TSTP Solution File: SET079+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET079+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 : n011.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 15:05:29 EDT 2024
% Result : Theorem 0.19s 0.36s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 80
% Syntax : Number of formulae : 239 ( 69 unt; 0 def)
% Number of atoms : 643 ( 67 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 610 ( 206 ~; 202 |; 115 &)
% ( 68 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 52 ( 50 usr; 46 prp; 0-2 aty)
% Number of functors : 29 ( 29 usr; 8 con; 0-3 aty)
% Number of variables : 326 ( 299 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f534,plain,
$false,
inference(avatar_sat_refutation,[],[f272,f277,f282,f287,f291,f295,f300,f304,f309,f314,f318,f322,f326,f332,f336,f340,f344,f348,f352,f356,f360,f365,f369,f373,f377,f381,f385,f400,f404,f409,f413,f417,f421,f425,f429,f433,f437,f441,f445,f474,f478,f482,f486,f490,f494,f533]) ).
fof(f533,plain,
( ~ spl7_5
| ~ spl7_40 ),
inference(avatar_contradiction_clause,[],[f531]) ).
fof(f531,plain,
( $false
| ~ spl7_5
| ~ spl7_40 ),
inference(resolution,[],[f473,f290]) ).
fof(f290,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f289,plain,
( spl7_5
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_5])]) ).
fof(f473,plain,
( member(sK0,null_class)
| ~ spl7_40 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f471,plain,
( spl7_40
<=> member(sK0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_40])]) ).
fof(f494,plain,
spl7_45,
inference(avatar_split_clause,[],[f186,f492]) ).
fof(f492,plain,
( spl7_45
<=> ! [X0,X1] :
( member(sK4(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_45])]) ).
fof(f186,plain,
! [X0,X1] :
( member(sK4(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK4(X0,X1),X1)
& member(X0,sK4(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f110,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK4(X0,X1),X1)
& member(X0,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f110,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,[],[f109]) ).
fof(f109,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(f490,plain,
spl7_44,
inference(avatar_split_clause,[],[f185,f488]) ).
fof(f488,plain,
( spl7_44
<=> ! [X0,X1] :
( member(X0,sK4(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_44])]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,sK4(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f486,plain,
spl7_43,
inference(avatar_split_clause,[],[f173,f484]) ).
fof(f484,plain,
( spl7_43
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_43])]) ).
fof(f173,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK3(X0,X1),X1)
& member(sK3(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f100,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,[],[f99]) ).
fof(f99,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,[],[f80]) ).
fof(f80,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(f482,plain,
spl7_42,
inference(avatar_split_clause,[],[f172,f480]) ).
fof(f480,plain,
( spl7_42
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_42])]) ).
fof(f172,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,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(f478,plain,
spl7_41,
inference(avatar_split_clause,[],[f171,f476]) ).
fof(f476,plain,
( spl7_41
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_41])]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f97]) ).
fof(f97,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(f474,plain,
( ~ spl7_1
| spl7_40
| ~ spl7_2
| ~ spl7_38 ),
inference(avatar_split_clause,[],[f467,f439,f274,f471,f269]) ).
fof(f269,plain,
( spl7_1
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_1])]) ).
fof(f274,plain,
( spl7_2
<=> null_class = unordered_pair(sK0,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_2])]) ).
fof(f439,plain,
( spl7_38
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_38])]) ).
fof(f467,plain,
( member(sK0,null_class)
| ~ member(sK0,universal_class)
| ~ spl7_2
| ~ spl7_38 ),
inference(superposition,[],[f440,f276]) ).
fof(f276,plain,
( null_class = unordered_pair(sK0,sK0)
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f440,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl7_38 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f445,plain,
spl7_39,
inference(avatar_split_clause,[],[f267,f443]) ).
fof(f443,plain,
( spl7_39
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_39])]) ).
fof(f267,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f205]) ).
fof(f205,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[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(flattening,[],[f121]) ).
fof(f121,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(f441,plain,
spl7_38,
inference(avatar_split_clause,[],[f266,f439]) ).
fof(f266,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f206]) ).
fof(f206,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f122]) ).
fof(f437,plain,
spl7_37,
inference(avatar_split_clause,[],[f203,f435]) ).
fof(f435,plain,
( spl7_37
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_37])]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f433,plain,
spl7_36,
inference(avatar_split_clause,[],[f202,f431]) ).
fof(f431,plain,
( spl7_36
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_36])]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[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(flattening,[],[f119]) ).
fof(f119,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(f429,plain,
spl7_35,
inference(avatar_split_clause,[],[f201,f427]) ).
fof(f427,plain,
( spl7_35
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_35])]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f425,plain,
spl7_34,
inference(avatar_split_clause,[],[f198,f423]) ).
fof(f423,plain,
( spl7_34
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_34])]) ).
fof(f198,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[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(flattening,[],[f117]) ).
fof(f117,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(f421,plain,
spl7_33,
inference(avatar_split_clause,[],[f197,f419]) ).
fof(f419,plain,
( spl7_33
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_33])]) ).
fof(f197,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f417,plain,
spl7_32,
inference(avatar_split_clause,[],[f175,f415]) ).
fof(f415,plain,
( spl7_32
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK3(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_32])]) ).
fof(f175,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f413,plain,
spl7_31,
inference(avatar_split_clause,[],[f174,f411]) ).
fof(f411,plain,
( spl7_31
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK3(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_31])]) ).
fof(f174,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK3(X0,X1),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f409,plain,
( ~ spl7_30
| ~ spl7_5
| ~ spl7_11 ),
inference(avatar_split_clause,[],[f327,f316,f289,f406]) ).
fof(f406,plain,
( spl7_30
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_30])]) ).
fof(f316,plain,
( spl7_11
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_11])]) ).
fof(f327,plain,
( ~ inductive(null_class)
| ~ spl7_5
| ~ spl7_11 ),
inference(resolution,[],[f317,f290]) ).
fof(f317,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f404,plain,
spl7_29,
inference(avatar_split_clause,[],[f146,f402]) ).
fof(f402,plain,
( spl7_29
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_29])]) ).
fof(f146,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(f400,plain,
spl7_28,
inference(avatar_split_clause,[],[f145,f398]) ).
fof(f398,plain,
( spl7_28
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_28])]) ).
fof(f145,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(f385,plain,
spl7_27,
inference(avatar_split_clause,[],[f182,f383]) ).
fof(f383,plain,
( spl7_27
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_27])]) ).
fof(f182,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[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(flattening,[],[f107]) ).
fof(f107,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(f381,plain,
spl7_26,
inference(avatar_split_clause,[],[f180,f379]) ).
fof(f379,plain,
( spl7_26
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_26])]) ).
fof(f180,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[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(flattening,[],[f105]) ).
fof(f105,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(f377,plain,
spl7_25,
inference(avatar_split_clause,[],[f179,f375]) ).
fof(f375,plain,
( spl7_25
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_25])]) ).
fof(f179,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f373,plain,
spl7_24,
inference(avatar_split_clause,[],[f177,f371]) ).
fof(f371,plain,
( spl7_24
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_24])]) ).
fof(f177,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[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(flattening,[],[f103]) ).
fof(f103,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(f369,plain,
spl7_23,
inference(avatar_split_clause,[],[f176,f367]) ).
fof(f367,plain,
( spl7_23
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_23])]) ).
fof(f176,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f365,plain,
( spl7_22
| ~ spl7_2
| ~ spl7_12 ),
inference(avatar_split_clause,[],[f328,f320,f274,f362]) ).
fof(f362,plain,
( spl7_22
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_22])]) ).
fof(f320,plain,
( spl7_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_12])]) ).
fof(f328,plain,
( member(null_class,universal_class)
| ~ spl7_2
| ~ spl7_12 ),
inference(superposition,[],[f321,f276]) ).
fof(f321,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f360,plain,
spl7_21,
inference(avatar_split_clause,[],[f162,f358]) ).
fof(f358,plain,
( spl7_21
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_21])]) ).
fof(f162,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(f356,plain,
spl7_20,
inference(avatar_split_clause,[],[f158,f354]) ).
fof(f354,plain,
( spl7_20
<=> ! [X0] :
( member(sK2(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_20])]) ).
fof(f158,plain,
! [X0] :
( member(sK2(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK2(X0),sK2(X0)) = X0
& member(sK2(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f94,f95]) ).
fof(f95,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK2(X0),sK2(X0)) = X0
& member(sK2(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f94,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,[],[f93]) ).
fof(f93,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(f352,plain,
spl7_19,
inference(avatar_split_clause,[],[f155,f350]) ).
fof(f350,plain,
( spl7_19
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_19])]) ).
fof(f155,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f91]) ).
fof(f91,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(f348,plain,
spl7_18,
inference(avatar_split_clause,[],[f151,f346]) ).
fof(f346,plain,
( spl7_18
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_18])]) ).
fof(f151,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,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(f344,plain,
spl7_17,
inference(avatar_split_clause,[],[f150,f342]) ).
fof(f342,plain,
( spl7_17
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_17])]) ).
fof(f150,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,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(f340,plain,
spl7_16,
inference(avatar_split_clause,[],[f149,f338]) ).
fof(f338,plain,
( spl7_16
<=> ! [X0] :
( disjoint(sK1(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_16])]) ).
fof(f149,plain,
! [X0] :
( disjoint(sK1(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0] :
( ( disjoint(sK1(X0),X0)
& member(sK1(X0),X0)
& member(sK1(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f72,f87]) ).
fof(f87,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK1(X0),X0)
& member(sK1(X0),X0)
& member(sK1(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f72,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(f336,plain,
spl7_15,
inference(avatar_split_clause,[],[f148,f334]) ).
fof(f334,plain,
( spl7_15
<=> ! [X0] :
( member(sK1(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_15])]) ).
fof(f148,plain,
! [X0] :
( member(sK1(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f332,plain,
spl7_14,
inference(avatar_split_clause,[],[f147,f330]) ).
fof(f330,plain,
( spl7_14
<=> ! [X0] :
( member(sK1(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_14])]) ).
fof(f147,plain,
! [X0] :
( member(sK1(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f326,plain,
spl7_13,
inference(avatar_split_clause,[],[f223,f324]) ).
fof(f324,plain,
( spl7_13
<=> ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_13])]) ).
fof(f223,plain,
! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) )
& inductive(sK6)
& member(sK6,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f84,f133]) ).
fof(f133,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK6,X1)
| ~ inductive(X1) )
& inductive(sK6)
& member(sK6,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f84,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(f322,plain,
spl7_12,
inference(avatar_split_clause,[],[f161,f320]) ).
fof(f161,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(f318,plain,
spl7_11,
inference(avatar_split_clause,[],[f152,f316]) ).
fof(f152,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[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(flattening,[],[f89]) ).
fof(f89,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(f314,plain,
spl7_10,
inference(avatar_split_clause,[],[f138,f311]) ).
fof(f311,plain,
( spl7_10
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_10])]) ).
fof(f138,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(f309,plain,
spl7_9,
inference(avatar_split_clause,[],[f137,f306]) ).
fof(f306,plain,
( spl7_9
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_9])]) ).
fof(f137,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(f304,plain,
spl7_8,
inference(avatar_split_clause,[],[f263,f302]) ).
fof(f302,plain,
( spl7_8
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_8])]) ).
fof(f263,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f98]) ).
fof(f300,plain,
spl7_7,
inference(avatar_split_clause,[],[f221,f297]) ).
fof(f297,plain,
( spl7_7
<=> member(sK6,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_7])]) ).
fof(f221,plain,
member(sK6,universal_class),
inference(cnf_transformation,[],[f134]) ).
fof(f295,plain,
spl7_6,
inference(avatar_split_clause,[],[f140,f293]) ).
fof(f293,plain,
( spl7_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_6])]) ).
fof(f140,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(f291,plain,
spl7_5,
inference(avatar_split_clause,[],[f139,f289]) ).
fof(f139,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(f287,plain,
spl7_4,
inference(avatar_split_clause,[],[f222,f284]) ).
fof(f284,plain,
( spl7_4
<=> inductive(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_4])]) ).
fof(f222,plain,
inductive(sK6),
inference(cnf_transformation,[],[f134]) ).
fof(f282,plain,
spl7_3,
inference(avatar_split_clause,[],[f219,f279]) ).
fof(f279,plain,
( spl7_3
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl7_3])]) ).
fof(f219,plain,
function(sK5),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f83,f131]) ).
fof(f131,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK5,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,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(f277,plain,
spl7_2,
inference(avatar_split_clause,[],[f229,f274]) ).
fof(f229,plain,
null_class = unordered_pair(sK0,sK0),
inference(definition_unfolding,[],[f136,f142]) ).
fof(f142,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(f136,plain,
null_class = singleton(sK0),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( null_class = singleton(sK0)
& member(sK0,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f85]) ).
fof(f85,plain,
( ? [X0] :
( singleton(X0) = null_class
& member(X0,universal_class) )
=> ( null_class = singleton(sK0)
& member(sK0,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0] :
( singleton(X0) = null_class
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0] :
( member(X0,universal_class)
=> singleton(X0) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_set_in_its_singleton) ).
fof(f272,plain,
spl7_1,
inference(avatar_split_clause,[],[f135,f269]) ).
fof(f135,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Apr 30 01:21:16 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (14458)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (14463)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)
% 0.14/0.36 % (14461)WARNING: value z3 for option sas not known
% 0.14/0.36 % (14463)First to succeed.
% 0.14/0.36 % (14459)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (14461)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)
% 0.14/0.36 % (14462)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (14460)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 % (14464)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)
% 0.14/0.36 % (14465)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)
% 0.19/0.36 % (14463)Refutation found. Thanks to Tanya!
% 0.19/0.36 % SZS status Theorem for theBenchmark
% 0.19/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.37 % (14463)------------------------------
% 0.19/0.37 % (14463)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.37 % (14463)Termination reason: Refutation
% 0.19/0.37
% 0.19/0.37 % (14463)Memory used [KB]: 1036
% 0.19/0.37 % (14463)Time elapsed: 0.009 s
% 0.19/0.37 % (14463)Instructions burned: 20 (million)
% 0.19/0.37 % (14463)------------------------------
% 0.19/0.37 % (14463)------------------------------
% 0.19/0.37 % (14458)Success in time 0.02 s
%------------------------------------------------------------------------------