TSTP Solution File: SET095-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET095-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 09:11:09 EDT 2024
% Result : Unsatisfiable 0.16s 0.35s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 154
% Syntax : Number of formulae : 277 ( 109 unt; 0 def)
% Number of atoms : 540 ( 74 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 434 ( 171 ~; 185 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 89 ( 87 usr; 79 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 10 con; 0-3 aty)
% Number of variables : 274 ( 274 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f771,plain,
$false,
inference(avatar_sat_refutation,[],[f246,f251,f256,f261,f265,f270,f274,f278,f282,f287,f291,f295,f299,f304,f309,f313,f317,f322,f328,f332,f336,f340,f344,f348,f356,f360,f364,f368,f372,f376,f380,f385,f398,f402,f406,f410,f414,f418,f422,f426,f430,f434,f438,f442,f446,f450,f454,f458,f462,f466,f486,f508,f512,f516,f520,f525,f529,f533,f537,f567,f603,f607,f611,f615,f622,f626,f640,f644,f649,f653,f657,f661,f665,f669,f673,f677,f681,f685,f770]) ).
fof(f770,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_71 ),
inference(avatar_split_clause,[],[f719,f655,f248,f243]) ).
fof(f243,plain,
( spl0_1
<=> member(x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f248,plain,
( spl0_2
<=> subclass(unordered_pair(x,x),y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f655,plain,
( spl0_71
<=> ! [X4,X0,X1] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f719,plain,
( ~ member(x,y)
| spl0_2
| ~ spl0_71 ),
inference(duplicate_literal_removal,[],[f713]) ).
fof(f713,plain,
( ~ member(x,y)
| ~ member(x,y)
| spl0_2
| ~ spl0_71 ),
inference(resolution,[],[f656,f250]) ).
fof(f250,plain,
( ~ subclass(unordered_pair(x,x),y)
| spl0_2 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f656,plain,
( ! [X0,X1,X4] :
( subclass(unordered_pair(X0,X1),X4)
| ~ member(X1,X4)
| ~ member(X0,X4) )
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f685,plain,
spl0_78,
inference(avatar_split_clause,[],[f223,f683]) ).
fof(f683,plain,
( spl0_78
<=> ! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f223,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f169,f158]) ).
fof(f158,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction2) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restriction1) ).
fof(f169,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f141]) ).
fof(f141,plain,
! [X0] : sum_class(X0) = domain_of(intersection(cross_product(universal_class,X0),element_relation)),
inference(definition_unfolding,[],[f53,f29]) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class2) ).
fof(f681,plain,
spl0_77,
inference(avatar_split_clause,[],[f187,f679]) ).
fof(f679,plain,
( spl0_77
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f187,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ),
inference(definition_unfolding,[],[f133,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
fof(f133,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists4) ).
fof(f677,plain,
spl0_76,
inference(avatar_split_clause,[],[f186,f675]) ).
fof(f675,plain,
( spl0_76
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of1(X0),member_of1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f186,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of1(X0),member_of1(X0)) = X0 ),
inference(definition_unfolding,[],[f136,f12]) ).
fof(f136,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of1(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique2) ).
fof(f673,plain,
spl0_75,
inference(avatar_split_clause,[],[f165,f671]) ).
fof(f671,plain,
( spl0_75
<=> ! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f165,plain,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f61,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f61,axiom,
! [X0] :
( single_valued_class(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f669,plain,
spl0_74,
inference(avatar_split_clause,[],[f164,f667]) ).
fof(f667,plain,
( spl0_74
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f164,plain,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f63,f38]) ).
fof(f63,axiom,
! [X8] :
( ~ function(X8)
| subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function2) ).
fof(f665,plain,
spl0_73,
inference(avatar_split_clause,[],[f160,f663]) ).
fof(f663,plain,
( spl0_73
<=> ! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f160,plain,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f60,f38]) ).
fof(f60,axiom,
! [X0] :
( ~ single_valued_class(X0)
| subclass(compose(X0,inverse(X0)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f661,plain,
spl0_72,
inference(avatar_split_clause,[],[f158,f659]) ).
fof(f659,plain,
( spl0_72
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f657,plain,
spl0_71,
inference(avatar_split_clause,[],[f119,f655]) ).
fof(f119,axiom,
! [X0,X1,X4] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(f653,plain,
spl0_70,
inference(avatar_split_clause,[],[f113,f651]) ).
fof(f651,plain,
( spl0_70
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f113,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f649,plain,
( spl0_69
| ~ spl0_5
| ~ spl0_60 ),
inference(avatar_split_clause,[],[f616,f565,f263,f646]) ).
fof(f646,plain,
( spl0_69
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f263,plain,
( spl0_5
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f565,plain,
( spl0_60
<=> ! [X0] :
( ~ subclass(y,X0)
| member(x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f616,plain,
( member(x,universal_class)
| ~ spl0_5
| ~ spl0_60 ),
inference(resolution,[],[f566,f264]) ).
fof(f264,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f566,plain,
( ! [X0] :
( ~ subclass(y,X0)
| member(x,X0) )
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f644,plain,
spl0_68,
inference(avatar_split_clause,[],[f23,f642]) ).
fof(f642,plain,
( spl0_68
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
fof(f640,plain,
spl0_67,
inference(avatar_split_clause,[],[f8,f638]) ).
fof(f638,plain,
( spl0_67
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f626,plain,
spl0_66,
inference(avatar_split_clause,[],[f195,f624]) ).
fof(f624,plain,
( spl0_66
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f195,plain,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f73,f38]) ).
fof(f73,axiom,
! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(inverse(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one3) ).
fof(f622,plain,
spl0_65,
inference(avatar_split_clause,[],[f180,f620]) ).
fof(f620,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f180,plain,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f112,f12]) ).
fof(f112,axiom,
! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f615,plain,
spl0_64,
inference(avatar_split_clause,[],[f179,f613]) ).
fof(f613,plain,
( spl0_64
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f179,plain,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ),
inference(definition_unfolding,[],[f111,f12]) ).
fof(f111,axiom,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = singleton(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f611,plain,
spl0_63,
inference(avatar_split_clause,[],[f178,f609]) ).
fof(f609,plain,
( spl0_63
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(member_of(X0),member_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f178,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(member_of(X0),member_of(X0)) != X0 ),
inference(definition_unfolding,[],[f137,f12]) ).
fof(f137,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(member_of(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(f607,plain,
spl0_62,
inference(avatar_split_clause,[],[f83,f605]) ).
fof(f605,plain,
( spl0_62
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible2) ).
fof(f603,plain,
spl0_61,
inference(avatar_split_clause,[],[f25,f601]) ).
fof(f601,plain,
( spl0_61
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
fof(f567,plain,
( spl0_60
| ~ spl0_1
| ~ spl0_52 ),
inference(avatar_split_clause,[],[f551,f506,f243,f565]) ).
fof(f506,plain,
( spl0_52
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f551,plain,
( ! [X0] :
( ~ subclass(y,X0)
| member(x,X0) )
| ~ spl0_1
| ~ spl0_52 ),
inference(resolution,[],[f507,f245]) ).
fof(f245,plain,
( member(x,y)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f507,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f537,plain,
spl0_59,
inference(avatar_split_clause,[],[f171,f535]) ).
fof(f535,plain,
( spl0_59
<=> ! [X1] :
( ~ member(X1,universal_class)
| member(member_of(unordered_pair(X1,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f171,plain,
! [X1] :
( ~ member(X1,universal_class)
| member(member_of(unordered_pair(X1,X1)),universal_class) ),
inference(definition_unfolding,[],[f130,f12]) ).
fof(f130,axiom,
! [X1] :
( ~ member(X1,universal_class)
| member(member_of(singleton(X1)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists1) ).
fof(f533,plain,
spl0_58,
inference(avatar_split_clause,[],[f170,f531]) ).
fof(f531,plain,
( spl0_58
<=> ! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f170,plain,
! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ),
inference(definition_unfolding,[],[f134,f12]) ).
fof(f134,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member_of(singleton(X2)) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).
fof(f529,plain,
spl0_57,
inference(avatar_split_clause,[],[f157,f527]) ).
fof(f527,plain,
( spl0_57
<=> ! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f157,plain,
! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f121,f12,f12]) ).
fof(f121,axiom,
! [X0,X1] : member(singleton(X1),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).
fof(f525,plain,
spl0_56,
inference(avatar_split_clause,[],[f154,f522]) ).
fof(f522,plain,
( spl0_56
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f154,plain,
identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation),
inference(definition_unfolding,[],[f75,f38]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f520,plain,
spl0_55,
inference(avatar_split_clause,[],[f97,f518]) ).
fof(f518,plain,
( spl0_55
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f516,plain,
spl0_54,
inference(avatar_split_clause,[],[f67,f514]) ).
fof(f514,plain,
( spl0_54
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f512,plain,
spl0_53,
inference(avatar_split_clause,[],[f7,f510]) ).
fof(f510,plain,
( spl0_53
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f508,plain,
spl0_52,
inference(avatar_split_clause,[],[f1,f506]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).
fof(f486,plain,
( spl0_51
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f387,f366,f342,f484]) ).
fof(f484,plain,
( spl0_51
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f342,plain,
( spl0_23
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f366,plain,
( spl0_28
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f387,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_23
| ~ spl0_28 ),
inference(resolution,[],[f367,f343]) ).
fof(f343,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f367,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f466,plain,
spl0_50,
inference(avatar_split_clause,[],[f177,f464]) ).
fof(f464,plain,
( spl0_50
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f177,plain,
! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ),
inference(definition_unfolding,[],[f126,f12]) ).
fof(f126,axiom,
! [X0] :
( member(X0,universal_class)
| singleton(X0) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f462,plain,
spl0_49,
inference(avatar_split_clause,[],[f173,f460]) ).
fof(f460,plain,
( spl0_49
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f173,plain,
! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ),
inference(definition_unfolding,[],[f125,f12]) ).
fof(f125,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(X1,singleton(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f458,plain,
spl0_48,
inference(avatar_split_clause,[],[f161,f456]) ).
fof(f456,plain,
( spl0_48
<=> ! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f161,plain,
! [X8] :
( ~ one_to_one(X8)
| function(domain_of(flip(cross_product(X8,universal_class)))) ),
inference(definition_unfolding,[],[f72,f38]) ).
fof(f72,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(inverse(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one2) ).
fof(f454,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f381,f354,f311,f452]) ).
fof(f452,plain,
( spl0_47
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f311,plain,
( spl0_16
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f354,plain,
( spl0_25
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f381,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f355,f312]) ).
fof(f312,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f355,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f450,plain,
spl0_46,
inference(avatar_split_clause,[],[f135,f448]) ).
fof(f448,plain,
( spl0_46
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f135,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of1(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).
fof(f446,plain,
spl0_45,
inference(avatar_split_clause,[],[f132,f444]) ).
fof(f444,plain,
( spl0_45
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f132,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists3) ).
fof(f442,plain,
spl0_44,
inference(avatar_split_clause,[],[f117,f440]) ).
fof(f440,plain,
( spl0_44
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f438,plain,
spl0_43,
inference(avatar_split_clause,[],[f116,f436]) ).
fof(f436,plain,
( spl0_43
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f116,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| unordered_pair(X0,X1) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f434,plain,
spl0_42,
inference(avatar_split_clause,[],[f106,f432]) ).
fof(f432,plain,
( spl0_42
<=> ! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f106,axiom,
! [X4] :
( null_class = X4
| member(not_subclass_element(X4,null_class),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f430,plain,
spl0_41,
inference(avatar_split_clause,[],[f88,f428]) ).
fof(f428,plain,
( spl0_41
<=> ! [X9,X11,X10] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f88,axiom,
! [X10,X11,X9] :
( ~ homomorphism(X9,X10,X11)
| compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism3) ).
fof(f426,plain,
spl0_40,
inference(avatar_split_clause,[],[f35,f424]) ).
fof(f424,plain,
( spl0_40
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip1) ).
fof(f422,plain,
spl0_39,
inference(avatar_split_clause,[],[f32,f420]) ).
fof(f420,plain,
( spl0_39
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate1) ).
fof(f418,plain,
spl0_38,
inference(avatar_split_clause,[],[f22,f416]) ).
fof(f416,plain,
( spl0_38
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
fof(f414,plain,
spl0_37,
inference(avatar_split_clause,[],[f21,f412]) ).
fof(f412,plain,
( spl0_37
<=> ! [X4,X0,X1] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( member(X4,X0)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
fof(f410,plain,
spl0_36,
inference(avatar_split_clause,[],[f10,f408]) ).
fof(f408,plain,
( spl0_36
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f10,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| member(X1,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f406,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f404]) ).
fof(f404,plain,
( spl0_35
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f9,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| member(X0,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f402,plain,
spl0_34,
inference(avatar_split_clause,[],[f3,f400]) ).
fof(f400,plain,
( spl0_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f398,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f396]) ).
fof(f396,plain,
( spl0_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f385,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f349,f342,f311,f383]) ).
fof(f383,plain,
( spl0_32
<=> ! [X0] : ~ inductive(intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f349,plain,
( ! [X0] : ~ inductive(intersection(complement(X0),X0))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f343,f312]) ).
fof(f380,plain,
spl0_31,
inference(avatar_split_clause,[],[f156,f378]) ).
fof(f378,plain,
( spl0_31
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f156,plain,
! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f110,f12]) ).
fof(f110,axiom,
! [X0,X1] : subclass(singleton(X1),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f376,plain,
spl0_30,
inference(avatar_split_clause,[],[f155,f374]) ).
fof(f374,plain,
( spl0_30
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f155,plain,
! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)),
inference(definition_unfolding,[],[f109,f12]) ).
fof(f109,axiom,
! [X0,X1] : subclass(singleton(X0),unordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f372,plain,
spl0_29,
inference(avatar_split_clause,[],[f108,f370]) ).
fof(f370,plain,
( spl0_29
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f108,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f368,plain,
spl0_28,
inference(avatar_split_clause,[],[f66,f366]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f364,plain,
spl0_27,
inference(avatar_split_clause,[],[f62,f362]) ).
fof(f362,plain,
( spl0_27
<=> ! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f62,axiom,
! [X8] :
( ~ function(X8)
| subclass(X8,cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function1) ).
fof(f360,plain,
spl0_26,
inference(avatar_split_clause,[],[f57,f358]) ).
fof(f358,plain,
( spl0_26
<=> ! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose1) ).
fof(f356,plain,
spl0_25,
inference(avatar_split_clause,[],[f24,f354]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f348,plain,
spl0_24,
inference(avatar_split_clause,[],[f105,f346]) ).
fof(f346,plain,
( spl0_24
<=> ! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f105,axiom,
! [X0] :
( ~ subclass(X0,null_class)
| null_class = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f344,plain,
spl0_23,
inference(avatar_split_clause,[],[f102,f342]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f340,plain,
spl0_22,
inference(avatar_split_clause,[],[f87,f338]) ).
fof(f338,plain,
( spl0_22
<=> ! [X9,X11,X10] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f87,axiom,
! [X10,X11,X9] :
( operation(X11)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism2) ).
fof(f336,plain,
spl0_21,
inference(avatar_split_clause,[],[f86,f334]) ).
fof(f334,plain,
( spl0_21
<=> ! [X9,X11,X10] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f86,axiom,
! [X10,X11,X9] :
( operation(X10)
| ~ homomorphism(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',homomorphism1) ).
fof(f332,plain,
spl0_20,
inference(avatar_split_clause,[],[f82,f330]) ).
fof(f330,plain,
( spl0_20
<=> ! [X9,X11,X10] :
( function(X9)
| ~ compatible(X9,X10,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f82,axiom,
! [X10,X11,X9] :
( function(X9)
| ~ compatible(X9,X10,X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible1) ).
fof(f328,plain,
( ~ spl0_19
| ~ spl0_8
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f323,f311,f276,f325]) ).
fof(f325,plain,
( spl0_19
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f276,plain,
( spl0_8
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f323,plain,
( ~ inductive(null_class)
| ~ spl0_8
| ~ spl0_16 ),
inference(resolution,[],[f312,f277]) ).
fof(f277,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f322,plain,
spl0_18,
inference(avatar_split_clause,[],[f152,f319]) ).
fof(f319,plain,
( spl0_18
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f152,plain,
member(null_class,unordered_pair(null_class,null_class)),
inference(definition_unfolding,[],[f124,f12]) ).
fof(f124,axiom,
member(null_class,singleton(null_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
fof(f317,plain,
spl0_17,
inference(avatar_split_clause,[],[f51,f315]) ).
fof(f315,plain,
( spl0_17
<=> ! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f51,axiom,
! [X1] :
( ~ inductive(X1)
| subclass(omega,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f313,plain,
spl0_16,
inference(avatar_split_clause,[],[f47,f311]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f309,plain,
spl0_15,
inference(avatar_split_clause,[],[f44,f306]) ).
fof(f306,plain,
( spl0_15
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation1) ).
fof(f304,plain,
spl0_14,
inference(avatar_split_clause,[],[f18,f301]) ).
fof(f301,plain,
( spl0_14
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation1) ).
fof(f299,plain,
spl0_13,
inference(avatar_split_clause,[],[f11,f297]) ).
fof(f297,plain,
( spl0_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f295,plain,
spl0_12,
inference(avatar_split_clause,[],[f78,f293]) ).
fof(f293,plain,
( spl0_12
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f291,plain,
spl0_11,
inference(avatar_split_clause,[],[f71,f289]) ).
fof(f289,plain,
( spl0_11
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f287,plain,
spl0_10,
inference(avatar_split_clause,[],[f107,f284]) ).
fof(f284,plain,
( spl0_10
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f282,plain,
spl0_9,
inference(avatar_split_clause,[],[f104,f280]) ).
fof(f280,plain,
( spl0_9
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f278,plain,
spl0_8,
inference(avatar_split_clause,[],[f103,f276]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f274,plain,
spl0_7,
inference(avatar_split_clause,[],[f96,f272]) ).
fof(f272,plain,
( spl0_7
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f270,plain,
spl0_6,
inference(avatar_split_clause,[],[f52,f267]) ).
fof(f267,plain,
( spl0_6
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f265,plain,
spl0_5,
inference(avatar_split_clause,[],[f4,f263]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f261,plain,
spl0_4,
inference(avatar_split_clause,[],[f69,f258]) ).
fof(f258,plain,
( spl0_4
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f256,plain,
spl0_3,
inference(avatar_split_clause,[],[f50,f253]) ).
fof(f253,plain,
( spl0_3
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f251,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f151,f248]) ).
fof(f151,plain,
~ subclass(unordered_pair(x,x),y),
inference(definition_unfolding,[],[f140,f12]) ).
fof(f140,axiom,
~ subclass(singleton(x),y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons2_2) ).
fof(f246,plain,
spl0_1,
inference(avatar_split_clause,[],[f139,f243]) ).
fof(f139,axiom,
member(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_singletons2_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET095-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.30 % Computer : n010.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Fri May 3 16:41:38 EDT 2024
% 0.11/0.30 % CPUTime :
% 0.11/0.30 % (11866)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (11869)WARNING: value z3 for option sas not known
% 0.16/0.32 % (11869)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)
% 0.16/0.32 % (11872)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)
% 0.16/0.32 % (11867)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32 % (11873)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)
% 0.16/0.32 % (11868)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.32 % (11871)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)
% 0.16/0.32 % (11870)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.34 % (11871)First to succeed.
% 0.16/0.34 % (11871)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-11866"
% 0.16/0.35 % (11871)Refutation found. Thanks to Tanya!
% 0.16/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.16/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.35 % (11871)------------------------------
% 0.16/0.35 % (11871)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.35 % (11871)Termination reason: Refutation
% 0.16/0.35
% 0.16/0.35 % (11871)Memory used [KB]: 1285
% 0.16/0.35 % (11871)Time elapsed: 0.022 s
% 0.16/0.35 % (11871)Instructions burned: 38 (million)
% 0.16/0.35 % (11866)Success in time 0.039 s
%------------------------------------------------------------------------------