TSTP Solution File: SET075-6 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET075-6 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:05:28 EDT 2024
% Result : Unsatisfiable 0.15s 0.41s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 104
% Syntax : Number of formulae : 372 ( 54 unt; 0 def)
% Number of atoms : 846 ( 95 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 916 ( 442 ~; 449 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 26 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 12 con; 0-3 aty)
% Number of variables : 427 ( 427 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f636,plain,
$false,
inference(avatar_sat_refutation,[],[f114,f125,f139,f208,f228,f242,f258,f284,f301,f323,f345,f357,f382,f420,f484,f486,f505,f507,f509,f511,f513,f545,f575,f577,f630,f634]) ).
fof(f634,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f633,plain,
( $false
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f632,f119]) ).
fof(f119,plain,
( member(y,universal_class)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f118,plain,
( spl0_3
<=> member(y,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f632,plain,
( ~ member(y,universal_class)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(subsumption_resolution,[],[f625,f94]) ).
fof(f94,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass1) ).
fof(f625,plain,
( ~ subclass(null_class,null_class)
| ~ member(y,universal_class)
| ~ spl0_1
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[],[f389,f588]) ).
fof(f588,plain,
( null_class = complement(universal_class)
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[],[f466,f108]) ).
fof(f108,plain,
( member(x,universal_class)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f107,plain,
( spl0_1
<=> member(x,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f466,plain,
( ! [X0] :
( ~ member(x,X0)
| complement(X0) = null_class )
| ~ spl0_2 ),
inference(resolution,[],[f462,f24]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f462,plain,
( ! [X0] :
( member(x,X0)
| null_class = X0 )
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f461,f94]) ).
fof(f461,plain,
( ! [X0] :
( ~ subclass(null_class,null_class)
| member(x,X0)
| null_class = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f368,f67]) ).
fof(f67,axiom,
! [X0] :
( null_class = intersection(X0,regular(X0))
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f368,plain,
( ! [X0,X1] :
( ~ subclass(null_class,intersection(X0,X1))
| member(x,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f359,f21]) ).
fof(f21,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f359,plain,
( ! [X0] :
( member(x,X0)
| ~ subclass(null_class,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f113,f1]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f113,plain,
( member(x,null_class)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f111]) ).
fof(f111,plain,
( spl0_2
<=> member(x,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f389,plain,
( ! [X0] :
( ~ subclass(null_class,complement(X0))
| ~ member(y,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f384,f24]) ).
fof(f384,plain,
( ! [X0] :
( member(y,X0)
| ~ subclass(null_class,X0) )
| ~ spl0_4 ),
inference(resolution,[],[f124,f1]) ).
fof(f124,plain,
( member(y,null_class)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f122]) ).
fof(f122,plain,
( spl0_4
<=> member(y,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f630,plain,
( ~ spl0_1
| ~ spl0_2 ),
inference(avatar_contradiction_clause,[],[f629]) ).
fof(f629,plain,
( $false
| ~ spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f628,f108]) ).
fof(f628,plain,
( ~ member(x,universal_class)
| ~ spl0_1
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f622,f94]) ).
fof(f622,plain,
( ~ subclass(null_class,null_class)
| ~ member(x,universal_class)
| ~ spl0_1
| ~ spl0_2 ),
inference(superposition,[],[f366,f588]) ).
fof(f366,plain,
( ! [X0] :
( ~ subclass(null_class,complement(X0))
| ~ member(x,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f359,f24]) ).
fof(f577,plain,
( ~ spl0_2
| spl0_24 ),
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f576,plain,
( $false
| ~ spl0_2
| spl0_24 ),
inference(subsumption_resolution,[],[f572,f113]) ).
fof(f572,plain,
( ~ member(x,null_class)
| ~ spl0_2
| spl0_24 ),
inference(superposition,[],[f546,f555]) ).
fof(f555,plain,
( null_class = identity_relation
| ~ spl0_2
| spl0_24 ),
inference(resolution,[],[f546,f462]) ).
fof(f546,plain,
( ~ member(x,identity_relation)
| spl0_24 ),
inference(resolution,[],[f539,f129]) ).
fof(f129,plain,
! [X0] :
( member(X0,inverse(subset_relation))
| ~ member(X0,identity_relation) ),
inference(superposition,[],[f21,f75]) ).
fof(f75,axiom,
identity_relation = intersection(inverse(subset_relation),subset_relation),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f539,plain,
( ~ member(x,inverse(subset_relation))
| spl0_24 ),
inference(avatar_component_clause,[],[f538]) ).
fof(f538,plain,
( spl0_24
<=> member(x,inverse(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f575,plain,
( ~ spl0_2
| spl0_24
| spl0_25 ),
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f574,plain,
( $false
| ~ spl0_2
| spl0_24
| spl0_25 ),
inference(subsumption_resolution,[],[f571,f94]) ).
fof(f571,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_2
| spl0_24
| spl0_25 ),
inference(superposition,[],[f544,f555]) ).
fof(f544,plain,
( ~ subclass(null_class,identity_relation)
| spl0_25 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f542,plain,
( spl0_25
<=> subclass(null_class,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f545,plain,
( spl0_24
| ~ spl0_25
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f460,f111,f542,f538]) ).
fof(f460,plain,
( ~ subclass(null_class,identity_relation)
| member(x,inverse(subset_relation))
| ~ spl0_2 ),
inference(superposition,[],[f368,f75]) ).
fof(f513,plain,
( ~ spl0_2
| spl0_7
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f512]) ).
fof(f512,plain,
( $false
| ~ spl0_2
| spl0_7
| spl0_22 ),
inference(global_subsumption,[],[f29,f28,f13,f77,f40,f41,f27,f74,f95,f30,f17,f58,f33,f36,f65,f49,f64,f23,f16,f20,f70,f31,f8,f96,f89,f59,f34,f37,f81,f85,f90,f91,f50,f69,f4,f52,f94,f93,f11,f97,f18,f44,f47,f51,f92,f12,f98,f39,f75,f24,f99,f43,f48,f54,f56,f57,f62,f66,f100,f2,f101,f3,f9,f104,f105,f10,f115,f19,f21,f127,f128,f126,f130,f129,f141,f22,f145,f146,f147,f32,f144,f35,f38,f53,f55,f150,f151,f152,f63,f76,f153,f154,f155,f148,f157,f1,f159,f160,f165,f166,f167,f168,f169,f171,f172,f163,f7,f181,f182,f183,f184,f185,f186,f188,f189,f175,f164,f196,f179,f190,f202,f176,f177,f178,f213,f42,f162,f215,f216,f217,f193,f218,f219,f199,f170,f230,f231,f232,f233,f229,f191,f245,f246,f244,f247,f248,f45,f249,f192,f260,f243,f261,f262,f259,f158,f265,f267,f268,f270,f272,f266,f67,f286,f287,f288,f290,f285,f161,f303,f304,f305,f306,f187,f313,f68,f314,f194,f195,f289,f214,f329,f325,f333,f324,f331,f332,f330,f14,f347,f346,f348,f355,f113,f359,f369,f352,f370,f371,f15,f373,f372,f374,f378,f379,f380,f366,f395,f396,f377,f397,f398,f25,f404,f405,f409,f407,f408,f353,f411,f410,f414,f421,f422,f424,f425,f354,f429,f26,f432,f433,f434,f435,f436,f437,f438,f439,f440,f441,f442,f443,f444,f445,f446,f447,f448,f450,f451,f367,f458,f459,f368,f462,f465,f466,f467,f468,f469,f464,f488,f489,f492,f503,f494,f496,f502]) ).
fof(f502,plain,
( ~ subclass(u,null_class)
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f424,f464]) ).
fof(f496,plain,
( null_class != identity_relation
| ~ spl0_2
| spl0_7
| spl0_22 ),
inference(superposition,[],[f202,f464]) ).
fof(f494,plain,
( subclass(identity_relation,null_class)
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f157,f464]) ).
fof(f503,plain,
( ! [X0] :
( subclass(X0,null_class)
| ~ member(not_subclass_element(X0,null_class),identity_relation) )
| ~ spl0_2
| spl0_22 ),
inference(forward_demodulation,[],[f493,f464]) ).
fof(f493,plain,
( ! [X0] :
( ~ member(not_subclass_element(X0,null_class),identity_relation)
| subclass(X0,subset_relation) )
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f148,f464]) ).
fof(f492,plain,
( ! [X0] :
( member(X0,null_class)
| ~ member(X0,identity_relation) )
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f147,f464]) ).
fof(f489,plain,
( ! [X0] :
( member(X0,inverse(null_class))
| ~ member(X0,identity_relation) )
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f129,f464]) ).
fof(f488,plain,
( identity_relation = intersection(inverse(null_class),null_class)
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f75,f464]) ).
fof(f464,plain,
( null_class = subset_relation
| ~ spl0_2
| spl0_22 ),
inference(resolution,[],[f462,f414]) ).
fof(f469,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,X1)
| member(x,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f462,f1]) ).
fof(f468,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| member(x,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f462,f21]) ).
fof(f467,plain,
( ! [X0,X1] :
( intersection(X0,X1) = null_class
| member(x,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f462,f22]) ).
fof(f465,plain,
( null_class = identity_relation
| ~ spl0_2
| spl0_22 ),
inference(resolution,[],[f462,f421]) ).
fof(f459,plain,
( ! [X0,X1] :
( null_class = X0
| ~ subclass(regular(X0),X1)
| member(x,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f458,f1]) ).
fof(f458,plain,
( ! [X0] :
( member(x,regular(X0))
| null_class = X0 )
| ~ spl0_2 ),
inference(subsumption_resolution,[],[f457,f94]) ).
fof(f457,plain,
( ! [X0] :
( ~ subclass(null_class,null_class)
| member(x,regular(X0))
| null_class = X0 )
| ~ spl0_2 ),
inference(superposition,[],[f367,f67]) ).
fof(f367,plain,
( ! [X0,X1] :
( ~ subclass(null_class,intersection(X0,X1))
| member(x,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f359,f22]) ).
fof(f451,plain,
! [X0,X1] :
( ~ subclass(v,union(X0,X1))
| ~ member(y,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f377,f26]) ).
fof(f450,plain,
( ! [X0,X1] :
( ~ subclass(null_class,union(X0,X1))
| ~ member(x,intersection(complement(X0),complement(X1))) )
| ~ spl0_2 ),
inference(superposition,[],[f366,f26]) ).
fof(f448,plain,
! [X0,X1] :
( ~ subclass(u,union(X0,X1))
| ~ member(x,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f352,f26]) ).
fof(f447,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| ~ subclass(universal_class,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f324,f26]) ).
fof(f446,plain,
! [X0,X1] :
( ~ inductive(image(element_relation,union(X0,X1)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f244,f26]) ).
fof(f445,plain,
! [X0,X1] :
( ~ subclass(universal_class,image(element_relation,union(X0,X1)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f243,f26]) ).
fof(f444,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| ~ member(omega,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f193,f26]) ).
fof(f443,plain,
! [X0,X1] :
( ~ member(null_class,image(element_relation,union(X0,X1)))
| ~ subclass(universal_class,power_class(intersection(complement(X0),complement(X1)))) ),
inference(superposition,[],[f191,f26]) ).
fof(f442,plain,
! [X0,X1] :
( ~ subclass(universal_class,union(X0,X1))
| ~ member(null_class,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f175,f26]) ).
fof(f441,plain,
! [X0,X1] :
( ~ inductive(union(X0,X1))
| ~ member(null_class,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f99,f26]) ).
fof(f440,plain,
! [X0,X1] : power_class(intersection(complement(X0),complement(X1))) = complement(image(element_relation,union(X0,X1))),
inference(superposition,[],[f55,f26]) ).
fof(f439,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| member(X2,intersection(complement(X0),complement(X1)))
| ~ member(X2,universal_class) ),
inference(superposition,[],[f25,f26]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| ~ member(X2,intersection(complement(X0),complement(X1))) ),
inference(superposition,[],[f24,f26]) ).
fof(f437,plain,
! [X2,X0,X1] : union(X2,intersection(complement(X0),complement(X1))) = complement(intersection(complement(X2),union(X0,X1))),
inference(superposition,[],[f26,f26]) ).
fof(f436,plain,
! [X0,X1] : union(X1,domain_of(intersection(X0,identity_relation))) = complement(intersection(complement(X1),diagonalise(X0))),
inference(superposition,[],[f26,f76]) ).
fof(f435,plain,
! [X0,X1] : union(X1,image(element_relation,complement(X0))) = complement(intersection(complement(X1),power_class(X0))),
inference(superposition,[],[f26,f55]) ).
fof(f434,plain,
! [X2,X0,X1] : union(intersection(complement(X0),complement(X1)),X2) = complement(intersection(union(X0,X1),complement(X2))),
inference(superposition,[],[f26,f26]) ).
fof(f433,plain,
! [X0,X1] : union(domain_of(intersection(X0,identity_relation)),X1) = complement(intersection(diagonalise(X0),complement(X1))),
inference(superposition,[],[f26,f76]) ).
fof(f432,plain,
! [X0,X1] : union(image(element_relation,complement(X0)),X1) = complement(intersection(power_class(X0),complement(X1))),
inference(superposition,[],[f26,f55]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f429,plain,
! [X0] :
( ~ subclass(u,null_class)
| member(x,X0)
| null_class = X0 ),
inference(superposition,[],[f354,f67]) ).
fof(f354,plain,
! [X0,X1] :
( ~ subclass(u,intersection(X0,X1))
| member(x,X0) ),
inference(resolution,[],[f348,f21]) ).
fof(f425,plain,
( ~ subclass(null_class,identity_relation)
| ~ spl0_2
| spl0_22 ),
inference(resolution,[],[f421,f359]) ).
fof(f424,plain,
( ~ subclass(u,subset_relation)
| spl0_22 ),
inference(resolution,[],[f414,f348]) ).
fof(f422,plain,
( ~ subclass(null_class,subset_relation)
| ~ spl0_2
| spl0_22 ),
inference(resolution,[],[f414,f359]) ).
fof(f421,plain,
( ~ member(x,identity_relation)
| spl0_22 ),
inference(resolution,[],[f414,f147]) ).
fof(f414,plain,
( ~ member(x,subset_relation)
| spl0_22 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f413,plain,
( spl0_22
<=> member(x,subset_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f410,plain,
( ~ subclass(u,identity_relation)
| member(x,subset_relation) ),
inference(superposition,[],[f353,f75]) ).
fof(f411,plain,
! [X0] :
( ~ subclass(u,null_class)
| member(x,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f353,f67]) ).
fof(f353,plain,
! [X0,X1] :
( ~ subclass(u,intersection(X0,X1))
| member(x,X1) ),
inference(resolution,[],[f348,f22]) ).
fof(f408,plain,
! [X0,X1] :
( member(X1,diagonalise(X0))
| member(X1,domain_of(intersection(X0,identity_relation)))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f76]) ).
fof(f407,plain,
! [X0,X1] :
( member(X1,power_class(X0))
| member(X1,image(element_relation,complement(X0)))
| ~ member(X1,universal_class) ),
inference(superposition,[],[f25,f55]) ).
fof(f409,plain,
! [X0,X1] :
( member(singleton(X0),X1)
| ~ subclass(universal_class,complement(complement(X1))) ),
inference(subsumption_resolution,[],[f406,f98]) ).
fof(f406,plain,
! [X0,X1] :
( member(singleton(X0),X1)
| ~ member(singleton(X0),universal_class)
| ~ subclass(universal_class,complement(complement(X1))) ),
inference(resolution,[],[f25,f214]) ).
fof(f405,plain,
! [X0,X1] :
( member(not_subclass_element(X0,complement(X1)),X1)
| ~ member(not_subclass_element(X0,complement(X1)),universal_class)
| subclass(X0,complement(X1)) ),
inference(resolution,[],[f25,f3]) ).
fof(f404,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,universal_class)
| ~ subclass(complement(X1),X2)
| member(X0,X2) ),
inference(resolution,[],[f25,f1]) ).
fof(f25,axiom,
! [X0,X4] :
( member(X4,complement(X0))
| member(X4,X0)
| ~ member(X4,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f398,plain,
! [X0] :
( ~ subclass(v,diagonalise(X0))
| ~ member(y,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f377,f76]) ).
fof(f397,plain,
! [X0] :
( ~ subclass(v,power_class(X0))
| ~ member(y,image(element_relation,complement(X0))) ),
inference(superposition,[],[f377,f55]) ).
fof(f377,plain,
! [X0] :
( ~ subclass(v,complement(X0))
| ~ member(y,X0) ),
inference(resolution,[],[f374,f24]) ).
fof(f396,plain,
( ! [X0] :
( ~ subclass(null_class,diagonalise(X0))
| ~ member(x,domain_of(intersection(X0,identity_relation))) )
| ~ spl0_2 ),
inference(superposition,[],[f366,f76]) ).
fof(f395,plain,
( ! [X0] :
( ~ subclass(null_class,power_class(X0))
| ~ member(x,image(element_relation,complement(X0))) )
| ~ spl0_2 ),
inference(superposition,[],[f366,f55]) ).
fof(f380,plain,
! [X0,X1] :
( ~ subclass(v,X0)
| ~ subclass(X0,X1)
| member(y,X1) ),
inference(resolution,[],[f374,f1]) ).
fof(f379,plain,
! [X0,X1] :
( ~ subclass(v,intersection(X0,X1))
| member(y,X0) ),
inference(resolution,[],[f374,f21]) ).
fof(f378,plain,
! [X0,X1] :
( ~ subclass(v,intersection(X0,X1))
| member(y,X1) ),
inference(resolution,[],[f374,f22]) ).
fof(f374,plain,
! [X0] :
( member(y,X0)
| ~ subclass(v,X0) ),
inference(resolution,[],[f372,f1]) ).
fof(f372,plain,
member(y,v),
inference(resolution,[],[f15,f92]) ).
fof(f373,plain,
! [X0,X1] :
( member(y,X0)
| ~ subclass(cross_product(u,v),cross_product(X1,X0)) ),
inference(resolution,[],[f15,f170]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f371,plain,
! [X0] :
( ~ subclass(u,diagonalise(X0))
| ~ member(x,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f352,f76]) ).
fof(f370,plain,
! [X0] :
( ~ subclass(u,power_class(X0))
| ~ member(x,image(element_relation,complement(X0))) ),
inference(superposition,[],[f352,f55]) ).
fof(f352,plain,
! [X0] :
( ~ subclass(u,complement(X0))
| ~ member(x,X0) ),
inference(resolution,[],[f348,f24]) ).
fof(f369,plain,
( ! [X0,X1] :
( ~ subclass(null_class,X0)
| ~ subclass(X0,X1)
| member(x,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f359,f1]) ).
fof(f355,plain,
! [X0,X1] :
( ~ subclass(u,X0)
| ~ subclass(X0,X1)
| member(x,X1) ),
inference(resolution,[],[f348,f1]) ).
fof(f348,plain,
! [X0] :
( member(x,X0)
| ~ subclass(u,X0) ),
inference(resolution,[],[f346,f1]) ).
fof(f346,plain,
member(x,u),
inference(resolution,[],[f14,f92]) ).
fof(f347,plain,
! [X0,X1] :
( member(x,X0)
| ~ subclass(cross_product(u,v),cross_product(X0,X1)) ),
inference(resolution,[],[f14,f170]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( ~ member(ordered_pair(X2,X3),cross_product(X0,X1))
| member(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f330,plain,
! [X0] :
( ~ subclass(universal_class,complement(subset_relation))
| ~ member(singleton(X0),identity_relation) ),
inference(resolution,[],[f214,f147]) ).
fof(f332,plain,
! [X0,X1] : ~ subclass(universal_class,complement(unordered_pair(X0,singleton(X1)))),
inference(subsumption_resolution,[],[f327,f98]) ).
fof(f327,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(X0,singleton(X1))))
| ~ member(singleton(X1),universal_class) ),
inference(resolution,[],[f214,f10]) ).
fof(f331,plain,
! [X0,X1] : ~ subclass(universal_class,complement(unordered_pair(singleton(X0),X1))),
inference(subsumption_resolution,[],[f326,f98]) ).
fof(f326,plain,
! [X0,X1] :
( ~ subclass(universal_class,complement(unordered_pair(singleton(X0),X1)))
| ~ member(singleton(X0),universal_class) ),
inference(resolution,[],[f214,f9]) ).
fof(f324,plain,
! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f214,f162]) ).
fof(f333,plain,
! [X0] : ~ subclass(universal_class,complement(singleton(singleton(X0)))),
inference(subsumption_resolution,[],[f328,f98]) ).
fof(f328,plain,
! [X0] :
( ~ subclass(universal_class,complement(singleton(singleton(X0))))
| ~ member(singleton(X0),universal_class) ),
inference(resolution,[],[f214,f105]) ).
fof(f325,plain,
~ subclass(universal_class,complement(universal_class)),
inference(resolution,[],[f214,f98]) ).
fof(f329,plain,
! [X0] :
( ~ subclass(universal_class,complement(inverse(subset_relation)))
| ~ member(singleton(X0),identity_relation) ),
inference(resolution,[],[f214,f129]) ).
fof(f214,plain,
! [X0,X1] :
( ~ member(singleton(X1),X0)
| ~ subclass(universal_class,complement(X0)) ),
inference(resolution,[],[f162,f24]) ).
fof(f289,plain,
! [X0] :
( ~ inductive(null_class)
| member(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f126,f67]) ).
fof(f195,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(omega,X0) ),
inference(resolution,[],[f164,f21]) ).
fof(f194,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(omega,X1) ),
inference(resolution,[],[f164,f22]) ).
fof(f314,plain,
! [X0,X1] :
( member(apply(X0,X1),universal_class)
| ~ member(image(X0,singleton(X1)),universal_class) ),
inference(superposition,[],[f54,f68]) ).
fof(f68,axiom,
! [X1,X8] : sum_class(image(X8,singleton(X1))) = apply(X8,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply) ).
fof(f313,plain,
( omega = image(successor_relation,omega)
| ~ inductive(image(successor_relation,omega)) ),
inference(subsumption_resolution,[],[f310,f50]) ).
fof(f310,plain,
( omega = image(successor_relation,omega)
| ~ inductive(image(successor_relation,omega))
| ~ inductive(omega) ),
inference(resolution,[],[f187,f48]) ).
fof(f187,plain,
! [X0] :
( ~ subclass(X0,omega)
| omega = X0
| ~ inductive(X0) ),
inference(resolution,[],[f7,f51]) ).
fof(f306,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f161,f1]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X0) ),
inference(resolution,[],[f161,f21]) ).
fof(f304,plain,
! [X2,X3,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(unordered_pair(X2,X3),X1) ),
inference(resolution,[],[f161,f22]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,complement(X0))
| ~ member(unordered_pair(X1,X2),X0) ),
inference(resolution,[],[f161,f24]) ).
fof(f161,plain,
! [X2,X0,X1] :
( member(unordered_pair(X1,X2),X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f11]) ).
fof(f285,plain,
! [X0] :
( ~ subclass(universal_class,null_class)
| member(null_class,X0)
| null_class = X0 ),
inference(superposition,[],[f177,f67]) ).
fof(f290,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,X0)
| null_class = X0 ),
inference(superposition,[],[f21,f67]) ).
fof(f288,plain,
! [X0,X1] :
( ~ member(X1,null_class)
| member(X1,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f22,f67]) ).
fof(f287,plain,
! [X0] :
( ~ inductive(null_class)
| member(null_class,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f144,f67]) ).
fof(f286,plain,
! [X0] :
( ~ subclass(universal_class,null_class)
| member(null_class,regular(X0))
| null_class = X0 ),
inference(superposition,[],[f176,f67]) ).
fof(f266,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(element_relation) ),
inference(resolution,[],[f158,f18]) ).
fof(f272,plain,
! [X0,X1] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(compose(X0,X1)) ),
inference(resolution,[],[f158,f57]) ).
fof(f270,plain,
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(successor_relation) ),
inference(resolution,[],[f158,f44]) ).
fof(f268,plain,
! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(flip(X0)) ),
inference(resolution,[],[f158,f35]) ).
fof(f267,plain,
! [X0] :
( member(null_class,cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ inductive(rotate(X0)) ),
inference(resolution,[],[f158,f32]) ).
fof(f265,plain,
! [X0] :
( member(null_class,cross_product(universal_class,universal_class))
| ~ inductive(X0)
| ~ function(X0) ),
inference(resolution,[],[f158,f62]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(null_class,X1)
| ~ inductive(X0) ),
inference(resolution,[],[f1,f47]) ).
fof(f259,plain,
! [X0] :
( ~ subclass(universal_class,domain_of(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(resolution,[],[f192,f163]) ).
fof(f262,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,diagonalise(X0)))
| ~ subclass(universal_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f243,f76]) ).
fof(f261,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,power_class(X0)))
| ~ subclass(universal_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f243,f55]) ).
fof(f243,plain,
! [X0] :
( ~ subclass(universal_class,image(element_relation,complement(X0)))
| ~ subclass(universal_class,power_class(X0)) ),
inference(resolution,[],[f191,f163]) ).
fof(f260,plain,
! [X0] :
( ~ inductive(domain_of(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(resolution,[],[f192,f47]) ).
fof(f192,plain,
! [X0] :
( ~ member(null_class,domain_of(intersection(X0,identity_relation)))
| ~ subclass(universal_class,diagonalise(X0)) ),
inference(superposition,[],[f175,f76]) ).
fof(f249,plain,
( y = successor(x)
| ~ subclass(cross_product(u,v),successor_relation) ),
inference(resolution,[],[f45,f170]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),successor_relation)
| successor(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).
fof(f248,plain,
! [X0] :
( ~ inductive(image(element_relation,diagonalise(X0)))
| ~ subclass(universal_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f244,f76]) ).
fof(f247,plain,
! [X0] :
( ~ inductive(image(element_relation,power_class(X0)))
| ~ subclass(universal_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f244,f55]) ).
fof(f244,plain,
! [X0] :
( ~ inductive(image(element_relation,complement(X0)))
| ~ subclass(universal_class,power_class(X0)) ),
inference(resolution,[],[f191,f47]) ).
fof(f246,plain,
! [X0] :
( ~ member(null_class,image(element_relation,diagonalise(X0)))
| ~ subclass(universal_class,power_class(domain_of(intersection(X0,identity_relation)))) ),
inference(superposition,[],[f191,f76]) ).
fof(f245,plain,
! [X0] :
( ~ member(null_class,image(element_relation,power_class(X0)))
| ~ subclass(universal_class,power_class(image(element_relation,complement(X0)))) ),
inference(superposition,[],[f191,f55]) ).
fof(f191,plain,
! [X0] :
( ~ member(null_class,image(element_relation,complement(X0)))
| ~ subclass(universal_class,power_class(X0)) ),
inference(superposition,[],[f175,f55]) ).
fof(f229,plain,
( ~ subclass(cross_product(u,v),element_relation)
| member(x,y) ),
inference(resolution,[],[f170,f19]) ).
fof(f233,plain,
! [X0,X1] :
( ~ subclass(cross_product(u,v),X0)
| ~ subclass(X0,X1)
| member(ordered_pair(x,y),X1) ),
inference(resolution,[],[f170,f1]) ).
fof(f232,plain,
! [X0,X1] :
( ~ subclass(cross_product(u,v),intersection(X0,X1))
| member(ordered_pair(x,y),X0) ),
inference(resolution,[],[f170,f21]) ).
fof(f231,plain,
! [X0,X1] :
( ~ subclass(cross_product(u,v),intersection(X0,X1))
| member(ordered_pair(x,y),X1) ),
inference(resolution,[],[f170,f22]) ).
fof(f230,plain,
! [X0] :
( ~ subclass(cross_product(u,v),complement(X0))
| ~ member(ordered_pair(x,y),X0) ),
inference(resolution,[],[f170,f24]) ).
fof(f170,plain,
! [X0] :
( member(ordered_pair(x,y),X0)
| ~ subclass(cross_product(u,v),X0) ),
inference(resolution,[],[f1,f92]) ).
fof(f199,plain,
( universal_class = cross_product(universal_class,universal_class)
| ~ function(universal_class) ),
inference(resolution,[],[f179,f62]) ).
fof(f219,plain,
! [X0] :
( ~ subclass(universal_class,diagonalise(X0))
| ~ member(omega,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f193,f76]) ).
fof(f218,plain,
! [X0] :
( ~ subclass(universal_class,power_class(X0))
| ~ member(omega,image(element_relation,complement(X0))) ),
inference(superposition,[],[f193,f55]) ).
fof(f193,plain,
! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ member(omega,X0) ),
inference(resolution,[],[f164,f24]) ).
fof(f217,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(singleton(X2),X1) ),
inference(resolution,[],[f162,f1]) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(singleton(X2),X0) ),
inference(resolution,[],[f162,f21]) ).
fof(f215,plain,
! [X2,X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(singleton(X2),X1) ),
inference(resolution,[],[f162,f22]) ).
fof(f162,plain,
! [X0,X1] :
( member(singleton(X1),X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f98]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
fof(f213,plain,
! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| member(null_class,X0)
| ~ function(universal_class) ),
inference(resolution,[],[f178,f62]) ).
fof(f178,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(null_class,X1) ),
inference(resolution,[],[f163,f1]) ).
fof(f177,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(null_class,X0) ),
inference(resolution,[],[f163,f21]) ).
fof(f176,plain,
! [X0,X1] :
( ~ subclass(universal_class,intersection(X0,X1))
| member(null_class,X1) ),
inference(resolution,[],[f163,f22]) ).
fof(f202,plain,
( identity_relation != subset_relation
| spl0_7 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f201,plain,
( spl0_7
<=> identity_relation = subset_relation ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f190,plain,
( ~ subclass(subset_relation,identity_relation)
| identity_relation = subset_relation ),
inference(resolution,[],[f7,f157]) ).
fof(f179,plain,
! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ),
inference(resolution,[],[f7,f4]) ).
fof(f196,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| ~ subclass(X0,X1)
| member(omega,X1) ),
inference(resolution,[],[f164,f1]) ).
fof(f164,plain,
! [X0] :
( member(omega,X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f52]) ).
fof(f175,plain,
! [X0] :
( ~ subclass(universal_class,complement(X0))
| ~ member(null_class,X0) ),
inference(resolution,[],[f163,f24]) ).
fof(f189,plain,
! [X0] :
( ~ subclass(identity_relation,compose(X0,inverse(X0)))
| compose(X0,inverse(X0)) = identity_relation
| ~ function(X0) ),
inference(resolution,[],[f7,f63]) ).
fof(f188,plain,
! [X0,X1] :
( ~ subclass(cross_product(universal_class,universal_class),compose(X0,X1))
| cross_product(universal_class,universal_class) = compose(X0,X1) ),
inference(resolution,[],[f7,f57]) ).
fof(f186,plain,
( ~ subclass(cross_product(universal_class,universal_class),successor_relation)
| cross_product(universal_class,universal_class) = successor_relation ),
inference(resolution,[],[f7,f44]) ).
fof(f185,plain,
! [X0] :
( ~ subclass(X0,image(successor_relation,X0))
| image(successor_relation,X0) = X0
| ~ inductive(X0) ),
inference(resolution,[],[f7,f48]) ).
fof(f184,plain,
! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),flip(X0))
| cross_product(cross_product(universal_class,universal_class),universal_class) = flip(X0) ),
inference(resolution,[],[f7,f35]) ).
fof(f183,plain,
! [X0] :
( ~ subclass(cross_product(cross_product(universal_class,universal_class),universal_class),rotate(X0))
| rotate(X0) = cross_product(cross_product(universal_class,universal_class),universal_class) ),
inference(resolution,[],[f7,f32]) ).
fof(f182,plain,
( ~ subclass(cross_product(universal_class,universal_class),element_relation)
| element_relation = cross_product(universal_class,universal_class) ),
inference(resolution,[],[f7,f18]) ).
fof(f181,plain,
! [X0] :
( ~ subclass(cross_product(universal_class,universal_class),X0)
| cross_product(universal_class,universal_class) = X0
| ~ function(X0) ),
inference(resolution,[],[f7,f62]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f163,plain,
! [X0] :
( member(null_class,X0)
| ~ subclass(universal_class,X0) ),
inference(resolution,[],[f1,f97]) ).
fof(f172,plain,
! [X0,X1] :
( ~ subclass(subset_relation,X0)
| member(X1,X0)
| ~ member(X1,identity_relation) ),
inference(resolution,[],[f1,f147]) ).
fof(f171,plain,
! [X0,X1] :
( ~ subclass(inverse(subset_relation),X0)
| member(X1,X0)
| ~ member(X1,identity_relation) ),
inference(resolution,[],[f1,f129]) ).
fof(f169,plain,
! [X0,X1] :
( ~ subclass(singleton(X0),X1)
| member(X0,X1)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1,f105]) ).
fof(f168,plain,
! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X1,X2)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f10]) ).
fof(f167,plain,
! [X2,X0,X1] :
( ~ subclass(unordered_pair(X0,X1),X2)
| member(X0,X2)
| ~ member(X0,universal_class) ),
inference(resolution,[],[f1,f9]) ).
fof(f166,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| member(power_class(X1),X0)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f56]) ).
fof(f165,plain,
! [X0,X1] :
( ~ subclass(universal_class,X0)
| member(sum_class(X1),X0)
| ~ member(X1,universal_class) ),
inference(resolution,[],[f1,f54]) ).
fof(f160,plain,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| member(not_subclass_element(X0,X2),X1)
| subclass(X0,X2) ),
inference(resolution,[],[f1,f2]) ).
fof(f159,plain,
! [X0,X1] :
( ~ subclass(X0,X1)
| member(regular(X0),X1)
| null_class = X0 ),
inference(resolution,[],[f1,f66]) ).
fof(f157,plain,
subclass(identity_relation,subset_relation),
inference(duplicate_literal_removal,[],[f156]) ).
fof(f156,plain,
( subclass(identity_relation,subset_relation)
| subclass(identity_relation,subset_relation) ),
inference(resolution,[],[f148,f2]) ).
fof(f148,plain,
! [X0] :
( ~ member(not_subclass_element(X0,subset_relation),identity_relation)
| subclass(X0,subset_relation) ),
inference(resolution,[],[f147,f3]) ).
fof(f155,plain,
! [X0,X1] :
( ~ member(X1,diagonalise(X0))
| ~ member(X1,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f24,f76]) ).
fof(f154,plain,
! [X0] :
( ~ inductive(diagonalise(X0))
| ~ member(null_class,domain_of(intersection(X0,identity_relation))) ),
inference(superposition,[],[f99,f76]) ).
fof(f153,plain,
! [X0] : power_class(domain_of(intersection(X0,identity_relation))) = complement(image(element_relation,diagonalise(X0))),
inference(superposition,[],[f55,f76]) ).
fof(f76,axiom,
! [X5] : complement(domain_of(intersection(X5,identity_relation))) = diagonalise(X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diagonalisation) ).
fof(f63,axiom,
! [X8] :
( subclass(compose(X8,inverse(X8)),identity_relation)
| ~ function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f152,plain,
! [X0,X1] :
( ~ member(X1,power_class(X0))
| ~ member(X1,image(element_relation,complement(X0))) ),
inference(superposition,[],[f24,f55]) ).
fof(f151,plain,
! [X0] :
( ~ inductive(power_class(X0))
| ~ member(null_class,image(element_relation,complement(X0))) ),
inference(superposition,[],[f99,f55]) ).
fof(f150,plain,
! [X0] : power_class(image(element_relation,complement(X0))) = complement(image(element_relation,power_class(X0))),
inference(superposition,[],[f55,f55]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
fof(f53,axiom,
! [X0] : domain_of(restrict(element_relation,universal_class,X0)) = sum_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f35,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip1) ).
fof(f144,plain,
! [X0,X1] :
( ~ inductive(intersection(X1,X0))
| member(null_class,X0) ),
inference(resolution,[],[f22,f47]) ).
fof(f32,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate1) ).
fof(f147,plain,
! [X0] :
( member(X0,subset_relation)
| ~ member(X0,identity_relation) ),
inference(superposition,[],[f22,f75]) ).
fof(f146,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X1)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f22,f2]) ).
fof(f145,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X1)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f22,f66]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f141,plain,
! [X0] :
( ~ member(not_subclass_element(X0,inverse(subset_relation)),identity_relation)
| subclass(X0,inverse(subset_relation)) ),
inference(resolution,[],[f129,f3]) ).
fof(f130,plain,
( ~ inductive(identity_relation)
| member(null_class,inverse(subset_relation)) ),
inference(superposition,[],[f126,f75]) ).
fof(f126,plain,
! [X0,X1] :
( ~ inductive(intersection(X0,X1))
| member(null_class,X0) ),
inference(resolution,[],[f21,f47]) ).
fof(f128,plain,
! [X2,X0,X1] :
( member(not_subclass_element(intersection(X0,X1),X2),X0)
| subclass(intersection(X0,X1),X2) ),
inference(resolution,[],[f21,f2]) ).
fof(f127,plain,
! [X0,X1] :
( member(regular(intersection(X0,X1)),X0)
| intersection(X0,X1) = null_class ),
inference(resolution,[],[f21,f66]) ).
fof(f19,axiom,
! [X0,X1] :
( ~ member(ordered_pair(X0,X1),element_relation)
| member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f115,plain,
( member(y,null_class)
| ~ member(y,universal_class) ),
inference(superposition,[],[f10,f93]) ).
fof(f10,axiom,
! [X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f105,plain,
! [X0] :
( member(X0,singleton(X0))
| ~ member(X0,universal_class) ),
inference(superposition,[],[f9,f12]) ).
fof(f104,plain,
( member(x,null_class)
| ~ member(x,universal_class) ),
inference(superposition,[],[f9,f93]) ).
fof(f9,axiom,
! [X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f3,axiom,
! [X0,X1] :
( ~ member(not_subclass_element(X0,X1),X1)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f101,plain,
! [X0,X1] :
( subclass(complement(X0),X1)
| ~ member(not_subclass_element(complement(X0),X1),X0) ),
inference(resolution,[],[f2,f24]) ).
fof(f2,axiom,
! [X0,X1] :
( member(not_subclass_element(X0,X1),X0)
| subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f100,plain,
! [X0] :
( complement(X0) = null_class
| ~ member(regular(complement(X0)),X0) ),
inference(resolution,[],[f66,f24]) ).
fof(f66,axiom,
! [X0] :
( member(regular(X0),X0)
| null_class = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f62,axiom,
! [X8] :
( subclass(X8,cross_product(universal_class,universal_class))
| ~ function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f57,axiom,
! [X7,X5] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f56,axiom,
! [X2] :
( member(power_class(X2),universal_class)
| ~ member(X2,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
fof(f54,axiom,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
fof(f48,axiom,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f99,plain,
! [X0] :
( ~ inductive(complement(X0))
| ~ member(null_class,X0) ),
inference(resolution,[],[f24,f47]) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
fof(f98,plain,
! [X0] : member(singleton(X0),universal_class),
inference(superposition,[],[f11,f12]) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
fof(f92,axiom,
member(ordered_pair(x,y),cross_product(u,v)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_1) ).
fof(f51,axiom,
! [X1] :
( subclass(omega,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f47,axiom,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f44,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f18,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f97,plain,
member(null_class,universal_class),
inference(superposition,[],[f11,f93]) ).
fof(f11,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f93,axiom,
null_class = unordered_pair(x,y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_unordered_pair_axiom3_2) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f91,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| apply(X11,ordered_pair(apply(X9,not_homomorphism1(X9,X10,X11)),apply(X9,not_homomorphism2(X9,X10,X11)))) != apply(X9,apply(X10,ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism6) ).
fof(f90,axiom,
! [X10,X11,X9] :
( ~ operation(X10)
| ~ operation(X11)
| ~ compatible(X9,X10,X11)
| homomorphism(X9,X10,X11)
| member(ordered_pair(not_homomorphism1(X9,X10,X11),not_homomorphism2(X9,X10,X11)),domain_of(X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism5) ).
fof(f85,axiom,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible4) ).
fof(f81,axiom,
! [X8] :
( ~ function(X8)
| operation(X8)
| ~ subclass(range_of(X8),domain_of(domain_of(X8)))
| domain_of(X8) != cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation4) ).
fof(f37,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip3) ).
fof(f34,axiom,
! [X2,X3,X0,X6] :
( ~ member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate3) ).
fof(f59,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),cross_product(universal_class,universal_class))
| member(ordered_pair(X1,X4),compose(X7,X5))
| ~ member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose3) ).
fof(f89,axiom,
! [X10,X0,X11,X1,X9] :
( ~ homomorphism(X9,X10,X11)
| ~ member(ordered_pair(X0,X1),domain_of(X10))
| apply(X11,ordered_pair(apply(X9,X0),apply(X9,X1))) = apply(X9,apply(X10,ordered_pair(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',homomorphism4) ).
fof(f96,plain,
! [X0] :
( member(ordered_pair(X0,successor(X0)),successor_relation)
| ~ member(ordered_pair(X0,successor(X0)),cross_product(universal_class,universal_class)) ),
inference(equality_resolution,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] :
( successor(X0) != X1
| member(ordered_pair(X0,X1),successor_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation3) ).
fof(f8,axiom,
! [X2,X0,X1] :
( X1 = X2
| X0 = X2
| ~ member(X2,unordered_pair(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
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/sandbox/benchmark/theBenchmark.p',domain2) ).
fof(f70,axiom,
! [X1] :
( ~ member(X1,universal_class)
| null_class = X1
| member(apply(choice,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice2) ).
fof(f20,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| member(ordered_pair(X0,X1),element_relation)
| ~ member(ordered_pair(X0,X1),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation3) ).
fof(f16,axiom,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product3) ).
fof(f23,axiom,
! [X0,X1,X4] :
( ~ member(X4,X0)
| ~ member(X4,X1)
| member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f64,axiom,
! [X8] :
( function(X8)
| ~ subclass(X8,cross_product(universal_class,universal_class))
| ~ subclass(compose(X8,inverse(X8)),identity_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',function3) ).
fof(f49,axiom,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive3) ).
fof(f65,axiom,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replacement) ).
fof(f36,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',flip2) ).
fof(f33,axiom,
! [X2,X3,X0,X6] :
( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
| ~ member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rotate2) ).
fof(f58,axiom,
! [X1,X7,X4,X5] :
( ~ member(ordered_pair(X1,X4),compose(X7,X5))
| member(X4,image(X7,image(X5,singleton(X1)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose2) ).
fof(f17,axiom,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product4) ).
fof(f30,axiom,
! [X0,X4] :
( ~ member(X4,domain_of(X0))
| restrict(X0,singleton(X4),universal_class) != null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f95,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( X0 != X1
| subclass(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_implies_subclass2) ).
fof(f74,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_relation) ).
fof(f27,axiom,
! [X0,X1] : intersection(complement(intersection(X0,X1)),complement(intersection(complement(X0),complement(X1)))) = symmetric_difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetric_difference) ).
fof(f41,axiom,
! [X0,X1,X4] : second(not_subclass_element(restrict(X4,singleton(X0),X1),null_class)) = range(X4,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range) ).
fof(f40,axiom,
! [X0,X1,X4] : first(not_subclass_element(restrict(X4,X0,singleton(X1)),null_class)) = domain(X4,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain) ).
fof(f77,axiom,
! [X0] : intersection(domain_of(X0),diagonalise(compose(inverse(element_relation),X0))) = cantor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cantor_class) ).
fof(f13,axiom,
! [X0,X1] : unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))) = ordered_pair(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f28,axiom,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = restrict(X5,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction1) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
fof(f511,plain,
( ~ spl0_2
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f510]) ).
fof(f510,plain,
( $false
| ~ spl0_2
| spl0_22 ),
inference(subsumption_resolution,[],[f500,f94]) ).
fof(f500,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f422,f464]) ).
fof(f509,plain,
( ~ spl0_2
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f508]) ).
fof(f508,plain,
( $false
| ~ spl0_2
| spl0_22 ),
inference(subsumption_resolution,[],[f499,f113]) ).
fof(f499,plain,
( ~ member(x,null_class)
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f414,f464]) ).
fof(f507,plain,
( ~ spl0_2
| spl0_7
| spl0_21
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f506]) ).
fof(f506,plain,
( $false
| ~ spl0_2
| spl0_7
| spl0_21
| spl0_22 ),
inference(global_subsumption,[],[f498,f29,f28,f13,f77,f40,f41,f27,f74,f95,f30,f17,f58,f33,f36,f65,f49,f64,f23,f16,f20,f70,f31,f8,f96,f89,f59,f34,f37,f81,f85,f90,f91,f50,f69,f4,f52,f94,f93,f11,f97,f18,f44,f47,f51,f92,f12,f98,f39,f75,f24,f99,f43,f48,f54,f56,f57,f62,f66,f100,f2,f101,f3,f9,f104,f105,f10,f115,f19,f21,f127,f128,f126,f130,f129,f141,f22,f145,f146,f147,f32,f144,f35,f38,f53,f55,f150,f151,f152,f63,f76,f153,f154,f155,f148,f157,f1,f159,f160,f165,f166,f167,f168,f169,f171,f172,f163,f7,f181,f182,f183,f184,f185,f186,f188,f189,f175,f164,f196,f179,f190,f202,f176,f177,f178,f213,f42,f162,f215,f216,f217,f193,f218,f219,f199,f170,f230,f231,f232,f233,f229,f191,f245,f246,f244,f247,f248,f45,f249,f192,f260,f243,f261,f262,f259,f158,f265,f267,f268,f270,f272,f266,f67,f286,f287,f288,f290,f285,f161,f303,f304,f305,f306,f187,f313,f68,f314,f194,f195,f289,f214,f329,f325,f333,f324,f331,f332,f330,f14,f347,f346,f348,f355,f113,f359,f369,f352,f370,f371,f15,f373,f372,f374,f378,f379,f380,f366,f395,f396,f377,f397,f398,f25,f404,f405,f409,f407,f408,f353,f411,f410,f414,f421,f422,f424,f425,f354,f429,f26,f432,f433,f434,f435,f436,f437,f438,f439,f440,f441,f442,f443,f444,f445,f446,f447,f448,f450,f451,f367,f458,f459,f368,f462,f465,f466,f467,f468,f469,f464,f488,f489,f492,f503,f494,f496]) ).
fof(f498,plain,
( ~ subclass(universal_class,complement(null_class))
| ~ spl0_2
| spl0_21
| spl0_22 ),
inference(superposition,[],[f344,f464]) ).
fof(f344,plain,
( ~ subclass(universal_class,complement(subset_relation))
| spl0_21 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f342,plain,
( spl0_21
<=> subclass(universal_class,complement(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f505,plain,
( ~ spl0_2
| spl0_7
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f504]) ).
fof(f504,plain,
( $false
| ~ spl0_2
| spl0_7
| spl0_22 ),
inference(global_subsumption,[],[f29,f28,f13,f77,f40,f41,f27,f74,f95,f30,f17,f58,f33,f36,f65,f49,f64,f23,f16,f20,f70,f31,f8,f96,f89,f59,f34,f37,f81,f85,f90,f91,f50,f69,f4,f52,f94,f93,f11,f97,f18,f44,f47,f51,f92,f12,f98,f39,f75,f24,f99,f43,f48,f54,f56,f57,f62,f66,f100,f2,f101,f3,f9,f104,f105,f10,f115,f19,f21,f127,f128,f126,f130,f129,f141,f22,f145,f146,f147,f32,f144,f35,f38,f53,f55,f150,f151,f152,f63,f76,f153,f154,f155,f148,f157,f1,f159,f160,f165,f166,f167,f168,f169,f171,f172,f163,f7,f181,f182,f183,f184,f185,f186,f188,f189,f175,f164,f196,f179,f190,f202,f176,f177,f178,f213,f42,f162,f215,f216,f217,f193,f218,f219,f199,f170,f230,f231,f232,f233,f229,f191,f245,f246,f244,f247,f248,f45,f249,f192,f260,f243,f261,f262,f259,f158,f265,f267,f268,f270,f272,f266,f67,f286,f287,f288,f290,f285,f161,f303,f304,f305,f306,f187,f313,f68,f314,f194,f195,f289,f214,f329,f325,f333,f324,f331,f332,f330,f14,f347,f346,f348,f355,f113,f359,f369,f352,f370,f371,f15,f373,f372,f374,f378,f379,f380,f366,f395,f396,f377,f397,f398,f25,f404,f405,f409,f407,f408,f353,f411,f410,f414,f421,f422,f424,f425,f354,f429,f26,f432,f433,f434,f435,f436,f437,f438,f439,f440,f441,f442,f443,f444,f445,f446,f447,f448,f450,f451,f367,f458,f459,f368,f462,f465,f466,f467,f468,f469,f464,f488,f489,f492,f503,f494,f496]) ).
fof(f486,plain,
( ~ spl0_2
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f485]) ).
fof(f485,plain,
( $false
| ~ spl0_2
| spl0_11 ),
inference(subsumption_resolution,[],[f478,f94]) ).
fof(f478,plain,
( ~ subclass(null_class,null_class)
| ~ spl0_2
| spl0_11 ),
inference(superposition,[],[f365,f463]) ).
fof(f463,plain,
( null_class = y
| ~ spl0_2
| spl0_11 ),
inference(resolution,[],[f462,f236]) ).
fof(f236,plain,
( ~ member(x,y)
| spl0_11 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f235,plain,
( spl0_11
<=> member(x,y) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f365,plain,
( ~ subclass(null_class,y)
| ~ spl0_2
| spl0_11 ),
inference(resolution,[],[f359,f236]) ).
fof(f484,plain,
( ~ spl0_2
| spl0_11 ),
inference(avatar_contradiction_clause,[],[f483]) ).
fof(f483,plain,
( $false
| ~ spl0_2
| spl0_11 ),
inference(subsumption_resolution,[],[f475,f113]) ).
fof(f475,plain,
( ~ member(x,null_class)
| ~ spl0_2
| spl0_11 ),
inference(superposition,[],[f236,f463]) ).
fof(f420,plain,
( spl0_22
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f410,f417,f413]) ).
fof(f417,plain,
( spl0_23
<=> subclass(u,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f382,plain,
spl0_3,
inference(avatar_contradiction_clause,[],[f381]) ).
fof(f381,plain,
( $false
| spl0_3 ),
inference(subsumption_resolution,[],[f375,f4]) ).
fof(f375,plain,
( ~ subclass(v,universal_class)
| spl0_3 ),
inference(resolution,[],[f374,f120]) ).
fof(f120,plain,
( ~ member(y,universal_class)
| spl0_3 ),
inference(avatar_component_clause,[],[f118]) ).
fof(f357,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f356,plain,
( $false
| spl0_1 ),
inference(subsumption_resolution,[],[f349,f4]) ).
fof(f349,plain,
( ~ subclass(u,universal_class)
| spl0_1 ),
inference(resolution,[],[f348,f109]) ).
fof(f109,plain,
( ~ member(x,universal_class)
| spl0_1 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f345,plain,
( spl0_20
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f330,f342,f339]) ).
fof(f339,plain,
( spl0_20
<=> ! [X0] : ~ member(singleton(X0),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f323,plain,
( spl0_17
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f289,f320,f295]) ).
fof(f295,plain,
( spl0_17
<=> ! [X0] :
( member(null_class,X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f320,plain,
( spl0_19
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f301,plain,
( spl0_17
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f285,f298,f295]) ).
fof(f298,plain,
( spl0_18
<=> subclass(universal_class,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f284,plain,
( ~ spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f266,f281,f277]) ).
fof(f277,plain,
( spl0_15
<=> inductive(element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f281,plain,
( spl0_16
<=> member(null_class,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f258,plain,
( ~ spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f249,f255,f251]) ).
fof(f251,plain,
( spl0_13
<=> subclass(cross_product(u,v),successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f255,plain,
( spl0_14
<=> y = successor(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f242,plain,
( spl0_11
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f229,f239,f235]) ).
fof(f239,plain,
( spl0_12
<=> subclass(cross_product(u,v),element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f228,plain,
( ~ spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f199,f225,f221]) ).
fof(f221,plain,
( spl0_9
<=> function(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f225,plain,
( spl0_10
<=> universal_class = cross_product(universal_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f208,plain,
( spl0_7
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f190,f205,f201]) ).
fof(f205,plain,
( spl0_8
<=> subclass(subset_relation,identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f139,plain,
( spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f130,f136,f132]) ).
fof(f132,plain,
( spl0_5
<=> member(null_class,inverse(subset_relation)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f136,plain,
( spl0_6
<=> inductive(identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f125,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f115,f122,f118]) ).
fof(f114,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f104,f111,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET075-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 01:22:17 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (7717)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (7724)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)
% 0.15/0.38 % (7720)WARNING: value z3 for option sas not known
% 0.15/0.38 % (7718)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (7719)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (7721)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (7720)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)
% 0.15/0.38 % (7722)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)
% 0.15/0.38 % (7723)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)
% 0.15/0.40 % (7720)First to succeed.
% 0.15/0.41 % (7720)Refutation found. Thanks to Tanya!
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.41 % (7720)------------------------------
% 0.15/0.41 % (7720)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.41 % (7720)Termination reason: Refutation
% 0.15/0.41
% 0.15/0.41 % (7720)Memory used [KB]: 1170
% 0.15/0.41 % (7720)Time elapsed: 0.029 s
% 0.15/0.41 % (7720)Instructions burned: 45 (million)
% 0.15/0.41 % (7720)------------------------------
% 0.15/0.41 % (7720)------------------------------
% 0.15/0.41 % (7717)Success in time 0.049 s
%------------------------------------------------------------------------------