TSTP Solution File: SET104-7 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET104-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:16:12 EDT 2024
% Result : Unsatisfiable 0.15s 0.36s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 207
% Syntax : Number of formulae : 395 ( 142 unt; 0 def)
% Number of atoms : 818 ( 150 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 708 ( 285 ~; 318 |; 0 &)
% ( 105 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 116 ( 114 usr; 106 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 10 con; 0-3 aty)
% Number of variables : 443 ( 443 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1160,plain,
$false,
inference(avatar_sat_refutation,[],[f264,f269,f274,f278,f283,f287,f291,f295,f300,f304,f308,f313,f317,f322,f327,f331,f335,f340,f346,f350,f354,f358,f362,f366,f374,f378,f382,f386,f390,f394,f398,f403,f416,f420,f424,f428,f432,f436,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f480,f484,f488,f508,f532,f536,f540,f544,f549,f553,f557,f561,f566,f629,f633,f653,f657,f661,f665,f681,f685,f689,f693,f697,f701,f705,f709,f713,f717,f721,f729,f799,f826,f830,f836,f840,f844,f848,f857,f861,f947,f951,f955,f959,f963,f968,f972,f1001,f1005,f1022,f1028,f1072,f1076,f1080,f1084,f1088,f1092,f1158]) ).
fof(f1158,plain,
( spl0_12
| ~ spl0_29
| ~ spl0_61
| ~ spl0_91 ),
inference(avatar_contradiction_clause,[],[f1157]) ).
fof(f1157,plain,
( $false
| spl0_12
| ~ spl0_29
| ~ spl0_61
| ~ spl0_91 ),
inference(trivial_inequality_removal,[],[f1156]) ).
fof(f1156,plain,
( unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y)))
| spl0_12
| ~ spl0_29
| ~ spl0_61
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1155,f389]) ).
fof(f389,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f388]) ).
fof(f388,plain,
( spl0_29
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1155,plain,
( unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y))) != unordered_pair(null_class,unordered_pair(unordered_pair(x,y),x))
| spl0_12
| ~ spl0_29
| ~ spl0_61
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1154,f954]) ).
fof(f954,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f953]) ).
fof(f953,plain,
( spl0_91
<=> ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1154,plain,
( unordered_pair(null_class,unordered_pair(unordered_pair(x,y),unordered_pair(x,y))) != unordered_pair(null_class,unordered_pair(x,unordered_pair(x,y)))
| spl0_12
| ~ spl0_29
| ~ spl0_61
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1153,f565]) ).
fof(f565,plain,
( null_class = unordered_pair(x,x)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f563]) ).
fof(f563,plain,
( spl0_61
<=> null_class = unordered_pair(x,x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1153,plain,
( unordered_pair(null_class,unordered_pair(unordered_pair(x,y),unordered_pair(x,y))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(x,y)))
| spl0_12
| ~ spl0_29
| ~ spl0_91 ),
inference(forward_demodulation,[],[f1132,f389]) ).
fof(f1132,plain,
( unordered_pair(null_class,unordered_pair(unordered_pair(y,x),unordered_pair(y,x))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,x)))
| spl0_12
| ~ spl0_91 ),
inference(superposition,[],[f312,f954]) ).
fof(f312,plain,
( unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))
| spl0_12 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f310,plain,
( spl0_12
<=> unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))) = unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1092,plain,
spl0_105,
inference(avatar_split_clause,[],[f219,f1090]) ).
fof(f1090,plain,
( spl0_105
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f219,plain,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| null_class = intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f31,f29,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set) ).
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(f31,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
fof(f1088,plain,
spl0_104,
inference(avatar_split_clause,[],[f212,f1086]) ).
fof(f1086,plain,
( spl0_104
<=> ! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f212,plain,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ),
inference(definition_unfolding,[],[f64,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function3) ).
fof(f1084,plain,
spl0_103,
inference(avatar_split_clause,[],[f196,f1082]) ).
fof(f1082,plain,
( spl0_103
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f196,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f94,f154]) ).
fof(f154,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f13,f12,f12]) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair) ).
fof(f94,axiom,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f1080,plain,
spl0_102,
inference(avatar_split_clause,[],[f195,f1078]) ).
fof(f1078,plain,
( spl0_102
<=> ! [X0,X3,X2,X1] :
( member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f195,plain,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f95,f154]) ).
fof(f95,axiom,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f1076,plain,
spl0_101,
inference(avatar_split_clause,[],[f190,f1074]) ).
fof(f1074,plain,
( spl0_101
<=> ! [X0,X3,X2,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f190,plain,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f15,f154]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f1072,plain,
spl0_100,
inference(avatar_split_clause,[],[f189,f1070]) ).
fof(f1070,plain,
( spl0_100
<=> ! [X0,X3,X2,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f189,plain,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f14,f154]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f1028,plain,
( spl0_99
| ~ spl0_29
| ~ spl0_91
| ~ spl0_98 ),
inference(avatar_split_clause,[],[f1024,f1020,f953,f388,f1026]) ).
fof(f1026,plain,
( spl0_99
<=> ! [X1] :
( unordered_pair(X1,X1) = unordered_pair(x,member_of(unordered_pair(X1,X1)))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1020,plain,
( spl0_98
<=> ! [X1] :
( ~ member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1024,plain,
( ! [X1] :
( unordered_pair(X1,X1) = unordered_pair(x,member_of(unordered_pair(X1,X1)))
| ~ member(X1,universal_class) )
| ~ spl0_29
| ~ spl0_91
| ~ spl0_98 ),
inference(forward_demodulation,[],[f1023,f389]) ).
fof(f1023,plain,
( ! [X1] :
( unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),x)
| ~ member(X1,universal_class) )
| ~ spl0_91
| ~ spl0_98 ),
inference(forward_demodulation,[],[f1021,f954]) ).
fof(f1021,plain,
( ! [X1] :
( ~ member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1022,plain,
spl0_98,
inference(avatar_split_clause,[],[f186,f1020]) ).
fof(f186,plain,
! [X1] :
( ~ member(X1,universal_class)
| unordered_pair(X1,X1) = unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) ),
inference(definition_unfolding,[],[f131,f12,f12,f12]) ).
fof(f131,axiom,
! [X1] :
( ~ member(X1,universal_class)
| singleton(X1) = singleton(member_of(singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists2) ).
fof(f1005,plain,
( spl0_97
| spl0_1
| ~ spl0_66 ),
inference(avatar_split_clause,[],[f673,f659,f261,f1003]) ).
fof(f1003,plain,
( spl0_97
<=> ! [X0] : unordered_pair(X0,X0) = unordered_pair(x,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f261,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f659,plain,
( spl0_66
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f673,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(x,X0)
| spl0_1
| ~ spl0_66 ),
inference(resolution,[],[f660,f263]) ).
fof(f263,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f660,plain,
( ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) )
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1001,plain,
spl0_96,
inference(avatar_split_clause,[],[f170,f999]) ).
fof(f999,plain,
( spl0_96
<=> ! [X0,X1] : member(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f170,plain,
! [X0,X1] : member(unordered_pair(X0,unordered_pair(X1,X1)),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),
inference(definition_unfolding,[],[f147,f12,f154]) ).
fof(f147,axiom,
! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(f972,plain,
spl0_95,
inference(avatar_split_clause,[],[f239,f970]) ).
fof(f970,plain,
( spl0_95
<=> ! [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,[spl0_95])]) ).
fof(f239,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(forward_demodulation,[],[f175,f171]) ).
fof(f171,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
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(f175,plain,
! [X0] :
( ~ inductive(X0)
| subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f48,f152]) ).
fof(f152,plain,
! [X0,X5] : image(X5,X0) = domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X5),universal_class)))),
inference(definition_unfolding,[],[f42,f151,f29]) ).
fof(f151,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive2) ).
fof(f968,plain,
( spl0_94
| spl0_1
| ~ spl0_66
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f964,f961,f659,f261,f966]) ).
fof(f966,plain,
( spl0_94
<=> ! [X0,X1] :
( unordered_pair(x,member_of(X0)) != X0
| ~ member(X1,X0)
| member_of(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f961,plain,
( spl0_93
<=> ! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| unordered_pair(member_of(X0),member_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f964,plain,
( ! [X0,X1] :
( unordered_pair(x,member_of(X0)) != X0
| ~ member(X1,X0)
| member_of(X0) = X1 )
| spl0_1
| ~ spl0_66
| ~ spl0_93 ),
inference(forward_demodulation,[],[f962,f673]) ).
fof(f962,plain,
( ! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| unordered_pair(member_of(X0),member_of(X0)) != X0 )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f961]) ).
fof(f963,plain,
spl0_93,
inference(avatar_split_clause,[],[f214,f961]) ).
fof(f214,plain,
! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| unordered_pair(member_of(X0),member_of(X0)) != X0 ),
inference(definition_unfolding,[],[f138,f12]) ).
fof(f138,axiom,
! [X0,X1] :
( ~ member(X1,X0)
| member_of(X0) = X1
| singleton(member_of(X0)) != X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons1) ).
fof(f959,plain,
spl0_92,
inference(avatar_split_clause,[],[f198,f957]) ).
fof(f957,plain,
( spl0_92
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f198,plain,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f84,f151]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatible3) ).
fof(f955,plain,
( spl0_91
| spl0_1
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f669,f655,f261,f953]) ).
fof(f655,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f669,plain,
( ! [X0] : unordered_pair(X0,X0) = unordered_pair(X0,x)
| spl0_1
| ~ spl0_65 ),
inference(resolution,[],[f656,f263]) ).
fof(f656,plain,
( ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f655]) ).
fof(f951,plain,
spl0_90,
inference(avatar_split_clause,[],[f188,f949]) ).
fof(f949,plain,
( spl0_90
<=> ! [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,[spl0_90])]) ).
fof(f188,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,[],[f19,f154]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation2) ).
fof(f947,plain,
spl0_89,
inference(avatar_split_clause,[],[f160,f945]) ).
fof(f945,plain,
( spl0_89
<=> ! [X0,X1] : unordered_pair(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(unordered_pair(X1,X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f160,plain,
! [X0,X1] : unordered_pair(X0,X1) = complement(intersection(complement(unordered_pair(X0,X0)),complement(unordered_pair(X1,X1)))),
inference(definition_unfolding,[],[f144,f26,f12,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
fof(f144,axiom,
! [X0,X1] : unordered_pair(X0,X1) = union(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).
fof(f861,plain,
spl0_88,
inference(avatar_split_clause,[],[f222,f859]) ).
fof(f859,plain,
( spl0_88
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f222,plain,
! [X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0 ),
inference(definition_unfolding,[],[f140,f12,f12]) ).
fof(f140,axiom,
! [X0,X1] :
( null_class = X0
| ~ subclass(X0,singleton(X1))
| singleton(X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f857,plain,
spl0_87,
inference(avatar_split_clause,[],[f216,f855]) ).
fof(f855,plain,
( spl0_87
<=> ! [X0,X1] :
( ~ member(X1,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f216,plain,
! [X0,X1] :
( ~ member(X1,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f128,f12,f12]) ).
fof(f128,axiom,
! [X0,X1] :
( ~ member(X1,universal_class)
| X0 = X1
| singleton(X0) != singleton(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element2) ).
fof(f848,plain,
spl0_86,
inference(avatar_split_clause,[],[f197,f846]) ).
fof(f846,plain,
( spl0_86
<=> ! [X4,X0] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f197,plain,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| null_class != intersection(cross_product(unordered_pair(X4,X4),universal_class),X0) ),
inference(definition_unfolding,[],[f30,f29,f12]) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
fof(f844,plain,
spl0_85,
inference(avatar_split_clause,[],[f101,f842]) ).
fof(f842,plain,
( spl0_85
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f101,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality4) ).
fof(f840,plain,
spl0_84,
inference(avatar_split_clause,[],[f99,f838]) ).
fof(f838,plain,
( spl0_84
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X0,X1),X1)
| member(not_subclass_element(X1,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f99,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X0,X1),X1)
| member(not_subclass_element(X1,X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality2) ).
fof(f836,plain,
spl0_83,
inference(avatar_split_clause,[],[f98,f834]) ).
fof(f834,plain,
( spl0_83
<=> ! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality1) ).
fof(f830,plain,
spl0_82,
inference(avatar_split_clause,[],[f176,f828]) ).
fof(f828,plain,
( spl0_82
<=> ! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f176,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f151]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation3) ).
fof(f826,plain,
spl0_81,
inference(avatar_split_clause,[],[f79,f824]) ).
fof(f824,plain,
( spl0_81
<=> ! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation2) ).
fof(f799,plain,
( spl0_80
| ~ spl0_29
| ~ spl0_68 ),
inference(avatar_split_clause,[],[f724,f679,f388,f797]) ).
fof(f797,plain,
( spl0_80
<=> ! [X0] : member(null_class,unordered_pair(null_class,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f679,plain,
( spl0_68
<=> ! [X0] : member(null_class,unordered_pair(X0,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f724,plain,
( ! [X0] : member(null_class,unordered_pair(null_class,X0))
| ~ spl0_29
| ~ spl0_68 ),
inference(superposition,[],[f680,f389]) ).
fof(f680,plain,
( ! [X0] : member(null_class,unordered_pair(X0,null_class))
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f729,plain,
spl0_79,
inference(avatar_split_clause,[],[f241,f727]) ).
fof(f727,plain,
( spl0_79
<=> ! [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_79])]) ).
fof(f241,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f183,f171]) ).
fof(f183,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f150]) ).
fof(f150,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(f721,plain,
spl0_78,
inference(avatar_split_clause,[],[f201,f719]) ).
fof(f719,plain,
( spl0_78
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f201,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ),
inference(definition_unfolding,[],[f133,f12]) ).
fof(f133,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_exists4) ).
fof(f717,plain,
spl0_77,
inference(avatar_split_clause,[],[f200,f715]) ).
fof(f715,plain,
( spl0_77
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of1(X0),member_of1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f200,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(f713,plain,
spl0_76,
inference(avatar_split_clause,[],[f178,f711]) ).
fof(f711,plain,
( spl0_76
<=> ! [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_76])]) ).
fof(f178,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(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(f709,plain,
spl0_75,
inference(avatar_split_clause,[],[f177,f707]) ).
fof(f707,plain,
( spl0_75
<=> ! [X8] :
( ~ function(X8)
| subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f177,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(f705,plain,
spl0_74,
inference(avatar_split_clause,[],[f173,f703]) ).
fof(f703,plain,
( spl0_74
<=> ! [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_74])]) ).
fof(f173,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(f701,plain,
spl0_73,
inference(avatar_split_clause,[],[f171,f699]) ).
fof(f699,plain,
( spl0_73
<=> ! [X5,X1,X0] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f697,plain,
spl0_72,
inference(avatar_split_clause,[],[f119,f695]) ).
fof(f695,plain,
( spl0_72
<=> ! [X4,X0,X1] :
( ~ member(X0,X4)
| ~ member(X1,X4)
| subclass(unordered_pair(X0,X1),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
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(f693,plain,
spl0_71,
inference(avatar_split_clause,[],[f113,f691]) ).
fof(f691,plain,
( spl0_71
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(X0,X1) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
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(f689,plain,
spl0_70,
inference(avatar_split_clause,[],[f23,f687]) ).
fof(f687,plain,
( spl0_70
<=> ! [X4,X0,X1] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
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(f685,plain,
spl0_69,
inference(avatar_split_clause,[],[f8,f683]) ).
fof(f683,plain,
( spl0_69
<=> ! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
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(f681,plain,
( spl0_68
| ~ spl0_58
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f643,f563,f551,f679]) ).
fof(f551,plain,
( spl0_58
<=> ! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f643,plain,
( ! [X0] : member(null_class,unordered_pair(X0,null_class))
| ~ spl0_58
| ~ spl0_61 ),
inference(superposition,[],[f552,f565]) ).
fof(f552,plain,
( ! [X0,X1] : member(unordered_pair(X1,X1),unordered_pair(X0,unordered_pair(X1,X1)))
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f665,plain,
spl0_67,
inference(avatar_split_clause,[],[f209,f663]) ).
fof(f663,plain,
( spl0_67
<=> ! [X8] :
( ~ function(X8)
| one_to_one(X8)
| ~ function(domain_of(flip(cross_product(X8,universal_class)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f209,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(f661,plain,
spl0_66,
inference(avatar_split_clause,[],[f194,f659]) ).
fof(f194,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(f657,plain,
spl0_65,
inference(avatar_split_clause,[],[f193,f655]) ).
fof(f193,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(f653,plain,
spl0_64,
inference(avatar_split_clause,[],[f192,f651]) ).
fof(f651,plain,
( spl0_64
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(member_of(X0),member_of(X0)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f192,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(f633,plain,
spl0_63,
inference(avatar_split_clause,[],[f83,f631]) ).
fof(f631,plain,
( spl0_63
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
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(f629,plain,
spl0_62,
inference(avatar_split_clause,[],[f25,f627]) ).
fof(f627,plain,
( spl0_62
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
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(f566,plain,
( spl0_61
| spl0_1
| ~ spl0_51 ),
inference(avatar_split_clause,[],[f527,f486,f261,f563]) ).
fof(f486,plain,
( spl0_51
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f527,plain,
( null_class = unordered_pair(x,x)
| spl0_1
| ~ spl0_51 ),
inference(resolution,[],[f487,f263]) ).
fof(f487,plain,
( ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class )
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f561,plain,
spl0_60,
inference(avatar_split_clause,[],[f185,f559]) ).
fof(f559,plain,
( spl0_60
<=> ! [X1] :
( ~ member(X1,universal_class)
| member(member_of(unordered_pair(X1,X1)),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f185,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(f557,plain,
spl0_59,
inference(avatar_split_clause,[],[f184,f555]) ).
fof(f555,plain,
( spl0_59
<=> ! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f184,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(f553,plain,
spl0_58,
inference(avatar_split_clause,[],[f169,f551]) ).
fof(f169,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(f549,plain,
spl0_57,
inference(avatar_split_clause,[],[f165,f546]) ).
fof(f546,plain,
( spl0_57
<=> identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f165,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(f544,plain,
spl0_56,
inference(avatar_split_clause,[],[f97,f542]) ).
fof(f542,plain,
( spl0_56
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
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(f540,plain,
spl0_55,
inference(avatar_split_clause,[],[f67,f538]) ).
fof(f538,plain,
( spl0_55
<=> ! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f67,axiom,
! [X0] :
( null_class = X0
| null_class = intersection(X0,regular(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity2) ).
fof(f536,plain,
spl0_54,
inference(avatar_split_clause,[],[f7,f534]) ).
fof(f534,plain,
( spl0_54
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f532,plain,
spl0_53,
inference(avatar_split_clause,[],[f1,f530]) ).
fof(f530,plain,
( spl0_53
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
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(f508,plain,
( spl0_52
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f405,f384,f360,f506]) ).
fof(f506,plain,
( spl0_52
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f360,plain,
( spl0_23
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f384,plain,
( spl0_28
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f405,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_23
| ~ spl0_28 ),
inference(resolution,[],[f385,f361]) ).
fof(f361,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f385,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f488,plain,
spl0_51,
inference(avatar_split_clause,[],[f191,f486]) ).
fof(f191,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(f484,plain,
spl0_50,
inference(avatar_split_clause,[],[f187,f482]) ).
fof(f482,plain,
( spl0_50
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f187,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(f480,plain,
spl0_49,
inference(avatar_split_clause,[],[f179,f478]) ).
fof(f478,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f179,plain,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ),
inference(definition_unfolding,[],[f139,f12]) ).
fof(f139,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| subclass(singleton(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(f476,plain,
spl0_48,
inference(avatar_split_clause,[],[f174,f474]) ).
fof(f474,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(f174,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(f472,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f399,f372,f329,f470]) ).
fof(f470,plain,
( spl0_47
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f329,plain,
( spl0_16
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f372,plain,
( spl0_25
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f399,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f373,f330]) ).
fof(f330,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f373,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f372]) ).
fof(f468,plain,
spl0_46,
inference(avatar_split_clause,[],[f135,f466]) ).
fof(f466,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(f464,plain,
spl0_45,
inference(avatar_split_clause,[],[f132,f462]) ).
fof(f462,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(f460,plain,
spl0_44,
inference(avatar_split_clause,[],[f117,f458]) ).
fof(f458,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(f456,plain,
spl0_43,
inference(avatar_split_clause,[],[f116,f454]) ).
fof(f454,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(f452,plain,
spl0_42,
inference(avatar_split_clause,[],[f106,f450]) ).
fof(f450,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(f448,plain,
spl0_41,
inference(avatar_split_clause,[],[f88,f446]) ).
fof(f446,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(f444,plain,
spl0_40,
inference(avatar_split_clause,[],[f35,f442]) ).
fof(f442,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(f440,plain,
spl0_39,
inference(avatar_split_clause,[],[f32,f438]) ).
fof(f438,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(f436,plain,
spl0_38,
inference(avatar_split_clause,[],[f22,f434]) ).
fof(f434,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(f432,plain,
spl0_37,
inference(avatar_split_clause,[],[f21,f430]) ).
fof(f430,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(f428,plain,
spl0_36,
inference(avatar_split_clause,[],[f10,f426]) ).
fof(f426,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(f424,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f422]) ).
fof(f422,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(f420,plain,
spl0_34,
inference(avatar_split_clause,[],[f3,f418]) ).
fof(f418,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(f416,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f414]) ).
fof(f414,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(f403,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f367,f360,f329,f401]) ).
fof(f401,plain,
( spl0_32
<=> ! [X0] : ~ inductive(intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f367,plain,
( ! [X0] : ~ inductive(intersection(complement(X0),X0))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f361,f330]) ).
fof(f398,plain,
spl0_31,
inference(avatar_split_clause,[],[f167,f396]) ).
fof(f396,plain,
( spl0_31
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f167,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(f394,plain,
spl0_30,
inference(avatar_split_clause,[],[f166,f392]) ).
fof(f392,plain,
( spl0_30
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f166,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(f390,plain,
spl0_29,
inference(avatar_split_clause,[],[f108,f388]) ).
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(f386,plain,
spl0_28,
inference(avatar_split_clause,[],[f66,f384]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity1) ).
fof(f382,plain,
spl0_27,
inference(avatar_split_clause,[],[f62,f380]) ).
fof(f380,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(f378,plain,
spl0_26,
inference(avatar_split_clause,[],[f57,f376]) ).
fof(f376,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(f374,plain,
spl0_25,
inference(avatar_split_clause,[],[f24,f372]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
fof(f366,plain,
spl0_24,
inference(avatar_split_clause,[],[f105,f364]) ).
fof(f364,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(f362,plain,
spl0_23,
inference(avatar_split_clause,[],[f102,f360]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f358,plain,
spl0_22,
inference(avatar_split_clause,[],[f87,f356]) ).
fof(f356,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(f354,plain,
spl0_21,
inference(avatar_split_clause,[],[f86,f352]) ).
fof(f352,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(f350,plain,
spl0_20,
inference(avatar_split_clause,[],[f82,f348]) ).
fof(f348,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(f346,plain,
( ~ spl0_19
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f341,f329,f289,f343]) ).
fof(f343,plain,
( spl0_19
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f289,plain,
( spl0_7
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f341,plain,
( ~ inductive(null_class)
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f330,f290]) ).
fof(f290,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f340,plain,
spl0_18,
inference(avatar_split_clause,[],[f162,f337]) ).
fof(f337,plain,
( spl0_18
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f162,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(f335,plain,
spl0_17,
inference(avatar_split_clause,[],[f51,f333]) ).
fof(f333,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(f331,plain,
spl0_16,
inference(avatar_split_clause,[],[f47,f329]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive1) ).
fof(f327,plain,
spl0_15,
inference(avatar_split_clause,[],[f44,f324]) ).
fof(f324,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(f322,plain,
spl0_14,
inference(avatar_split_clause,[],[f18,f319]) ).
fof(f319,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(f317,plain,
spl0_13,
inference(avatar_split_clause,[],[f11,f315]) ).
fof(f315,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(f313,plain,
~ spl0_12,
inference(avatar_split_clause,[],[f161,f310]) ).
fof(f161,plain,
unordered_pair(null_class,unordered_pair(unordered_pair(y,y),unordered_pair(y,y))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(definition_unfolding,[],[f148,f12,f12,f154]) ).
fof(f148,axiom,
unordered_pair(null_class,singleton(singleton(y))) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_2) ).
fof(f308,plain,
spl0_11,
inference(avatar_split_clause,[],[f78,f306]) ).
fof(f306,plain,
( spl0_11
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',operation1) ).
fof(f304,plain,
spl0_10,
inference(avatar_split_clause,[],[f71,f302]) ).
fof(f302,plain,
( spl0_10
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_to_one1) ).
fof(f300,plain,
spl0_9,
inference(avatar_split_clause,[],[f107,f297]) ).
fof(f297,plain,
( spl0_9
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f295,plain,
spl0_8,
inference(avatar_split_clause,[],[f104,f293]) ).
fof(f293,plain,
( spl0_8
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f291,plain,
spl0_7,
inference(avatar_split_clause,[],[f103,f289]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f287,plain,
spl0_6,
inference(avatar_split_clause,[],[f96,f285]) ).
fof(f285,plain,
( spl0_6
<=> ! [X0] : subclass(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f96,axiom,
! [X0] : subclass(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f283,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f280]) ).
fof(f280,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f278,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f276]) ).
fof(f276,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f274,plain,
spl0_3,
inference(avatar_split_clause,[],[f69,f271]) ).
fof(f271,plain,
( spl0_3
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice1) ).
fof(f269,plain,
spl0_2,
inference(avatar_split_clause,[],[f50,f266]) ).
fof(f266,plain,
( spl0_2
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f264,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f149,f261]) ).
fof(f149,axiom,
~ member(x,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_2_of_ordered_pair_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SET104-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.05/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.09/0.30 % Computer : n021.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon May 20 11:12:22 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % (15934)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.32 % (15937)WARNING: value z3 for option sas not known
% 0.15/0.32 % (15935)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.32 % (15936)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.32 % (15938)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.32 % (15940)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)
% 0.15/0.32 % (15937)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)
% 0.15/0.32 % (15939)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)
% 0.15/0.32 % (15941)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)
% 0.15/0.35 % (15939)First to succeed.
% 0.15/0.36 % (15940)Also succeeded, but the first one will report.
% 0.15/0.36 % (15939)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15934"
% 0.15/0.36 % (15939)Refutation found. Thanks to Tanya!
% 0.15/0.36 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.36 % (15939)------------------------------
% 0.15/0.36 % (15939)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.36 % (15939)Termination reason: Refutation
% 0.15/0.36
% 0.15/0.36 % (15939)Memory used [KB]: 1487
% 0.15/0.36 % (15939)Time elapsed: 0.033 s
% 0.15/0.36 % (15939)Instructions burned: 63 (million)
% 0.15/0.36 % (15934)Success in time 0.055 s
%------------------------------------------------------------------------------