TSTP Solution File: SET648+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SET648+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_sat --cores 0 -t %d %s
% Computer : n004.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 18:25:13 EDT 2022
% Result : Theorem 2.09s 0.63s
% Output : Refutation 2.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 18
% Syntax : Number of formulae : 98 ( 19 unt; 0 def)
% Number of atoms : 412 ( 3 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 525 ( 211 ~; 205 |; 58 &)
% ( 11 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 201 ( 187 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f931,plain,
$false,
inference(subsumption_resolution,[],[f930,f162]) ).
fof(f162,plain,
~ ilf_type(sK1,sF15),
inference(definition_folding,[],[f112,f161,f160]) ).
fof(f160,plain,
domain_of(sK1) = sF14,
introduced(function_definition,[]) ).
fof(f161,plain,
sF15 = relation_type(sF14,sK0),
introduced(function_definition,[]) ).
fof(f112,plain,
~ ilf_type(sK1,relation_type(domain_of(sK1),sK0)),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
( ilf_type(sK1,binary_relation_type)
& ~ ilf_type(sK1,relation_type(domain_of(sK1),sK0))
& subset(range_of(sK1),sK0)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f42,f67,f66]) ).
fof(f66,plain,
( ? [X0] :
( ? [X1] :
( ilf_type(X1,binary_relation_type)
& ~ ilf_type(X1,relation_type(domain_of(X1),X0))
& subset(range_of(X1),X0) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ilf_type(X1,binary_relation_type)
& ~ ilf_type(X1,relation_type(domain_of(X1),sK0))
& subset(range_of(X1),sK0) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
( ? [X1] :
( ilf_type(X1,binary_relation_type)
& ~ ilf_type(X1,relation_type(domain_of(X1),sK0))
& subset(range_of(X1),sK0) )
=> ( ilf_type(sK1,binary_relation_type)
& ~ ilf_type(sK1,relation_type(domain_of(sK1),sK0))
& subset(range_of(sK1),sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0] :
( ? [X1] :
( ilf_type(X1,binary_relation_type)
& ~ ilf_type(X1,relation_type(domain_of(X1),X0))
& subset(range_of(X1),X0) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
? [X0] :
( ? [X1] :
( ~ ilf_type(X1,relation_type(domain_of(X1),X0))
& subset(range_of(X1),X0)
& ilf_type(X1,binary_relation_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
inference(negated_conjecture,[],[f27]) ).
fof(f27,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,binary_relation_type)
=> ( subset(range_of(X1),X0)
=> ilf_type(X1,relation_type(domain_of(X1),X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_10) ).
fof(f930,plain,
ilf_type(sK1,sF15),
inference(forward_demodulation,[],[f928,f161]) ).
fof(f928,plain,
ilf_type(sK1,relation_type(sF14,sK0)),
inference(resolution,[],[f925,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,subset_type(cross_product(X0,X1)))
| ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f180,f145]) ).
fof(f145,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(f180,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) ),
inference(subsumption_resolution,[],[f127,f145]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X2,subset_type(cross_product(X0,X1))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [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)) ) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [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)) ) ) )
| ~ ilf_type(X0,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(f925,plain,
ilf_type(sK1,subset_type(cross_product(sF14,sK0))),
inference(resolution,[],[f906,f197]) ).
fof(f197,plain,
! [X2,X3] :
( ~ member(X3,power_set(X2))
| ilf_type(X3,subset_type(X2)) ),
inference(subsumption_resolution,[],[f195,f175]) ).
fof(f175,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f125,f145]) ).
fof(f125,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,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(f195,plain,
! [X2,X3] :
( ilf_type(X3,subset_type(X2))
| ~ member(X3,power_set(X2))
| empty(power_set(X2)) ),
inference(resolution,[],[f174,f169]) ).
fof(f169,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f168,f145]) ).
fof(f168,plain,
! [X0,X1] :
( ~ ilf_type(X1,member_type(power_set(X0)))
| ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f156,f145]) ).
fof(f156,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [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)) )
& ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ) ) ) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [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)) ) ) ),
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(f174,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| empty(X1)
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f173,f145]) ).
fof(f173,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ ilf_type(X0,set_type)
| ~ member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f159,f145]) ).
fof(f159,plain,
! [X0,X1] :
( ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type)
| ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [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) ) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) ) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p22) ).
fof(f906,plain,
member(sK1,power_set(cross_product(sF14,sK0))),
inference(subsumption_resolution,[],[f905,f145]) ).
fof(f905,plain,
( member(sK1,power_set(cross_product(sF14,sK0)))
| ~ ilf_type(cross_product(sF14,sK0),set_type) ),
inference(subsumption_resolution,[],[f904,f145]) ).
fof(f904,plain,
( ~ ilf_type(sK1,set_type)
| ~ ilf_type(cross_product(sF14,sK0),set_type)
| member(sK1,power_set(cross_product(sF14,sK0))) ),
inference(duplicate_literal_removal,[],[f902]) ).
fof(f902,plain,
( member(sK1,power_set(cross_product(sF14,sK0)))
| ~ ilf_type(sK1,set_type)
| ~ ilf_type(cross_product(sF14,sK0),set_type)
| member(sK1,power_set(cross_product(sF14,sK0))) ),
inference(resolution,[],[f713,f131]) ).
fof(f131,plain,
! [X0,X1] :
( ~ member(sK5(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK5(X0,X1),X1)
& ilf_type(sK5(X0,X1),set_type)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f81,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) )
=> ( ~ member(sK5(X0,X1),X1)
& ilf_type(sK5(X0,X1),set_type)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(f713,plain,
! [X4] :
( member(sK5(sK1,X4),cross_product(sF14,sK0))
| member(sK1,power_set(X4)) ),
inference(resolution,[],[f692,f264]) ).
fof(f264,plain,
! [X2,X3,X4] :
( ~ subset(X3,X4)
| member(X3,power_set(X2))
| member(sK5(X3,X2),X4) ),
inference(subsumption_resolution,[],[f263,f145]) ).
fof(f263,plain,
! [X2,X3,X4] :
( member(X3,power_set(X2))
| ~ subset(X3,X4)
| member(sK5(X3,X2),X4)
| ~ ilf_type(X3,set_type) ),
inference(subsumption_resolution,[],[f262,f145]) ).
fof(f262,plain,
! [X2,X3,X4] :
( member(sK5(X3,X2),X4)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| member(X3,power_set(X2))
| ~ subset(X3,X4) ),
inference(resolution,[],[f129,f186]) ).
fof(f186,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| ~ subset(X0,X1)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f185,f145]) ).
fof(f185,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f184,f145]) ).
fof(f184,plain,
! [X3,X0,X1] :
( ~ member(X3,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1)
| member(X3,X1) ),
inference(subsumption_resolution,[],[f119,f145]) ).
fof(f119,plain,
! [X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(X3,X0)
| ~ ilf_type(X0,set_type)
| member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& ilf_type(sK4(X0,X1),set_type)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f76,f77]) ).
fof(f77,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& ilf_type(sK4(X0,X1),set_type)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(rectify,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& ilf_type(X2,set_type)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0) ) )
| ~ ilf_type(X1,set_type) ) ),
inference(flattening,[],[f39]) ).
fof(f39,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,[],[f12]) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',p12) ).
fof(f129,plain,
! [X0,X1] :
( member(sK5(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f83]) ).
fof(f692,plain,
subset(sK1,cross_product(sF14,sK0)),
inference(resolution,[],[f649,f164]) ).
fof(f164,plain,
subset(sF16,sK0),
inference(definition_folding,[],[f111,f163]) ).
fof(f163,plain,
range_of(sK1) = sF16,
introduced(function_definition,[]) ).
fof(f111,plain,
subset(range_of(sK1),sK0),
inference(cnf_transformation,[],[f68]) ).
fof(f649,plain,
! [X13] :
( ~ subset(sF16,X13)
| subset(sK1,cross_product(sF14,X13)) ),
inference(resolution,[],[f454,f215]) ).
fof(f215,plain,
subset(sK1,cross_product(sF14,sF16)),
inference(forward_demodulation,[],[f214,f163]) ).
fof(f214,plain,
subset(sK1,cross_product(sF14,range_of(sK1))),
inference(subsumption_resolution,[],[f212,f113]) ).
fof(f113,plain,
ilf_type(sK1,binary_relation_type),
inference(cnf_transformation,[],[f68]) ).
fof(f212,plain,
( subset(sK1,cross_product(sF14,range_of(sK1)))
| ~ ilf_type(sK1,binary_relation_type) ),
inference(superposition,[],[f135,f160]) ).
fof(f135,plain,
! [X0] :
( subset(X0,cross_product(domain_of(X0),range_of(X0)))
| ~ ilf_type(X0,binary_relation_type) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,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/sandbox/benchmark/theBenchmark.p',p2) ).
fof(f454,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cross_product(X0,X1))
| subset(X3,cross_product(X0,X2))
| ~ subset(X1,X2) ),
inference(subsumption_resolution,[],[f453,f145]) ).
fof(f453,plain,
! [X2,X3,X0,X1] :
( ~ subset(X1,X2)
| subset(X3,cross_product(X0,X2))
| ~ subset(X3,cross_product(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f452,f145]) ).
fof(f452,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cross_product(X0,X1))
| ~ ilf_type(X3,set_type)
| subset(X3,cross_product(X0,X2))
| ~ ilf_type(X0,set_type)
| ~ subset(X1,X2) ),
inference(subsumption_resolution,[],[f451,f145]) ).
fof(f451,plain,
! [X2,X3,X0,X1] :
( ~ subset(X3,cross_product(X0,X1))
| subset(X3,cross_product(X0,X2))
| ~ subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X3,set_type) ),
inference(subsumption_resolution,[],[f450,f145]) ).
fof(f450,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(cross_product(X0,X2),set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X3,cross_product(X0,X1))
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| subset(X3,cross_product(X0,X2))
| ~ ilf_type(X1,set_type) ),
inference(subsumption_resolution,[],[f449,f145]) ).
fof(f449,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(cross_product(X0,X1),set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(cross_product(X0,X2),set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X3,cross_product(X0,X1))
| subset(X3,cross_product(X0,X2))
| ~ subset(X1,X2) ),
inference(subsumption_resolution,[],[f448,f145]) ).
fof(f448,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(cross_product(X0,X2),set_type)
| ~ subset(X3,cross_product(X0,X1))
| ~ ilf_type(cross_product(X0,X1),set_type)
| subset(X3,cross_product(X0,X2))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X1,X2) ),
inference(resolution,[],[f132,f134]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ subset(X1,X2)
| ~ subset(X0,X1)
| subset(X0,X2)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( subset(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2)
| ~ subset(X0,X1) ) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f58]) ).
fof(f58,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(f132,plain,
! [X2,X0,X1] :
( subset(cross_product(X2,X0),cross_product(X2,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X0,set_type)
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ! [X1] :
( ~ ilf_type(X1,set_type)
| ! [X2] :
( ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) )
| ~ ilf_type(X2,set_type)
| ~ subset(X0,X1) ) ) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) )
| ~ subset(X0,X1)
| ~ 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)
=> ( subset(X0,X1)
=> ( subset(cross_product(X0,X2),cross_product(X1,X2))
& subset(cross_product(X2,X0),cross_product(X2,X1)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET648+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n004.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 : Tue Aug 30 14:06:19 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.50 % (10700)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.50 % (10692)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.51 % (10684)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.51 % (10680)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51 % (10685)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.51 % (10683)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.51 % (10681)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.52 % (10680)Instruction limit reached!
% 0.20/0.52 % (10680)------------------------------
% 0.20/0.52 % (10680)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52 % (10674)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.52 % (10680)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52 % (10680)Termination reason: Unknown
% 0.20/0.52 % (10680)Termination phase: Blocked clause elimination
% 0.20/0.52
% 0.20/0.52 % (10680)Memory used [KB]: 1023
% 0.20/0.52 % (10680)Time elapsed: 0.004 s
% 0.20/0.52 % (10680)Instructions burned: 3 (million)
% 0.20/0.52 % (10680)------------------------------
% 0.20/0.52 % (10680)------------------------------
% 0.20/0.53 % (10678)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (10690)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.53 % (10672)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.53 % (10676)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (10677)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.53 % (10675)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53 % (10673)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 % (10682)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.53 TRYING [1]
% 0.20/0.54 % (10673)Refutation not found, incomplete strategy% (10673)------------------------------
% 0.20/0.54 % (10673)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.54 % (10673)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.54 % (10673)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.54
% 0.20/0.54 % (10673)Memory used [KB]: 5500
% 0.20/0.54 % (10673)Time elapsed: 0.137 s
% 0.20/0.54 % (10673)Instructions burned: 5 (million)
% 0.20/0.54 % (10673)------------------------------
% 0.20/0.54 % (10673)------------------------------
% 0.20/0.54 TRYING [2]
% 0.20/0.54 % (10686)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (10701)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.54 % (10698)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.54 % (10694)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.54 % (10696)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55 % (10697)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.55 % (10699)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.55 % (10679)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55 % (10688)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.55 % (10691)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (10689)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.55 % (10695)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.55 TRYING [1]
% 0.20/0.55 % (10679)Instruction limit reached!
% 0.20/0.55 % (10679)------------------------------
% 0.20/0.55 % (10679)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (10679)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (10679)Termination reason: Unknown
% 0.20/0.55 % (10679)Termination phase: Saturation
% 0.20/0.55
% 0.20/0.55 % (10679)Memory used [KB]: 5500
% 0.20/0.55 % (10679)Time elapsed: 0.133 s
% 0.20/0.55 % (10679)Instructions burned: 7 (million)
% 0.20/0.55 % (10679)------------------------------
% 0.20/0.55 % (10679)------------------------------
% 0.20/0.55 TRYING [2]
% 0.20/0.55 % (10693)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.56 % (10687)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.56 TRYING [3]
% 0.20/0.56 TRYING [1]
% 0.20/0.56 TRYING [2]
% 0.20/0.56 TRYING [3]
% 0.20/0.58 TRYING [3]
% 0.20/0.60 % (10681)Instruction limit reached!
% 0.20/0.60 % (10681)------------------------------
% 0.20/0.60 % (10681)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.60 % (10681)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.60 % (10681)Termination reason: Unknown
% 0.20/0.60 % (10681)Termination phase: Saturation
% 0.20/0.60
% 0.20/0.60 % (10681)Memory used [KB]: 1407
% 0.20/0.60 % (10681)Time elapsed: 0.182 s
% 0.20/0.60 % (10681)Instructions burned: 51 (million)
% 0.20/0.60 % (10681)------------------------------
% 0.20/0.60 % (10681)------------------------------
% 1.76/0.60 % (10674)Instruction limit reached!
% 1.76/0.60 % (10674)------------------------------
% 1.76/0.60 % (10674)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.76/0.60 % (10674)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.76/0.60 % (10674)Termination reason: Unknown
% 1.76/0.60 % (10674)Termination phase: Saturation
% 1.76/0.60
% 1.76/0.60 % (10674)Memory used [KB]: 1535
% 1.76/0.60 % (10674)Time elapsed: 0.208 s
% 1.76/0.60 % (10674)Instructions burned: 38 (million)
% 1.76/0.60 % (10674)------------------------------
% 1.76/0.60 % (10674)------------------------------
% 1.76/0.61 % (10678)Instruction limit reached!
% 1.76/0.61 % (10678)------------------------------
% 1.76/0.61 % (10678)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.76/0.61 % (10678)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.76/0.61 % (10678)Termination reason: Unknown
% 1.76/0.61 % (10678)Termination phase: Finite model building SAT solving
% 1.76/0.61
% 1.76/0.61 % (10678)Memory used [KB]: 6780
% 1.76/0.61 % (10678)Time elapsed: 0.131 s
% 1.76/0.61 % (10678)Instructions burned: 53 (million)
% 1.76/0.61 % (10678)------------------------------
% 1.76/0.61 % (10678)------------------------------
% 1.76/0.62 % (10682)Instruction limit reached!
% 1.76/0.62 % (10682)------------------------------
% 1.76/0.62 % (10682)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.76/0.62 % (10682)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.76/0.62 % (10682)Termination reason: Unknown
% 1.76/0.62 % (10682)Termination phase: Saturation
% 1.76/0.62
% 1.76/0.62 % (10682)Memory used [KB]: 6012
% 1.76/0.62 % (10682)Time elapsed: 0.220 s
% 1.76/0.62 % (10682)Instructions burned: 50 (million)
% 1.76/0.62 % (10682)------------------------------
% 1.76/0.62 % (10682)------------------------------
% 1.76/0.62 TRYING [4]
% 1.76/0.62 % (10677)Instruction limit reached!
% 1.76/0.62 % (10677)------------------------------
% 1.76/0.62 % (10677)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.76/0.62 % (10677)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.76/0.62 % (10677)Termination reason: Unknown
% 1.76/0.62 % (10677)Termination phase: Saturation
% 1.76/0.62
% 1.76/0.62 % (10677)Memory used [KB]: 6140
% 1.76/0.62 % (10677)Time elapsed: 0.223 s
% 1.76/0.62 % (10677)Instructions burned: 49 (million)
% 1.76/0.62 % (10677)------------------------------
% 1.76/0.62 % (10677)------------------------------
% 2.09/0.63 % (10699)First to succeed.
% 2.09/0.63 % (10699)Refutation found. Thanks to Tanya!
% 2.09/0.63 % SZS status Theorem for theBenchmark
% 2.09/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 2.09/0.63 % (10699)------------------------------
% 2.09/0.63 % (10699)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.09/0.63 % (10699)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.09/0.63 % (10699)Termination reason: Refutation
% 2.09/0.63
% 2.09/0.63 % (10699)Memory used [KB]: 1535
% 2.09/0.63 % (10699)Time elapsed: 0.234 s
% 2.09/0.63 % (10699)Instructions burned: 38 (million)
% 2.09/0.63 % (10699)------------------------------
% 2.09/0.63 % (10699)------------------------------
% 2.09/0.63 % (10671)Success in time 0.269 s
%------------------------------------------------------------------------------