_29155,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(superposition,[status(thm)],[c_24253,c_1058]) ).
cnf(c_29157,plain,
ilf_type(sK14,sP2_iProver_def),
inference(light_normalisation,[status(thm)],[c_29155,c_1734]) ).
cnf(c_29158,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_29157,c_1738]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET649+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 2 20:36:03 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.46/1.67 % SZS status Started for theBenchmark.p
% 7.46/1.67 % SZS status Theorem for theBenchmark.p
% 7.46/1.67
% 7.46/1.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 7.46/1.67
% 7.46/1.67 ------ iProver source info
% 7.46/1.67
% 7.46/1.67 git: date: 2024-05-02 19:28:25 +0000
% 7.46/1.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 7.46/1.67 git: non_committed_changes: false
% 7.46/1.67
% 7.46/1.67 ------ Parsing...
% 7.46/1.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 7.46/1.67
% 7.46/1.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 7.46/1.67
% 7.46/1.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 7.46/1.67
% 7.46/1.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.46/1.67 ------ Proving...
% 7.46/1.67 ------ Problem Properties
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67 clauses 42
% 7.46/1.67 conjectures 4
% 7.46/1.67 EPR 13
% 7.46/1.67 Horn 36
% 7.46/1.67 unary 13
% 7.46/1.67 binary 19
% 7.46/1.67 lits 81
% 7.46/1.67 lits eq 5
% 7.46/1.67 fd_pure 0
% 7.46/1.67 fd_pseudo 0
% 7.46/1.67 fd_cond 0
% 7.46/1.67 fd_pseudo_cond 0
% 7.46/1.67 AC symbols 0
% 7.46/1.67
% 7.46/1.67 ------ Schedule dynamic 5 is on
% 7.46/1.67
% 7.46/1.67 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67 ------
% 7.46/1.67 Current options:
% 7.46/1.67 ------
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67 ------ Proving...
% 7.46/1.67
% 7.46/1.67
% 7.46/1.67 % SZS status Theorem for theBenchmark.p
% 7.46/1.67
% 7.46/1.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.46/1.68
% 7.46/1.68
%------------------------------------------------------------------------------