TSTP Solution File: SET081+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET081+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 : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 09:11:01 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 101
% Syntax : Number of formulae : 311 ( 98 unt; 0 def)
% Number of atoms : 817 ( 99 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 783 ( 277 ~; 275 |; 128 &)
% ( 84 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 66 ( 64 usr; 60 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 9 con; 0-3 aty)
% Number of variables : 445 ( 416 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f633,plain,
$false,
inference(avatar_sat_refutation,[],[f272,f277,f282,f287,f291,f295,f300,f304,f309,f314,f318,f322,f326,f331,f335,f339,f343,f347,f351,f355,f359,f364,f368,f372,f376,f380,f384,f399,f403,f411,f415,f419,f423,f427,f431,f435,f439,f443,f447,f474,f478,f482,f486,f490,f494,f535,f539,f543,f575,f579,f583,f587,f591,f615,f619,f623,f627,f631,f632]) ).
fof(f632,plain,
( spl8_1
| ~ spl8_2
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f610,f581,f274,f269]) ).
fof(f269,plain,
( spl8_1
<=> sK0 = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f274,plain,
( spl8_2
<=> member(sK1,unordered_pair(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f581,plain,
( spl8_52
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
fof(f610,plain,
( sK0 = sK1
| ~ spl8_2
| ~ spl8_52 ),
inference(duplicate_literal_removal,[],[f606]) ).
fof(f606,plain,
( sK0 = sK1
| sK0 = sK1
| ~ spl8_2
| ~ spl8_52 ),
inference(resolution,[],[f582,f276]) ).
fof(f276,plain,
( member(sK1,unordered_pair(sK0,sK0))
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f274]) ).
fof(f582,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f631,plain,
spl8_59,
inference(avatar_split_clause,[],[f246,f629]) ).
fof(f629,plain,
( spl8_59
<=> ! [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_59])]) ).
fof(f246,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,[],[f192,f227]) ).
fof(f227,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f165,f142,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(f165,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(f192,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[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(flattening,[],[f115]) ).
fof(f115,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(f627,plain,
spl8_58,
inference(avatar_split_clause,[],[f243,f625]) ).
fof(f625,plain,
( spl8_58
<=> ! [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_58])]) ).
fof(f243,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,[],[f188,f227]) ).
fof(f188,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[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(flattening,[],[f113]) ).
fof(f113,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(f623,plain,
spl8_57,
inference(avatar_split_clause,[],[f242,f621]) ).
fof(f621,plain,
( spl8_57
<=> ! [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_57])]) ).
fof(f242,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,[],[f189,f227]) ).
fof(f189,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f114]) ).
fof(f619,plain,
spl8_56,
inference(avatar_split_clause,[],[f231,f617]) ).
fof(f617,plain,
( spl8_56
<=> ! [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_56])]) ).
fof(f231,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,[],[f153,f226]) ).
fof(f226,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,[],[f164,f225,f195]) ).
fof(f195,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(f225,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f141,f144]) ).
fof(f144,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(f141,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(f164,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(f153,plain,
! [X0] :
( subclass(image(successor_relation,X0),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(f615,plain,
spl8_55,
inference(avatar_split_clause,[],[f240,f613]) ).
fof(f613,plain,
( spl8_55
<=> ! [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_55])]) ).
fof(f240,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f183,f195,f142]) ).
fof(f183,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(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(f591,plain,
( spl8_54
| ~ spl8_41
| ~ spl8_44 ),
inference(avatar_split_clause,[],[f531,f484,f471,f589]) ).
fof(f589,plain,
( spl8_54
<=> ! [X0] :
( member(sK1,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
fof(f471,plain,
( spl8_41
<=> member(sK1,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
fof(f484,plain,
( spl8_44
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
fof(f531,plain,
( ! [X0] :
( member(sK1,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_41
| ~ spl8_44 ),
inference(resolution,[],[f473,f485]) ).
fof(f485,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl8_44 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f473,plain,
( member(sK1,universal_class)
| ~ spl8_41 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f587,plain,
spl8_53,
inference(avatar_split_clause,[],[f233,f585]) ).
fof(f585,plain,
( spl8_53
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
fof(f233,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f156,f144]) ).
fof(f156,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ 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(f583,plain,
spl8_52,
inference(avatar_split_clause,[],[f204,f581]) ).
fof(f204,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
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(f579,plain,
spl8_51,
inference(avatar_split_clause,[],[f200,f577]) ).
fof(f577,plain,
( spl8_51
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
fof(f200,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,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(f575,plain,
spl8_50,
inference(avatar_split_clause,[],[f199,f573]) ).
fof(f573,plain,
( spl8_50
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
fof(f199,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
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(f543,plain,
spl8_49,
inference(avatar_split_clause,[],[f187,f541]) ).
fof(f541,plain,
( spl8_49
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
fof(f187,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,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])],[f110,f111]) ).
fof(f111,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK5(X0,X1),X1)
& member(X0,sK5(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(f539,plain,
spl8_48,
inference(avatar_split_clause,[],[f181,f537]) ).
fof(f537,plain,
( spl8_48
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
fof(f181,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
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(f535,plain,
spl8_47,
inference(avatar_split_clause,[],[f178,f533]) ).
fof(f533,plain,
( spl8_47
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
fof(f178,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
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(f494,plain,
spl8_46,
inference(avatar_split_clause,[],[f186,f492]) ).
fof(f492,plain,
( spl8_46
<=> ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
fof(f186,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f490,plain,
spl8_45,
inference(avatar_split_clause,[],[f185,f488]) ).
fof(f488,plain,
( spl8_45
<=> ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f112]) ).
fof(f486,plain,
spl8_44,
inference(avatar_split_clause,[],[f173,f484]) ).
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(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])],[f100,f101]) ).
fof(f101,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(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,
spl8_43,
inference(avatar_split_clause,[],[f172,f480]) ).
fof(f480,plain,
( spl8_43
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
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,
spl8_42,
inference(avatar_split_clause,[],[f171,f476]) ).
fof(f476,plain,
( spl8_42
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
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,
( spl8_41
| ~ spl8_2
| ~ spl8_38 ),
inference(avatar_split_clause,[],[f465,f437,f274,f471]) ).
fof(f437,plain,
( spl8_38
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f465,plain,
( member(sK1,universal_class)
| ~ spl8_2
| ~ spl8_38 ),
inference(resolution,[],[f438,f276]) ).
fof(f438,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) )
| ~ spl8_38 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f447,plain,
spl8_40,
inference(avatar_split_clause,[],[f267,f445]) ).
fof(f445,plain,
( spl8_40
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
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(f443,plain,
spl8_39,
inference(avatar_split_clause,[],[f266,f441]) ).
fof(f441,plain,
( spl8_39
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
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(f439,plain,
spl8_38,
inference(avatar_split_clause,[],[f203,f437]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f435,plain,
spl8_37,
inference(avatar_split_clause,[],[f202,f433]) ).
fof(f433,plain,
( spl8_37
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f120]) ).
fof(f431,plain,
spl8_36,
inference(avatar_split_clause,[],[f201,f429]) ).
fof(f429,plain,
( spl8_36
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f427,plain,
spl8_35,
inference(avatar_split_clause,[],[f198,f425]) ).
fof(f425,plain,
( spl8_35
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f198,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f423,plain,
spl8_34,
inference(avatar_split_clause,[],[f197,f421]) ).
fof(f421,plain,
( spl8_34
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f197,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
fof(f419,plain,
spl8_33,
inference(avatar_split_clause,[],[f175,f417]) ).
fof(f417,plain,
( spl8_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f175,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f415,plain,
spl8_32,
inference(avatar_split_clause,[],[f174,f413]) ).
fof(f413,plain,
( spl8_32
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f174,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f411,plain,
( spl8_30
| spl8_31
| ~ spl8_11
| ~ spl8_23 ),
inference(avatar_split_clause,[],[f386,f366,f316,f408,f405]) ).
fof(f405,plain,
( spl8_30
<=> ! [X0] : ~ inductive(complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f408,plain,
( spl8_31
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f316,plain,
( spl8_11
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f366,plain,
( spl8_23
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f386,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(complement(X0)) )
| ~ spl8_11
| ~ spl8_23 ),
inference(resolution,[],[f367,f317]) ).
fof(f317,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| member(X1,universal_class) )
| ~ spl8_23 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f403,plain,
spl8_29,
inference(avatar_split_clause,[],[f146,f401]) ).
fof(f401,plain,
( spl8_29
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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(f399,plain,
spl8_28,
inference(avatar_split_clause,[],[f145,f397]) ).
fof(f397,plain,
( spl8_28
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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(f384,plain,
spl8_27,
inference(avatar_split_clause,[],[f182,f382]) ).
fof(f382,plain,
( spl8_27
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f182,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f380,plain,
spl8_26,
inference(avatar_split_clause,[],[f180,f378]) ).
fof(f378,plain,
( spl8_26
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f180,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f376,plain,
spl8_25,
inference(avatar_split_clause,[],[f179,f374]) ).
fof(f374,plain,
( spl8_25
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f179,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f372,plain,
spl8_24,
inference(avatar_split_clause,[],[f177,f370]) ).
fof(f370,plain,
( spl8_24
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f177,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f368,plain,
spl8_23,
inference(avatar_split_clause,[],[f176,f366]) ).
fof(f176,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f104]) ).
fof(f364,plain,
( ~ spl8_22
| ~ spl8_5
| ~ spl8_11 ),
inference(avatar_split_clause,[],[f327,f316,f289,f361]) ).
fof(f361,plain,
( spl8_22
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f289,plain,
( spl8_5
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f327,plain,
( ~ inductive(null_class)
| ~ spl8_5
| ~ spl8_11 ),
inference(resolution,[],[f317,f290]) ).
fof(f290,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f359,plain,
spl8_21,
inference(avatar_split_clause,[],[f162,f357]) ).
fof(f357,plain,
( spl8_21
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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(f355,plain,
spl8_20,
inference(avatar_split_clause,[],[f158,f353]) ).
fof(f353,plain,
( spl8_20
<=> ! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f158,plain,
! [X0] :
( member(sK3(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(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f94,f95]) ).
fof(f95,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(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(f351,plain,
spl8_19,
inference(avatar_split_clause,[],[f155,f349]) ).
fof(f349,plain,
( spl8_19
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f155,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f347,plain,
spl8_18,
inference(avatar_split_clause,[],[f151,f345]) ).
fof(f345,plain,
( spl8_18
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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(f343,plain,
spl8_17,
inference(avatar_split_clause,[],[f150,f341]) ).
fof(f341,plain,
( spl8_17
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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(f339,plain,
spl8_16,
inference(avatar_split_clause,[],[f149,f337]) ).
fof(f337,plain,
( spl8_16
<=> ! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f149,plain,
! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,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])],[f72,f87]) ).
fof(f87,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(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(f335,plain,
spl8_15,
inference(avatar_split_clause,[],[f148,f333]) ).
fof(f333,plain,
( spl8_15
<=> ! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f148,plain,
! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f331,plain,
spl8_14,
inference(avatar_split_clause,[],[f147,f329]) ).
fof(f329,plain,
( spl8_14
<=> ! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f147,plain,
! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f88]) ).
fof(f326,plain,
spl8_13,
inference(avatar_split_clause,[],[f223,f324]) ).
fof(f324,plain,
( spl8_13
<=> ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f223,plain,
! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f84,f133]) ).
fof(f133,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(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,
spl8_12,
inference(avatar_split_clause,[],[f161,f320]) ).
fof(f320,plain,
( spl8_12
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
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,
spl8_11,
inference(avatar_split_clause,[],[f152,f316]) ).
fof(f152,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f314,plain,
spl8_10,
inference(avatar_split_clause,[],[f138,f311]) ).
fof(f311,plain,
( spl8_10
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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,
spl8_9,
inference(avatar_split_clause,[],[f137,f306]) ).
fof(f306,plain,
( spl8_9
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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,
spl8_8,
inference(avatar_split_clause,[],[f263,f302]) ).
fof(f302,plain,
( spl8_8
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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,
spl8_7,
inference(avatar_split_clause,[],[f221,f297]) ).
fof(f297,plain,
( spl8_7
<=> member(sK7,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f221,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f134]) ).
fof(f295,plain,
spl8_6,
inference(avatar_split_clause,[],[f140,f293]) ).
fof(f293,plain,
( spl8_6
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_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,
spl8_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,
spl8_4,
inference(avatar_split_clause,[],[f222,f284]) ).
fof(f284,plain,
( spl8_4
<=> inductive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f222,plain,
inductive(sK7),
inference(cnf_transformation,[],[f134]) ).
fof(f282,plain,
spl8_3,
inference(avatar_split_clause,[],[f219,f279]) ).
fof(f279,plain,
( spl8_3
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f219,plain,
function(sK6),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f83,f131]) ).
fof(f131,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(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,
spl8_2,
inference(avatar_split_clause,[],[f229,f274]) ).
fof(f229,plain,
member(sK1,unordered_pair(sK0,sK0)),
inference(definition_unfolding,[],[f135,f142]) ).
fof(f135,plain,
member(sK1,singleton(sK0)),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
( sK0 != sK1
& member(sK1,singleton(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f71,f85]) ).
fof(f85,plain,
( ? [X0,X1] :
( X0 != X1
& member(X1,singleton(X0)) )
=> ( sK0 != sK1
& member(sK1,singleton(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
? [X0,X1] :
( X0 != X1
& member(X1,singleton(X0)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( member(X1,singleton(X0))
=> X0 = X1 ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X0,X1] :
( member(X1,singleton(X0))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f272,plain,
~ spl8_1,
inference(avatar_split_clause,[],[f136,f269]) ).
fof(f136,plain,
sK0 != sK1,
inference(cnf_transformation,[],[f86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET081+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 17:00:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (27951)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (27956)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)
% 0.14/0.37 % (27954)WARNING: value z3 for option sas not known
% 0.14/0.37 % (27952)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (27953)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (27955)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (27957)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)
% 0.14/0.37 % (27958)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)
% 0.14/0.37 % (27954)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)
% 0.14/0.38 % (27956)First to succeed.
% 0.14/0.38 % (27956)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27951"
% 0.14/0.38 % (27956)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.39 % (27956)------------------------------
% 0.14/0.39 % (27956)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.39 % (27956)Termination reason: Refutation
% 0.14/0.39
% 0.14/0.39 % (27956)Memory used [KB]: 1092
% 0.14/0.39 % (27956)Time elapsed: 0.015 s
% 0.14/0.39 % (27956)Instructions burned: 25 (million)
% 0.14/0.39 % (27951)Success in time 0.03 s
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