TSTP Solution File: SET646+3 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET646+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 : Wed May 1 03:48:28 EDT 2024
% Result : Theorem 0.57s 0.76s
% Output : Refutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 14 unt; 0 def)
% Number of atoms : 465 ( 40 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 601 ( 224 ~; 209 |; 109 &)
% ( 16 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-2 aty)
% Number of variables : 222 ( 188 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f370,plain,
$false,
inference(subsumption_resolution,[],[f369,f110]) ).
fof(f110,plain,
member(sK2,sK0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
( ~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1))
& member(sK3,sK1)
& member(sK2,sK0)
& ilf_type(sK3,set_type)
& ilf_type(sK2,set_type)
& ilf_type(sK1,set_type)
& ilf_type(sK0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f30,f64,f63,f62,f61]) ).
fof(f61,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,X1))
& member(X3,X1)
& member(X2,sK0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK0,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f62,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,X1))
& member(X3,X1)
& member(X2,sK0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,sK1))
& member(X3,sK1)
& member(X2,sK0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK1,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f63,plain,
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(sK0,sK1))
& member(X3,sK1)
& member(X2,sK0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(sK2,X3)),relation_type(sK0,sK1))
& member(X3,sK1)
& member(sK2,sK0)
& ilf_type(X3,set_type) )
& ilf_type(sK2,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f64,plain,
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(sK2,X3)),relation_type(sK0,sK1))
& member(X3,sK1)
& member(sK2,sK0)
& ilf_type(X3,set_type) )
=> ( ~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1))
& member(sK3,sK1)
& member(sK2,sK0)
& ilf_type(sK3,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ~ ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1))
& member(X3,X1)
& member(X2,X0)
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
inference(negated_conjecture,[],[f26]) ).
fof(f26,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( member(X3,X1)
& member(X2,X0) )
=> ilf_type(singleton(ordered_pair(X2,X3)),relation_type(X0,X1)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',prove_relset_1_8) ).
fof(f369,plain,
~ member(sK2,sK0),
inference(subsumption_resolution,[],[f362,f111]) ).
fof(f111,plain,
member(sK3,sK1),
inference(cnf_transformation,[],[f65]) ).
fof(f362,plain,
( ~ member(sK3,sK1)
| ~ member(sK2,sK0) ),
inference(resolution,[],[f348,f208]) ).
fof(f208,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(subsumption_resolution,[],[f207,f113]) ).
fof(f113,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p25) ).
fof(f207,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f206,f113]) ).
fof(f206,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f205,f113]) ).
fof(f205,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f133,f113]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) )
| ~ ilf_type(X3,set_type) )
| ~ 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] :
( ! [X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) )
| ~ ilf_type(X3,set_type) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,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)
=> ( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p2) ).
fof(f348,plain,
~ member(ordered_pair(sK2,sK3),cross_product(sK0,sK1)),
inference(backward_demodulation,[],[f304,f346]) ).
fof(f346,plain,
ordered_pair(sK2,sK3) = sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),
inference(resolution,[],[f303,f194]) ).
fof(f194,plain,
! [X1,X4] :
( ~ member(X4,singleton(X1))
| X1 = X4 ),
inference(subsumption_resolution,[],[f193,f113]) ).
fof(f193,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f192,f113]) ).
fof(f192,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f191,f113]) ).
fof(f191,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f171,f113]) ).
fof(f171,plain,
! [X0,X1,X4] :
( X1 = X4
| ~ member(X4,singleton(X1))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(singleton(X1),set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(equality_resolution,[],[f117]) ).
fof(f117,plain,
! [X2,X0,X1,X4] :
( X1 = X4
| ~ member(X4,X2)
| ~ ilf_type(X4,set_type)
| singleton(X1) != X2
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ( ( sK4(X1,X2) != X1
| ~ member(sK4(X1,X2),X2) )
& ( sK4(X1,X2) = X1
| member(sK4(X1,X2),X2) )
& ilf_type(sK4(X1,X2),set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f69,f70]) ).
fof(f70,plain,
! [X1,X2] :
( ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) )
=> ( ( sK4(X1,X2) != X1
| ~ member(sK4(X1,X2),X2) )
& ( sK4(X1,X2) = X1
| member(sK4(X1,X2),X2) )
& ilf_type(sK4(X1,X2),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X4] :
( ( ( member(X4,X2)
| X1 != X4 )
& ( X1 = X4
| ~ member(X4,X2) ) )
| ~ ilf_type(X4,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X1 = X3
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( singleton(X1) = X2
| ? [X3] :
( ( X1 != X3
| ~ member(X3,X2) )
& ( X1 = X3
| member(X3,X2) )
& ilf_type(X3,set_type) ) )
& ( ! [X3] :
( ( ( member(X3,X2)
| X1 != X3 )
& ( X1 = X3
| ~ member(X3,X2) ) )
| ~ ilf_type(X3,set_type) )
| singleton(X1) != X2 ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( singleton(X1) = X2
<=> ! [X3] :
( ( member(X3,X2)
<=> X1 = X3 )
| ~ ilf_type(X3,set_type) ) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( singleton(X1) = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X2)
<=> X1 = X3 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p5) ).
fof(f303,plain,
member(sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),singleton(ordered_pair(sK2,sK3))),
inference(resolution,[],[f301,f258]) ).
fof(f258,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK14(X0,X1),X0) ),
inference(subsumption_resolution,[],[f257,f113]) ).
fof(f257,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK14(X0,X1),X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f165,f113]) ).
fof(f165,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| member(sK14(X0,X1),X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK14(X0,X1),X1)
& member(sK14(X0,X1),X0)
& ilf_type(sK14(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,[sK14])],[f103,f104]) ).
fof(f104,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK14(X0,X1),X1)
& member(sK14(X0,X1),X0)
& ilf_type(sK14(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f103,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,[],[f102]) ).
fof(f102,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,[],[f60]) ).
fof(f60,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,[],[f59]) ).
fof(f59,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,[],[f17]) ).
fof(f17,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.uggCXQGWln/Vampire---4.8_29530',p17) ).
fof(f301,plain,
~ member(singleton(ordered_pair(sK2,sK3)),power_set(cross_product(sK0,sK1))),
inference(resolution,[],[f298,f251]) ).
fof(f251,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1) ),
inference(subsumption_resolution,[],[f250,f247]) ).
fof(f247,plain,
! [X2,X0] :
( ~ empty(X0)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f246,f113]) ).
fof(f246,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f155,f113]) ).
fof(f155,plain,
! [X2,X0] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type)
| ~ empty(X0)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( ( empty(X0)
| ( member(sK12(X0),X0)
& ilf_type(sK12(X0),set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f96,f97]) ).
fof(f97,plain,
! [X0] :
( ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) )
=> ( member(sK12(X0),X0)
& ilf_type(sK12(X0),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f96,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X2] :
( ~ member(X2,X0)
| ~ ilf_type(X2,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(rectify,[],[f95]) ).
fof(f95,plain,
! [X0] :
( ( ( empty(X0)
| ? [X1] :
( member(X1,X0)
& ilf_type(X1,set_type) ) )
& ( ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) )
| ~ empty(X0) ) )
| ~ ilf_type(X0,set_type) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ( empty(X0)
<=> ! [X1] :
( ~ member(X1,X0)
| ~ ilf_type(X1,set_type) ) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( empty(X0)
<=> ! [X1] :
( ilf_type(X1,set_type)
=> ~ member(X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.uggCXQGWln/Vampire---4.8_29530',p21) ).
fof(f250,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1) ),
inference(subsumption_resolution,[],[f249,f113]) ).
fof(f249,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f160,f113]) ).
fof(f160,plain,
! [X0,X1] :
( ilf_type(X0,member_type(X1))
| ~ member(X0,X1)
| ~ ilf_type(X1,set_type)
| empty(X1)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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,[],[f57]) ).
fof(f57,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,[],[f56]) ).
fof(f56,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,[],[f19]) ).
fof(f19,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.uggCXQGWln/Vampire---4.8_29530',p19) ).
fof(f298,plain,
~ ilf_type(singleton(ordered_pair(sK2,sK3)),member_type(power_set(cross_product(sK0,sK1)))),
inference(resolution,[],[f296,f242]) ).
fof(f242,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0))) ),
inference(subsumption_resolution,[],[f241,f113]) ).
fof(f241,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f154,f113]) ).
fof(f154,plain,
! [X0,X1] :
( ilf_type(X1,subset_type(X0))
| ~ ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,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,[],[f52]) ).
fof(f52,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,[],[f12]) ).
fof(f12,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.uggCXQGWln/Vampire---4.8_29530',p12) ).
fof(f296,plain,
~ ilf_type(singleton(ordered_pair(sK2,sK3)),subset_type(cross_product(sK0,sK1))),
inference(resolution,[],[f222,f112]) ).
fof(f112,plain,
~ ilf_type(singleton(ordered_pair(sK2,sK3)),relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f65]) ).
fof(f222,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f221,f113]) ).
fof(f221,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f135,f113]) ).
fof(f135,plain,
! [X3,X0,X1] :
( ilf_type(X3,relation_type(X0,X1))
| ~ ilf_type(X3,subset_type(cross_product(X0,X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,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,[],[f28]) ).
fof(f28,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,[],[f3]) ).
fof(f3,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.uggCXQGWln/Vampire---4.8_29530',p3) ).
fof(f304,plain,
~ member(sK14(singleton(ordered_pair(sK2,sK3)),cross_product(sK0,sK1)),cross_product(sK0,sK1)),
inference(resolution,[],[f301,f256]) ).
fof(f256,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK14(X0,X1),X1) ),
inference(subsumption_resolution,[],[f255,f113]) ).
fof(f255,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK14(X0,X1),X1)
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f166,f113]) ).
fof(f166,plain,
! [X0,X1] :
( member(X0,power_set(X1))
| ~ member(sK14(X0,X1),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET646+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.15 % 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
% 0.14/0.35 % Computer : n012.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 Apr 30 17:12:11 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36 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.uggCXQGWln/Vampire---4.8_29530
% 0.57/0.75 % (29755)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)
% 0.57/0.75 % (29761)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)
% 0.57/0.75 % (29757)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.57/0.75 % (29756)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)
% 0.57/0.75 % (29758)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)
% 0.57/0.75 % (29759)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)
% 0.57/0.75 % (29760)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)
% 0.57/0.75 % (29755)Refutation not found, incomplete strategy% (29755)------------------------------
% 0.57/0.75 % (29755)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75 % (29755)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (29755)Memory used [KB]: 1098
% 0.57/0.75 % (29755)Time elapsed: 0.004 s
% 0.57/0.75 % (29755)Instructions burned: 8 (million)
% 0.57/0.75 % (29755)------------------------------
% 0.57/0.75 % (29755)------------------------------
% 0.57/0.75 % (29760)Refutation not found, incomplete strategy% (29760)------------------------------
% 0.57/0.75 % (29760)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75 % (29760)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (29760)Memory used [KB]: 1030
% 0.57/0.75 % (29760)Time elapsed: 0.003 s
% 0.57/0.75 % (29760)Instructions burned: 3 (million)
% 0.57/0.75 % (29760)------------------------------
% 0.57/0.75 % (29760)------------------------------
% 0.57/0.75 % (29758)Refutation not found, incomplete strategy% (29758)------------------------------
% 0.57/0.75 % (29758)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75 % (29758)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (29758)Memory used [KB]: 1032
% 0.57/0.75 % (29762)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)
% 0.57/0.75 % (29758)Time elapsed: 0.003 s
% 0.57/0.75 % (29758)Instructions burned: 3 (million)
% 0.57/0.75 % (29758)------------------------------
% 0.57/0.75 % (29758)------------------------------
% 0.57/0.75 % (29759)Refutation not found, incomplete strategy% (29759)------------------------------
% 0.57/0.75 % (29759)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75 % (29759)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (29759)Memory used [KB]: 1113
% 0.57/0.75 % (29759)Time elapsed: 0.004 s
% 0.57/0.75 % (29759)Instructions burned: 6 (million)
% 0.57/0.75 % (29759)------------------------------
% 0.57/0.75 % (29759)------------------------------
% 0.57/0.75 % (29762)Refutation not found, incomplete strategy% (29762)------------------------------
% 0.57/0.75 % (29762)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.75 % (29762)Termination reason: Refutation not found, incomplete strategy
% 0.57/0.75
% 0.57/0.75 % (29762)Memory used [KB]: 1032
% 0.57/0.75 % (29762)Time elapsed: 0.003 s
% 0.57/0.75 % (29763)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)
% 0.57/0.75 % (29762)Instructions burned: 4 (million)
% 0.57/0.75 % (29762)------------------------------
% 0.57/0.75 % (29762)------------------------------
% 0.57/0.76 % (29764)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.57/0.76 % (29765)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)
% 0.57/0.76 % (29766)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2996ds/52Mi)
% 0.57/0.76 % (29767)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2996ds/518Mi)
% 0.57/0.76 % (29757)First to succeed.
% 0.57/0.76 % (29757)Refutation found. Thanks to Tanya!
% 0.57/0.76 % SZS status Theorem for Vampire---4
% 0.57/0.76 % SZS output start Proof for Vampire---4
% See solution above
% 0.57/0.76 % (29757)------------------------------
% 0.57/0.76 % (29757)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.57/0.76 % (29757)Termination reason: Refutation
% 0.57/0.76
% 0.57/0.76 % (29757)Memory used [KB]: 1171
% 0.57/0.76 % (29757)Time elapsed: 0.012 s
% 0.57/0.76 % (29757)Instructions burned: 18 (million)
% 0.57/0.76 % (29757)------------------------------
% 0.57/0.76 % (29757)------------------------------
% 0.57/0.76 % (29725)Success in time 0.393 s
% 0.57/0.76 % Vampire---4.8 exiting
%------------------------------------------------------------------------------