TSTP Solution File: SET669+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET669+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 03:01:11 EDT 2024
% Result : Theorem 0.45s 1.13s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named definition)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ( subset(X1,X0)
& subset(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f7,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',p7) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,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(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(f21,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',p21) ).
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(f31,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',p31) ).
fof(f32,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p32) ).
fof(f33,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_32) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f36,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f44,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,[],[f7]) ).
fof(f45,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,[],[f44]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,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(f58,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(f59,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,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f61,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(f62,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,[],[f61]) ).
fof(f74,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,[],[f31]) ).
fof(f75,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f76,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f75]) ).
fof(f81,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,[],[f45]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(f84,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])],[f82,f83]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f48]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( ( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| X0 != X1 ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f90]) ).
fof(f96,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,[],[f54]) ).
fof(f99,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,[],[f59]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK6(X0,X1),X1)
& member(sK6(X0,X1),X0)
& ilf_type(sK6(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,[sK6])],[f100,f101]) ).
fof(f103,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,[],[f62]) ).
fof(f116,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ( range(sK12,X1,X2) != X1
| ~ subset(X1,domain(sK12,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(sK12,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f117,plain,
( ? [X1] :
( ? [X2] :
( ( range(sK12,X1,X2) != X1
| ~ subset(X1,domain(sK12,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(sK12,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ( sK13 != range(sK12,sK13,X2)
| ~ subset(sK13,domain(sK12,sK13,X2)) )
& subset(identity_relation_of(sK13),X2)
& ilf_type(X2,relation_type(sK12,sK13)) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
( ? [X2] :
( ( sK13 != range(sK12,sK13,X2)
| ~ subset(sK13,domain(sK12,sK13,X2)) )
& subset(identity_relation_of(sK13),X2)
& ilf_type(X2,relation_type(sK12,sK13)) )
=> ( ( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) )
& subset(identity_relation_of(sK13),sK14)
& ilf_type(sK14,relation_type(sK12,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( ( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) )
& subset(identity_relation_of(sK13),sK14)
& ilf_type(sK14,relation_type(sK12,sK13))
& ilf_type(sK13,set_type)
& ilf_type(sK12,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13,sK14])],[f76,f118,f117,f116]) ).
fof(f120,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f37]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( subset(X2,domain(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f122,plain,
! [X2,X3,X0,X1] :
( subset(X2,range(X0,X1,X3))
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f132,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK1(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f133,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f84]) ).
fof(f141,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f91]) ).
fof(f150,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,[],[f96]) ).
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,[],[f102]) ).
fof(f159,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f60]) ).
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,[],[f103]) ).
fof(f178,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,[],[f74]) ).
fof(f179,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f182,plain,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f119]) ).
fof(f183,plain,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f119]) ).
fof(f184,plain,
( sK13 != range(sK12,sK13,sK14)
| ~ subset(sK13,domain(sK12,sK13,sK14)) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_49,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(X3,range(X1,X2,X0)) ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_51,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(X3,domain(X1,X2,X0)) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_59,plain,
( ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_60,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_68,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(cnf_transformation,[],[f141]) ).
cnf(c_79,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,[],[f150]) ).
cnf(c_86,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_88,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_90,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_106,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,[],[f178]) ).
cnf(c_107,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f179]) ).
cnf(c_108,negated_conjecture,
( range(sK12,sK13,sK14) != sK13
| ~ subset(sK13,domain(sK12,sK13,sK14)) ),
inference(cnf_transformation,[],[f184]) ).
cnf(c_109,negated_conjecture,
subset(identity_relation_of(sK13),sK14),
inference(cnf_transformation,[],[f183]) ).
cnf(c_110,negated_conjecture,
ilf_type(sK14,relation_type(sK12,sK13)),
inference(cnf_transformation,[],[f182]) ).
cnf(c_167,plain,
~ empty(power_set(X0)),
inference(global_subsumption_just,[status(thm)],[c_88,c_107,c_88]) ).
cnf(c_224,plain,
( ~ ilf_type(X1,set_type)
| member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_60,c_107,c_60]) ).
cnf(c_225,plain,
( ~ ilf_type(X0,set_type)
| member(sK1(X1,X0),X1)
| subset(X1,X0) ),
inference(renaming,[status(thm)],[c_224]) ).
cnf(c_226,plain,
( member(sK1(X1,X0),X1)
| subset(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_225,c_107,c_225]) ).
cnf(c_227,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_226]) ).
cnf(c_238,plain,
( ~ member(sK1(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| subset(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_107,c_59]) ).
cnf(c_240,plain,
( ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| empty(X1) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_107,c_90]) ).
cnf(c_247,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_79,c_107,c_79]) ).
cnf(c_259,plain,
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_49,c_107,c_68]) ).
cnf(c_260,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| ~ ilf_type(X1,set_type)
| X0 = X1 ),
inference(renaming,[status(thm)],[c_259]) ).
cnf(c_271,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_86,c_107,c_86]) ).
cnf(c_272,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_271]) ).
cnf(c_429,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_106,c_107]) ).
cnf(c_434,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[c_260,c_107]) ).
cnf(c_435,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_272,c_107]) ).
cnf(c_437,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_238,c_107]) ).
cnf(c_439,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(X3,domain(X1,X2,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_51,c_107]) ).
cnf(c_448,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| subset(X3,range(X1,X2,X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_50,c_107]) ).
cnf(c_450,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[c_247,c_107]) ).
cnf(c_453,plain,
( ~ ilf_type(X0,member_type(X1))
| member(X0,X1)
| empty(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_240,c_107]) ).
cnf(c_628,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_429,c_107]) ).
cnf(c_687,plain,
( ~ member(X0,power_set(X1))
| ~ member(X2,X0)
| member(X2,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_435,c_107]) ).
cnf(c_718,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| subset(X3,domain(X1,X2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_439,c_107,c_107]) ).
cnf(c_734,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ subset(identity_relation_of(X3),X0)
| subset(X3,range(X1,X2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_448,c_107,c_107]) ).
cnf(c_1310,plain,
( ~ ilf_type(X0,subset_type(X1))
| ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_450]) ).
cnf(c_1312,plain,
( subset(X0,X1)
| ~ member(sK1(X0,X1),X1) ),
inference(prop_impl_just,[status(thm)],[c_437]) ).
cnf(c_1313,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1312]) ).
cnf(c_1314,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_227]) ).
cnf(c_1315,plain,
( member(sK1(X0,X1),X0)
| subset(X0,X1) ),
inference(renaming,[status(thm)],[c_1314]) ).
cnf(c_1324,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(range(X1,X2,X0),subset_type(X2)) ),
inference(prop_impl_just,[status(thm)],[c_628]) ).
cnf(c_1908,plain,
relation_type(sK12,sK13) = sP0_iProver_def,
definition ).
cnf(c_1909,plain,
identity_relation_of(sK13) = sP1_iProver_def,
definition ).
cnf(c_1910,plain,
range(sK12,sK13,sK14) = sP2_iProver_def,
definition ).
cnf(c_1911,plain,
domain(sK12,sK13,sK14) = sP3_iProver_def,
definition ).
cnf(c_1912,negated_conjecture,
ilf_type(sK14,sP0_iProver_def),
inference(demodulation,[status(thm)],[c_110,c_1908]) ).
cnf(c_1913,negated_conjecture,
subset(sP1_iProver_def,sK14),
inference(demodulation,[status(thm)],[c_109,c_1909]) ).
cnf(c_1914,negated_conjecture,
( sP2_iProver_def != sK13
| ~ subset(sK13,sP3_iProver_def) ),
inference(demodulation,[status(thm)],[c_108,c_1911,c_1910]) ).
cnf(c_2934,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1))
| empty(power_set(X1)) ),
inference(superposition,[status(thm)],[c_1310,c_453]) ).
cnf(c_2935,plain,
( ~ ilf_type(X0,subset_type(X1))
| member(X0,power_set(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2934,c_167]) ).
cnf(c_3130,plain,
( ~ ilf_type(sK14,relation_type(sK12,sK13))
| ~ subset(identity_relation_of(X0),sK14)
| subset(X0,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_1911,c_718]) ).
cnf(c_3132,plain,
( ~ subset(identity_relation_of(X0),sK14)
| ~ ilf_type(sK14,sP0_iProver_def)
| subset(X0,sP3_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_3130,c_1908]) ).
cnf(c_3133,plain,
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,sP3_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3132,c_1912]) ).
cnf(c_3173,plain,
( ~ ilf_type(sK14,relation_type(sK12,sK13))
| ilf_type(sP2_iProver_def,subset_type(sK13)) ),
inference(superposition,[status(thm)],[c_1910,c_1324]) ).
cnf(c_3175,plain,
( ~ ilf_type(sK14,sP0_iProver_def)
| ilf_type(sP2_iProver_def,subset_type(sK13)) ),
inference(light_normalisation,[status(thm)],[c_3173,c_1908]) ).
cnf(c_3176,plain,
ilf_type(sP2_iProver_def,subset_type(sK13)),
inference(forward_subsumption_resolution,[status(thm)],[c_3175,c_1912]) ).
cnf(c_3181,plain,
member(sP2_iProver_def,power_set(sK13)),
inference(superposition,[status(thm)],[c_3176,c_2935]) ).
cnf(c_3191,plain,
( ~ subset(sP1_iProver_def,sK14)
| subset(sK13,sP3_iProver_def) ),
inference(superposition,[status(thm)],[c_1909,c_3133]) ).
cnf(c_3192,plain,
subset(sK13,sP3_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_3191,c_1913]) ).
cnf(c_3195,plain,
sK13 != sP2_iProver_def,
inference(backward_subsumption_resolution,[status(thm)],[c_1914,c_3192]) ).
cnf(c_3240,plain,
( ~ ilf_type(sK14,relation_type(sK12,sK13))
| ~ subset(identity_relation_of(X0),sK14)
| subset(X0,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_1910,c_734]) ).
cnf(c_3242,plain,
( ~ subset(identity_relation_of(X0),sK14)
| ~ ilf_type(sK14,sP0_iProver_def)
| subset(X0,sP2_iProver_def) ),
inference(light_normalisation,[status(thm)],[c_3240,c_1908]) ).
cnf(c_3243,plain,
( ~ subset(identity_relation_of(X0),sK14)
| subset(X0,sP2_iProver_def) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3242,c_1912]) ).
cnf(c_3347,plain,
( ~ subset(sP1_iProver_def,sK14)
| subset(sK13,sP2_iProver_def) ),
inference(superposition,[status(thm)],[c_1909,c_3243]) ).
cnf(c_3348,plain,
subset(sK13,sP2_iProver_def),
inference(forward_subsumption_resolution,[status(thm)],[c_3347,c_1913]) ).
cnf(c_3356,plain,
( ~ subset(sP2_iProver_def,sK13)
| sK13 = sP2_iProver_def ),
inference(superposition,[status(thm)],[c_3348,c_434]) ).
cnf(c_3357,plain,
~ subset(sP2_iProver_def,sK13),
inference(forward_subsumption_resolution,[status(thm)],[c_3356,c_3195]) ).
cnf(c_4214,plain,
( ~ member(X0,sP2_iProver_def)
| member(X0,sK13) ),
inference(superposition,[status(thm)],[c_3181,c_687]) ).
cnf(c_4383,plain,
( member(sK1(sP2_iProver_def,X0),sK13)
| subset(sP2_iProver_def,X0) ),
inference(superposition,[status(thm)],[c_1315,c_4214]) ).
cnf(c_5348,plain,
subset(sP2_iProver_def,sK13),
inference(superposition,[status(thm)],[c_4383,c_1313]) ).
cnf(c_5351,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5348,c_3357]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11 % Command : run_iprover %s %d THM
% 0.12/0.32 % Computer : n008.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu May 2 20:28:27 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.45/1.13 % SZS status Started for theBenchmark.p
% 0.45/1.13 % SZS status Theorem for theBenchmark.p
% 0.45/1.13
% 0.45/1.13 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 0.45/1.13
% 0.45/1.13 ------ iProver source info
% 0.45/1.13
% 0.45/1.13 git: date: 2024-05-02 19:28:25 +0000
% 0.45/1.13 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 0.45/1.13 git: non_committed_changes: false
% 0.45/1.13
% 0.45/1.13 ------ Parsing...
% 0.45/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.45/1.13
% 0.45/1.13 ------ 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
% 0.45/1.13
% 0.45/1.13 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.45/1.13
% 0.45/1.13 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.13 ------ Proving...
% 0.45/1.13 ------ Problem Properties
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 clauses 48
% 0.45/1.13 conjectures 3
% 0.45/1.13 EPR 12
% 0.45/1.13 Horn 41
% 0.45/1.13 unary 13
% 0.45/1.13 binary 26
% 0.45/1.13 lits 94
% 0.45/1.13 lits eq 11
% 0.45/1.13 fd_pure 0
% 0.45/1.13 fd_pseudo 0
% 0.45/1.13 fd_cond 0
% 0.45/1.13 fd_pseudo_cond 2
% 0.45/1.13 AC symbols 0
% 0.45/1.13
% 0.45/1.13 ------ Schedule dynamic 5 is on
% 0.45/1.13
% 0.45/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 ------
% 0.45/1.13 Current options:
% 0.45/1.13 ------
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 ------ Proving...
% 0.45/1.13
% 0.45/1.13
% 0.45/1.13 % SZS status Theorem for theBenchmark.p
% 0.45/1.13
% 0.45/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.45/1.13
% 0.45/1.13
%------------------------------------------------------------------------------