TSTP Solution File: SET652+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET652+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 92.11s 13.19s
% Output : CNFRefutation 92.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f157)
% Comments :
%------------------------------------------------------------------------------
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(f6,axiom,
! [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',p6) ).
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/sandbox/benchmark/theBenchmark.p',p9) ).
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(f18,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',p18) ).
fof(f20,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',p20) ).
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(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,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X2,X0))
=> ( subset(range_of(X3),X1)
=> ilf_type(X3,relation_type(X2,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(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(f37,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,[],[f6]) ).
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,[],[f9]) ).
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(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(f49,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,[],[f18]) ).
fof(f50,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,[],[f49]) ).
fof(f52,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,[],[f20]) ).
fof(f53,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,[],[f52]) ).
fof(f58,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(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] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f63,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f70,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(f71,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,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0)
& ilf_type(sK2(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK2(X0,X1),X1)
& member(sK2(X0,X1),X0)
& ilf_type(sK2(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,[sK2])],[f71,f72]) ).
fof(f78,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(f81,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,[],[f50]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(f84,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f82,f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f53]) ).
fof(f94,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(f95,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,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK10(X0),X0)
& ilf_type(sK10(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f95,f96]) ).
fof(f98,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK11)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f99,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,X1))
& subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK11)) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK12))
& subset(range_of(X3),sK12)
& ilf_type(X3,relation_type(X2,sK11)) )
& ilf_type(X2,set_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(X3,relation_type(X2,sK12))
& subset(range_of(X3),sK12)
& ilf_type(X3,relation_type(X2,sK11)) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(X3,relation_type(sK13,sK12))
& subset(range_of(X3),sK12)
& ilf_type(X3,relation_type(sK13,sK11)) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X3] :
( ~ ilf_type(X3,relation_type(sK13,sK12))
& subset(range_of(X3),sK12)
& ilf_type(X3,relation_type(sK13,sK11)) )
=> ( ~ ilf_type(sK14,relation_type(sK13,sK12))
& subset(range_of(sK14),sK12)
& ilf_type(sK14,relation_type(sK13,sK11)) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK12))
& subset(range_of(sK14),sK12)
& ilf_type(sK14,relation_type(sK13,sK11))
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14])],[f63,f101,f100,f99,f98]) ).
fof(f104,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f32]) ).
fof(f105,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(f106,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(f107,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,[],[f35]) ).
fof(f109,plain,
! [X2,X0,X1] :
( subset(domain_of(X2),X0)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f115,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f73]) ).
fof(f127,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,[],[f78]) ).
fof(f132,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f133,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f137,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f85]) ).
fof(f145,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,[],[f58]) ).
fof(f146,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f97]) ).
fof(f150,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f154,plain,
ilf_type(sK14,relation_type(sK13,sK11)),
inference(cnf_transformation,[],[f102]) ).
fof(f155,plain,
subset(range_of(sK14),sK12),
inference(cnf_transformation,[],[f102]) ).
fof(f156,plain,
~ ilf_type(sK14,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f102]) ).
cnf(c_50,plain,
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f104]) ).
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,[],[f105]) ).
cnf(c_52,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,[],[f107]) ).
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,[],[f106]) ).
cnf(c_56,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(domain_of(X0),X1) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_64,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,[],[f115]) ).
cnf(c_68,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f157]) ).
cnf(c_71,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,[],[f127]) ).
cnf(c_75,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_76,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_81,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,[],[f137]) ).
cnf(c_90,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,[],[f145]) ).
cnf(c_93,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f146]) ).
cnf(c_95,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f150]) ).
cnf(c_96,negated_conjecture,
~ ilf_type(sK14,relation_type(sK13,sK12)),
inference(cnf_transformation,[],[f156]) ).
cnf(c_97,negated_conjecture,
subset(range_of(sK14),sK12),
inference(cnf_transformation,[],[f155]) ).
cnf(c_98,negated_conjecture,
ilf_type(sK14,relation_type(sK13,sK11)),
inference(cnf_transformation,[],[f154]) ).
cnf(c_185,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_68,c_95,c_68]) ).
cnf(c_233,plain,
( ~ ilf_type(X1,set_type)
| member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_76,c_95,c_76]) ).
cnf(c_234,plain,
( ~ ilf_type(X0,set_type)
| member(sK5(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(renaming,[status(thm)],[c_233]) ).
cnf(c_235,plain,
( member(sK5(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_234,c_95,c_234]) ).
cnf(c_236,plain,
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_235]) ).
cnf(c_246,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_71,c_95,c_71]) ).
cnf(c_250,plain,
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_75,c_95,c_75]) ).
cnf(c_252,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_81,c_95,c_93,c_81]) ).
cnf(c_253,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_252]) ).
cnf(c_270,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_64,c_95,c_64]) ).
cnf(c_271,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_270]) ).
cnf(c_276,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_95,c_51]) ).
cnf(c_277,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_276]) ).
cnf(c_282,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_253,c_95]) ).
cnf(c_283,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_90,c_95]) ).
cnf(c_286,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_271,c_95]) ).
cnf(c_289,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_277,c_95]) ).
cnf(c_291,plain,
( ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_250,c_95]) ).
cnf(c_292,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_246,c_95]) ).
cnf(c_294,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_52,c_95]) ).
cnf(c_295,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_95]) ).
cnf(c_296,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| subset(domain_of(X0),X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_56,c_95]) ).
cnf(c_392,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_283,c_95]) ).
cnf(c_414,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(domain_of(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_296,c_95]) ).
cnf(c_454,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_294,c_95]) ).
cnf(c_465,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_295,c_95]) ).
cnf(c_477,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_286,c_95]) ).
cnf(c_520,plain,
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_289,c_95,c_95]) ).
cnf(c_754,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_465]) ).
cnf(c_755,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_754]) ).
cnf(c_758,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_292]) ).
cnf(c_759,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_758]) ).
cnf(c_768,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(domain_of(X0),X1) ),
inference(prop_impl_just,[status(thm)],[c_414]) ).
cnf(c_770,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_392,c_454]) ).
cnf(c_774,plain,
( ~ relation_like(X0)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(prop_impl_just,[status(thm)],[c_50,c_185]) ).
cnf(c_782,plain,
( ~ member(sK5(X0,X1),X1)
| member(X0,power_set(X1)) ),
inference(prop_impl_just,[status(thm)],[c_291]) ).
cnf(c_786,plain,
( member(X0,power_set(X1))
| member(sK5(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_236]) ).
cnf(c_787,plain,
( member(sK5(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_786]) ).
cnf(c_788,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_282]) ).
cnf(c_1886,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK11))
| relation_like(sK14) ),
inference(instantiation,[status(thm)],[c_770]) ).
cnf(c_1894,plain,
( ~ ilf_type(sK14,relation_type(sK13,sK11))
| subset(domain_of(sK14),sK13) ),
inference(instantiation,[status(thm)],[c_768]) ).
cnf(c_1939,plain,
( ~ member(X0,power_set(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(instantiation,[status(thm)],[c_788]) ).
cnf(c_1953,plain,
( ~ relation_like(sK14)
| subset(sK14,cross_product(domain_of(sK14),range_of(sK14))) ),
inference(instantiation,[status(thm)],[c_774]) ).
cnf(c_1984,plain,
( ~ ilf_type(X0,member_type(power_set(cross_product(X1,X2))))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(instantiation,[status(thm)],[c_759]) ).
cnf(c_2259,plain,
( ~ member(X0,power_set(cross_product(X1,X2)))
| ilf_type(X0,member_type(power_set(cross_product(X1,X2)))) ),
inference(instantiation,[status(thm)],[c_1939]) ).
cnf(c_12438,plain,
( ~ ilf_type(sK14,subset_type(cross_product(sK13,sK12)))
| ilf_type(sK14,relation_type(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_755]) ).
cnf(c_12967,plain,
( ~ ilf_type(sK14,member_type(power_set(cross_product(sK13,sK12))))
| ilf_type(sK14,subset_type(cross_product(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_1984]) ).
cnf(c_20181,plain,
( ~ member(sK14,power_set(cross_product(sK13,sK12)))
| ilf_type(sK14,member_type(power_set(cross_product(sK13,sK12)))) ),
inference(instantiation,[status(thm)],[c_2259]) ).
cnf(c_52302,plain,
( member(sK5(X0,cross_product(X1,X2)),X0)
| member(X0,power_set(cross_product(X1,X2))) ),
inference(instantiation,[status(thm)],[c_787]) ).
cnf(c_52303,plain,
( ~ member(sK5(X0,cross_product(X1,X2)),cross_product(X1,X2))
| member(X0,power_set(cross_product(X1,X2))) ),
inference(instantiation,[status(thm)],[c_782]) ).
cnf(c_60194,plain,
( ~ member(sK5(sK14,X0),sK14)
| ~ subset(sK14,X1)
| member(sK5(sK14,X0),X1) ),
inference(instantiation,[status(thm)],[c_477]) ).
cnf(c_67793,plain,
( member(sK5(sK14,cross_product(sK13,sK12)),sK14)
| member(sK14,power_set(cross_product(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_52302]) ).
cnf(c_68006,plain,
( ~ subset(sK14,cross_product(domain_of(sK14),range_of(sK14)))
| ~ member(sK5(sK14,X0),sK14)
| member(sK5(sK14,X0),cross_product(domain_of(sK14),range_of(sK14))) ),
inference(instantiation,[status(thm)],[c_60194]) ).
cnf(c_78036,plain,
( ~ member(sK5(sK14,X0),cross_product(domain_of(sK14),range_of(sK14)))
| ~ subset(cross_product(domain_of(sK14),range_of(sK14)),X1)
| member(sK5(sK14,X0),X1) ),
inference(instantiation,[status(thm)],[c_477]) ).
cnf(c_87713,plain,
( ~ member(sK5(sK14,cross_product(sK13,sK12)),cross_product(sK13,sK12))
| member(sK14,power_set(cross_product(sK13,sK12))) ),
inference(instantiation,[status(thm)],[c_52303]) ).
cnf(c_89468,plain,
( ~ subset(domain_of(sK14),X0)
| ~ subset(range_of(sK14),X1)
| subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(X0,X1)) ),
inference(instantiation,[status(thm)],[c_520]) ).
cnf(c_99273,plain,
( ~ subset(sK14,cross_product(domain_of(sK14),range_of(sK14)))
| ~ member(sK5(sK14,cross_product(sK13,sK12)),sK14)
| member(sK5(sK14,cross_product(sK13,sK12)),cross_product(domain_of(sK14),range_of(sK14))) ),
inference(instantiation,[status(thm)],[c_68006]) ).
cnf(c_113043,plain,
( ~ member(sK5(sK14,cross_product(X0,X1)),cross_product(domain_of(sK14),range_of(sK14)))
| ~ subset(cross_product(domain_of(sK14),range_of(sK14)),X2)
| member(sK5(sK14,cross_product(X0,X1)),X2) ),
inference(instantiation,[status(thm)],[c_78036]) ).
cnf(c_118138,plain,
( ~ subset(range_of(sK14),X0)
| ~ subset(domain_of(sK14),sK13)
| subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,X0)) ),
inference(instantiation,[status(thm)],[c_89468]) ).
cnf(c_123815,plain,
( ~ subset(domain_of(sK14),sK13)
| ~ subset(range_of(sK14),sK12)
| subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_118138]) ).
cnf(c_130660,plain,
( ~ member(sK5(sK14,cross_product(X0,X1)),cross_product(domain_of(sK14),range_of(sK14)))
| ~ subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12))
| member(sK5(sK14,cross_product(X0,X1)),cross_product(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_113043]) ).
cnf(c_140087,plain,
( ~ member(sK5(sK14,cross_product(sK13,sK12)),cross_product(domain_of(sK14),range_of(sK14)))
| ~ subset(cross_product(domain_of(sK14),range_of(sK14)),cross_product(sK13,sK12))
| member(sK5(sK14,cross_product(sK13,sK12)),cross_product(sK13,sK12)) ),
inference(instantiation,[status(thm)],[c_130660]) ).
cnf(c_140088,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_140087,c_123815,c_99273,c_87713,c_67793,c_20181,c_12967,c_12438,c_1953,c_1894,c_1886,c_96,c_98,c_97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET652+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.11 % Command : run_iprover %s %d THM
% 0.11/0.31 % Computer : n011.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu May 2 20:32:03 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 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
% 92.11/13.19 % SZS status Started for theBenchmark.p
% 92.11/13.19 % SZS status Theorem for theBenchmark.p
% 92.11/13.19
% 92.11/13.19 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 92.11/13.19
% 92.11/13.19 ------ iProver source info
% 92.11/13.19
% 92.11/13.19 git: date: 2024-05-02 19:28:25 +0000
% 92.11/13.19 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 92.11/13.19 git: non_committed_changes: false
% 92.11/13.19
% 92.11/13.19 ------ Parsing...
% 92.11/13.19 ------ Clausification by vclausify_rel & Parsing by iProver...
% 92.11/13.19
% 92.11/13.19 ------ 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
% 92.11/13.19
% 92.11/13.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 92.11/13.19
% 92.11/13.19 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 92.11/13.19 ------ Proving...
% 92.11/13.19 ------ Problem Properties
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19 clauses 38
% 92.11/13.19 conjectures 3
% 92.11/13.19 EPR 9
% 92.11/13.19 Horn 32
% 92.11/13.19 unary 9
% 92.11/13.19 binary 21
% 92.11/13.19 lits 75
% 92.11/13.19 lits eq 2
% 92.11/13.19 fd_pure 0
% 92.11/13.19 fd_pseudo 0
% 92.11/13.19 fd_cond 0
% 92.11/13.19 fd_pseudo_cond 0
% 92.11/13.19 AC symbols 0
% 92.11/13.19
% 92.11/13.19 ------ Input Options Time Limit: Unbounded
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19 ------
% 92.11/13.19 Current options:
% 92.11/13.19 ------
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19 ------ Proving...
% 92.11/13.19
% 92.11/13.19
% 92.11/13.19 % SZS status Theorem for theBenchmark.p
% 92.11/13.19
% 92.11/13.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 92.11/13.19
% 92.11/13.20
%------------------------------------------------------------------------------