TSTP Solution File: SET806+4 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET806+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n024.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 09:08:33 EDT 2024
% Result : Theorem 0.55s 0.72s
% Output : Refutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 130 ( 8 unt; 0 def)
% Number of atoms : 443 ( 0 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 494 ( 181 ~; 171 |; 101 &)
% ( 19 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 17 ( 16 usr; 11 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 188 ( 150 !; 38 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f317,plain,
$false,
inference(avatar_sat_refutation,[],[f111,f117,f207,f225,f235,f261,f267,f272,f273,f278,f293,f316]) ).
fof(f316,plain,
( ~ spl9_3
| ~ spl9_14
| ~ spl9_15 ),
inference(avatar_contradiction_clause,[],[f315]) ).
fof(f315,plain,
( $false
| ~ spl9_3
| ~ spl9_14
| ~ spl9_15 ),
inference(subsumption_resolution,[],[f314,f259]) ).
fof(f259,plain,
( member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f258,plain,
( spl9_14
<=> member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f314,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl9_3
| ~ spl9_15 ),
inference(subsumption_resolution,[],[f309,f270]) ).
fof(f270,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f269,plain,
( spl9_15
<=> member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f309,plain,
( ~ member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl9_3 ),
inference(resolution,[],[f93,f182]) ).
fof(f182,plain,
! [X0] :
( ~ sP0(equal_set_predicate,X0)
| ~ member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK2(equal_set_predicate,X0))
| ~ member(sK8(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0)),sK4(equal_set_predicate,X0)) ),
inference(resolution,[],[f146,f73]) ).
fof(f73,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sK8(X0,X1),X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f46,f47]) ).
fof(f47,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK8(X0,X1),X1)
& member(sK8(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f46,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',subset) ).
fof(f146,plain,
! [X0] :
( ~ subset(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0))
| ~ sP0(equal_set_predicate,X0)
| ~ member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK2(equal_set_predicate,X0)) ),
inference(resolution,[],[f129,f73]) ).
fof(f129,plain,
! [X0] :
( ~ subset(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0))
| ~ subset(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0))
| ~ sP0(equal_set_predicate,X0) ),
inference(resolution,[],[f124,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ apply(X0,sK2(X0,X1),sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( ~ apply(X0,sK2(X0,X1),sK4(X0,X1))
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& apply(X0,sK2(X0,X1),sK3(X0,X1))
& member(sK4(X0,X1),X1)
& member(sK3(X0,X1),X1)
& member(sK2(X0,X1),X1) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f38,f39]) ).
fof(f39,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ~ apply(X0,sK2(X0,X1),sK4(X0,X1))
& apply(X0,sK3(X0,X1),sK4(X0,X1))
& apply(X0,sK2(X0,X1),sK3(X0,X1))
& member(sK4(X0,X1),X1)
& member(sK3(X0,X1),X1)
& member(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( ~ apply(X0,X2,X4)
& apply(X0,X3,X4)
& apply(X0,X2,X3)
& member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ~ sP0(X1,X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ~ sP0(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f124,plain,
! [X0,X1] :
( apply(equal_set_predicate,X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(resolution,[],[f50,f54]) ).
fof(f54,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( ( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) )
& ( ( subset(X1,X0)
& subset(X0,X1) )
| ~ equal_set(X0,X1) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',equal_set) ).
fof(f50,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( ( apply(equal_set_predicate,X0,X1)
| ~ equal_set(X0,X1) )
& ( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ) ),
inference(nnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( apply(equal_set_predicate,X0,X1)
<=> equal_set(X0,X1) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X2,X4] :
( apply(equal_set_predicate,X2,X4)
<=> equal_set(X2,X4) ),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',rel_equal_set) ).
fof(f93,plain,
( sP0(equal_set_predicate,power_set(sK1))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f91,plain,
( spl9_3
<=> sP0(equal_set_predicate,power_set(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f293,plain,
( ~ spl9_6
| spl9_13 ),
inference(avatar_contradiction_clause,[],[f292]) ).
fof(f292,plain,
( $false
| ~ spl9_6
| spl9_13 ),
inference(subsumption_resolution,[],[f289,f282]) ).
fof(f282,plain,
( member(sK5(power_set(sK1),equal_set_predicate),power_set(sK6(power_set(sK1),equal_set_predicate)))
| ~ spl9_6 ),
inference(resolution,[],[f109,f126]) ).
fof(f126,plain,
! [X0,X1] :
( ~ apply(equal_set_predicate,X0,X1)
| member(X0,power_set(X1)) ),
inference(resolution,[],[f118,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( member(X0,power_set(X1))
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ member(X0,power_set(X1)) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f22,plain,
! [X0,X1] :
( member(X0,power_set(X1))
<=> subset(X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X2,X0] :
( member(X2,power_set(X0))
<=> subset(X2,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',power_set) ).
fof(f118,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[],[f49,f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f49,plain,
! [X0,X1] :
( equal_set(X0,X1)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
fof(f109,plain,
( apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl9_6
<=> apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f289,plain,
( ~ member(sK5(power_set(sK1),equal_set_predicate),power_set(sK6(power_set(sK1),equal_set_predicate)))
| spl9_13 ),
inference(resolution,[],[f224,f55]) ).
fof(f55,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f224,plain,
( ~ subset(sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| spl9_13 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f222,plain,
( spl9_13
<=> subset(sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f278,plain,
( ~ spl9_3
| ~ spl9_11
| spl9_15 ),
inference(avatar_contradiction_clause,[],[f277]) ).
fof(f277,plain,
( $false
| ~ spl9_3
| ~ spl9_11
| spl9_15 ),
inference(subsumption_resolution,[],[f276,f271]) ).
fof(f271,plain,
( ~ member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| spl9_15 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f276,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl9_3
| ~ spl9_11 ),
inference(resolution,[],[f275,f243]) ).
fof(f243,plain,
( ! [X0] :
( ~ member(X0,sK3(equal_set_predicate,power_set(sK1)))
| member(X0,sK2(equal_set_predicate,power_set(sK1))) )
| ~ spl9_3 ),
inference(resolution,[],[f93,f141]) ).
fof(f141,plain,
! [X0,X1] :
( ~ sP0(equal_set_predicate,X1)
| member(X0,sK2(equal_set_predicate,X1))
| ~ member(X0,sK3(equal_set_predicate,X1)) ),
inference(resolution,[],[f127,f60]) ).
fof(f60,plain,
! [X0,X1] :
( apply(X0,sK2(X0,X1),sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f127,plain,
! [X2,X0,X1] :
( ~ apply(equal_set_predicate,X0,X1)
| ~ member(X2,X1)
| member(X2,X0) ),
inference(resolution,[],[f119,f71]) ).
fof(f71,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f119,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ apply(equal_set_predicate,X0,X1) ),
inference(resolution,[],[f49,f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ equal_set(X0,X1)
| subset(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f275,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl9_3
| ~ spl9_11 ),
inference(resolution,[],[f197,f242]) ).
fof(f242,plain,
( ! [X0] :
( ~ member(X0,sK4(equal_set_predicate,power_set(sK1)))
| member(X0,sK3(equal_set_predicate,power_set(sK1))) )
| ~ spl9_3 ),
inference(resolution,[],[f93,f140]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sP0(equal_set_predicate,X1)
| member(X0,sK3(equal_set_predicate,X1))
| ~ member(X0,sK4(equal_set_predicate,X1)) ),
inference(resolution,[],[f127,f61]) ).
fof(f61,plain,
! [X0,X1] :
( apply(X0,sK3(X0,X1),sK4(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f197,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f195,plain,
( spl9_11
<=> member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f273,plain,
( spl9_10
| spl9_11
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f247,f91,f195,f186]) ).
fof(f186,plain,
( spl9_10
<=> member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f247,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl9_3 ),
inference(resolution,[],[f93,f166]) ).
fof(f166,plain,
! [X0] :
( ~ sP0(equal_set_predicate,X0)
| member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK4(equal_set_predicate,X0))
| member(sK8(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0)),sK2(equal_set_predicate,X0)) ),
inference(resolution,[],[f145,f72]) ).
fof(f72,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sK8(X0,X1),X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f145,plain,
! [X0] :
( ~ subset(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0))
| ~ sP0(equal_set_predicate,X0)
| member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK4(equal_set_predicate,X0)) ),
inference(resolution,[],[f129,f72]) ).
fof(f272,plain,
( spl9_10
| ~ spl9_15
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f263,f91,f269,f186]) ).
fof(f263,plain,
( ~ member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl9_3 ),
inference(resolution,[],[f181,f93]) ).
fof(f181,plain,
! [X0] :
( ~ sP0(equal_set_predicate,X0)
| ~ member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK2(equal_set_predicate,X0))
| member(sK8(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0)),sK2(equal_set_predicate,X0)) ),
inference(resolution,[],[f146,f72]) ).
fof(f267,plain,
( ~ spl9_10
| ~ spl9_3
| spl9_14 ),
inference(avatar_split_clause,[],[f264,f258,f91,f186]) ).
fof(f264,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK2(equal_set_predicate,power_set(sK1)))
| ~ spl9_3
| spl9_14 ),
inference(resolution,[],[f262,f241]) ).
fof(f241,plain,
( ! [X0] :
( member(X0,sK3(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK2(equal_set_predicate,power_set(sK1))) )
| ~ spl9_3 ),
inference(resolution,[],[f93,f138]) ).
fof(f138,plain,
! [X0,X1] :
( ~ sP0(equal_set_predicate,X1)
| member(X0,sK3(equal_set_predicate,X1))
| ~ member(X0,sK2(equal_set_predicate,X1)) ),
inference(resolution,[],[f125,f60]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ apply(equal_set_predicate,X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(resolution,[],[f118,f71]) ).
fof(f262,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK3(equal_set_predicate,power_set(sK1)))
| ~ spl9_3
| spl9_14 ),
inference(resolution,[],[f260,f240]) ).
fof(f240,plain,
( ! [X0] :
( member(X0,sK4(equal_set_predicate,power_set(sK1)))
| ~ member(X0,sK3(equal_set_predicate,power_set(sK1))) )
| ~ spl9_3 ),
inference(resolution,[],[f93,f137]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sP0(equal_set_predicate,X1)
| member(X0,sK4(equal_set_predicate,X1))
| ~ member(X0,sK3(equal_set_predicate,X1)) ),
inference(resolution,[],[f125,f61]) ).
fof(f260,plain,
( ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| spl9_14 ),
inference(avatar_component_clause,[],[f258]) ).
fof(f261,plain,
( ~ spl9_14
| spl9_11
| ~ spl9_3 ),
inference(avatar_split_clause,[],[f256,f91,f195,f258]) ).
fof(f256,plain,
( member(sK8(sK4(equal_set_predicate,power_set(sK1)),sK2(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ member(sK8(sK2(equal_set_predicate,power_set(sK1)),sK4(equal_set_predicate,power_set(sK1))),sK4(equal_set_predicate,power_set(sK1)))
| ~ spl9_3 ),
inference(resolution,[],[f167,f93]) ).
fof(f167,plain,
! [X0] :
( ~ sP0(equal_set_predicate,X0)
| member(sK8(sK4(equal_set_predicate,X0),sK2(equal_set_predicate,X0)),sK4(equal_set_predicate,X0))
| ~ member(sK8(sK2(equal_set_predicate,X0),sK4(equal_set_predicate,X0)),sK4(equal_set_predicate,X0)) ),
inference(resolution,[],[f145,f73]) ).
fof(f235,plain,
( ~ spl9_6
| spl9_12 ),
inference(avatar_split_clause,[],[f226,f218,f107]) ).
fof(f218,plain,
( spl9_12
<=> subset(sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f226,plain,
( ~ apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| spl9_12 ),
inference(resolution,[],[f220,f119]) ).
fof(f220,plain,
( ~ subset(sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl9_12 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f225,plain,
( ~ spl9_12
| ~ spl9_13
| spl9_7 ),
inference(avatar_split_clause,[],[f216,f113,f222,f218]) ).
fof(f113,plain,
( spl9_7
<=> apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f216,plain,
( ~ subset(sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ subset(sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl9_7 ),
inference(resolution,[],[f115,f124]) ).
fof(f115,plain,
( ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| spl9_7 ),
inference(avatar_component_clause,[],[f113]) ).
fof(f207,plain,
spl9_4,
inference(avatar_contradiction_clause,[],[f206]) ).
fof(f206,plain,
( $false
| spl9_4 ),
inference(subsumption_resolution,[],[f204,f203]) ).
fof(f203,plain,
( member(sK8(sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)),sK7(power_set(sK1),equal_set_predicate))
| spl9_4 ),
inference(resolution,[],[f200,f72]) ).
fof(f200,plain,
( ~ subset(sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl9_4 ),
inference(duplicate_literal_removal,[],[f199]) ).
fof(f199,plain,
( ~ subset(sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| ~ subset(sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl9_4 ),
inference(resolution,[],[f98,f124]) ).
fof(f98,plain,
( ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate))
| spl9_4 ),
inference(avatar_component_clause,[],[f96]) ).
fof(f96,plain,
( spl9_4
<=> apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f204,plain,
( ~ member(sK8(sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)),sK7(power_set(sK1),equal_set_predicate))
| spl9_4 ),
inference(resolution,[],[f200,f73]) ).
fof(f117,plain,
( ~ spl9_4
| ~ spl9_7
| spl9_3 ),
inference(avatar_split_clause,[],[f81,f91,f113,f96]) ).
fof(f81,plain,
( sP0(equal_set_predicate,power_set(sK1))
| ~ apply(equal_set_predicate,sK6(power_set(sK1),equal_set_predicate),sK5(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[],[f51,f70]) ).
fof(f70,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ( ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
& apply(X1,sK5(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X0)
& member(sK5(X0,X1),X0) )
| ( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
& member(sK7(X0,X1),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f41,f43,f42]) ).
fof(f42,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ apply(X1,X3,X2)
& apply(X1,X2,X3)
& member(X3,X0)
& member(X2,X0) )
=> ( ~ apply(X1,sK6(X0,X1),sK5(X0,X1))
& apply(X1,sK5(X0,X1),sK6(X0,X1))
& member(sK6(X0,X1),X0)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f43,plain,
! [X0,X1] :
( ? [X4] :
( ~ apply(X1,X4,X4)
& member(X4,X0) )
=> ( ~ apply(X1,sK7(X0,X1),sK7(X0,X1))
& member(sK7(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ? [X2,X3] :
( ~ apply(X1,X3,X2)
& apply(X1,X2,X3)
& member(X3,X0)
& member(X2,X0) )
| ? [X4] :
( ~ apply(X1,X4,X4)
& member(X4,X0) ) ),
inference(rectify,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(definition_folding,[],[f27,f29]) ).
fof(f27,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0,X1] :
( equivalence(X1,X0)
| ? [X2,X3,X4] :
( ~ apply(X1,X2,X4)
& apply(X1,X3,X4)
& apply(X1,X2,X3)
& member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
| ? [X5,X6] :
( ~ apply(X1,X6,X5)
& apply(X1,X5,X6)
& member(X6,X0)
& member(X5,X0) )
| ? [X7] :
( ~ apply(X1,X7,X7)
& member(X7,X0) ) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) )
=> equivalence(X1,X0) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X0)
& member(X3,X0)
& member(X2,X0) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X2,X3) )
=> apply(X1,X2,X4) ) )
& ! [X5,X6] :
( ( member(X6,X0)
& member(X5,X0) )
=> ( apply(X1,X5,X6)
=> apply(X1,X6,X5) ) )
& ! [X7] :
( member(X7,X0)
=> apply(X1,X7,X7) ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X6] :
( equivalence(X6,X0)
<=> ( ! [X2,X4,X5] :
( ( member(X5,X0)
& member(X4,X0)
& member(X2,X0) )
=> ( ( apply(X6,X4,X5)
& apply(X6,X2,X4) )
=> apply(X6,X2,X5) ) )
& ! [X2,X4] :
( ( member(X4,X0)
& member(X2,X0) )
=> ( apply(X6,X2,X4)
=> apply(X6,X4,X2) ) )
& ! [X2] :
( member(X2,X0)
=> apply(X6,X2,X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',equivalence) ).
fof(f51,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
~ equivalence(equal_set_predicate,power_set(sK1)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f25,f32]) ).
fof(f32,plain,
( ? [X0] : ~ equivalence(equal_set_predicate,power_set(X0))
=> ~ equivalence(equal_set_predicate,power_set(sK1)) ),
introduced(choice_axiom,[]) ).
fof(f25,plain,
? [X0] : ~ equivalence(equal_set_predicate,power_set(X0)),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0] : equivalence(equal_set_predicate,power_set(X0)),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X3] : equivalence(equal_set_predicate,power_set(X3)),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X3] : equivalence(equal_set_predicate,power_set(X3)),
file('/export/starexec/sandbox2/tmp/tmp.gnUU0pP7QU/Vampire---4.8_16138',thIII13) ).
fof(f111,plain,
( ~ spl9_4
| spl9_6
| spl9_3 ),
inference(avatar_split_clause,[],[f79,f91,f107,f96]) ).
fof(f79,plain,
( sP0(equal_set_predicate,power_set(sK1))
| apply(equal_set_predicate,sK5(power_set(sK1),equal_set_predicate),sK6(power_set(sK1),equal_set_predicate))
| ~ apply(equal_set_predicate,sK7(power_set(sK1),equal_set_predicate),sK7(power_set(sK1),equal_set_predicate)) ),
inference(resolution,[],[f51,f68]) ).
fof(f68,plain,
! [X0,X1] :
( equivalence(X1,X0)
| sP0(X1,X0)
| apply(X1,sK5(X0,X1),sK6(X0,X1))
| ~ apply(X1,sK7(X0,X1),sK7(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SET806+4 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14 % 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
% 0.15/0.34 % Computer : n024.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 3 16:19:08 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.15/0.34 This is a FOF_THM_RFO_SEQ problem
% 0.15/0.34 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.gnUU0pP7QU/Vampire---4.8_16138
% 0.55/0.72 % (16529)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)
% 0.55/0.72 % (16522)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)
% 0.55/0.72 % (16525)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)
% 0.55/0.72 % (16524)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.55/0.72 % (16523)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)
% 0.55/0.72 % (16526)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)
% 0.55/0.72 % (16527)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)
% 0.55/0.72 % (16528)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)
% 0.55/0.72 % (16529)First to succeed.
% 0.55/0.72 % (16522)Refutation not found, incomplete strategy% (16522)------------------------------
% 0.55/0.72 % (16522)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.72 % (16528)Refutation not found, incomplete strategy% (16528)------------------------------
% 0.55/0.72 % (16528)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.72 % (16528)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.72
% 0.55/0.72 % (16528)Memory used [KB]: 1044
% 0.55/0.72 % (16528)Time elapsed: 0.003 s
% 0.55/0.72 % (16527)Refutation not found, incomplete strategy% (16527)------------------------------
% 0.55/0.72 % (16527)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.72 % (16528)Instructions burned: 3 (million)
% 0.55/0.72 % (16527)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.72
% 0.55/0.72 % (16527)Memory used [KB]: 1064
% 0.55/0.72 % (16527)Time elapsed: 0.003 s
% 0.55/0.72 % (16527)Instructions burned: 4 (million)
% 0.55/0.72 % (16522)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.72
% 0.55/0.72 % (16522)Memory used [KB]: 1075
% 0.55/0.72 % (16522)Time elapsed: 0.004 s
% 0.55/0.72 % (16522)Instructions burned: 4 (million)
% 0.55/0.72 % (16526)Refutation not found, incomplete strategy% (16526)------------------------------
% 0.55/0.72 % (16526)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.72 % (16526)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.72
% 0.55/0.72 % (16526)Memory used [KB]: 1067
% 0.55/0.72 % (16526)Time elapsed: 0.004 s
% 0.55/0.72 % (16526)Instructions burned: 4 (million)
% 0.55/0.72 % (16525)Refutation not found, incomplete strategy% (16525)------------------------------
% 0.55/0.72 % (16525)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.72 % (16528)------------------------------
% 0.55/0.72 % (16528)------------------------------
% 0.55/0.72 % (16527)------------------------------
% 0.55/0.72 % (16527)------------------------------
% 0.55/0.72 % (16525)Termination reason: Refutation not found, incomplete strategy
% 0.55/0.72
% 0.55/0.72 % (16525)Memory used [KB]: 1065
% 0.55/0.72 % (16525)Time elapsed: 0.004 s
% 0.55/0.72 % (16522)------------------------------
% 0.55/0.72 % (16522)------------------------------
% 0.55/0.72 % (16525)Instructions burned: 4 (million)
% 0.55/0.72 % (16526)------------------------------
% 0.55/0.72 % (16526)------------------------------
% 0.55/0.72 % (16525)------------------------------
% 0.55/0.72 % (16525)------------------------------
% 0.55/0.72 % (16529)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16345"
% 0.55/0.72 % (16529)Refutation found. Thanks to Tanya!
% 0.55/0.72 % SZS status Theorem for Vampire---4
% 0.55/0.72 % SZS output start Proof for Vampire---4
% See solution above
% 0.55/0.73 % (16529)------------------------------
% 0.55/0.73 % (16529)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.55/0.73 % (16529)Termination reason: Refutation
% 0.55/0.73
% 0.55/0.73 % (16529)Memory used [KB]: 1127
% 0.55/0.73 % (16529)Time elapsed: 0.005 s
% 0.55/0.73 % (16529)Instructions burned: 12 (million)
% 0.55/0.73 % (16345)Success in time 0.372 s
% 0.55/0.73 % Vampire---4.8 exiting
%------------------------------------------------------------------------------