TSTP Solution File: SET663+3 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : SET663+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.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 03:01:10 EDT 2024
% Result : Theorem 3.73s 1.18s
% Output : CNFRefutation 3.73s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f189)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( subset(X0,empty_set)
=> empty_set = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,binary_relation_type)
=> ( ( empty_set = range_of(X0)
| empty_set = domain_of(X0) )
=> empty_set = 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,relation_type(X0,X1))
=> ( subset(range_of(X2),X1)
& subset(domain_of(X2),X0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ~ member(X0,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(f5,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5a) ).
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/sandbox/benchmark/theBenchmark.p',p6) ).
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/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f22,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',p21) ).
fof(f23,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',p22) ).
fof(f25,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',p24) ).
fof(f28,axiom,
! [X0] :
( ( ilf_type(X0,set_type)
& empty(X0) )
=> relation_like(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(f29,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',p28) ).
fof(f34,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).
fof(f35,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> empty_set = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_26) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( ilf_type(X2,relation_type(empty_set,X1))
=> empty_set = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f37,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(f39,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f42,plain,
! [X0] :
( empty_set = X0
| ( empty_set != range_of(X0)
& empty_set != domain_of(X0) )
| ~ ilf_type(X0,binary_relation_type) ),
inference(flattening,[],[f41]) ).
fof(f43,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,[],[f3]) ).
fof(f44,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f45,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,[],[f37]) ).
fof(f53,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(f61,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f62,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,[],[f23]) ).
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(flattening,[],[f62]) ).
fof(f65,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,[],[f25]) ).
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(flattening,[],[f65]) ).
fof(f71,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f72,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(flattening,[],[f71]) ).
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,[],[f29]) ).
fof(f78,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f36]) ).
fof(f79,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f78]) ).
fof(f92,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,[],[f53]) ).
fof(f99,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,[],[f61]) ).
fof(f100,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,[],[f99]) ).
fof(f101,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK6(X0),X0)
& ilf_type(sK6(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f102,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK6(X0),X0)
& ilf_type(sK6(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,[sK6])],[f100,f101]) ).
fof(f103,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,[],[f63]) ).
fof(f104,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,[],[f103]) ).
fof(f105,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f106,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(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,[sK7])],[f104,f105]) ).
fof(f107,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,[],[f66]) ).
fof(f116,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& 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] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,X1))
& ilf_type(X2,relation_type(sK12,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,sK13))
& ilf_type(X2,relation_type(sK12,sK13)) )
& ilf_type(sK13,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f118,plain,
( ? [X2] :
( empty_set != X2
& ilf_type(X2,relation_type(empty_set,sK13))
& ilf_type(X2,relation_type(sK12,sK13)) )
=> ( empty_set != sK14
& ilf_type(sK14,relation_type(empty_set,sK13))
& ilf_type(sK14,relation_type(sK12,sK13)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
( empty_set != sK14
& ilf_type(sK14,relation_type(empty_set,sK13))
& 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])],[f79,f118,f117,f116]) ).
fof(f120,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f121,plain,
! [X0] :
( empty_set = X0
| empty_set != domain_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f42]) ).
fof(f122,plain,
! [X0] :
( empty_set = X0
| empty_set != range_of(X0)
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f42]) ).
fof(f123,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,[],[f43]) ).
fof(f124,plain,
! [X2,X0,X1] :
( subset(range_of(X2),X1)
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f43]) ).
fof(f125,plain,
! [X0] :
( ~ member(X0,empty_set)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f44]) ).
fof(f126,plain,
empty(empty_set),
inference(cnf_transformation,[],[f5]) ).
fof(f127,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,[],[f45]) ).
fof(f128,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,[],[f45]) ).
fof(f145,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,[],[f92]) ).
fof(f154,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f102]) ).
fof(f159,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f106]) ).
fof(f164,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,[],[f107]) ).
fof(f172,plain,
! [X0] :
( relation_like(X0)
| ~ ilf_type(X0,set_type)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f173,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(f178,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f34]) ).
fof(f182,plain,
ilf_type(sK14,relation_type(empty_set,sK13)),
inference(cnf_transformation,[],[f119]) ).
fof(f183,plain,
empty_set != sK14,
inference(cnf_transformation,[],[f119]) ).
cnf(c_49,plain,
( ~ subset(X0,empty_set)
| ~ ilf_type(X0,set_type)
| X0 = empty_set ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_50,plain,
( range_of(X0) != empty_set
| ~ ilf_type(X0,binary_relation_type)
| X0 = empty_set ),
inference(cnf_transformation,[],[f122]) ).
cnf(c_51,plain,
( domain_of(X0) != empty_set
| ~ ilf_type(X0,binary_relation_type)
| X0 = empty_set ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_52,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| subset(range_of(X0),X2) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_53,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,[],[f123]) ).
cnf(c_54,plain,
( ~ ilf_type(X0,set_type)
| ~ member(X0,empty_set) ),
inference(cnf_transformation,[],[f125]) ).
cnf(c_55,plain,
empty(empty_set),
inference(cnf_transformation,[],[f126]) ).
cnf(c_56,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,[],[f128]) ).
cnf(c_57,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,[],[f127]) ).
cnf(c_69,plain,
( ~ ilf_type(X0,set_type)
| ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f189]) ).
cnf(c_72,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,[],[f145]) ).
cnf(c_83,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f154]) ).
cnf(c_85,plain,
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f159]) ).
cnf(c_90,plain,
( ~ member(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(cnf_transformation,[],[f164]) ).
cnf(c_99,plain,
( ~ ilf_type(X0,set_type)
| ~ empty(X0)
| relation_like(X0) ),
inference(cnf_transformation,[],[f172]) ).
cnf(c_100,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,[],[f173]) ).
cnf(c_105,plain,
ilf_type(X0,set_type),
inference(cnf_transformation,[],[f178]) ).
cnf(c_106,negated_conjecture,
empty_set != sK14,
inference(cnf_transformation,[],[f183]) ).
cnf(c_107,negated_conjecture,
ilf_type(sK14,relation_type(empty_set,sK13)),
inference(cnf_transformation,[],[f182]) ).
cnf(c_164,plain,
~ member(X0,empty_set),
inference(global_subsumption_just,[status(thm)],[c_54,c_105,c_54]) ).
cnf(c_167,plain,
( ~ empty(X0)
| relation_like(X0) ),
inference(global_subsumption_just,[status(thm)],[c_99,c_105,c_99]) ).
cnf(c_188,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(global_subsumption_just,[status(thm)],[c_69,c_105,c_69]) ).
cnf(c_227,plain,
( ~ ilf_type(X1,set_type)
| member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_105,c_85]) ).
cnf(c_228,plain,
( ~ ilf_type(X0,set_type)
| member(sK7(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(renaming,[status(thm)],[c_227]) ).
cnf(c_229,plain,
( member(sK7(X1,X0),X1)
| member(X1,power_set(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_228,c_105,c_228]) ).
cnf(c_230,plain,
( member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_229]) ).
cnf(c_236,plain,
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| ~ member(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_90,c_105,c_83,c_90]) ).
cnf(c_237,plain,
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(renaming,[status(thm)],[c_236]) ).
cnf(c_243,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_72,c_105,c_72]) ).
cnf(c_259,plain,
( ~ relation_like(X0)
| ilf_type(X0,binary_relation_type) ),
inference(prop_impl_just,[status(thm)],[c_188]) ).
cnf(c_267,plain,
( relation_like(X0)
| ~ empty(X0) ),
inference(prop_impl_just,[status(thm)],[c_167]) ).
cnf(c_268,plain,
( ~ empty(X0)
| relation_like(X0) ),
inference(renaming,[status(thm)],[c_267]) ).
cnf(c_396,plain,
( range_of(X0) != empty_set
| ~ relation_like(X0)
| X0 = empty_set ),
inference(bin_hyper_res,[status(thm)],[c_50,c_259]) ).
cnf(c_397,plain,
( domain_of(X0) != empty_set
| ~ relation_like(X0)
| X0 = empty_set ),
inference(bin_hyper_res,[status(thm)],[c_51,c_259]) ).
cnf(c_416,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| subset(range_of(X0),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_52,c_105]) ).
cnf(c_419,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_237,c_105]) ).
cnf(c_421,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_100,c_105]) ).
cnf(c_427,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_57,c_105]) ).
cnf(c_428,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_56,c_105]) ).
cnf(c_429,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_243,c_105]) ).
cnf(c_430,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_53,c_105]) ).
cnf(c_536,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| relation_like(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_421,c_105]) ).
cnf(c_547,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(range_of(X0),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_416,c_105]) ).
cnf(c_569,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(domain_of(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_430,c_105]) ).
cnf(c_586,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_427,c_105]) ).
cnf(c_597,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_428,c_105]) ).
cnf(c_891,plain,
( X0 != empty_set
| relation_like(X0) ),
inference(resolution_lifted,[status(thm)],[c_55,c_268]) ).
cnf(c_892,plain,
relation_like(empty_set),
inference(unflattening,[status(thm)],[c_891]) ).
cnf(c_1531,plain,
( ilf_type(X0,relation_type(X1,X2))
| ~ ilf_type(X0,subset_type(cross_product(X1,X2))) ),
inference(prop_impl_just,[status(thm)],[c_586]) ).
cnf(c_1532,plain,
( ~ ilf_type(X0,subset_type(cross_product(X1,X2)))
| ilf_type(X0,relation_type(X1,X2)) ),
inference(renaming,[status(thm)],[c_1531]) ).
cnf(c_1535,plain,
( ilf_type(X0,subset_type(X1))
| ~ ilf_type(X0,member_type(power_set(X1))) ),
inference(prop_impl_just,[status(thm)],[c_429]) ).
cnf(c_1536,plain,
( ~ ilf_type(X0,member_type(power_set(X1)))
| ilf_type(X0,subset_type(X1)) ),
inference(renaming,[status(thm)],[c_1535]) ).
cnf(c_1539,plain,
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(prop_impl_just,[status(thm)],[c_105,c_49]) ).
cnf(c_1541,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(range_of(X0),X2) ),
inference(prop_impl_just,[status(thm)],[c_547]) ).
cnf(c_1543,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| subset(domain_of(X0),X1) ),
inference(prop_impl_just,[status(thm)],[c_569]) ).
cnf(c_1545,plain,
( ~ ilf_type(X0,relation_type(X1,X2))
| relation_like(X0) ),
inference(prop_impl_just,[status(thm)],[c_536,c_597]) ).
cnf(c_1575,plain,
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1)) ),
inference(prop_impl_just,[status(thm)],[c_419]) ).
cnf(c_1583,plain,
( member(X0,power_set(X1))
| member(sK7(X0,X1),X0) ),
inference(prop_impl_just,[status(thm)],[c_230]) ).
cnf(c_1584,plain,
( member(sK7(X0,X1),X0)
| member(X0,power_set(X1)) ),
inference(renaming,[status(thm)],[c_1583]) ).
cnf(c_2228,plain,
relation_type(empty_set,sK13) = sP1_iProver_def,
definition ).
cnf(c_2230,negated_conjecture,
ilf_type(sK14,sP1_iProver_def),
inference(demodulation,[status(thm)],[c_107,c_2228]) ).
cnf(c_2234,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_3151,plain,
( ~ ilf_type(X0,sP1_iProver_def)
| relation_like(X0) ),
inference(superposition,[status(thm)],[c_2228,c_1545]) ).
cnf(c_3183,plain,
relation_like(sK14),
inference(superposition,[status(thm)],[c_2230,c_3151]) ).
cnf(c_3262,plain,
( ~ ilf_type(X0,sP1_iProver_def)
| subset(domain_of(X0),empty_set) ),
inference(superposition,[status(thm)],[c_2228,c_1543]) ).
cnf(c_3302,plain,
( ~ ilf_type(X0,sP1_iProver_def)
| domain_of(X0) = empty_set ),
inference(superposition,[status(thm)],[c_3262,c_1539]) ).
cnf(c_3357,plain,
member(empty_set,power_set(X0)),
inference(superposition,[status(thm)],[c_1584,c_164]) ).
cnf(c_3402,plain,
domain_of(sK14) = empty_set,
inference(superposition,[status(thm)],[c_2230,c_3302]) ).
cnf(c_3412,plain,
( ~ member(X0,power_set(X1))
| ilf_type(X0,subset_type(X1)) ),
inference(superposition,[status(thm)],[c_1575,c_1536]) ).
cnf(c_3437,plain,
ilf_type(empty_set,subset_type(X0)),
inference(superposition,[status(thm)],[c_3357,c_3412]) ).
cnf(c_3530,plain,
( empty_set != X0
| sK14 != X0
| empty_set = sK14 ),
inference(instantiation,[status(thm)],[c_2234]) ).
cnf(c_3600,plain,
ilf_type(empty_set,relation_type(X0,X1)),
inference(superposition,[status(thm)],[c_3437,c_1532]) ).
cnf(c_3611,plain,
subset(range_of(empty_set),X0),
inference(superposition,[status(thm)],[c_3600,c_1541]) ).
cnf(c_3632,plain,
range_of(empty_set) = empty_set,
inference(superposition,[status(thm)],[c_3611,c_1539]) ).
cnf(c_3660,plain,
( empty_set != empty_set
| sK14 != empty_set
| empty_set = sK14 ),
inference(instantiation,[status(thm)],[c_3530]) ).
cnf(c_3662,plain,
( range_of(empty_set) != empty_set
| ~ relation_like(empty_set)
| empty_set = empty_set ),
inference(instantiation,[status(thm)],[c_396]) ).
cnf(c_4732,plain,
( domain_of(sK14) != empty_set
| ~ relation_like(sK14)
| sK14 = empty_set ),
inference(instantiation,[status(thm)],[c_397]) ).
cnf(c_4735,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4732,c_3662,c_3660,c_3632,c_3402,c_3183,c_892,c_106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET663+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.14 % Command : run_iprover %s %d THM
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 2 21:15:01 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 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
% 3.73/1.18 % SZS status Started for theBenchmark.p
% 3.73/1.18 % SZS status Theorem for theBenchmark.p
% 3.73/1.18
% 3.73/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.73/1.18
% 3.73/1.18 ------ iProver source info
% 3.73/1.18
% 3.73/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.73/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.73/1.18 git: non_committed_changes: false
% 3.73/1.18
% 3.73/1.18 ------ Parsing...
% 3.73/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.73/1.18
% 3.73/1.18 ------ 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
% 3.73/1.18
% 3.73/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.73/1.18
% 3.73/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.73/1.18 ------ Proving...
% 3.73/1.18 ------ Problem Properties
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18 clauses 46
% 3.73/1.18 conjectures 3
% 3.73/1.18 EPR 14
% 3.73/1.18 Horn 39
% 3.73/1.18 unary 13
% 3.73/1.18 binary 25
% 3.73/1.18 lits 91
% 3.73/1.18 lits eq 14
% 3.73/1.18 fd_pure 0
% 3.73/1.18 fd_pseudo 0
% 3.73/1.18 fd_cond 3
% 3.73/1.18 fd_pseudo_cond 2
% 3.73/1.18 AC symbols 0
% 3.73/1.18
% 3.73/1.18 ------ Schedule dynamic 5 is on
% 3.73/1.18
% 3.73/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18 ------
% 3.73/1.18 Current options:
% 3.73/1.18 ------
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18 ------ Proving...
% 3.73/1.18
% 3.73/1.18
% 3.73/1.18 % SZS status Theorem for theBenchmark.p
% 3.73/1.18
% 3.73/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.73/1.19
% 3.73/1.19
%------------------------------------------------------------------------------