TSTP Solution File: SET083+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET083+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n027.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 : Tue Apr 30 15:05:31 EDT 2024
% Result : Theorem 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 142
% Syntax : Number of formulae : 473 ( 133 unt; 0 def)
% Number of atoms : 1257 ( 156 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1249 ( 465 ~; 470 |; 166 &)
% ( 124 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 98 ( 96 usr; 92 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 9 con; 0-3 aty)
% Number of variables : 777 ( 746 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f914,plain,
$false,
inference(avatar_sat_refutation,[],[f274,f279,f284,f289,f294,f298,f302,f307,f311,f316,f321,f325,f329,f333,f339,f343,f347,f351,f355,f359,f364,f368,f372,f376,f380,f384,f388,f392,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f451,f455,f479,f487,f491,f495,f499,f503,f532,f547,f551,f555,f586,f590,f597,f601,f625,f630,f634,f638,f642,f646,f650,f654,f673,f677,f681,f685,f689,f709,f713,f717,f721,f736,f740,f744,f778,f782,f797,f801,f828,f838,f844,f855,f859,f870,f874,f878,f888,f892,f911,f913]) ).
fof(f913,plain,
( spl8_2
| ~ spl8_54
| ~ spl8_86 ),
inference(avatar_split_clause,[],[f905,f867,f595,f276]) ).
fof(f276,plain,
( spl8_2
<=> sK0 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f595,plain,
( spl8_54
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
fof(f867,plain,
( spl8_86
<=> member(sK0,unordered_pair(sK1,sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
fof(f905,plain,
( sK0 = sK1
| ~ spl8_54
| ~ spl8_86 ),
inference(duplicate_literal_removal,[],[f901]) ).
fof(f901,plain,
( sK0 = sK1
| sK0 = sK1
| ~ spl8_54
| ~ spl8_86 ),
inference(resolution,[],[f869,f596]) ).
fof(f596,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl8_54 ),
inference(avatar_component_clause,[],[f595]) ).
fof(f869,plain,
( member(sK0,unordered_pair(sK1,sK1))
| ~ spl8_86 ),
inference(avatar_component_clause,[],[f867]) ).
fof(f911,plain,
( spl8_91
| ~ spl8_3
| ~ spl8_54 ),
inference(avatar_split_clause,[],[f620,f595,f281,f909]) ).
fof(f909,plain,
( spl8_91
<=> ! [X0] :
( ~ member(X0,unordered_pair(sK1,sK1))
| sK0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
fof(f281,plain,
( spl8_3
<=> unordered_pair(sK0,sK0) = unordered_pair(sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f620,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK1,sK1))
| sK0 = X0 )
| ~ spl8_3
| ~ spl8_54 ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,plain,
( ! [X0] :
( ~ member(X0,unordered_pair(sK1,sK1))
| sK0 = X0
| sK0 = X0 )
| ~ spl8_3
| ~ spl8_54 ),
inference(superposition,[],[f596,f283]) ).
fof(f283,plain,
( unordered_pair(sK0,sK0) = unordered_pair(sK1,sK1)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f892,plain,
spl8_90,
inference(avatar_split_clause,[],[f260,f890]) ).
fof(f890,plain,
( spl8_90
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
fof(f260,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f220,f229,f229,f229,f229,f229,f229]) ).
fof(f229,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f167,f144,f144]) ).
fof(f144,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f167,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f220,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
<=> ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2,X3,X6,X0] :
( member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip_defn) ).
fof(f888,plain,
spl8_89,
inference(avatar_split_clause,[],[f257,f886]) ).
fof(f886,plain,
( spl8_89
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
fof(f257,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f217,f229,f229,f229,f229,f229,f229]) ).
fof(f217,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(nnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X2,X3,X6] :
( member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate_defn) ).
fof(f878,plain,
spl8_88,
inference(avatar_split_clause,[],[f262,f876]) ).
fof(f876,plain,
( spl8_88
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
fof(f262,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f218,f229,f229,f229,f229]) ).
fof(f218,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f874,plain,
spl8_87,
inference(avatar_split_clause,[],[f259,f872]) ).
fof(f872,plain,
( spl8_87
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
fof(f259,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f215,f229,f229,f229,f229]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f870,plain,
( ~ spl8_1
| spl8_86
| ~ spl8_3
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f481,f449,f281,f867,f271]) ).
fof(f271,plain,
( spl8_1
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f449,plain,
( spl8_40
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
fof(f481,plain,
( member(sK0,unordered_pair(sK1,sK1))
| ~ member(sK0,universal_class)
| ~ spl8_3
| ~ spl8_40 ),
inference(superposition,[],[f450,f283]) ).
fof(f450,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f859,plain,
spl8_85,
inference(avatar_split_clause,[],[f261,f857]) ).
fof(f857,plain,
( spl8_85
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
fof(f261,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f219,f229,f229,f229,f229]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f855,plain,
spl8_84,
inference(avatar_split_clause,[],[f258,f853]) ).
fof(f853,plain,
( spl8_84
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
fof(f258,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f216,f229,f229,f229,f229]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f844,plain,
spl8_83,
inference(avatar_split_clause,[],[f251,f842]) ).
fof(f842,plain,
( spl8_83
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
fof(f251,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ),
inference(definition_unfolding,[],[f211,f229,f228,f228,f144]) ).
fof(f228,plain,
! [X0,X1] : image(X1,X0) = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f166,f227,f197]) ).
fof(f197,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X5,X1] : restrict(X5,X0,X1) = intersection(X5,cross_product(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restrict_defn) ).
fof(f227,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f143,f146]) ).
fof(f146,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1] : inverse(X1) = domain_of(flip(cross_product(X1,universal_class))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_defn) ).
fof(f143,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X4] : range_of(X4) = domain_of(inverse(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of_defn) ).
fof(f166,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X5] : image(X5,X0) = range_of(restrict(X5,X0,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image_defn) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X2,X3),compose(X1,X0))
<=> ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X5,X7,X2,X3] :
( member(ordered_pair(X2,X3),compose(X7,X5))
<=> ( member(X3,image(X7,image(X5,singleton(X2))))
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn2) ).
fof(f838,plain,
spl8_82,
inference(avatar_split_clause,[],[f252,f836]) ).
fof(f836,plain,
( spl8_82
<=> ! [X0,X3,X2,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
fof(f252,plain,
! [X2,X3,X0,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f210,f228,f228,f144,f229]) ).
fof(f210,plain,
! [X2,X3,X0,X1] :
( member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f828,plain,
spl8_81,
inference(avatar_split_clause,[],[f267,f826]) ).
fof(f826,plain,
( spl8_81
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
fof(f267,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(equality_resolution,[],[f246]) ).
fof(f246,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f196,f229,f226]) ).
fof(f226,plain,
! [X0] : successor(X0) = union(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f145,f144]) ).
fof(f145,plain,
! [X0] : successor(X0) = union(X0,singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : successor(X0) = union(X0,singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_defn) ).
fof(f196,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
<=> ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn2) ).
fof(f801,plain,
spl8_80,
inference(avatar_split_clause,[],[f263,f799]) ).
fof(f799,plain,
( spl8_80
<=> ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
fof(f263,plain,
! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f222,f230]) ).
fof(f230,plain,
! [X0,X1] : apply(X0,X1) = sum_class(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f165,f228,f144]) ).
fof(f165,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X1] : apply(X8,X1) = sum_class(image(X8,singleton(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_defn) ).
fof(f222,plain,
! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f132]) ).
fof(f132,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f69]) ).
fof(f69,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice) ).
fof(f797,plain,
spl8_79,
inference(avatar_split_clause,[],[f250,f795]) ).
fof(f795,plain,
( spl8_79
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_79])]) ).
fof(f250,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f198,f229]) ).
fof(f198,plain,
! [X2,X0,X1] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( member(X2,cross_product(X0,X1))
=> ordered_pair(first(X2),second(X2)) = X2 ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X4] :
( member(X4,cross_product(X0,X1))
=> ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product) ).
fof(f782,plain,
spl8_78,
inference(avatar_split_clause,[],[f254,f780]) ).
fof(f780,plain,
( spl8_78
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
fof(f254,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(definition_unfolding,[],[f214,f229]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,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)) ) ),
inference(flattening,[],[f126]) ).
fof(f126,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)) ) ),
inference(nnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
<=> ( member(X3,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f778,plain,
spl8_77,
inference(avatar_split_clause,[],[f237,f776]) ).
fof(f776,plain,
( spl8_77
<=> ! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
fof(f237,plain,
! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ),
inference(definition_unfolding,[],[f161,f229]) ).
fof(f161,plain,
! [X0] :
( ordered_pair(sK3(X0),sK3(X0)) = X0
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f95,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f95,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(rectify,[],[f94]) ).
fof(f94,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( member(X0,identity_relation)
<=> ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X4] :
( member(X4,identity_relation)
<=> ? [X0] :
( ordered_pair(X0,X0) = X4
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f744,plain,
spl8_76,
inference(avatar_split_clause,[],[f247,f742]) ).
fof(f742,plain,
( spl8_76
<=> ! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
fof(f247,plain,
! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f195,f226,f229]) ).
fof(f195,plain,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f740,plain,
spl8_75,
inference(avatar_split_clause,[],[f240,f738]) ).
fof(f738,plain,
( spl8_75
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
fof(f240,plain,
! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f169,f229]) ).
fof(f169,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( member(X1,universal_class)
& member(X0,universal_class) )
=> ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',first_second) ).
fof(f736,plain,
spl8_74,
inference(avatar_split_clause,[],[f239,f734]) ).
fof(f734,plain,
( spl8_74
<=> ! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
fof(f239,plain,
! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f170,f229]) ).
fof(f170,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f79]) ).
fof(f721,plain,
spl8_73,
inference(avatar_split_clause,[],[f243,f719]) ).
fof(f719,plain,
( spl8_73
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
fof(f243,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f192,f229]) ).
fof(f192,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
<=> ( member(X0,X1)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation_defn) ).
fof(f717,plain,
spl8_72,
inference(avatar_split_clause,[],[f238,f715]) ).
fof(f715,plain,
( spl8_72
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
fof(f238,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f168,f228]) ).
fof(f168,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ( function(X1)
& member(X0,universal_class) )
=> member(image(X1,X0),universal_class) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X8] :
( ( function(X8)
& member(X0,universal_class) )
=> member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
fof(f713,plain,
spl8_71,
inference(avatar_split_clause,[],[f232,f711]) ).
fof(f711,plain,
( spl8_71
<=> ! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
fof(f232,plain,
! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ),
inference(definition_unfolding,[],[f156,f228]) ).
fof(f156,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive_defn) ).
fof(f709,plain,
( ~ spl8_69
| spl8_70
| ~ spl8_20
| ~ spl8_48 ),
inference(avatar_split_clause,[],[f593,f530,f357,f706,f702]) ).
fof(f702,plain,
( spl8_69
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
fof(f706,plain,
( spl8_70
<=> member(sK0,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
fof(f357,plain,
( spl8_20
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f530,plain,
( spl8_48
<=> ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
fof(f593,plain,
( member(sK0,cross_product(universal_class,universal_class))
| ~ function(universal_class)
| ~ spl8_20
| ~ spl8_48 ),
inference(resolution,[],[f531,f358]) ).
fof(f358,plain,
( ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) )
| ~ spl8_20 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f531,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(sK0,X0) )
| ~ spl8_48 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f689,plain,
spl8_68,
inference(avatar_split_clause,[],[f256,f687]) ).
fof(f687,plain,
( spl8_68
<=> ! [X0,X3,X2,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
fof(f256,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f212,f229]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f685,plain,
spl8_67,
inference(avatar_split_clause,[],[f255,f683]) ).
fof(f683,plain,
( spl8_67
<=> ! [X0,X3,X2,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
fof(f255,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f213,f229]) ).
fof(f213,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f681,plain,
spl8_66,
inference(avatar_split_clause,[],[f253,f679]) ).
fof(f679,plain,
( spl8_66
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
fof(f253,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f209,f229]) ).
fof(f209,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f125]) ).
fof(f677,plain,
spl8_65,
inference(avatar_split_clause,[],[f241,f675]) ).
fof(f675,plain,
( spl8_65
<=> ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
fof(f241,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f186,f197,f144]) ).
fof(f186,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(flattening,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X4] :
( member(X4,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X4),universal_class)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of) ).
fof(f673,plain,
spl8_64,
inference(avatar_split_clause,[],[f234,f671]) ).
fof(f671,plain,
( spl8_64
<=> ! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
fof(f234,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f159,f146]) ).
fof(f159,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( function(X0)
<=> ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X8] :
( function(X8)
<=> ( subclass(compose(X8,inverse(X8)),identity_relation)
& subclass(X8,cross_product(universal_class,universal_class)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function_defn) ).
fof(f654,plain,
spl8_63,
inference(avatar_split_clause,[],[f264,f652]) ).
fof(f652,plain,
( spl8_63
<=> ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
fof(f264,plain,
! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f236]) ).
fof(f236,plain,
! [X0,X1] :
( member(X0,identity_relation)
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))) != X0
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f162,f229]) ).
fof(f162,plain,
! [X0,X1] :
( member(X0,identity_relation)
| ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f97]) ).
fof(f650,plain,
spl8_62,
inference(avatar_split_clause,[],[f249,f648]) ).
fof(f648,plain,
( spl8_62
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
fof(f249,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f193,f229]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f646,plain,
spl8_61,
inference(avatar_split_clause,[],[f248,f644]) ).
fof(f644,plain,
( spl8_61
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
fof(f248,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f194,f229]) ).
fof(f194,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f117]) ).
fof(f642,plain,
spl8_60,
inference(avatar_split_clause,[],[f245,f640]) ).
fof(f640,plain,
( spl8_60
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
fof(f245,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f190,f229]) ).
fof(f190,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f115]) ).
fof(f638,plain,
( spl8_59
| ~ spl8_1
| ~ spl8_51 ),
inference(avatar_split_clause,[],[f572,f553,f271,f636]) ).
fof(f636,plain,
( spl8_59
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
fof(f553,plain,
( spl8_51
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
fof(f572,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) )
| ~ spl8_1
| ~ spl8_51 ),
inference(resolution,[],[f554,f273]) ).
fof(f273,plain,
( member(sK0,universal_class)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum_class(X1))
| ~ member(X0,X2) )
| ~ spl8_51 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f634,plain,
spl8_58,
inference(avatar_split_clause,[],[f244,f632]) ).
fof(f632,plain,
( spl8_58
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
fof(f244,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f191,f229]) ).
fof(f191,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f115]) ).
fof(f630,plain,
spl8_57,
inference(avatar_split_clause,[],[f233,f628]) ).
fof(f628,plain,
( spl8_57
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
fof(f233,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f155,f228]) ).
fof(f155,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f625,plain,
spl8_56,
inference(avatar_split_clause,[],[f242,f623]) ).
fof(f623,plain,
( spl8_56
<=> ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
fof(f242,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f185,f197,f144]) ).
fof(f185,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(X1),universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f601,plain,
spl8_55,
inference(avatar_split_clause,[],[f235,f599]) ).
fof(f599,plain,
( spl8_55
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
fof(f235,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f158,f146]) ).
fof(f158,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f597,plain,
spl8_54,
inference(avatar_split_clause,[],[f206,f595]) ).
fof(f206,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f590,plain,
spl8_53,
inference(avatar_split_clause,[],[f202,f588]) ).
fof(f588,plain,
( spl8_53
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,union(X0,X1))
<=> ( member(X4,X1)
| member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f586,plain,
spl8_52,
inference(avatar_split_clause,[],[f201,f584]) ).
fof(f584,plain,
( spl8_52
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,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)) ) ),
inference(flattening,[],[f118]) ).
fof(f118,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)) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
<=> ( member(X4,X1)
& member(X4,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f555,plain,
spl8_51,
inference(avatar_split_clause,[],[f189,f553]) ).
fof(f189,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f111,f112]) ).
fof(f112,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f111,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum_class(X1)) ) ),
inference(rectify,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum_class(X1)) ) ),
inference(nnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( member(X0,sum_class(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X2,X0] :
( member(X2,sum_class(X0))
<=> ? [X1] :
( member(X1,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_defn) ).
fof(f551,plain,
spl8_50,
inference(avatar_split_clause,[],[f183,f549]) ).
fof(f549,plain,
( spl8_50
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
fof(f183,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( member(X0,power_class(X1))
<=> ( subclass(X0,X1)
& member(X0,universal_class) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X2,X0] :
( member(X2,power_class(X0))
<=> ( subclass(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_defn) ).
fof(f547,plain,
spl8_49,
inference(avatar_split_clause,[],[f180,f545]) ).
fof(f545,plain,
( spl8_49
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
fof(f180,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(flattening,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X4] :
( member(X4,complement(X0))
<=> ( ~ member(X4,X0)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
fof(f532,plain,
( spl8_48
| ~ spl8_1
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f521,f493,f271,f530]) ).
fof(f493,plain,
( spl8_45
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
fof(f521,plain,
( ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_1
| ~ spl8_45 ),
inference(resolution,[],[f494,f273]) ).
fof(f494,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f503,plain,
spl8_47,
inference(avatar_split_clause,[],[f188,f501]) ).
fof(f501,plain,
( spl8_47
<=> ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
fof(f188,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f499,plain,
spl8_46,
inference(avatar_split_clause,[],[f187,f497]) ).
fof(f497,plain,
( spl8_46
<=> ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
fof(f187,plain,
! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f495,plain,
spl8_45,
inference(avatar_split_clause,[],[f175,f493]) ).
fof(f175,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f101,f102]) ).
fof(f102,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_defn) ).
fof(f491,plain,
spl8_44,
inference(avatar_split_clause,[],[f174,f489]) ).
fof(f489,plain,
( spl8_44
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f487,plain,
spl8_43,
inference(avatar_split_clause,[],[f173,f485]) ).
fof(f485,plain,
( spl8_43
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality) ).
fof(f479,plain,
( spl8_42
| ~ spl8_6
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f458,f421,f296,f477]) ).
fof(f477,plain,
( spl8_42
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
fof(f296,plain,
( spl8_6
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f421,plain,
( spl8_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f458,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl8_6
| ~ spl8_33 ),
inference(resolution,[],[f422,f297]) ).
fof(f297,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f422,plain,
( ! [X0,X1] :
( member(sK4(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f455,plain,
spl8_41,
inference(avatar_split_clause,[],[f269,f453]) ).
fof(f453,plain,
( spl8_41
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
fof(f269,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f207]) ).
fof(f207,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f123]) ).
fof(f451,plain,
spl8_40,
inference(avatar_split_clause,[],[f268,f449]) ).
fof(f268,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f208]) ).
fof(f208,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f123]) ).
fof(f447,plain,
spl8_39,
inference(avatar_split_clause,[],[f205,f445]) ).
fof(f445,plain,
( spl8_39
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
fof(f205,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f123]) ).
fof(f443,plain,
spl8_38,
inference(avatar_split_clause,[],[f204,f441]) ).
fof(f441,plain,
( spl8_38
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f204,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f121]) ).
fof(f439,plain,
spl8_37,
inference(avatar_split_clause,[],[f203,f437]) ).
fof(f437,plain,
( spl8_37
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f435,plain,
spl8_36,
inference(avatar_split_clause,[],[f200,f433]) ).
fof(f433,plain,
( spl8_36
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f200,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f431,plain,
spl8_35,
inference(avatar_split_clause,[],[f199,f429]) ).
fof(f429,plain,
( spl8_35
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f199,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f427,plain,
spl8_34,
inference(avatar_split_clause,[],[f177,f425]) ).
fof(f425,plain,
( spl8_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f177,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f423,plain,
spl8_33,
inference(avatar_split_clause,[],[f176,f421]) ).
fof(f176,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f419,plain,
spl8_32,
inference(avatar_split_clause,[],[f148,f417]) ).
fof(f417,plain,
( spl8_32
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f148,plain,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip) ).
fof(f415,plain,
spl8_31,
inference(avatar_split_clause,[],[f147,f413]) ).
fof(f413,plain,
( spl8_31
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f147,plain,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate) ).
fof(f411,plain,
( spl8_29
| spl8_30
| ~ spl8_12
| ~ spl8_24 ),
inference(avatar_split_clause,[],[f394,f374,f323,f408,f405]) ).
fof(f405,plain,
( spl8_29
<=> ! [X0] : ~ inductive(complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
fof(f408,plain,
( spl8_30
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f323,plain,
( spl8_12
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f374,plain,
( spl8_24
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f394,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(complement(X0)) )
| ~ spl8_12
| ~ spl8_24 ),
inference(resolution,[],[f375,f324]) ).
fof(f324,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f375,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| member(X1,universal_class) )
| ~ spl8_24 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f392,plain,
spl8_28,
inference(avatar_split_clause,[],[f184,f390]) ).
fof(f390,plain,
( spl8_28
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
fof(f184,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f109]) ).
fof(f388,plain,
spl8_27,
inference(avatar_split_clause,[],[f182,f386]) ).
fof(f386,plain,
( spl8_27
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f182,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f384,plain,
spl8_26,
inference(avatar_split_clause,[],[f181,f382]) ).
fof(f382,plain,
( spl8_26
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f181,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f107]) ).
fof(f380,plain,
spl8_25,
inference(avatar_split_clause,[],[f179,f378]) ).
fof(f378,plain,
( spl8_25
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f179,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f376,plain,
spl8_24,
inference(avatar_split_clause,[],[f178,f374]) ).
fof(f178,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f105]) ).
fof(f372,plain,
spl8_23,
inference(avatar_split_clause,[],[f164,f370]) ).
fof(f370,plain,
( spl8_23
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f164,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_defn1) ).
fof(f368,plain,
spl8_22,
inference(avatar_split_clause,[],[f160,f366]) ).
fof(f366,plain,
( spl8_22
<=> ! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f160,plain,
! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f97]) ).
fof(f364,plain,
( ~ spl8_21
| ~ spl8_6
| ~ spl8_12 ),
inference(avatar_split_clause,[],[f334,f323,f296,f361]) ).
fof(f361,plain,
( spl8_21
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
fof(f334,plain,
( ~ inductive(null_class)
| ~ spl8_6
| ~ spl8_12 ),
inference(resolution,[],[f324,f297]) ).
fof(f359,plain,
spl8_20,
inference(avatar_split_clause,[],[f157,f357]) ).
fof(f157,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f355,plain,
spl8_19,
inference(avatar_split_clause,[],[f153,f353]) ).
fof(f353,plain,
( spl8_19
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f153,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( member(X0,universal_class)
=> member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class) ).
fof(f351,plain,
spl8_18,
inference(avatar_split_clause,[],[f152,f349]) ).
fof(f349,plain,
( spl8_18
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f152,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( member(X0,universal_class)
=> member(power_class(X0),universal_class) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X2] :
( member(X2,universal_class)
=> member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class) ).
fof(f347,plain,
spl8_17,
inference(avatar_split_clause,[],[f151,f345]) ).
fof(f345,plain,
( spl8_17
<=> ! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
fof(f151,plain,
! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f73,f88]) ).
fof(f88,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity) ).
fof(f343,plain,
spl8_16,
inference(avatar_split_clause,[],[f150,f341]) ).
fof(f341,plain,
( spl8_16
<=> ! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f150,plain,
! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f339,plain,
spl8_15,
inference(avatar_split_clause,[],[f149,f337]) ).
fof(f337,plain,
( spl8_15
<=> ! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f149,plain,
! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f89]) ).
fof(f333,plain,
spl8_14,
inference(avatar_split_clause,[],[f225,f331]) ).
fof(f331,plain,
( spl8_14
<=> ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f225,plain,
! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f85,f134]) ).
fof(f134,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infinity) ).
fof(f329,plain,
spl8_13,
inference(avatar_split_clause,[],[f163,f327]) ).
fof(f327,plain,
( spl8_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f163,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
fof(f325,plain,
spl8_12,
inference(avatar_split_clause,[],[f154,f323]) ).
fof(f154,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f321,plain,
spl8_11,
inference(avatar_split_clause,[],[f140,f318]) ).
fof(f318,plain,
( spl8_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f140,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f316,plain,
spl8_10,
inference(avatar_split_clause,[],[f139,f313]) ).
fof(f313,plain,
( spl8_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f139,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation) ).
fof(f311,plain,
spl8_9,
inference(avatar_split_clause,[],[f265,f309]) ).
fof(f309,plain,
( spl8_9
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f265,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f172]) ).
fof(f172,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f99]) ).
fof(f307,plain,
spl8_8,
inference(avatar_split_clause,[],[f223,f304]) ).
fof(f304,plain,
( spl8_8
<=> member(sK7,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f223,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f135]) ).
fof(f302,plain,
spl8_7,
inference(avatar_split_clause,[],[f142,f300]) ).
fof(f300,plain,
( spl8_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f142,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f298,plain,
spl8_6,
inference(avatar_split_clause,[],[f141,f296]) ).
fof(f141,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_defn) ).
fof(f294,plain,
spl8_5,
inference(avatar_split_clause,[],[f224,f291]) ).
fof(f291,plain,
( spl8_5
<=> inductive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f224,plain,
inductive(sK7),
inference(cnf_transformation,[],[f135]) ).
fof(f289,plain,
spl8_4,
inference(avatar_split_clause,[],[f221,f286]) ).
fof(f286,plain,
( spl8_4
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f221,plain,
function(sK6),
inference(cnf_transformation,[],[f133]) ).
fof(f284,plain,
spl8_3,
inference(avatar_split_clause,[],[f231,f281]) ).
fof(f231,plain,
unordered_pair(sK0,sK0) = unordered_pair(sK1,sK1),
inference(definition_unfolding,[],[f136,f144,f144]) ).
fof(f136,plain,
singleton(sK0) = singleton(sK1),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( sK0 != sK1
& member(sK0,universal_class)
& singleton(sK0) = singleton(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f72,f86]) ).
fof(f86,plain,
( ? [X0,X1] :
( X0 != X1
& member(X0,universal_class)
& singleton(X0) = singleton(X1) )
=> ( sK0 != sK1
& member(sK0,universal_class)
& singleton(sK0) = singleton(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0,X1] :
( X0 != X1
& member(X0,universal_class)
& singleton(X0) = singleton(X1) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
? [X0,X1] :
( X0 != X1
& member(X0,universal_class)
& singleton(X0) = singleton(X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( ( member(X0,universal_class)
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1] :
( ( member(X0,universal_class)
& singleton(X0) = singleton(X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
fof(f279,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f138,f276]) ).
fof(f138,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f87]) ).
fof(f274,plain,
spl8_1,
inference(avatar_split_clause,[],[f137,f271]) ).
fof(f137,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET083+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 01:33:32 EDT 2024
% 0.22/0.36 % CPUTime :
% 0.22/0.37 % (2428)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (2431)WARNING: value z3 for option sas not known
% 0.22/0.39 % (2432)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.39 % (2429)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.39 % (2431)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.39 % (2433)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.22/0.39 % (2430)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.39 % (2434)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.22/0.39 % (2435)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.22/0.41 % (2433)First to succeed.
% 0.22/0.41 TRYING [1]
% 0.22/0.41 TRYING [1]
% 0.22/0.41 TRYING [2]
% 0.22/0.41 TRYING [2]
% 0.22/0.42 TRYING [1]
% 0.22/0.42 % (2433)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Theorem for theBenchmark
% 0.22/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.42 % (2433)------------------------------
% 0.22/0.42 % (2433)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.42 % (2433)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (2433)Memory used [KB]: 1280
% 0.22/0.42 % (2433)Time elapsed: 0.033 s
% 0.22/0.42 % (2433)Instructions burned: 53 (million)
% 0.22/0.42 % (2433)------------------------------
% 0.22/0.42 % (2433)------------------------------
% 0.22/0.42 % (2428)Success in time 0.052 s
%------------------------------------------------------------------------------