TSTP Solution File: SET650+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 0.46s 1.16s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f170)
% Comments :
%------------------------------------------------------------------------------
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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,domain_of(X0))
<=> ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X1,range_of(X0))
<=> ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(f8,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',p8) ).
fof(f10,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',p10) ).
fof(f23,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/sandbox/benchmark/theBenchmark.p',p23) ).
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,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
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,[],[f8]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(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(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ( member(X3,X1)
& member(X2,X0) )
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(X0,X1)) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0] :
( ! [X1] :
( ( member(X1,domain_of(X0))
<=> ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( ( member(X1,range_of(X0))
<=> ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f38,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(f40,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,[],[f10]) ).
fof(f41,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,[],[f40]) ).
fof(f57,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,[],[f23]) ).
fof(f61,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X1,X2),X0)
& ilf_type(X2,set_type) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f34]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X1,X3),X0)
& ilf_type(X3,set_type) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X1,X3),X0)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(X1,sK2(X0,X1)),X0)
& ilf_type(sK2(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,domain_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X1,X2),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(X1,sK2(X0,X1)),X0)
& ilf_type(sK2(X0,X1),set_type) )
| ~ member(X1,domain_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f71,f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X2] :
( member(ordered_pair(X2,X1),X0)
& ilf_type(X2,set_type) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(nnf_transformation,[],[f36]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ? [X3] :
( member(ordered_pair(X3,X1),X0)
& ilf_type(X3,set_type) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( ? [X3] :
( member(ordered_pair(X3,X1),X0)
& ilf_type(X3,set_type) )
=> ( member(ordered_pair(sK3(X0,X1),X1),X0)
& ilf_type(sK3(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
! [X0] :
( ! [X1] :
( ( ( member(X1,range_of(X0))
| ! [X2] :
( ~ member(ordered_pair(X2,X1),X0)
| ~ ilf_type(X2,set_type) ) )
& ( ( member(ordered_pair(sK3(X0,X1),X1),X0)
& ilf_type(sK3(X0,X1),set_type) )
| ~ member(X1,range_of(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f75,f76]) ).
fof(f80,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,[],[f41]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0)
& ilf_type(sK5(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,[sK5])],[f81,f82]) ).
fof(f108,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),X0) )
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),sK14) )
& ilf_type(X2,relation_type(sK14,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK14,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
( ? [X1] :
( ? [X2] :
( ( ~ subset(range_of(X2),X1)
| ~ subset(domain_of(X2),sK14) )
& ilf_type(X2,relation_type(sK14,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( ~ subset(range_of(X2),sK15)
| ~ subset(domain_of(X2),sK14) )
& ilf_type(X2,relation_type(sK14,sK15)) )
& ilf_type(sK15,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f110,plain,
( ? [X2] :
( ( ~ subset(range_of(X2),sK15)
| ~ subset(domain_of(X2),sK14) )
& ilf_type(X2,relation_type(sK14,sK15)) )
=> ( ( ~ subset(range_of(sK16),sK15)
| ~ subset(domain_of(sK16),sK14) )
& ilf_type(sK16,relation_type(sK14,sK15)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
( ( ~ subset(range_of(sK16),sK15)
| ~ subset(domain_of(sK16),sK14) )
& ilf_type(sK16,relation_type(sK14,sK15))
& ilf_type(sK15,set_type)
& ilf_type(sK14,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15,sK16])],[f61,f110,f109,f108]) ).
fof(f118,plain,
! [X2,X3,X0,X1,X4] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(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,[],[f33]) ).
fof(f119,plain,
! [X2,X3,X0,X1,X4] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X4,relation_type(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,[],[f33]) ).
fof(f121,plain,
! [X0,X1] :
( member(ordered_pair(X1,sK2(X0,X1)),X0)
| ~ member(X1,domain_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f125,plain,
! [X0,X1] :
( member(ordered_pair(sK3(X0,X1),X1),X0)
| ~ member(X1,range_of(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f77]) ).
fof(f129,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,[],[f38]) ).
fof(f133,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f160,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,[],[f57]) ).
fof(f165,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f168,plain,
ilf_type(sK16,relation_type(sK14,sK15)),
inference(cnf_transformation,[],[f111]) ).
fof(f169,plain,
( ~ subset(range_of(sK16),sK15)
| ~ subset(domain_of(sK16),sK14) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_55,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_56,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_58,plain,
( ~ member(X0,domain_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK2(X1,X0)),X1) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_62,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK3(X1,X0),X0),X1) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_65,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,[],[f129]) ).
cnf(c_68,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_69,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_74,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f170]) ).
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,[],[f160]) ).
cnf(c_101,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f165]) ).
cnf(c_102,negated_conjecture,
( ~ subset(domain_of(sK16),sK14)
| ~ subset(range_of(sK16),sK15) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_103,negated_conjecture,
ilf_type(sK16,relation_type(sK14,sK15)),
inference(cnf_transformation,[],[f168]) ).
cnf(c_180,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_74,c_101,c_74]) ).
cnf(c_207,plain,
( ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_101,c_69]) ).
cnf(c_208,plain,
( ~ ilf_type(X0,set_type)
| member(sK5(X1,X0),X1)
| subset(X1,X0) ),
inference(renaming,[status(thm)],[c_207]) ).
cnf(c_209,plain,
( member(sK5(X1,X0),X1)
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_208,c_101,c_208]) ).
cnf(c_210,plain,
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_209]) ).
cnf(c_221,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_101,c_68]) ).
cnf(c_250,plain,
( ~ member(X0,range_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(sK3(X1,X0),X0),X1) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_101,c_62]) ).
cnf(c_253,plain,
( ~ member(X0,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type)
| member(ordered_pair(X0,sK2(X1,X0)),X1) ),
inference(global_subsumption_just,[status(thm)],[c_58,c_101,c_58]) ).
cnf(c_278,plain,
( ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(global_subsumption_just,[status(thm)],[c_56,c_101,c_56]) ).
cnf(c_279,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(renaming,[status(thm)],[c_278]) ).
cnf(c_280,plain,
( ~ ilf_type(X2,relation_type(X3,X4))
| ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(global_subsumption_just,[status(thm)],[c_55,c_101,c_55]) ).
cnf(c_281,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(renaming,[status(thm)],[c_280]) ).
cnf(c_430,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X1,X4) ),
inference(backward_subsumption_resolution,[status(thm)],[c_281,c_101]) ).
cnf(c_431,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| member(X0,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[c_279,c_101]) ).
cnf(c_437,plain,
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_221,c_101]) ).
cnf(c_443,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_101]) ).
cnf(c_445,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_65,c_101]) ).
cnf(c_534,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_443,c_101]) ).
cnf(c_609,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_445,c_101]) ).
cnf(c_650,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X1,X4) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430,c_101,c_101]) ).
cnf(c_666,plain,
( ~ member(ordered_pair(X0,X1),X2)
| ~ ilf_type(X2,relation_type(X3,X4))
| member(X0,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_431,c_101,c_101]) ).
cnf(c_897,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_180]) ).
cnf(c_907,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_534,c_609]) ).
cnf(c_909,plain,
( ~ member(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_437]) ).
cnf(c_913,plain,
( subset(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_210]) ).
cnf(c_914,plain,
( member(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_913]) ).
cnf(c_2352,plain,
( ~ ilf_type(sK16,relation_type(sK14,sK15))
| relation_like(sK16) ),
inference(instantiation,[status(thm)],[c_907]) ).
cnf(c_3512,plain,
( ~ relation_like(sK16)
| ilf_type(sK16,binary_relation_type) ),
inference(instantiation,[status(thm)],[c_897]) ).
cnf(c_4400,plain,
( ~ member(ordered_pair(X0,X1),sK16)
| member(X1,sK15) ),
inference(resolution,[status(thm)],[c_650,c_103]) ).
cnf(c_4495,plain,
( ~ member(ordered_pair(X0,X1),sK16)
| member(X0,sK14) ),
inference(resolution,[status(thm)],[c_666,c_103]) ).
cnf(c_4645,plain,
( ~ member(X0,range_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| member(X0,sK15) ),
inference(resolution,[status(thm)],[c_4400,c_250]) ).
cnf(c_4960,plain,
( ~ member(X0,range_of(sK16))
| member(X0,sK15) ),
inference(global_subsumption_just,[status(thm)],[c_4645,c_103,c_2352,c_3512,c_4645]) ).
cnf(c_4984,plain,
( member(sK5(range_of(sK16),X0),sK15)
| subset(range_of(sK16),X0) ),
inference(resolution,[status(thm)],[c_4960,c_914]) ).
cnf(c_5306,plain,
( ~ member(X0,domain_of(sK16))
| ~ ilf_type(sK16,binary_relation_type)
| member(X0,sK14) ),
inference(resolution,[status(thm)],[c_253,c_4495]) ).
cnf(c_5661,plain,
( ~ member(X0,domain_of(sK16))
| member(X0,sK14) ),
inference(global_subsumption_just,[status(thm)],[c_5306,c_103,c_2352,c_3512,c_5306]) ).
cnf(c_5678,plain,
( member(sK5(domain_of(sK16),X0),sK14)
| subset(domain_of(sK16),X0) ),
inference(resolution,[status(thm)],[c_5661,c_914]) ).
cnf(c_5812,plain,
subset(range_of(sK16),sK15),
inference(resolution,[status(thm)],[c_4984,c_909]) ).
cnf(c_5878,plain,
subset(domain_of(sK16),sK14),
inference(resolution,[status(thm)],[c_5678,c_909]) ).
cnf(c_5879,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_5878,c_5812,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.13 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 20:41:13 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 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
% 0.46/1.16 % SZS status Started for theBenchmark.p
% 0.46/1.16 % SZS status Theorem for theBenchmark.p
% 0.46/1.16
% 0.46/1.16 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.46/1.16
% 0.46/1.16 ------ iProver source info
% 0.46/1.16
% 0.46/1.16 git: date: 2024-05-02 19:28:25 +0000
% 0.46/1.16 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.46/1.16 git: non_committed_changes: false
% 0.46/1.16
% 0.46/1.16 ------ Parsing...
% 0.46/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.46/1.16
% 0.46/1.16 ------ 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
% 0.46/1.16
% 0.46/1.16 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.46/1.16
% 0.46/1.16 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.46/1.16 ------ Proving...
% 0.46/1.16 ------ Problem Properties
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 clauses 38
% 0.46/1.16 conjectures 2
% 0.46/1.16 EPR 8
% 0.46/1.16 Horn 32
% 0.46/1.16 unary 7
% 0.46/1.16 binary 19
% 0.46/1.16 lits 81
% 0.46/1.16 lits eq 2
% 0.46/1.16 fd_pure 0
% 0.46/1.16 fd_pseudo 0
% 0.46/1.16 fd_cond 0
% 0.46/1.16 fd_pseudo_cond 0
% 0.46/1.16 AC symbols 0
% 0.46/1.16
% 0.46/1.16 ------ Input Options Time Limit: Unbounded
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 ------
% 0.46/1.16 Current options:
% 0.46/1.16 ------
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 ------ Proving...
% 0.46/1.16
% 0.46/1.16
% 0.46/1.16 % SZS status Theorem for theBenchmark.p
% 0.46/1.16
% 0.46/1.16 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.46/1.16
% 0.46/1.16
%------------------------------------------------------------------------------