TSTP Solution File: SET656+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n012.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 : Sun May 5 09:07:51 EDT 2024
% Result : Theorem 0.56s 0.75s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 102 ( 13 unt; 0 def)
% Number of atoms : 396 ( 22 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 486 ( 192 ~; 181 |; 58 &)
% ( 16 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 4 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 190 ( 172 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f467,plain,
$false,
inference(avatar_sat_refutation,[],[f341,f425,f459,f466]) ).
fof(f466,plain,
~ spl18_6,
inference(avatar_contradiction_clause,[],[f465]) ).
fof(f465,plain,
( $false
| ~ spl18_6 ),
inference(subsumption_resolution,[],[f464,f126]) ).
fof(f126,plain,
sK2 != intersection(sK2,cross_product(sK0,sK1)),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( sK2 != intersection(sK2,cross_product(sK0,sK1))
& ilf_type(sK2,relation_type(sK0,sK1))
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f34,f73,f72,f71]) ).
fof(f71,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( intersection(X2,cross_product(X0,X1)) != X2
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( intersection(X2,cross_product(sK0,X1)) != X2
& ilf_type(X2,relation_type(sK0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
( ? [X1] :
( ? [X2] :
( intersection(X2,cross_product(sK0,X1)) != X2
& ilf_type(X2,relation_type(sK0,X1)) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( intersection(X2,cross_product(sK0,sK1)) != X2
& ilf_type(X2,relation_type(sK0,sK1)) )
& ilf_type(sK1,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
( ? [X2] :
( intersection(X2,cross_product(sK0,sK1)) != X2
& ilf_type(X2,relation_type(sK0,sK1)) )
=> ( sK2 != intersection(sK2,cross_product(sK0,sK1))
& ilf_type(sK2,relation_type(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( intersection(X2,cross_product(X0,X1)) != X2
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> intersection(X2,cross_product(X0,X1)) = X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',prove_relset_1_18) ).
fof(f464,plain,
( sK2 = intersection(sK2,cross_product(sK0,sK1))
| ~ spl18_6 ),
inference(resolution,[],[f420,f218]) ).
fof(f218,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(subsumption_resolution,[],[f217,f127]) ).
fof(f127,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p30) ).
fof(f217,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f134,f127]) ).
fof(f134,plain,
! [X0,X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( intersection(X0,X1) = X0
| ~ subset(X0,X1)
| ~ 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)
=> ( subset(X0,X1)
=> intersection(X0,X1) = X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p1) ).
fof(f420,plain,
( subset(sK2,cross_product(sK0,sK1))
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f418]) ).
fof(f418,plain,
( spl18_6
<=> subset(sK2,cross_product(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
fof(f459,plain,
spl18_7,
inference(avatar_contradiction_clause,[],[f458]) ).
fof(f458,plain,
( $false
| spl18_7 ),
inference(subsumption_resolution,[],[f456,f125]) ).
fof(f125,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f74]) ).
fof(f456,plain,
( ~ ilf_type(sK2,relation_type(sK0,sK1))
| spl18_7 ),
inference(resolution,[],[f451,f222]) ).
fof(f222,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f221,f127]) ).
fof(f221,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f137,f127]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ! [X1] :
( ( ! [X2] :
( ilf_type(X2,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X2,relation_type(X0,X1)) )
& ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,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,[],[f6]) ).
fof(f6,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/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p6) ).
fof(f451,plain,
( ~ ilf_type(sK2,subset_type(cross_product(sK0,sK1)))
| spl18_7 ),
inference(resolution,[],[f441,f268]) ).
fof(f268,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f267,f127]) ).
fof(f267,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f168,f127]) ).
fof(f168,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) )
& ( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,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/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p13) ).
fof(f441,plain,
( ~ ilf_type(sK2,member_type(power_set(cross_product(sK0,sK1))))
| spl18_7 ),
inference(subsumption_resolution,[],[f437,f278]) ).
fof(f278,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f183,f127]) ).
fof(f183,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p20) ).
fof(f437,plain,
( ~ ilf_type(sK2,member_type(power_set(cross_product(sK0,sK1))))
| empty(power_set(cross_product(sK0,sK1)))
| spl18_7 ),
inference(resolution,[],[f424,f277]) ).
fof(f277,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1) ),
inference(subsumption_resolution,[],[f276,f127]) ).
fof(f276,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f181,f127]) ).
fof(f181,plain,
! [X0,X1] :
( member(X0,X1)
| ~ ilf_type(X0,member_type(X1))
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ( ( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) )
& ( member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f63]) ).
fof(f63,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,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p21) ).
fof(f424,plain,
( ~ member(sK2,power_set(cross_product(sK0,sK1)))
| spl18_7 ),
inference(avatar_component_clause,[],[f422]) ).
fof(f422,plain,
( spl18_7
<=> member(sK2,power_set(cross_product(sK0,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
fof(f425,plain,
( spl18_6
| ~ spl18_7
| spl18_1 ),
inference(avatar_split_clause,[],[f409,f330,f422,f418]) ).
fof(f330,plain,
( spl18_1
<=> member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f409,plain,
( ~ member(sK2,power_set(cross_product(sK0,sK1)))
| subset(sK2,cross_product(sK0,sK1))
| spl18_1 ),
inference(resolution,[],[f345,f251]) ).
fof(f251,plain,
! [X0,X1] :
( member(sK7(X0,X1),X0)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f250,f127]) ).
fof(f250,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f155,f127]) ).
fof(f155,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK7(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f90,f91]) ).
fof(f91,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK7(X0,X1),X1)
& member(sK7(X0,X1),X0)
& ilf_type(sK7(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f49]) ).
fof(f49,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,[],[f17]) ).
fof(f17,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p17) ).
fof(f345,plain,
( ! [X0] :
( ~ member(sK7(sK2,cross_product(sK0,sK1)),X0)
| ~ member(X0,power_set(cross_product(sK0,sK1))) )
| spl18_1 ),
inference(resolution,[],[f332,f285]) ).
fof(f285,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f284,f127]) ).
fof(f284,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f283,f127]) ).
fof(f283,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f188,f127]) ).
fof(f188,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type)
| ~ member(X0,power_set(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK17(X0,X1),X1)
& member(sK17(X0,X1),X0)
& ilf_type(sK17(X0,X1),set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f120,f121]) ).
fof(f121,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK17(X0,X1),X1)
& member(sK17(X0,X1),X0)
& ilf_type(sK17(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ ilf_type(X3,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ member(X0,power_set(X1)) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f69]) ).
fof(f69,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,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p19) ).
fof(f332,plain,
( ~ member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1))
| spl18_1 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f341,plain,
~ spl18_1,
inference(avatar_split_clause,[],[f328,f330]) ).
fof(f328,plain,
~ member(sK7(sK2,cross_product(sK0,sK1)),cross_product(sK0,sK1)),
inference(superposition,[],[f311,f287]) ).
fof(f287,plain,
! [X0] : intersection(X0,X0) = X0,
inference(resolution,[],[f218,f247]) ).
fof(f247,plain,
! [X0] : subset(X0,X0),
inference(subsumption_resolution,[],[f152,f127]) ).
fof(f152,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( subset(X0,X0)
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> subset(X0,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p18) ).
fof(f311,plain,
! [X0] : ~ member(sK7(sK2,cross_product(sK0,sK1)),intersection(cross_product(sK0,sK1),X0)),
inference(trivial_inequality_removal,[],[f307]) ).
fof(f307,plain,
! [X0] :
( sK2 != sK2
| ~ member(sK7(sK2,cross_product(sK0,sK1)),intersection(cross_product(sK0,sK1),X0)) ),
inference(superposition,[],[f126,f298]) ).
fof(f298,plain,
! [X2,X0,X1] :
( intersection(X0,X1) = X0
| ~ member(sK7(X0,X1),intersection(X1,X2)) ),
inference(resolution,[],[f289,f216]) ).
fof(f216,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(subsumption_resolution,[],[f215,f127]) ).
fof(f215,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f214,f127]) ).
fof(f214,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f131,f127]) ).
fof(f131,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) )
| ~ ilf_type(X2,set_type) )
| ~ 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,set_type)
=> ( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657',p4) ).
fof(f289,plain,
! [X0,X1] :
( ~ member(sK7(X0,X1),X1)
| intersection(X0,X1) = X0 ),
inference(resolution,[],[f249,f218]) ).
fof(f249,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1) ),
inference(subsumption_resolution,[],[f248,f127]) ).
fof(f248,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f156,f127]) ).
fof(f156,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK7(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 16:50:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.35 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.dd5uJ1ntxE/Vampire---4.8_24657
% 0.56/0.73 % (24907)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.56/0.73 % (24901)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.73 % (24903)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.73 % (24902)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.56/0.73 % (24906)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.56/0.73 % (24904)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.56/0.73 % (24905)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.56/0.73 % (24906)Refutation not found, incomplete strategy% (24906)------------------------------
% 0.56/0.73 % (24906)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.73 % (24904)Refutation not found, incomplete strategy% (24904)------------------------------
% 0.56/0.73 % (24904)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.73 % (24904)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.73
% 0.56/0.73 % (24904)Memory used [KB]: 1041
% 0.56/0.73 % (24904)Time elapsed: 0.003 s
% 0.56/0.73 % (24904)Instructions burned: 3 (million)
% 0.56/0.73 % (24906)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.73
% 0.56/0.73 % (24906)Memory used [KB]: 1026
% 0.56/0.73 % (24906)Time elapsed: 0.003 s
% 0.56/0.73 % (24906)Instructions burned: 3 (million)
% 0.56/0.73 % (24904)------------------------------
% 0.56/0.73 % (24904)------------------------------
% 0.56/0.73 % (24906)------------------------------
% 0.56/0.73 % (24906)------------------------------
% 0.56/0.74 % (24908)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.56/0.74 % (24909)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.56/0.74 % (24908)Refutation not found, incomplete strategy% (24908)------------------------------
% 0.56/0.74 % (24908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.74 % (24908)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (24908)Memory used [KB]: 1040
% 0.56/0.74 % (24908)Time elapsed: 0.004 s
% 0.56/0.74 % (24908)Instructions burned: 3 (million)
% 0.56/0.74 % (24908)------------------------------
% 0.56/0.74 % (24908)------------------------------
% 0.56/0.74 % (24903)First to succeed.
% 0.56/0.75 % (24911)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/208Mi)
% 0.56/0.75 % (24903)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-24820"
% 0.56/0.75 % (24903)Refutation found. Thanks to Tanya!
% 0.56/0.75 % SZS status Theorem for Vampire---4
% 0.56/0.75 % SZS output start Proof for Vampire---4
% See solution above
% 0.56/0.75 % (24903)------------------------------
% 0.56/0.75 % (24903)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.75 % (24903)Termination reason: Refutation
% 0.56/0.75
% 0.56/0.75 % (24903)Memory used [KB]: 1184
% 0.56/0.75 % (24903)Time elapsed: 0.015 s
% 0.56/0.75 % (24903)Instructions burned: 23 (million)
% 0.56/0.75 % (24820)Success in time 0.387 s
% 0.56/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------