TSTP Solution File: SET647+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET647+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 : Thu Aug 31 15:08:54 EDT 2023
% Result : Theorem 4.33s 1.19s
% Output : CNFRefutation 4.33s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f159)
% 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/sandbox2/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/sandbox2/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)
=> ( subset(X0,X1)
=> ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).
fof(f24,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',p24) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_9) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(domain_of(X1),X0)
=> ilf_type(X1,relation_type(X0,range_of(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] :
( ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) )
| ~ subset(X0,X1)
| ~ 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] :
( ( subset(cross_product(X2,X0),cross_product(X2,X1))
& subset(cross_product(X0,X2),cross_product(X1,X2)) )
| ~ subset(X0,X1)
| ~ 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(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] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_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] :
( ~ ilf_type(X1,relation_type(X0,range_of(X1)))
& subset(domain_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ~ ilf_type(X1,relation_type(sK12,range_of(X1)))
& subset(domain_of(X1),sK12)
& ilf_type(X1,binary_relation_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
( ? [X1] :
( ~ ilf_type(X1,relation_type(sK12,range_of(X1)))
& subset(domain_of(X1),sK12)
& ilf_type(X1,binary_relation_type) )
=> ( ~ ilf_type(sK13,relation_type(sK12,range_of(sK13)))
& subset(domain_of(sK13),sK12)
& ilf_type(sK13,binary_relation_type) ) ),
introduced(choice_axiom,[]) ).
fof(f104,plain,
( ~ ilf_type(sK13,relation_type(sK12,range_of(sK13)))
& subset(domain_of(sK13),sK12)
& ilf_type(sK13,binary_relation_type)
& ilf_type(sK12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f63,f103,f102]) ).
fof(f105,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(f106,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f32]) ).
fof(f107,plain,
! [X2,X0,X1] :
( subset(cross_product(X0,X2),cross_product(X1,X2))
| ~ subset(X0,X1)
| ~ 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(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(f156,plain,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f104]) ).
fof(f157,plain,
subset(domain_of(sK13),sK12),
inference(cnf_transformation,[],[f104]) ).
fof(f158,plain,
~ ilf_type(sK13,relation_type(sK12,range_of(sK13))),
inference(cnf_transformation,[],[f104]) ).
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,[],[f105]) ).
cnf(c_50,plain,
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_52,plain,
( ~ subset(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_54,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_64,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_65,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_70,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_73,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_84,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_85,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_90,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_95,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f150]) ).
cnf(c_97,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f154]) ).
cnf(c_98,negated_conjecture,
~ ilf_type(sK13,relation_type(sK12,range_of(sK13))),
inference(cnf_transformation,[],[f158]) ).
cnf(c_99,negated_conjecture,
subset(domain_of(sK13),sK12),
inference(cnf_transformation,[],[f157]) ).
cnf(c_100,negated_conjecture,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f156]) ).
cnf(c_170,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_97,c_65]) ).
cnf(c_173,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_64,c_97,c_64]) ).
cnf(c_209,plain,
( ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_97,c_85]) ).
cnf(c_210,plain,
( ~ ilf_type(X0,set_type)
| member(sK9(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(renaming,[status(thm)],[c_209]) ).
cnf(c_211,plain,
( member(sK9(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_210,c_97,c_210]) ).
cnf(c_212,plain,
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_211]) ).
cnf(c_218,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_97,c_95,c_90]) ).
cnf(c_219,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_218]) ).
cnf(c_221,plain,
( ~ member(sK9(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_84,c_97,c_84]) ).
cnf(c_225,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_73,c_97,c_73]) ).
cnf(c_251,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_70,c_97,c_70]) ).
cnf(c_252,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_251]) ).
cnf(c_253,plain,
( ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_97,c_52]) ).
cnf(c_257,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_97,c_49]) ).
cnf(c_258,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_257]) ).
cnf(c_269,plain,
( ~ relation_like(X0)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(prop_impl_just,[status(thm)],[c_50,c_173]) ).
cnf(c_403,plain,
( ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_97]) ).
cnf(c_404,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_252,c_97]) ).
cnf(c_406,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_97]) ).
cnf(c_410,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_54,c_97]) ).
cnf(c_415,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_219,c_97]) ).
cnf(c_417,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_225,c_97]) ).
cnf(c_419,plain,
( ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_221,c_97]) ).
cnf(c_558,plain,
( ~ subset(X0,X1)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_403,c_97]) ).
cnf(c_586,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_410,c_97]) ).
cnf(c_609,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_404,c_97]) ).
cnf(c_623,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X2)
| subset(X0,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_406,c_97]) ).
cnf(c_921,plain,
( relation_like(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_170]) ).
cnf(c_922,plain,
( ~ ilf_type(X0,binary_relation_type)
| relation_like(X0) ),
inference(renaming,[status(thm)],[c_921]) ).
cnf(c_925,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_586]) ).
cnf(c_926,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_925]) ).
cnf(c_929,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_417]) ).
cnf(c_930,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_929]) ).
cnf(c_935,plain,
( ~ subset(X0,X1)
| subset(cross_product(X0,X2),cross_product(X1,X2)) ),
inference(prop_impl_just,[status(thm)],[c_558]) ).
cnf(c_943,plain,
( ~ relation_like(X0)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(prop_impl_just,[status(thm)],[c_269]) ).
cnf(c_955,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_415]) ).
cnf(c_959,plain,
( ~ member(sK9(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_419]) ).
cnf(c_963,plain,
( member(X0,power_set(X1))
| member(sK9(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_212]) ).
cnf(c_964,plain,
( member(sK9(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_963]) ).
cnf(c_2297,plain,
( ~ ilf_type(sK13,subset_type(cross_product(sK12,range_of(sK13))))
| ilf_type(sK13,relation_type(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_926]) ).
cnf(c_2301,plain,
( ~ ilf_type(sK13,member_type(power_set(cross_product(sK12,range_of(sK13)))))
| ilf_type(sK13,subset_type(cross_product(sK12,range_of(sK13)))) ),
inference(instantiation,[status(thm)],[c_930]) ).
cnf(c_2308,plain,
( ~ member(sK13,power_set(cross_product(sK12,range_of(sK13))))
| ilf_type(sK13,member_type(power_set(cross_product(sK12,range_of(sK13))))) ),
inference(instantiation,[status(thm)],[c_955]) ).
cnf(c_2329,plain,
( ~ member(sK9(sK13,cross_product(sK12,range_of(sK13))),cross_product(sK12,range_of(sK13)))
| member(sK13,power_set(cross_product(sK12,range_of(sK13)))) ),
inference(instantiation,[status(thm)],[c_959]) ).
cnf(c_2330,plain,
( member(sK9(sK13,cross_product(sK12,range_of(sK13))),sK13)
| member(sK13,power_set(cross_product(sK12,range_of(sK13)))) ),
inference(instantiation,[status(thm)],[c_964]) ).
cnf(c_2491,plain,
( ~ subset(X0,cross_product(sK12,range_of(sK13)))
| ~ subset(X1,X0)
| subset(X1,cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_623]) ).
cnf(c_2678,plain,
relation_like(sK13),
inference(superposition,[status(thm)],[c_100,c_922]) ).
cnf(c_2817,plain,
( ~ subset(X0,sK12)
| subset(cross_product(X0,range_of(sK13)),cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_935]) ).
cnf(c_2966,plain,
( ~ subset(cross_product(X0,range_of(sK13)),cross_product(sK12,range_of(sK13)))
| ~ subset(X1,cross_product(X0,range_of(sK13)))
| subset(X1,cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_2491]) ).
cnf(c_3219,plain,
( ~ member(sK9(sK13,X0),X1)
| ~ subset(X1,X0)
| member(sK9(sK13,X0),X0) ),
inference(instantiation,[status(thm)],[c_609]) ).
cnf(c_3783,plain,
( ~ relation_like(sK13)
| subset(sK13,cross_product(domain_of(sK13),range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_943]) ).
cnf(c_3925,plain,
( ~ subset(domain_of(sK13),sK12)
| subset(cross_product(domain_of(sK13),range_of(sK13)),cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_2817]) ).
cnf(c_4315,plain,
( ~ subset(cross_product(domain_of(sK13),range_of(sK13)),cross_product(sK12,range_of(sK13)))
| ~ subset(sK13,cross_product(domain_of(sK13),range_of(sK13)))
| subset(sK13,cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_2966]) ).
cnf(c_5420,plain,
( ~ member(sK9(sK13,cross_product(sK12,range_of(sK13))),sK13)
| ~ subset(sK13,cross_product(sK12,range_of(sK13)))
| member(sK9(sK13,cross_product(sK12,range_of(sK13))),cross_product(sK12,range_of(sK13))) ),
inference(instantiation,[status(thm)],[c_3219]) ).
cnf(c_5421,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5420,c_4315,c_3925,c_3783,c_2678,c_2329,c_2330,c_2308,c_2301,c_2297,c_98,c_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET647+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n015.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 : Sat Aug 26 10:10:23 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.33/1.19 % SZS status Started for theBenchmark.p
% 4.33/1.19 % SZS status Theorem for theBenchmark.p
% 4.33/1.19
% 4.33/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 4.33/1.19
% 4.33/1.19 ------ iProver source info
% 4.33/1.19
% 4.33/1.19 git: date: 2023-05-31 18:12:56 +0000
% 4.33/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 4.33/1.19 git: non_committed_changes: false
% 4.33/1.19 git: last_make_outside_of_git: false
% 4.33/1.19
% 4.33/1.19 ------ Parsing...
% 4.33/1.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 4.33/1.19
% 4.33/1.19 ------ 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
% 4.33/1.19
% 4.33/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 4.33/1.19
% 4.33/1.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.33/1.19 ------ Proving...
% 4.33/1.19 ------ Problem Properties
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19 clauses 39
% 4.33/1.19 conjectures 3
% 4.33/1.19 EPR 10
% 4.33/1.19 Horn 33
% 4.33/1.19 unary 9
% 4.33/1.19 binary 21
% 4.33/1.19 lits 78
% 4.33/1.19 lits eq 2
% 4.33/1.19 fd_pure 0
% 4.33/1.19 fd_pseudo 0
% 4.33/1.19 fd_cond 0
% 4.33/1.19 fd_pseudo_cond 0
% 4.33/1.19 AC symbols 0
% 4.33/1.19
% 4.33/1.19 ------ Input Options Time Limit: Unbounded
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19 ------
% 4.33/1.19 Current options:
% 4.33/1.19 ------
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19 ------ Proving...
% 4.33/1.19
% 4.33/1.19
% 4.33/1.19 % SZS status Theorem for theBenchmark.p
% 4.33/1.19
% 4.33/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.33/1.19
% 4.33/1.19
%------------------------------------------------------------------------------