TSTP Solution File: SET645+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET645+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 : n008.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 0.56s 0.75s
% Output : Refutation 0.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 16
% Syntax : Number of formulae : 91 ( 9 unt; 0 def)
% Number of atoms : 438 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 555 ( 208 ~; 209 |; 87 &)
% ( 12 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 201 ( 163 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f507,plain,
$false,
inference(avatar_sat_refutation,[],[f162,f341,f506]) ).
fof(f506,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f505]) ).
fof(f505,plain,
( $false
| spl15_2 ),
inference(subsumption_resolution,[],[f503,f161]) ).
fof(f161,plain,
( ~ member(sK12,sK10)
| spl15_2 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f159,plain,
( spl15_2
<=> member(sK12,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f503,plain,
member(sK12,sK10),
inference(resolution,[],[f391,f134]) ).
fof(f134,plain,
ilf_type(sK13,relation_type(sK9,sK10)),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),sK13)
& ilf_type(sK13,relation_type(sK9,sK10))
& ilf_type(sK12,set_type)
& ilf_type(sK11,set_type)
& ilf_type(sK10,set_type)
& ilf_type(sK9,set_type) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12,sK13])],[f51,f86,f85,f84,f83,f82]) ).
fof(f82,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,X0) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(sK9,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(sK10,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(X2,sK9) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
=> ( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
& ilf_type(sK11,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,X3),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(X3,set_type) )
=> ( ? [X4] :
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
& ilf_type(sK12,set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X4] :
( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),X4)
& ilf_type(X4,relation_type(sK9,sK10)) )
=> ( ( ~ member(sK12,sK10)
| ~ member(sK11,sK9) )
& member(ordered_pair(sK11,sK12),sK13)
& ilf_type(sK13,relation_type(sK9,sK10)) ) ),
introduced(choice_axiom,[]) ).
fof(f51,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,X0) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(X0,X1)) )
& ilf_type(X3,set_type) )
& ilf_type(X2,set_type) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ( ~ member(X3,X1)
| ~ member(X2,X0) )
& member(ordered_pair(X2,X3),X4)
& ilf_type(X4,relation_type(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,[],[f23]) ).
fof(f23,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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,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)
=> ! [X4] :
( ilf_type(X4,relation_type(X0,X1))
=> ( member(ordered_pair(X2,X3),X4)
=> ( member(X3,X1)
& member(X2,X0) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7sX5uTqycy/Vampire---4.8_30040',prove_relset_1_7) ).
fof(f391,plain,
! [X0,X1] :
( ~ ilf_type(sK13,relation_type(X1,X0))
| member(sK12,X0) ),
inference(subsumption_resolution,[],[f388,f129]) ).
fof(f129,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.7sX5uTqycy/Vampire---4.8_30040',p21) ).
fof(f388,plain,
! [X0,X1] :
( member(sK12,X0)
| ~ ilf_type(sK13,relation_type(X1,X0))
| ~ ilf_type(cross_product(X1,X0),set_type) ),
inference(resolution,[],[f387,f113]) ).
fof(f113,plain,
! [X0] :
( ~ empty(power_set(X0))
| ~ ilf_type(X0,set_type) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7sX5uTqycy/Vampire---4.8_30040',p14) ).
fof(f387,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(sK13,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f386,f129]) ).
fof(f386,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(sK13,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f384,f129]) ).
fof(f384,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(sK13,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f320,f95]) ).
fof(f95,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,[],[f28]) ).
fof(f28,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,[],[f24]) ).
fof(f24,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/sandbox2/tmp/tmp.7sX5uTqycy/Vampire---4.8_30040',p4) ).
fof(f320,plain,
! [X0,X1] :
( ~ ilf_type(sK13,subset_type(cross_product(X1,X0)))
| empty(power_set(cross_product(X1,X0)))
| member(sK12,X0) ),
inference(subsumption_resolution,[],[f319,f129]) ).
fof(f319,plain,
! [X0,X1] :
( member(sK12,X0)
| empty(power_set(cross_product(X1,X0)))
| ~ ilf_type(sK13,subset_type(cross_product(X1,X0)))
| ~ ilf_type(cross_product(X1,X0),set_type) ),
inference(subsumption_resolution,[],[f317,f129]) ).
fof(f317,plain,
! [X0,X1] :
( member(sK12,X0)
| empty(power_set(cross_product(X1,X0)))
| ~ ilf_type(sK13,subset_type(cross_product(X1,X0)))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(cross_product(X1,X0),set_type) ),
inference(resolution,[],[f268,f101]) ).
fof(f101,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,[],[f57]) ).
fof(f57,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,[],[f34]) ).
fof(f34,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,[],[f10]) ).
fof(f10,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.7sX5uTqycy/Vampire---4.8_30040',p10) ).
fof(f268,plain,
! [X0,X1] :
( ~ ilf_type(sK13,member_type(power_set(cross_product(X1,X0))))
| member(sK12,X0)
| empty(power_set(cross_product(X1,X0))) ),
inference(subsumption_resolution,[],[f267,f129]) ).
fof(f267,plain,
! [X0,X1] :
( member(sK12,X0)
| ~ ilf_type(sK13,member_type(power_set(cross_product(X1,X0))))
| empty(power_set(cross_product(X1,X0)))
| ~ ilf_type(sK13,set_type) ),
inference(subsumption_resolution,[],[f263,f129]) ).
fof(f263,plain,
! [X0,X1] :
( member(sK12,X0)
| ~ ilf_type(sK13,member_type(power_set(cross_product(X1,X0))))
| ~ ilf_type(power_set(cross_product(X1,X0)),set_type)
| empty(power_set(cross_product(X1,X0)))
| ~ ilf_type(sK13,set_type) ),
inference(resolution,[],[f231,f115]) ).
fof(f115,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,[],[f69]) ).
fof(f69,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,[],[f41]) ).
fof(f41,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,[],[f40]) ).
fof(f40,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,[],[f15]) ).
fof(f15,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.7sX5uTqycy/Vampire---4.8_30040',p15) ).
fof(f231,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK12,X1) ),
inference(subsumption_resolution,[],[f230,f129]) ).
fof(f230,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f229,f129]) ).
fof(f229,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f228,f129]) ).
fof(f228,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f214,f129]) ).
fof(f214,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK12,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(resolution,[],[f190,f89]) ).
fof(f89,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ 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(cnf_transformation,[],[f53]) ).
fof(f53,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,[],[f52]) ).
fof(f52,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,[],[f25]) ).
fof(f25,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,[],[f1]) ).
fof(f1,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.7sX5uTqycy/Vampire---4.8_30040',p1) ).
fof(f190,plain,
! [X0] :
( member(ordered_pair(sK11,sK12),X0)
| ~ member(sK13,power_set(X0)) ),
inference(subsumption_resolution,[],[f189,f129]) ).
fof(f189,plain,
! [X0] :
( member(ordered_pair(sK11,sK12),X0)
| ~ member(sK13,power_set(X0))
| ~ ilf_type(sK13,set_type) ),
inference(subsumption_resolution,[],[f188,f129]) ).
fof(f188,plain,
! [X0] :
( member(ordered_pair(sK11,sK12),X0)
| ~ member(sK13,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13,set_type) ),
inference(subsumption_resolution,[],[f182,f129]) ).
fof(f182,plain,
! [X0] :
( member(ordered_pair(sK11,sK12),X0)
| ~ ilf_type(ordered_pair(sK11,sK12),set_type)
| ~ member(sK13,power_set(X0))
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK13,set_type) ),
inference(resolution,[],[f135,f109]) ).
fof(f109,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,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( ( ( member(X0,power_set(X1))
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(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,[sK3])],[f66,f67]) ).
fof(f67,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0)
& ilf_type(X2,set_type) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0)
& ilf_type(sK3(X0,X1),set_type) ) ),
introduced(choice_axiom,[]) ).
fof(f66,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,[],[f65]) ).
fof(f65,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,[],[f38]) ).
fof(f38,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,[],[f37]) ).
fof(f37,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,[],[f13]) ).
fof(f13,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.7sX5uTqycy/Vampire---4.8_30040',p13) ).
fof(f135,plain,
member(ordered_pair(sK11,sK12),sK13),
inference(cnf_transformation,[],[f87]) ).
fof(f341,plain,
spl15_1,
inference(avatar_split_clause,[],[f337,f155]) ).
fof(f155,plain,
( spl15_1
<=> member(sK11,sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_1])]) ).
fof(f337,plain,
member(sK11,sK9),
inference(resolution,[],[f332,f134]) ).
fof(f332,plain,
! [X0,X1] :
( ~ ilf_type(sK13,relation_type(X0,X1))
| member(sK11,X0) ),
inference(subsumption_resolution,[],[f329,f129]) ).
fof(f329,plain,
! [X0,X1] :
( member(sK11,X0)
| ~ ilf_type(sK13,relation_type(X0,X1))
| ~ ilf_type(cross_product(X0,X1),set_type) ),
inference(resolution,[],[f324,f113]) ).
fof(f324,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(sK13,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f323,f129]) ).
fof(f323,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(sK13,relation_type(X0,X1))
| ~ ilf_type(X0,set_type) ),
inference(subsumption_resolution,[],[f321,f129]) ).
fof(f321,plain,
! [X0,X1] :
( empty(power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(sK13,relation_type(X0,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type) ),
inference(resolution,[],[f312,f95]) ).
fof(f312,plain,
! [X0,X1] :
( ~ ilf_type(sK13,subset_type(cross_product(X0,X1)))
| empty(power_set(cross_product(X0,X1)))
| member(sK11,X0) ),
inference(subsumption_resolution,[],[f311,f129]) ).
fof(f311,plain,
! [X0,X1] :
( member(sK11,X0)
| empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13,subset_type(cross_product(X0,X1)))
| ~ ilf_type(cross_product(X0,X1),set_type) ),
inference(subsumption_resolution,[],[f309,f129]) ).
fof(f309,plain,
! [X0,X1] :
( member(sK11,X0)
| empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13,subset_type(cross_product(X0,X1)))
| ~ ilf_type(sK13,set_type)
| ~ ilf_type(cross_product(X0,X1),set_type) ),
inference(resolution,[],[f259,f101]) ).
fof(f259,plain,
! [X0,X1] :
( ~ ilf_type(sK13,member_type(power_set(cross_product(X0,X1))))
| member(sK11,X0)
| empty(power_set(cross_product(X0,X1))) ),
inference(subsumption_resolution,[],[f258,f129]) ).
fof(f258,plain,
! [X0,X1] :
( member(sK11,X0)
| ~ ilf_type(sK13,member_type(power_set(cross_product(X0,X1))))
| empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13,set_type) ),
inference(subsumption_resolution,[],[f254,f129]) ).
fof(f254,plain,
! [X0,X1] :
( member(sK11,X0)
| ~ ilf_type(sK13,member_type(power_set(cross_product(X0,X1))))
| ~ ilf_type(power_set(cross_product(X0,X1)),set_type)
| empty(power_set(cross_product(X0,X1)))
| ~ ilf_type(sK13,set_type) ),
inference(resolution,[],[f227,f115]) ).
fof(f227,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK11,X0) ),
inference(subsumption_resolution,[],[f226,f129]) ).
fof(f226,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f225,f129]) ).
fof(f225,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f224,f129]) ).
fof(f224,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(subsumption_resolution,[],[f213,f129]) ).
fof(f213,plain,
! [X0,X1] :
( ~ member(sK13,power_set(cross_product(X0,X1)))
| member(sK11,X0)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X0,set_type)
| ~ ilf_type(sK12,set_type)
| ~ ilf_type(sK11,set_type) ),
inference(resolution,[],[f190,f88]) ).
fof(f88,plain,
! [X2,X3,X0,X1] :
( 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(cnf_transformation,[],[f53]) ).
fof(f162,plain,
( ~ spl15_1
| ~ spl15_2 ),
inference(avatar_split_clause,[],[f136,f159,f155]) ).
fof(f136,plain,
( ~ member(sK12,sK10)
| ~ member(sK11,sK9) ),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.14 % 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
% 0.15/0.35 % Computer : n008.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 17:13:57 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36 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.7sX5uTqycy/Vampire---4.8_30040
% 0.56/0.74 % (30240)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)
% 0.56/0.74 % (30246)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 % (30246)Refutation not found, incomplete strategy% (30246)------------------------------
% 0.56/0.74 % (30246)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.74 % (30246)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (30246)Memory used [KB]: 1025
% 0.56/0.74 % (30246)Time elapsed: 0.002 s
% 0.56/0.74 % (30246)Instructions burned: 2 (million)
% 0.56/0.74 % (30246)------------------------------
% 0.56/0.74 % (30246)------------------------------
% 0.56/0.74 % (30239)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)
% 0.56/0.74 % (30241)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.56/0.74 % (30242)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)
% 0.56/0.74 % (30243)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)
% 0.56/0.74 % (30244)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)
% 0.56/0.74 % (30245)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)
% 0.56/0.74 % (30244)Refutation not found, incomplete strategy% (30244)------------------------------
% 0.56/0.74 % (30244)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.74 % (30244)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (30244)Memory used [KB]: 1025
% 0.56/0.74 % (30244)Time elapsed: 0.003 s
% 0.56/0.74 % (30244)Instructions burned: 2 (million)
% 0.56/0.74 % (30244)------------------------------
% 0.56/0.74 % (30244)------------------------------
% 0.56/0.74 % (30242)Refutation not found, incomplete strategy% (30242)------------------------------
% 0.56/0.74 % (30242)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.74 % (30242)Termination reason: Refutation not found, incomplete strategy
% 0.56/0.74
% 0.56/0.74 % (30242)Memory used [KB]: 1026
% 0.56/0.74 % (30242)Time elapsed: 0.003 s
% 0.56/0.74 % (30242)Instructions burned: 3 (million)
% 0.56/0.74 % (30242)------------------------------
% 0.56/0.74 % (30242)------------------------------
% 0.56/0.74 % (30247)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)
% 0.56/0.75 % (30248)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)
% 0.56/0.75 % (30249)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 % (30243)First to succeed.
% 0.56/0.75 % (30243)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 % (30243)------------------------------
% 0.56/0.75 % (30243)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.56/0.75 % (30243)Termination reason: Refutation
% 0.56/0.75
% 0.56/0.75 % (30243)Memory used [KB]: 1189
% 0.56/0.75 % (30243)Time elapsed: 0.010 s
% 0.56/0.75 % (30243)Instructions burned: 16 (million)
% 0.56/0.75 % (30243)------------------------------
% 0.56/0.75 % (30243)------------------------------
% 0.56/0.75 % (30229)Success in time 0.388 s
% 0.56/0.75 % Vampire---4.8 exiting
%------------------------------------------------------------------------------