TSTP Solution File: SET657+3 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SET657+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.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 15:08:58 EDT 2023
% Result : Theorem 12.03s 2.67s
% Output : CNFRefutation 12.03s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f195)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(union(X0,X2),union(X1,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> field_of(X0) = union(domain_of(X0),range_of(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(f7,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',p7) ).
fof(f9,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',p9) ).
fof(f16,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',p16) ).
fof(f21,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',p21) ).
fof(f22,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',p22) ).
fof(f23,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',p23) ).
fof(f27,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',p27) ).
fof(f33,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> domain(X0,X1,X2) = domain_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p33) ).
fof(f34,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(domain(X0,X1,X2),subset_type(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p34) ).
fof(f35,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p35) ).
fof(f36,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p36) ).
fof(f37,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p37) ).
fof(f38,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> subset(field_of(X2),union(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_19) ).
fof(f39,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> subset(field_of(X2),union(X0,X1)) ) ) ),
inference(negated_conjecture,[],[f38]) ).
fof(f40,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,[],[f7]) ).
fof(f41,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(union(X0,X2),union(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,[],[f1]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( subset(union(X0,X2),union(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,[],[f41]) ).
fof(f46,plain,
! [X0] :
( field_of(X0) = union(domain_of(X0),range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,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,[],[f40]) ).
fof(f50,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,[],[f9]) ).
fof(f51,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,[],[f50]) ).
fof(f57,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,[],[f16]) ).
fof(f63,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,[],[f21]) ).
fof(f64,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,[],[f63]) ).
fof(f65,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f66,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,[],[f23]) ).
fof(f67,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,[],[f66]) ).
fof(f73,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,[],[f27]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f35]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f84,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(X0,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f39]) ).
fof(f89,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,[],[f51]) ).
fof(f90,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,[],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0)
& ilf_type(sK1(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK1(X0,X1),X1)
& member(sK1(X0,X1),X0)
& ilf_type(sK1(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,[sK1])],[f90,f91]) ).
fof(f97,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,[],[f57]) ).
fof(f100,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,[],[f64]) ).
fof(f101,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,[],[f100]) ).
fof(f102,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(f103,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f101,f102]) ).
fof(f104,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,[],[f67]) ).
fof(f122,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(X0,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(sK11,X1))
& ilf_type(X2,relation_type(sK11,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
( ? [X1] :
( ? [X2] :
( ~ subset(field_of(X2),union(sK11,X1))
& ilf_type(X2,relation_type(sK11,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ~ subset(field_of(X2),union(sK11,sK12))
& ilf_type(X2,relation_type(sK11,sK12)) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f124,plain,
( ? [X2] :
( ~ subset(field_of(X2),union(sK11,sK12))
& ilf_type(X2,relation_type(sK11,sK12)) )
=> ( ~ subset(field_of(sK13),union(sK11,sK12))
& ilf_type(sK13,relation_type(sK11,sK12)) ) ),
introduced(choice_axiom,[]) ).
fof(f125,plain,
( ~ subset(field_of(sK13),union(sK11,sK12))
& ilf_type(sK13,relation_type(sK11,sK12))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f84,f124,f123,f122]) ).
fof(f126,plain,
! [X2,X3,X0,X1] :
( subset(union(X0,X2),union(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,[],[f42]) ).
fof(f132,plain,
! [X0] :
( field_of(X0) = union(domain_of(X0),range_of(X0))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f46]) ).
fof(f135,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f48]) ).
fof(f139,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f140,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f149,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,[],[f97]) ).
fof(f155,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,[],[f103]) ).
fof(f159,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f161,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f104]) ).
fof(f175,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,[],[f73]) ).
fof(f183,plain,
! [X2,X0,X1] :
( domain(X0,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f184,plain,
! [X2,X0,X1] :
( ilf_type(domain(X0,X1,X2),subset_type(X0))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f185,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f82]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f187,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f37]) ).
fof(f190,plain,
ilf_type(sK13,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f125]) ).
fof(f191,plain,
~ subset(field_of(sK13),union(sK11,sK12)),
inference(cnf_transformation,[],[f125]) ).
cnf(c_49,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(union(X0,X2),union(X1,X3)) ),
inference(cnf_transformation,[],[f126]) ).
cnf(c_55,plain,
( ~ ilf_type(X0,binary_relation_type)
| union(domain_of(X0),range_of(X0)) = field_of(X0) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_57,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_60,plain,
( ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
cnf(c_61,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f139]) ).
cnf(c_68,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f195]) ).
cnf(c_72,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(cnf_transformation,[],[f149]) ).
cnf(c_79,plain,
( ~ member(X0,power_set(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,[],[f155]) ).
cnf(c_81,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_83,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_96,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_104,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(cnf_transformation,[],[f183]) ).
cnf(c_105,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_106,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(cnf_transformation,[],[f185]) ).
cnf(c_107,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(cnf_transformation,[],[f186]) ).
cnf(c_108,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f187]) ).
cnf(c_109,negated_conjecture,
~ subset(field_of(sK13),union(sK11,sK12)),
inference(cnf_transformation,[],[f191]) ).
cnf(c_110,negated_conjecture,
ilf_type(sK13,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f190]) ).
cnf(c_166,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_81,c_108,c_81]) ).
cnf(c_193,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_108,c_68]) ).
cnf(c_230,plain,
( ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_108,c_61]) ).
cnf(c_231,plain,
( ~ ilf_type(X0,set_type)
| member(sK1(X1,X0),X1)
| subset(X1,X0) ),
inference(renaming,[status(thm)],[c_230]) ).
cnf(c_232,plain,
( member(sK1(X1,X0),X1)
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_231,c_108,c_231]) ).
cnf(c_233,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_232]) ).
cnf(c_249,plain,
( ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_108,c_60]) ).
cnf(c_251,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_83,c_108,c_83]) ).
cnf(c_258,plain,
( ~ ilf_type(X0,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(power_set(X1))) ),
inference(global_subsumption_just,[status(thm)],[c_72,c_108,c_72]) ).
cnf(c_283,plain,
( ~ member(X2,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_79,c_108,c_79]) ).
cnf(c_284,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(renaming,[status(thm)],[c_283]) ).
cnf(c_287,plain,
( ~ subset(X2,X3)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(union(X0,X2),union(X1,X3)) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_108,c_49]) ).
cnf(c_288,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(union(X0,X2),union(X1,X3)) ),
inference(renaming,[status(thm)],[c_287]) ).
cnf(c_297,plain,
( ~ relation_like(X0)
| union(domain_of(X0),range_of(X0)) = field_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_55,c_193]) ).
cnf(c_447,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_284,c_108]) ).
cnf(c_449,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| range(X1,X2,X0) = range_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_106,c_108]) ).
cnf(c_460,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_258,c_108]) ).
cnf(c_461,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_249,c_108]) ).
cnf(c_463,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_108]) ).
cnf(c_465,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| domain(X1,X2,X0) = domain_of(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_104,c_108]) ).
cnf(c_466,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(union(X0,X2),union(X1,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_288,c_108]) ).
cnf(c_467,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X2,set_type)
| relation_like(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_108]) ).
cnf(c_469,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_57,c_108]) ).
cnf(c_470,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_105,c_108]) ).
cnf(c_471,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_107,c_108]) ).
cnf(c_584,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_467,c_108]) ).
cnf(c_635,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_469,c_108]) ).
cnf(c_646,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_470,c_108]) ).
cnf(c_657,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_471,c_108]) ).
cnf(c_668,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_449,c_108]) ).
cnf(c_679,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_465,c_108]) ).
cnf(c_705,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_447,c_108]) ).
cnf(c_765,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(union(X0,X2),union(X1,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_466,c_108,c_108]) ).
cnf(c_1217,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_460]) ).
cnf(c_1219,plain,
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_461]) ).
cnf(c_1220,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1219]) ).
cnf(c_1221,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_233]) ).
cnf(c_1222,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1221]) ).
cnf(c_1233,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_584,c_635]) ).
cnf(c_1235,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| domain(X1,X2,X0) = domain_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_679]) ).
cnf(c_1237,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(domain(X1,X2,X0),subset_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_646]) ).
cnf(c_1239,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| range(X1,X2,X0) = range_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_668]) ).
cnf(c_1241,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(prop_impl_just,[status(thm)],[c_657]) ).
cnf(c_1245,plain,
( ~ relation_like(X0)
| union(domain_of(X0),range_of(X0)) = field_of(X0) ),
inference(prop_impl_just,[status(thm)],[c_297]) ).
cnf(c_2872,plain,
relation_like(sK13),
inference(superposition,[status(thm)],[c_110,c_1233]) ).
cnf(c_2964,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1217,c_463]) ).
cnf(c_2965,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2964,c_166]) ).
cnf(c_3197,plain,
union(domain_of(sK13),range_of(sK13)) = field_of(sK13),
inference(superposition,[status(thm)],[c_2872,c_1245]) ).
cnf(c_3222,plain,
domain(sK11,sK12,sK13) = domain_of(sK13),
inference(superposition,[status(thm)],[c_110,c_1235]) ).
cnf(c_3228,plain,
( ~ ilf_type(sK13,relation_type(sK11,sK12))
| ilf_type(domain_of(sK13),subset_type(sK11)) ),
inference(superposition,[status(thm)],[c_3222,c_1237]) ).
cnf(c_3229,plain,
ilf_type(domain_of(sK13),subset_type(sK11)),
inference(forward_subsumption_resolution,[status(thm)],[c_3228,c_110]) ).
cnf(c_3230,plain,
member(domain_of(sK13),power_set(sK11)),
inference(superposition,[status(thm)],[c_3229,c_2965]) ).
cnf(c_3282,plain,
( ~ subset(domain_of(sK13),X0)
| ~ subset(range_of(sK13),X1)
| subset(field_of(sK13),union(X0,X1)) ),
inference(superposition,[status(thm)],[c_3197,c_765]) ).
cnf(c_3479,plain,
range(sK11,sK12,sK13) = range_of(sK13),
inference(superposition,[status(thm)],[c_110,c_1239]) ).
cnf(c_3624,plain,
( ~ ilf_type(sK13,relation_type(sK11,sK12))
| ilf_type(range_of(sK13),subset_type(sK12)) ),
inference(superposition,[status(thm)],[c_3479,c_1241]) ).
cnf(c_3625,plain,
ilf_type(range_of(sK13),subset_type(sK12)),
inference(forward_subsumption_resolution,[status(thm)],[c_3624,c_110]) ).
cnf(c_3626,plain,
member(range_of(sK13),power_set(sK12)),
inference(superposition,[status(thm)],[c_3625,c_2965]) ).
cnf(c_3828,plain,
( ~ member(X0,domain_of(sK13))
| member(X0,sK11) ),
inference(superposition,[status(thm)],[c_3230,c_705]) ).
cnf(c_3829,plain,
( ~ member(X0,range_of(sK13))
| member(X0,sK12) ),
inference(superposition,[status(thm)],[c_3626,c_705]) ).
cnf(c_4442,plain,
( ~ subset(domain_of(sK13),sK11)
| ~ subset(range_of(sK13),sK12) ),
inference(superposition,[status(thm)],[c_3282,c_109]) ).
cnf(c_5832,plain,
( member(sK1(domain_of(sK13),X0),sK11)
| subset(domain_of(sK13),X0) ),
inference(superposition,[status(thm)],[c_1222,c_3828]) ).
cnf(c_5893,plain,
( member(sK1(range_of(sK13),X0),sK12)
| subset(range_of(sK13),X0) ),
inference(superposition,[status(thm)],[c_1222,c_3829]) ).
cnf(c_51474,plain,
subset(domain_of(sK13),sK11),
inference(superposition,[status(thm)],[c_5832,c_1220]) ).
cnf(c_51486,plain,
~ subset(range_of(sK13),sK12),
inference(backward_subsumption_resolution,[status(thm)],[c_4442,c_51474]) ).
cnf(c_55076,plain,
subset(range_of(sK13),sK12),
inference(superposition,[status(thm)],[c_5893,c_1220]) ).
cnf(c_55083,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_55076,c_51486]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET657+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 12:08:31 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.03/2.67 % SZS status Started for theBenchmark.p
% 12.03/2.67 % SZS status Theorem for theBenchmark.p
% 12.03/2.67
% 12.03/2.67 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 12.03/2.67
% 12.03/2.67 ------ iProver source info
% 12.03/2.67
% 12.03/2.67 git: date: 2023-05-31 18:12:56 +0000
% 12.03/2.67 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 12.03/2.67 git: non_committed_changes: false
% 12.03/2.67 git: last_make_outside_of_git: false
% 12.03/2.67
% 12.03/2.67 ------ Parsing...
% 12.03/2.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 12.03/2.67
% 12.03/2.67 ------ 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
% 12.03/2.67
% 12.03/2.67 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 12.03/2.67
% 12.03/2.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 12.03/2.67 ------ Proving...
% 12.03/2.67 ------ Problem Properties
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67 clauses 44
% 12.03/2.67 conjectures 2
% 12.03/2.67 EPR 8
% 12.03/2.67 Horn 36
% 12.03/2.67 unary 9
% 12.03/2.67 binary 25
% 12.03/2.67 lits 89
% 12.03/2.67 lits eq 9
% 12.03/2.67 fd_pure 0
% 12.03/2.67 fd_pseudo 0
% 12.03/2.67 fd_cond 0
% 12.03/2.67 fd_pseudo_cond 2
% 12.03/2.67 AC symbols 0
% 12.03/2.67
% 12.03/2.67 ------ Schedule dynamic 5 is on
% 12.03/2.67
% 12.03/2.67 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67 ------
% 12.03/2.67 Current options:
% 12.03/2.67 ------
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67 ------ Proving...
% 12.03/2.67
% 12.03/2.67
% 12.03/2.67 % SZS status Theorem for theBenchmark.p
% 12.03/2.67
% 12.03/2.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.03/2.67
% 12.03/2.67
%------------------------------------------------------------------------------