TSTP Solution File: SET652+3 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : SET652+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 18:21:45 EDT 2022
% Result : Theorem 1.56s 0.55s
% Output : Refutation 1.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 98 ( 17 unt; 0 def)
% Number of atoms : 427 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 526 ( 197 ~; 178 |; 86 &)
% ( 15 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 177 ( 147 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f598,plain,
$false,
inference(avatar_sat_refutation,[],[f273,f587,f597]) ).
fof(f597,plain,
~ spl15_2,
inference(avatar_contradiction_clause,[],[f596]) ).
fof(f596,plain,
( $false
| ~ spl15_2 ),
inference(subsumption_resolution,[],[f588,f117]) ).
fof(f117,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(f588,plain,
( ~ ilf_type(cross_product(sK10,sK9),set_type)
| ~ spl15_2 ),
inference(unit_resulting_resolution,[],[f272,f129]) ).
fof(f129,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ~ empty(power_set(X0))
& ilf_type(power_set(X0),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(f272,plain,
( empty(power_set(cross_product(sK10,sK9)))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f270]) ).
fof(f270,plain,
( spl15_2
<=> empty(power_set(cross_product(sK10,sK9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f587,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f586]) ).
fof(f586,plain,
( $false
| spl15_1 ),
inference(subsumption_resolution,[],[f574,f353]) ).
fof(f353,plain,
( ~ member(sK3(sK11,cross_product(sK10,sK9)),cross_product(sK10,sK9))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f117,f117,f268,f108]) ).
fof(f108,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ member(sK3(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ilf_type(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) ) )
& ( ! [X3] :
( ~ ilf_type(X3,set_type)
| ~ member(X3,X0)
| member(X3,X1) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f70,f71]) ).
fof(f71,plain,
! [X0,X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& member(X2,X0)
& ~ member(X2,X1) )
=> ( ilf_type(sK3(X0,X1),set_type)
& member(sK3(X0,X1),X0)
& ~ member(sK3(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f69]) ).
fof(f69,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(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) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f55]) ).
fof(f55,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,[],[f18]) ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(f268,plain,
( ~ member(sK11,power_set(cross_product(sK10,sK9)))
| spl15_1 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f266,plain,
( spl15_1
<=> member(sK11,power_set(cross_product(sK10,sK9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f574,plain,
( member(sK3(sK11,cross_product(sK10,sK9)),cross_product(sK10,sK9))
| spl15_1 ),
inference(unit_resulting_resolution,[],[f117,f430,f117,f117,f352,f126]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ member(X2,X0)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| member(X2,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ( ilf_type(sK7(X0,X1),set_type)
& ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f85,f86]) ).
fof(f86,plain,
! [X0,X1] :
( ? [X3] :
( ilf_type(X3,set_type)
& ~ member(X3,X1)
& member(X3,X0) )
=> ( ilf_type(sK7(X0,X1),set_type)
& ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X3] :
( ilf_type(X3,set_type)
& ~ member(X3,X1)
& member(X3,X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f84]) ).
fof(f84,plain,
! [X0] :
( ! [X1] :
( ( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ? [X2] :
( ilf_type(X2,set_type)
& ~ member(X2,X1)
& member(X2,X0) ) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ~ ilf_type(X2,set_type)
| member(X2,X1)
| ~ member(X2,X0) )
<=> subset(X0,X1) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( ! [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(ennf_transformation,[],[f9]) ).
fof(f9,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) ) )
<=> subset(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p9) ).
fof(f352,plain,
( member(sK3(sK11,cross_product(sK10,sK9)),sK11)
| spl15_1 ),
inference(unit_resulting_resolution,[],[f117,f117,f268,f109]) ).
fof(f109,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| member(X0,power_set(X1))
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f430,plain,
subset(sK11,cross_product(sK10,sK9)),
inference(unit_resulting_resolution,[],[f117,f117,f189,f117,f315,f151]) ).
fof(f151,plain,
! [X2,X0,X1] :
( subset(X0,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| ~ ilf_type(X2,set_type)
| subset(X0,X2) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f38]) ).
fof(f38,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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(f315,plain,
subset(sK11,cross_product(domain_of(sK11),range_of(sK11))),
inference(unit_resulting_resolution,[],[f238,f105]) ).
fof(f105,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ ilf_type(X0,binary_relation_type)
| subset(X0,cross_product(domain_of(X0),range_of(X0))) ),
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/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(f238,plain,
ilf_type(sK11,binary_relation_type),
inference(unit_resulting_resolution,[],[f117,f207,f156]) ).
fof(f156,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(duplicate_literal_removal,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ilf_type(X0,binary_relation_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X0,set_type)
| ~ relation_like(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ( ilf_type(X0,binary_relation_type)
| ~ relation_like(X0)
| ~ ilf_type(X0,set_type) )
& ( ( relation_like(X0)
& ilf_type(X0,set_type) )
| ~ ilf_type(X0,binary_relation_type) ) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(X0,binary_relation_type)
<=> ( relation_like(X0)
& ilf_type(X0,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(f207,plain,
relation_like(sK11),
inference(unit_resulting_resolution,[],[f117,f117,f171,f132]) ).
fof(f132,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| relation_like(X2)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( relation_like(X2)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f23]) ).
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/sandbox2/benchmark/theBenchmark.p',p23) ).
fof(f171,plain,
ilf_type(sK11,subset_type(cross_product(sK10,sK8))),
inference(unit_resulting_resolution,[],[f117,f117,f136,f140]) ).
fof(f140,plain,
! [X3,X0,X1] :
( ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ! [X1] :
( ( ! [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)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ! [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))) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p4) ).
fof(f136,plain,
ilf_type(sK11,relation_type(sK10,sK8)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
( ilf_type(sK8,set_type)
& ilf_type(sK10,set_type)
& subset(range_of(sK11),sK9)
& ilf_type(sK11,relation_type(sK10,sK8))
& ~ ilf_type(sK11,relation_type(sK10,sK9))
& ilf_type(sK9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11])],[f43,f91,f90,f89,f88]) ).
fof(f88,plain,
( ? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0))
& ~ ilf_type(X3,relation_type(X2,X1)) ) )
& ilf_type(X1,set_type) ) )
=> ( ilf_type(sK8,set_type)
& ? [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK8))
& ~ ilf_type(X3,relation_type(X2,X1)) ) )
& ilf_type(X1,set_type) ) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( ? [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,sK8))
& ~ ilf_type(X3,relation_type(X2,X1)) ) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),sK9)
& ilf_type(X3,relation_type(X2,sK8))
& ~ ilf_type(X3,relation_type(X2,sK9)) ) )
& ilf_type(sK9,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),sK9)
& ilf_type(X3,relation_type(X2,sK8))
& ~ ilf_type(X3,relation_type(X2,sK9)) ) )
=> ( ilf_type(sK10,set_type)
& ? [X3] :
( subset(range_of(X3),sK9)
& ilf_type(X3,relation_type(sK10,sK8))
& ~ ilf_type(X3,relation_type(sK10,sK9)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
( ? [X3] :
( subset(range_of(X3),sK9)
& ilf_type(X3,relation_type(sK10,sK8))
& ~ ilf_type(X3,relation_type(sK10,sK9)) )
=> ( subset(range_of(sK11),sK9)
& ilf_type(sK11,relation_type(sK10,sK8))
& ~ ilf_type(sK11,relation_type(sK10,sK9)) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
? [X0] :
( ilf_type(X0,set_type)
& ? [X1] :
( ? [X2] :
( ilf_type(X2,set_type)
& ? [X3] :
( subset(range_of(X3),X1)
& ilf_type(X3,relation_type(X2,X0))
& ~ ilf_type(X3,relation_type(X2,X1)) ) )
& ilf_type(X1,set_type) ) ),
inference(flattening,[],[f42]) ).
fof(f42,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(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(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/sandbox2/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(f189,plain,
subset(cross_product(domain_of(sK11),range_of(sK11)),cross_product(sK10,sK9)),
inference(unit_resulting_resolution,[],[f137,f117,f117,f117,f117,f173,f142]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X2,X3)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,set_type)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ subset(X0,X1)
| ~ ilf_type(X3,set_type) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ subset(X0,X1)
| ~ subset(X2,X3)
| subset(cross_product(X0,X2),cross_product(X1,X3))
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f57]) ).
fof(f57,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/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(f173,plain,
subset(domain_of(sK11),sK10),
inference(unit_resulting_resolution,[],[f117,f117,f136,f131]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| subset(domain_of(X2),X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ~ ilf_type(X2,relation_type(X0,X1))
| ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(domain_of(X2),X0)
& subset(range_of(X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(f137,plain,
subset(range_of(sK11),sK9),
inference(cnf_transformation,[],[f92]) ).
fof(f273,plain,
( ~ spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f264,f270,f266]) ).
fof(f264,plain,
( empty(power_set(cross_product(sK10,sK9)))
| ~ member(sK11,power_set(cross_product(sK10,sK9))) ),
inference(subsumption_resolution,[],[f263,f117]) ).
fof(f263,plain,
( empty(power_set(cross_product(sK10,sK9)))
| ~ member(sK11,power_set(cross_product(sK10,sK9)))
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f262,f117]) ).
fof(f262,plain,
( empty(power_set(cross_product(sK10,sK9)))
| ~ ilf_type(power_set(cross_product(sK10,sK9)),set_type)
| ~ ilf_type(sK11,set_type)
| ~ member(sK11,power_set(cross_product(sK10,sK9))) ),
inference(resolution,[],[f204,f115]) ).
fof(f115,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| empty(X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) )
& ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| empty(X1)
| ( member(X0,X1)
<=> ilf_type(X0,member_type(X1)) ) ) ),
inference(flattening,[],[f40]) ).
fof(f40,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(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ( member(X0,X1)
<=> ilf_type(X0,member_type(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p20) ).
fof(f204,plain,
~ ilf_type(sK11,member_type(power_set(cross_product(sK10,sK9)))),
inference(unit_resulting_resolution,[],[f117,f117,f170,f150]) ).
fof(f150,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [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))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) ) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [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))) ) ) ),
inference(ennf_transformation,[],[f15]) ).
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/sandbox2/benchmark/theBenchmark.p',p15) ).
fof(f170,plain,
~ ilf_type(sK11,subset_type(cross_product(sK10,sK9))),
inference(subsumption_resolution,[],[f169,f117]) ).
fof(f169,plain,
( ~ ilf_type(sK11,subset_type(cross_product(sK10,sK9)))
| ~ ilf_type(sK9,set_type) ),
inference(subsumption_resolution,[],[f168,f117]) ).
fof(f168,plain,
( ~ ilf_type(sK10,set_type)
| ~ ilf_type(sK9,set_type)
| ~ ilf_type(sK11,subset_type(cross_product(sK10,sK9))) ),
inference(resolution,[],[f135,f141]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ilf_type(X2,relation_type(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
fof(f135,plain,
~ ilf_type(sK11,relation_type(sK10,sK9)),
inference(cnf_transformation,[],[f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET652+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 30 14:13:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.21/0.51 % (13356)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)
% 0.21/0.51 % (13350)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)
% 0.21/0.51 % (13371)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)
% 0.21/0.51 % (13362)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.21/0.51 % (13354)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)
% 0.21/0.51 % (13351)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)
% 0.21/0.52 % (13362)Instruction limit reached!
% 0.21/0.52 % (13362)------------------------------
% 0.21/0.52 % (13362)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.52 % (13362)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.52 % (13362)Termination reason: Unknown
% 0.21/0.52 % (13362)Termination phase: Saturation
% 0.21/0.52
% 0.21/0.52 % (13362)Memory used [KB]: 6140
% 0.21/0.52 % (13362)Time elapsed: 0.073 s
% 0.21/0.52 % (13362)Instructions burned: 8 (million)
% 0.21/0.52 % (13362)------------------------------
% 0.21/0.52 % (13362)------------------------------
% 0.21/0.52 % (13358)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)
% 0.21/0.53 % (13352)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)
% 0.21/0.53 % (13373)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)
% 0.21/0.53 % (13355)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)
% 1.36/0.53 % (13348)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)
% 1.36/0.53 % (13348)Instruction limit reached!
% 1.36/0.53 % (13348)------------------------------
% 1.36/0.53 % (13348)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (13348)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (13348)Termination reason: Unknown
% 1.36/0.53 % (13348)Termination phase: Saturation
% 1.36/0.53
% 1.36/0.53 % (13348)Memory used [KB]: 1535
% 1.36/0.53 % (13348)Time elapsed: 0.003 s
% 1.36/0.53 % (13348)Instructions burned: 3 (million)
% 1.36/0.53 % (13348)------------------------------
% 1.36/0.53 % (13348)------------------------------
% 1.36/0.53 % (13347)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)
% 1.36/0.53 % (13366)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)
% 1.36/0.53 % (13366)Instruction limit reached!
% 1.36/0.53 % (13366)------------------------------
% 1.36/0.53 % (13366)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (13366)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (13366)Termination reason: Unknown
% 1.36/0.53 % (13366)Termination phase: Preprocessing 2
% 1.36/0.53
% 1.36/0.53 % (13366)Memory used [KB]: 1407
% 1.36/0.53 % (13366)Time elapsed: 0.002 s
% 1.36/0.53 % (13366)Instructions burned: 2 (million)
% 1.36/0.53 % (13366)------------------------------
% 1.36/0.53 % (13366)------------------------------
% 1.36/0.53 % (13350)Instruction limit reached!
% 1.36/0.53 % (13350)------------------------------
% 1.36/0.53 % (13350)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (13350)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (13350)Termination reason: Unknown
% 1.36/0.53 % (13350)Termination phase: Saturation
% 1.36/0.53
% 1.36/0.53 % (13350)Memory used [KB]: 6140
% 1.36/0.53 % (13350)Time elapsed: 0.132 s
% 1.36/0.53 % (13350)Instructions burned: 14 (million)
% 1.36/0.53 % (13350)------------------------------
% 1.36/0.53 % (13350)------------------------------
% 1.36/0.53 % (13365)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.36/0.53 % (13374)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)
% 1.36/0.53 % (13365)Instruction limit reached!
% 1.36/0.53 % (13365)------------------------------
% 1.36/0.53 % (13365)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.53 % (13365)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.53 % (13365)Termination reason: Unknown
% 1.36/0.53 % (13365)Termination phase: Finite model building preprocessing
% 1.36/0.53
% 1.36/0.53 % (13365)Memory used [KB]: 1535
% 1.36/0.53 % (13365)Time elapsed: 0.003 s
% 1.36/0.53 % (13365)Instructions burned: 5 (million)
% 1.36/0.53 % (13365)------------------------------
% 1.36/0.53 % (13365)------------------------------
% 1.36/0.54 % (13346)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 1.36/0.54 % (13372)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)
% 1.36/0.54 % (13368)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 % (13377)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 % (13361)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)
% 1.36/0.54 % (13358)Instruction limit reached!
% 1.36/0.54 % (13358)------------------------------
% 1.36/0.54 % (13358)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (13358)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (13358)Termination reason: Unknown
% 1.36/0.54 % (13358)Termination phase: Saturation
% 1.36/0.54
% 1.36/0.54 % (13358)Memory used [KB]: 6140
% 1.36/0.54 % (13358)Time elapsed: 0.144 s
% 1.36/0.54 % (13358)Instructions burned: 7 (million)
% 1.36/0.54 % (13358)------------------------------
% 1.36/0.54 % (13358)------------------------------
% 1.36/0.54 % (13349)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)
% 1.36/0.54 % (13361)Instruction limit reached!
% 1.36/0.54 % (13361)------------------------------
% 1.36/0.54 % (13361)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (13361)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.54 % (13361)Termination reason: Unknown
% 1.36/0.54 % (13361)Termination phase: Saturation
% 1.36/0.54
% 1.36/0.54 % (13361)Memory used [KB]: 6012
% 1.36/0.54 % (13361)Time elapsed: 0.003 s
% 1.36/0.54 % (13361)Instructions burned: 3 (million)
% 1.36/0.54 % (13361)------------------------------
% 1.36/0.54 % (13361)------------------------------
% 1.36/0.54 % (13359)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)
% 1.36/0.54 % (13351)Instruction limit reached!
% 1.36/0.54 % (13351)------------------------------
% 1.36/0.54 % (13351)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.54 % (13367)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)
% 1.36/0.54 % (13354)First to succeed.
% 1.36/0.54 % (13370)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)
% 1.36/0.55 % (13367)Refutation not found, incomplete strategy% (13367)------------------------------
% 1.36/0.55 % (13367)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.36/0.55 % (13367)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.36/0.55 % (13367)Termination reason: Refutation not found, incomplete strategy
% 1.36/0.55
% 1.36/0.55 % (13367)Memory used [KB]: 6012
% 1.36/0.55 % (13367)Time elapsed: 0.147 s
% 1.36/0.55 % (13367)Instructions burned: 4 (million)
% 1.36/0.55 % (13367)------------------------------
% 1.36/0.55 % (13367)------------------------------
% 1.56/0.55 % (13369)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)
% 1.56/0.55 % (13354)Refutation found. Thanks to Tanya!
% 1.56/0.55 % SZS status Theorem for theBenchmark
% 1.56/0.55 % SZS output start Proof for theBenchmark
% See solution above
% 1.56/0.55 % (13354)------------------------------
% 1.56/0.55 % (13354)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.56/0.55 % (13354)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.56/0.55 % (13354)Termination reason: Refutation
% 1.56/0.55
% 1.56/0.55 % (13354)Memory used [KB]: 6396
% 1.56/0.55 % (13354)Time elapsed: 0.094 s
% 1.56/0.55 % (13354)Instructions burned: 23 (million)
% 1.56/0.55 % (13354)------------------------------
% 1.56/0.55 % (13354)------------------------------
% 1.56/0.55 % (13342)Success in time 0.188 s
%------------------------------------------------------------------------------