TSTP Solution File: SET649+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET649+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% Computer : n019.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 : Wed Aug 31 18:21:44 EDT 2022
% Result : Theorem 1.51s 0.55s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 85 ( 14 unt; 0 def)
% Number of atoms : 376 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 466 ( 175 ~; 156 |; 78 &)
% ( 13 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 147 ( 126 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f480,plain,
$false,
inference(avatar_sat_refutation,[],[f267,f447,f479]) ).
fof(f479,plain,
~ spl15_1,
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f478,plain,
( $false
| ~ spl15_1 ),
inference(subsumption_resolution,[],[f470,f110]) ).
fof(f110,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(f470,plain,
( ~ ilf_type(cross_product(sK11,sK12),set_type)
| ~ spl15_1 ),
inference(unit_resulting_resolution,[],[f262,f117]) ).
fof(f117,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(f262,plain,
( empty(power_set(cross_product(sK11,sK12)))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f260,plain,
( spl15_1
<=> empty(power_set(cross_product(sK11,sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f447,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f446]) ).
fof(f446,plain,
( $false
| spl15_2 ),
inference(subsumption_resolution,[],[f435,f274]) ).
fof(f274,plain,
( ~ member(sK10(sK13,cross_product(sK11,sK12)),cross_product(sK11,sK12))
| spl15_2 ),
inference(unit_resulting_resolution,[],[f110,f110,f266,f144]) ).
fof(f144,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(sK10(X0,X1),X1)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( member(X0,power_set(X1))
| ( member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type)
& ~ member(sK10(X0,X1),X1) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| member(X3,X1) )
| ~ member(X0,power_set(X1)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f93,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) )
=> ( member(sK10(X0,X1),X0)
& ilf_type(sK10(X0,X1),set_type)
& ~ member(sK10(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) ) )
& ( ! [X3] :
( ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| member(X3,X1) )
| ~ member(X0,power_set(X1)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( member(X0,power_set(X1))
| ? [X2] :
( member(X2,X0)
& ilf_type(X2,set_type)
& ~ member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) )
| ~ member(X0,power_set(X1)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( ! [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(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) )
<=> member(X0,power_set(X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f266,plain,
( ~ member(sK13,power_set(cross_product(sK11,sK12)))
| spl15_2 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f264,plain,
( spl15_2
<=> member(sK13,power_set(cross_product(sK11,sK12))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f435,plain,
( member(sK10(sK13,cross_product(sK11,sK12)),cross_product(sK11,sK12))
| spl15_2 ),
inference(unit_resulting_resolution,[],[f275,f110,f110,f110,f376,f133]) ).
fof(f133,plain,
! [X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| member(X3,X1)
| ~ member(X3,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ( ( subset(X0,X1)
| ( ilf_type(sK7(X0,X1),set_type)
& member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) )
| ~ subset(X0,X1) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f83,f84]) ).
fof(f84,plain,
! [X0,X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
=> ( ilf_type(sK7(X0,X1),set_type)
& member(sK7(X0,X1),X0)
& ~ member(sK7(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [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) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) )
| ~ subset(X0,X1) ) ) ) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [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) ) )
& ( ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) )
| ~ subset(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f45]) ).
fof(f45,plain,
! [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) ) ) ) ),
inference(flattening,[],[f44]) ).
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,[],[f12]) ).
fof(f12,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',p12) ).
fof(f376,plain,
subset(sK13,cross_product(sK11,sK12)),
inference(unit_resulting_resolution,[],[f110,f110,f163,f110,f200,f108]) ).
fof(f108,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| subset(X0,X2)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( subset(X0,X2)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ( subset(X1,X2)
& subset(X0,X1) )
=> subset(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(f200,plain,
subset(cross_product(domain_of(sK13),range_of(sK13)),cross_product(sK11,sK12)),
inference(unit_resulting_resolution,[],[f154,f110,f110,f110,f110,f156,f111]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ! [X3] :
( ~ subset(X2,X3)
| ~ ilf_type(X3,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1) )
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f50]) ).
fof(f50,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(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(f156,plain,
subset(domain_of(sK13),sK11),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( ilf_type(sK11,set_type)
& ilf_type(sK12,set_type)
& subset(domain_of(sK13),sK11)
& ~ ilf_type(sK13,relation_type(sK11,sK12))
& subset(range_of(sK13),sK12)
& ilf_type(sK13,binary_relation_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13])],[f31,f101,f100,f99]) ).
fof(f99,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( subset(domain_of(X2),X0)
& ~ ilf_type(X2,relation_type(X0,X1))
& subset(range_of(X2),X1)
& ilf_type(X2,binary_relation_type) ) ) )
=> ( ilf_type(sK11,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( subset(domain_of(X2),sK11)
& ~ ilf_type(X2,relation_type(sK11,X1))
& subset(range_of(X2),X1)
& ilf_type(X2,binary_relation_type) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( subset(domain_of(X2),sK11)
& ~ ilf_type(X2,relation_type(sK11,X1))
& subset(range_of(X2),X1)
& ilf_type(X2,binary_relation_type) ) )
=> ( ilf_type(sK12,set_type)
& ? [X2] :
( subset(domain_of(X2),sK11)
& ~ ilf_type(X2,relation_type(sK11,sK12))
& subset(range_of(X2),sK12)
& ilf_type(X2,binary_relation_type) ) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
( ? [X2] :
( subset(domain_of(X2),sK11)
& ~ ilf_type(X2,relation_type(sK11,sK12))
& subset(range_of(X2),sK12)
& ilf_type(X2,binary_relation_type) )
=> ( subset(domain_of(sK13),sK11)
& ~ ilf_type(sK13,relation_type(sK11,sK12))
& subset(range_of(sK13),sK12)
& ilf_type(sK13,binary_relation_type) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ilf_type(X1,set_type)
& ? [X2] :
( subset(domain_of(X2),X0)
& ~ ilf_type(X2,relation_type(X0,X1))
& subset(range_of(X2),X1)
& ilf_type(X2,binary_relation_type) ) ) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
& subset(domain_of(X2),X0)
& subset(range_of(X2),X1)
& ilf_type(X2,binary_relation_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) )
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) )
=> ilf_type(X2,relation_type(X0,X1)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_11) ).
fof(f154,plain,
subset(range_of(sK13),sK12),
inference(cnf_transformation,[],[f102]) ).
fof(f163,plain,
subset(sK13,cross_product(domain_of(sK13),range_of(sK13))),
inference(unit_resulting_resolution,[],[f153,f114]) ).
fof(f114,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(ennf_transformation,[],[f2]) ).
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(f153,plain,
ilf_type(sK13,binary_relation_type),
inference(cnf_transformation,[],[f102]) ).
fof(f275,plain,
( member(sK10(sK13,cross_product(sK11,sK12)),sK13)
| spl15_2 ),
inference(unit_resulting_resolution,[],[f110,f110,f266,f146]) ).
fof(f146,plain,
! [X0,X1] :
( member(sK10(X0,X1),X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f95]) ).
fof(f267,plain,
( spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f258,f264,f260]) ).
fof(f258,plain,
( ~ member(sK13,power_set(cross_product(sK11,sK12)))
| empty(power_set(cross_product(sK11,sK12))) ),
inference(subsumption_resolution,[],[f257,f110]) ).
fof(f257,plain,
( ~ ilf_type(sK13,set_type)
| ~ member(sK13,power_set(cross_product(sK11,sK12)))
| empty(power_set(cross_product(sK11,sK12))) ),
inference(subsumption_resolution,[],[f256,f110]) ).
fof(f256,plain,
( ~ ilf_type(power_set(cross_product(sK11,sK12)),set_type)
| ~ member(sK13,power_set(cross_product(sK11,sK12)))
| ~ ilf_type(sK13,set_type)
| empty(power_set(cross_product(sK11,sK12))) ),
inference(resolution,[],[f219,f148]) ).
fof(f148,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) ) ) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| empty(X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f219,plain,
~ ilf_type(sK13,member_type(power_set(cross_product(sK11,sK12)))),
inference(subsumption_resolution,[],[f218,f110]) ).
fof(f218,plain,
( ~ ilf_type(sK13,member_type(power_set(cross_product(sK11,sK12))))
| ~ ilf_type(sK13,set_type) ),
inference(subsumption_resolution,[],[f217,f110]) ).
fof(f217,plain,
( ~ ilf_type(sK13,member_type(power_set(cross_product(sK11,sK12))))
| ~ ilf_type(cross_product(sK11,sK12),set_type)
| ~ ilf_type(sK13,set_type) ),
inference(resolution,[],[f213,f131]) ).
fof(f131,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) )
& ( 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(nnf_transformation,[],[f56]) ).
fof(f56,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(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,member_type(power_set(X0)))
<=> ilf_type(X1,subset_type(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15) ).
fof(f213,plain,
~ ilf_type(sK13,subset_type(cross_product(sK11,sK12))),
inference(subsumption_resolution,[],[f212,f110]) ).
fof(f212,plain,
( ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK13,subset_type(cross_product(sK11,sK12))) ),
inference(subsumption_resolution,[],[f211,f110]) ).
fof(f211,plain,
( ~ ilf_type(sK11,set_type)
| ~ ilf_type(sK13,subset_type(cross_product(sK11,sK12)))
| ~ ilf_type(sK12,set_type) ),
inference(resolution,[],[f155,f128]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [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) ) ),
inference(rectify,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ! [X3] :
( ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ilf_type(X3,relation_type(X0,X1)) )
& ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(X2,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(ennf_transformation,[],[f29]) ).
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(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(f155,plain,
~ ilf_type(sK13,relation_type(sK11,sK12)),
inference(cnf_transformation,[],[f102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET649+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 14:13:20 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.51 % (12078)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 0.20/0.52 % (12066)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.20/0.52 % (12070)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.52 % (12086)dis+21_1:1_aac=none:abs=on:er=known:fde=none:fsr=off:nwc=5.0:s2a=on:s2at=4.0:sp=const_frequency:to=lpo:urr=ec_only:i=25:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/25Mi)
% 0.20/0.52 % (12083)dis+21_1:1_ep=RS:nwc=10.0:s2a=on:s2at=1.5:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.52 % (12060)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (12061)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.52 % (12063)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.20/0.52 % (12061)Refutation not found, incomplete strategy% (12061)------------------------------
% 0.20/0.52 % (12061)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (12061)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (12061)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.52
% 0.20/0.52 % (12061)Memory used [KB]: 6012
% 0.20/0.52 % (12061)Time elapsed: 0.123 s
% 0.20/0.52 % (12061)Instructions burned: 2 (million)
% 0.20/0.52 % (12061)------------------------------
% 0.20/0.52 % (12061)------------------------------
% 1.36/0.52 % (12075)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.36/0.53 % (12071)lrs+10_1:4_av=off:bs=unit_only:bsr=unit_only:ep=RS:s2a=on:sos=on:sp=frequency:to=lpo:i=16:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 1.36/0.53 % (12062)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.36/0.53 % (12073)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.36/0.53 % (12081)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 1.36/0.53 % (12059)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.36/0.53 % (12080)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.36/0.53 % (12078)Refutation not found, incomplete strategy% (12078)------------------------------
% 1.36/0.53 % (12078)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (12078)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (12078)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.53
% 1.36/0.53 % (12078)Memory used [KB]: 6012
% 1.36/0.53 % (12078)Time elapsed: 0.130 s
% 1.36/0.53 % (12078)Instructions burned: 3 (million)
% 1.36/0.53 % (12078)------------------------------
% 1.36/0.53 % (12078)------------------------------
% 1.36/0.53 % (12073)Instruction limit reached!
% 1.36/0.53 % (12073)------------------------------
% 1.36/0.53 % (12073)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (12073)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (12073)Termination reason: Unknown
% 1.36/0.53 % (12073)Termination phase: Saturation
% 1.36/0.53
% 1.36/0.53 % (12073)Memory used [KB]: 6012
% 1.36/0.53 % (12073)Time elapsed: 0.005 s
% 1.36/0.53 % (12073)Instructions burned: 3 (million)
% 1.36/0.53 % (12073)------------------------------
% 1.36/0.53 % (12073)------------------------------
% 1.36/0.53 % (12070)Instruction limit reached!
% 1.36/0.53 % (12070)------------------------------
% 1.36/0.53 % (12070)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (12070)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (12070)Termination reason: Unknown
% 1.36/0.53 % (12070)Termination phase: Saturation
% 1.36/0.53
% 1.36/0.53 % (12070)Memory used [KB]: 6140
% 1.36/0.53 % (12070)Time elapsed: 0.132 s
% 1.36/0.53 % (12070)Instructions burned: 7 (million)
% 1.36/0.53 % (12070)------------------------------
% 1.36/0.53 % (12070)------------------------------
% 1.36/0.54 % (12088)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 1.36/0.54 % (12076)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.36/0.54 % (12077)ott+1010_1:1_sd=2:sos=on:sp=occurrence:ss=axioms:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 1.36/0.54 % (12079)dis+1010_1:1_bs=on:ep=RS:erd=off:newcnf=on:nwc=10.0:s2a=on:sgt=32:ss=axioms:i=30:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/30Mi)
% 1.36/0.54 % (12065)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 1.36/0.54 % (12072)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.36/0.54 % (12067)dis+10_1:1_newcnf=on:sgt=8:sos=on:ss=axioms:to=lpo:urr=on:i=49:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/49Mi)
% 1.36/0.54 % (12071)Refutation not found, incomplete strategy% (12071)------------------------------
% 1.36/0.54 % (12071)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (12068)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 1.36/0.54 % (12071)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (12069)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.36/0.54 % (12071)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.54
% 1.36/0.54 % (12071)Memory used [KB]: 1535
% 1.36/0.54 % (12071)Time elapsed: 0.129 s
% 1.36/0.54 % (12071)Instructions burned: 5 (million)
% 1.36/0.54 % (12071)------------------------------
% 1.36/0.54 % (12071)------------------------------
% 1.36/0.54 % (12060)Refutation not found, incomplete strategy% (12060)------------------------------
% 1.36/0.54 % (12060)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (12060)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (12060)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.54
% 1.36/0.54 % (12060)Memory used [KB]: 6012
% 1.36/0.54 % (12060)Time elapsed: 0.142 s
% 1.36/0.54 % (12060)Instructions burned: 4 (million)
% 1.36/0.54 % (12060)------------------------------
% 1.36/0.54 % (12060)------------------------------
% 1.36/0.54 % (12064)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 1.36/0.54 % (12082)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 1.36/0.54 % (12084)lrs+11_1:1_plsq=on:plsqc=1:plsqr=32,1:ss=included:i=95:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/95Mi)
% 1.36/0.54 % (12087)dis+2_3:1_aac=none:abs=on:ep=R:lcm=reverse:nwc=10.0:sos=on:sp=const_frequency:spb=units:urr=ec_only:i=8:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/8Mi)
% 1.36/0.54 % (12077)Instruction limit reached!
% 1.36/0.54 % (12077)------------------------------
% 1.36/0.54 % (12077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (12077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (12077)Termination reason: Unknown
% 1.36/0.54 % (12077)Termination phase: Saturation
% 1.36/0.54
% 1.36/0.54 % (12077)Memory used [KB]: 6012
% 1.36/0.54 % (12077)Time elapsed: 0.004 s
% 1.36/0.54 % (12077)Instructions burned: 3 (million)
% 1.36/0.54 % (12077)------------------------------
% 1.36/0.54 % (12077)------------------------------
% 1.51/0.54 % (12085)lrs+1011_1:1_fd=preordered:fsd=on:sos=on:thsq=on:thsqc=64:thsqd=32:uwa=ground:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.51/0.54 % (12082)Refutation not found, incomplete strategy% (12082)------------------------------
% 1.51/0.54 % (12082)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.54 % (12082)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.54 % (12082)Termination reason: Refutation not found, incomplete strategy
% 1.51/0.54
% 1.51/0.54 % (12082)Memory used [KB]: 1535
% 1.51/0.54 % (12082)Time elapsed: 0.127 s
% 1.51/0.54 % (12082)Instructions burned: 4 (million)
% 1.51/0.54 % (12082)------------------------------
% 1.51/0.54 % (12082)------------------------------
% 1.51/0.55 % (12085)Refutation not found, incomplete strategy% (12085)------------------------------
% 1.51/0.55 % (12085)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.55 % (12085)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.55 % (12085)Termination reason: Refutation not found, incomplete strategy
% 1.51/0.55
% 1.51/0.55 % (12085)Memory used [KB]: 6012
% 1.51/0.55 % (12085)Time elapsed: 0.147 s
% 1.51/0.55 % (12085)Instructions burned: 3 (million)
% 1.51/0.55 % (12085)------------------------------
% 1.51/0.55 % (12085)------------------------------
% 1.51/0.55 % (12066)First to succeed.
% 1.51/0.55 % (12064)Instruction limit reached!
% 1.51/0.55 % (12064)------------------------------
% 1.51/0.55 % (12064)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.55 % (12064)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.55 % (12064)Termination reason: Unknown
% 1.51/0.55 % (12064)Termination phase: Saturation
% 1.51/0.55
% 1.51/0.55 % (12064)Memory used [KB]: 1663
% 1.51/0.55 % (12064)Time elapsed: 0.150 s
% 1.51/0.55 % (12064)Instructions burned: 15 (million)
% 1.51/0.55 % (12064)------------------------------
% 1.51/0.55 % (12064)------------------------------
% 1.51/0.55 % (12066)Refutation found. Thanks to Tanya!
% 1.51/0.55 % SZS status Theorem for theBenchmark
% 1.51/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.51/0.55 % (12066)------------------------------
% 1.51/0.55 % (12066)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.51/0.55 % (12066)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.51/0.55 % (12066)Termination reason: Refutation
% 1.51/0.55
% 1.51/0.55 % (12066)Memory used [KB]: 6268
% 1.51/0.55 % (12066)Time elapsed: 0.143 s
% 1.51/0.55 % (12066)Instructions burned: 14 (million)
% 1.51/0.55 % (12066)------------------------------
% 1.51/0.55 % (12066)------------------------------
% 1.51/0.55 % (12058)Success in time 0.192 s
%------------------------------------------------------------------------------