TSTP Solution File: SET116-7 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET116-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n025.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 15:05:45 EDT 2024
% Result : Unsatisfiable 0.17s 0.38s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 247
% Syntax : Number of formulae : 480 ( 166 unt; 0 def)
% Number of atoms : 1009 ( 192 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 883 ( 354 ~; 404 |; 0 &)
% ( 125 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 136 ( 134 usr; 126 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 9 con; 0-3 aty)
% Number of variables : 570 ( 570 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1354,plain,
$false,
inference(avatar_sat_refutation,[],[f288,f293,f298,f302,f307,f311,f315,f319,f324,f329,f333,f337,f341,f346,f351,f355,f359,f364,f370,f374,f378,f382,f386,f390,f398,f402,f406,f410,f414,f418,f422,f427,f440,f444,f448,f452,f456,f460,f464,f468,f472,f476,f480,f484,f488,f492,f496,f500,f504,f508,f512,f532,f555,f559,f563,f567,f572,f576,f580,f584,f651,f655,f659,f663,f667,f671,f675,f689,f693,f697,f701,f705,f709,f713,f717,f721,f725,f729,f733,f737,f807,f832,f836,f842,f846,f850,f854,f860,f864,f937,f941,f946,f950,f954,f958,f988,f1003,f1007,f1011,f1015,f1019,f1023,f1027,f1031,f1061,f1108,f1112,f1116,f1126,f1137,f1141,f1145,f1172,f1176,f1181,f1204,f1208,f1212,f1270,f1274,f1279,f1283,f1317,f1321,f1325,f1353]) ).
fof(f1353,plain,
( spl0_1
| spl0_10
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1264,f1210,f326,f285]) ).
fof(f285,plain,
( spl0_1
<=> x = second(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f326,plain,
( spl0_10
<=> x = unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1210,plain,
( spl0_118
<=> ! [X0] :
( second(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1264,plain,
( x = second(x)
| spl0_10
| ~ spl0_118 ),
inference(trivial_inequality_removal,[],[f1243]) ).
fof(f1243,plain,
( x != x
| x = second(x)
| spl0_10
| ~ spl0_118 ),
inference(superposition,[],[f328,f1211]) ).
fof(f1211,plain,
( ! [X0] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| second(X0) = X0 )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1210]) ).
fof(f328,plain,
( x != unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x))))
| spl0_10 ),
inference(avatar_component_clause,[],[f326]) ).
fof(f1325,plain,
spl0_125,
inference(avatar_split_clause,[],[f256,f1323]) ).
fof(f1323,plain,
( spl0_125
<=> ! [X9,X11,X10] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f256,plain,
! [X10,X11,X9] :
( ~ function(X9)
| compatible(X9,X10,X11)
| domain_of(domain_of(X10)) != domain_of(X9)
| ~ subclass(domain_of(domain_of(flip(cross_product(X9,universal_class)))),domain_of(domain_of(X11))) ),
inference(definition_unfolding,[],[f85,f163]) ).
fof(f163,plain,
! [X4] : range_of(X4) = domain_of(domain_of(flip(cross_product(X4,universal_class)))),
inference(definition_unfolding,[],[f39,f38]) ).
fof(f38,axiom,
! [X1] : domain_of(flip(cross_product(X1,universal_class))) = inverse(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f39,axiom,
! [X4] : domain_of(inverse(X4)) = range_of(X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',range_of) ).
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(f1321,plain,
spl0_124,
inference(avatar_split_clause,[],[f218,f1319]) ).
fof(f1319,plain,
( spl0_124
<=> ! [X0] :
( second(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f218,plain,
! [X0] :
( second(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f155,f166]) ).
fof(f166,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(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_set) ).
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(f155,axiom,
! [X0] :
( second(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
fof(f1317,plain,
spl0_123,
inference(avatar_split_clause,[],[f214,f1315]) ).
fof(f1315,plain,
( spl0_123
<=> ! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f214,plain,
! [X0] :
( first(X0) = X0
| member(unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))),cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f154,f166]) ).
fof(f154,axiom,
! [X0] :
( first(X0) = X0
| member(ordered_pair(first(X0),second(X0)),cross_product(universal_class,universal_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_2) ).
fof(f1283,plain,
spl0_122,
inference(avatar_split_clause,[],[f249,f1281]) ).
fof(f1281,plain,
( spl0_122
<=> ! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(null_class,null_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f249,plain,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(null_class,unordered_pair(null_class,null_class)) ),
inference(definition_unfolding,[],[f150,f166,f12]) ).
fof(f150,axiom,
! [X0,X1] :
( member(X1,universal_class)
| member(X0,universal_class)
| ordered_pair(X0,X1) = unordered_pair(null_class,singleton(null_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_3_of_ordered_pair) ).
fof(f1279,plain,
( spl0_121
| spl0_10
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1240,f1206,f326,f1276]) ).
fof(f1276,plain,
( spl0_121
<=> x = first(x) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1206,plain,
( spl0_117
<=> ! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1240,plain,
( x = first(x)
| spl0_10
| ~ spl0_117 ),
inference(trivial_inequality_removal,[],[f1219]) ).
fof(f1219,plain,
( x != x
| x = first(x)
| spl0_10
| ~ spl0_117 ),
inference(superposition,[],[f328,f1207]) ).
fof(f1207,plain,
( ! [X0] :
( unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0
| first(X0) = X0 )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f1274,plain,
spl0_120,
inference(avatar_split_clause,[],[f220,f1272]) ).
fof(f1272,plain,
( spl0_120
<=> ! [X4,X0,X1] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f220,plain,
! [X0,X1,X4] :
( ~ member(X4,cross_product(X0,X1))
| unordered_pair(unordered_pair(first(X4),first(X4)),unordered_pair(first(X4),unordered_pair(second(X4),second(X4)))) = X4 ),
inference(definition_unfolding,[],[f17,f166]) ).
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(f1270,plain,
spl0_119,
inference(avatar_split_clause,[],[f212,f1268]) ).
fof(f1268,plain,
( spl0_119
<=> ! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f212,plain,
! [X0,X1] :
( complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f45,f169,f166]) ).
fof(f169,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f43,f26,f12]) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
fof(f43,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor) ).
fof(f45,axiom,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_relation2) ).
fof(f1212,plain,
spl0_118,
inference(avatar_split_clause,[],[f217,f1210]) ).
fof(f217,plain,
! [X0] :
( second(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f157,f166]) ).
fof(f157,axiom,
! [X0] :
( second(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
fof(f1208,plain,
spl0_117,
inference(avatar_split_clause,[],[f213,f1206]) ).
fof(f213,plain,
! [X0] :
( first(X0) = X0
| unordered_pair(unordered_pair(first(X0),first(X0)),unordered_pair(first(X0),unordered_pair(second(X0),second(X0)))) = X0 ),
inference(definition_unfolding,[],[f156,f166]) ).
fof(f156,axiom,
! [X0] :
( first(X0) = X0
| ordered_pair(first(X0),second(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_1st_and_2nd_4) ).
fof(f1204,plain,
spl0_116,
inference(avatar_split_clause,[],[f209,f1202]) ).
fof(f1202,plain,
( spl0_116
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f209,plain,
! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,null_class)) ),
inference(definition_unfolding,[],[f148,f166,f12]) ).
fof(f148,axiom,
! [X0,X1] :
( member(X1,universal_class)
| ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,null_class)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).
fof(f1181,plain,
( ~ spl0_9
| spl0_115
| ~ spl0_4
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1132,f1114,f300,f1178,f321]) ).
fof(f321,plain,
( spl0_9
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1178,plain,
( spl0_115
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f300,plain,
( spl0_4
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1114,plain,
( spl0_108
<=> ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1132,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl0_4
| ~ spl0_108 ),
inference(resolution,[],[f1115,f301]) ).
fof(f301,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f1115,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) )
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1114]) ).
fof(f1176,plain,
spl0_114,
inference(avatar_split_clause,[],[f233,f1174]) ).
fof(f1174,plain,
( spl0_114
<=> ! [X0,X3,X2,X1] :
( ~ member(X2,X0)
| ~ 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_114])]) ).
fof(f233,plain,
! [X2,X3,X0,X1] :
( ~ member(X2,X0)
| ~ member(X3,X1)
| member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f16,f166]) ).
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(f1172,plain,
spl0_113,
inference(avatar_split_clause,[],[f184,f1169]) ).
fof(f1169,plain,
( spl0_113
<=> subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f184,plain,
subset_relation = intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),domain_of(flip(cross_product(element_relation,universal_class))))))),
inference(definition_unfolding,[],[f74,f38]) ).
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(f1145,plain,
spl0_112,
inference(avatar_split_clause,[],[f222,f1143]) ).
fof(f1143,plain,
( spl0_112
<=> ! [X0,X3,X2,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f92,f166]) ).
fof(f92,axiom,
! [X2,X3,X0,X1] :
( member(X0,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_unordered_pair) ).
fof(f1141,plain,
spl0_111,
inference(avatar_split_clause,[],[f221,f1139]) ).
fof(f1139,plain,
( spl0_111
<=> ! [X0,X3,X2,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f93,f166]) ).
fof(f93,axiom,
! [X2,X3,X0,X1] :
( member(X1,unordered_pair(X0,X1))
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_unordered_pair) ).
fof(f1137,plain,
spl0_110,
inference(avatar_split_clause,[],[f219,f1135]) ).
fof(f1135,plain,
( spl0_110
<=> ! [X0,X3,X2,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f219,plain,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f118,f166]) ).
fof(f118,axiom,
! [X2,X3,X0,X1] :
( unordered_pair(X0,X1) != null_class
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom3) ).
fof(f1126,plain,
( spl0_109
| ~ spl0_38
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f630,f569,f458,f1124]) ).
fof(f1124,plain,
( spl0_109
<=> ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f458,plain,
( spl0_38
<=> ! [X4,X0,X1] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f569,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(f630,plain,
( ! [X0] :
( ~ member(X0,identity_relation)
| member(X0,subset_relation) )
| ~ spl0_38
| ~ spl0_57 ),
inference(superposition,[],[f459,f571]) ).
fof(f571,plain,
( identity_relation = intersection(domain_of(flip(cross_product(subset_relation,universal_class))),subset_relation)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f459,plain,
( ! [X0,X1,X4] :
( ~ member(X4,intersection(X0,X1))
| member(X4,X1) )
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f1116,plain,
spl0_108,
inference(avatar_split_clause,[],[f266,f1114]) ).
fof(f266,plain,
! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) ),
inference(forward_demodulation,[],[f231,f183]) ).
fof(f183,plain,
! [X0,X1,X5] : intersection(X5,cross_product(X0,X1)) = intersection(cross_product(X0,X1),X5),
inference(definition_unfolding,[],[f28,f29]) ).
fof(f29,axiom,
! [X0,X1,X5] : restrict(X5,X0,X1) = intersection(cross_product(X0,X1),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',restriction2) ).
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(f231,plain,
! [X0] :
( inductive(X0)
| ~ member(null_class,X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),successor_relation),universal_class)))),X0) ),
inference(definition_unfolding,[],[f49,f164]) ).
fof(f164,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,f163,f29]) ).
fof(f42,axiom,
! [X0,X5] : range_of(restrict(X5,X0,universal_class)) = image(X5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image) ).
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(f1112,plain,
spl0_107,
inference(avatar_split_clause,[],[f264,f1110]) ).
fof(f1110,plain,
( spl0_107
<=> ! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f264,plain,
! [X2] :
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(X2),universal_class)),universal_class))))),universal_class)
| ~ member(X2,universal_class) ),
inference(forward_demodulation,[],[f194,f183]) ).
fof(f194,plain,
! [X2] :
( ~ member(X2,universal_class)
| member(complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X2),universal_class),element_relation),universal_class))))),universal_class) ),
inference(definition_unfolding,[],[f56,f170]) ).
fof(f170,plain,
! [X0] : power_class(X0) = complement(domain_of(domain_of(flip(cross_product(intersection(cross_product(complement(X0),universal_class),element_relation),universal_class))))),
inference(definition_unfolding,[],[f55,f164]) ).
fof(f55,axiom,
! [X0] : complement(image(element_relation,complement(X0))) = power_class(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class_definition) ).
fof(f56,axiom,
! [X2] :
( ~ member(X2,universal_class)
| member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_class2) ).
fof(f1108,plain,
spl0_106,
inference(avatar_split_clause,[],[f230,f1106]) ).
fof(f1106,plain,
( spl0_106
<=> ! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f230,plain,
! [X0,X8] :
( ~ function(X8)
| ~ member(X0,universal_class)
| member(domain_of(domain_of(flip(cross_product(intersection(cross_product(X0,universal_class),X8),universal_class)))),universal_class) ),
inference(definition_unfolding,[],[f65,f164]) ).
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(f1061,plain,
( spl0_105
| ~ spl0_8
| ~ spl0_56 ),
inference(avatar_split_clause,[],[f624,f565,f317,f1059]) ).
fof(f1059,plain,
( spl0_105
<=> ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f317,plain,
( spl0_8
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f565,plain,
( spl0_56
<=> ! [X4,X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f624,plain,
( ! [X0,X1] :
( ~ subclass(X0,null_class)
| subclass(X0,X1) )
| ~ spl0_8
| ~ spl0_56 ),
inference(resolution,[],[f566,f318]) ).
fof(f318,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f317]) ).
fof(f566,plain,
( ! [X0,X1,X4] :
( ~ subclass(X1,X4)
| ~ subclass(X0,X1)
| subclass(X0,X4) )
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f1031,plain,
spl0_104,
inference(avatar_split_clause,[],[f257,f1029]) ).
fof(f1029,plain,
( spl0_104
<=> ! [X4,X0,X1] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f257,plain,
! [X0,X1,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X4) ),
inference(definition_unfolding,[],[f129,f12]) ).
fof(f129,axiom,
! [X0,X1,X4] :
( ~ member(X0,universal_class)
| X0 = X4
| X0 = X1
| singleton(X0) != unordered_pair(X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair3) ).
fof(f1027,plain,
spl0_103,
inference(avatar_split_clause,[],[f242,f1025]) ).
fof(f1025,plain,
( spl0_103
<=> ! [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_103])]) ).
fof(f242,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(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(f1023,plain,
spl0_102,
inference(avatar_split_clause,[],[f232,f1021]) ).
fof(f1021,plain,
( spl0_102
<=> ! [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_102])]) ).
fof(f232,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(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(f1019,plain,
spl0_101,
inference(avatar_split_clause,[],[f208,f1017]) ).
fof(f1017,plain,
( spl0_101
<=> ! [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_101])]) ).
fof(f208,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,f166]) ).
fof(f95,axiom,
! [X2,X3,X0,X1] :
( member(X3,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
fof(f1015,plain,
spl0_100,
inference(avatar_split_clause,[],[f207,f1013]) ).
fof(f1013,plain,
( spl0_100
<=> ! [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_100])]) ).
fof(f207,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,f166]) ).
fof(f94,axiom,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_1_to_cartesian_product) ).
fof(f1011,plain,
spl0_99,
inference(avatar_split_clause,[],[f202,f1009]) ).
fof(f1009,plain,
( spl0_99
<=> ! [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_99])]) ).
fof(f202,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,f166]) ).
fof(f15,axiom,
! [X2,X3,X0,X1] :
( member(X3,X1)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product2) ).
fof(f1007,plain,
spl0_98,
inference(avatar_split_clause,[],[f201,f1005]) ).
fof(f1005,plain,
( spl0_98
<=> ! [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_98])]) ).
fof(f201,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,f166]) ).
fof(f14,axiom,
! [X2,X3,X0,X1] :
( member(X2,X0)
| ~ member(ordered_pair(X2,X3),cross_product(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartesian_product1) ).
fof(f1003,plain,
spl0_97,
inference(avatar_split_clause,[],[f198,f1001]) ).
fof(f1001,plain,
( spl0_97
<=> ! [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_97])]) ).
fof(f198,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/sandbox/benchmark/theBenchmark.p',member_exists2) ).
fof(f988,plain,
spl0_96,
inference(avatar_split_clause,[],[f182,f986]) ).
fof(f986,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(f182,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,f166]) ).
fof(f147,axiom,
! [X0,X1] : member(unordered_pair(X0,singleton(X1)),ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_member_of_ordered_pair) ).
fof(f958,plain,
spl0_95,
inference(avatar_split_clause,[],[f263,f956]) ).
fof(f956,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(f263,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,[],[f187,f183]) ).
fof(f187,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,f164]) ).
fof(f48,axiom,
! [X0] :
( ~ inductive(X0)
| subclass(image(successor_relation,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive2) ).
fof(f954,plain,
spl0_94,
inference(avatar_split_clause,[],[f234,f952]) ).
fof(f952,plain,
( spl0_94
<=> ! [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_94])]) ).
fof(f234,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/sandbox/benchmark/theBenchmark.p',property_of_singletons1) ).
fof(f950,plain,
spl0_93,
inference(avatar_split_clause,[],[f211,f948]) ).
fof(f948,plain,
( spl0_93
<=> ! [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_93])]) ).
fof(f211,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,f163]) ).
fof(f84,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| subclass(range_of(X9),domain_of(domain_of(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible3) ).
fof(f946,plain,
( spl0_92
| ~ spl0_3
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f855,f805,f295,f943]) ).
fof(f943,plain,
( spl0_92
<=> single_valued_class(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f295,plain,
( spl0_3
<=> function(choice) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f805,plain,
( spl0_81
<=> ! [X0] :
( single_valued_class(X0)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f855,plain,
( single_valued_class(choice)
| ~ spl0_3
| ~ spl0_81 ),
inference(resolution,[],[f806,f297]) ).
fof(f297,plain,
( function(choice)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f806,plain,
( ! [X0] :
( ~ function(X0)
| single_valued_class(X0) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f941,plain,
spl0_91,
inference(avatar_split_clause,[],[f200,f939]) ).
fof(f939,plain,
( spl0_91
<=> ! [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_91])]) ).
fof(f200,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,f166]) ).
fof(f19,axiom,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_relation2) ).
fof(f937,plain,
spl0_90,
inference(avatar_split_clause,[],[f172,f935]) ).
fof(f935,plain,
( spl0_90
<=> ! [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_90])]) ).
fof(f172,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(f144,axiom,
! [X0,X1] : unordered_pair(X0,X1) = union(singleton(X0),singleton(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pairs_and_singletons) ).
fof(f864,plain,
spl0_89,
inference(avatar_split_clause,[],[f245,f862]) ).
fof(f862,plain,
( spl0_89
<=> ! [X0,X1] :
( null_class = X0
| ~ subclass(X0,unordered_pair(X1,X1))
| unordered_pair(X1,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f245,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/sandbox/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
fof(f860,plain,
spl0_88,
inference(avatar_split_clause,[],[f236,f858]) ).
fof(f858,plain,
( spl0_88
<=> ! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f236,plain,
! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| unordered_pair(X0,X0) != unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f127,f12,f12]) ).
fof(f127,axiom,
! [X0,X1] :
( ~ member(X0,universal_class)
| X0 = X1
| singleton(X0) != singleton(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
fof(f854,plain,
spl0_87,
inference(avatar_split_clause,[],[f210,f852]) ).
fof(f852,plain,
( spl0_87
<=> ! [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_87])]) ).
fof(f210,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/sandbox/benchmark/theBenchmark.p',domain1) ).
fof(f850,plain,
spl0_86,
inference(avatar_split_clause,[],[f101,f848]) ).
fof(f848,plain,
( spl0_86
<=> ! [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_86])]) ).
fof(f101,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality4) ).
fof(f846,plain,
spl0_85,
inference(avatar_split_clause,[],[f100,f844]) ).
fof(f844,plain,
( spl0_85
<=> ! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| member(not_subclass_element(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f100,axiom,
! [X0,X1] :
( X0 = X1
| ~ member(not_subclass_element(X1,X0),X0)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality3) ).
fof(f842,plain,
spl0_84,
inference(avatar_split_clause,[],[f98,f840]) ).
fof(f840,plain,
( spl0_84
<=> ! [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_84])]) ).
fof(f98,axiom,
! [X0,X1] :
( X0 = X1
| member(not_subclass_element(X1,X0),X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
fof(f836,plain,
spl0_83,
inference(avatar_split_clause,[],[f188,f834]) ).
fof(f834,plain,
( spl0_83
<=> ! [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_83])]) ).
fof(f188,plain,
! [X8] :
( ~ operation(X8)
| subclass(domain_of(domain_of(flip(cross_product(X8,universal_class)))),domain_of(domain_of(X8))) ),
inference(definition_unfolding,[],[f80,f163]) ).
fof(f80,axiom,
! [X8] :
( ~ operation(X8)
| subclass(range_of(X8),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation3) ).
fof(f832,plain,
spl0_82,
inference(avatar_split_clause,[],[f79,f830]) ).
fof(f830,plain,
( spl0_82
<=> ! [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_82])]) ).
fof(f79,axiom,
! [X8] :
( ~ operation(X8)
| domain_of(X8) = cross_product(domain_of(domain_of(X8)),domain_of(domain_of(X8))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation2) ).
fof(f807,plain,
( spl0_81
| ~ spl0_75
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f785,f719,f715,f805]) ).
fof(f715,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(f719,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(f785,plain,
( ! [X0] :
( single_valued_class(X0)
| ~ function(X0) )
| ~ spl0_75
| ~ spl0_76 ),
inference(resolution,[],[f720,f716]) ).
fof(f716,plain,
( ! [X8] :
( subclass(compose(X8,domain_of(flip(cross_product(X8,universal_class)))),identity_relation)
| ~ function(X8) )
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f715]) ).
fof(f720,plain,
( ! [X0] :
( ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| single_valued_class(X0) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f737,plain,
spl0_80,
inference(avatar_split_clause,[],[f265,f735]) ).
fof(f735,plain,
( spl0_80
<=> ! [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_80])]) ).
fof(f265,plain,
! [X0] :
( member(domain_of(intersection(element_relation,cross_product(universal_class,X0))),universal_class)
| ~ member(X0,universal_class) ),
inference(forward_demodulation,[],[f195,f183]) ).
fof(f195,plain,
! [X0] :
( ~ member(X0,universal_class)
| member(domain_of(intersection(cross_product(universal_class,X0),element_relation)),universal_class) ),
inference(definition_unfolding,[],[f54,f162]) ).
fof(f162,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/sandbox/benchmark/theBenchmark.p',sum_class_definition) ).
fof(f54,axiom,
! [X0] :
( ~ member(X0,universal_class)
| member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_class2) ).
fof(f733,plain,
( spl0_79
| ~ spl0_4
| ~ spl0_54 ),
inference(avatar_split_clause,[],[f602,f557,f300,f731]) ).
fof(f731,plain,
( spl0_79
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f557,plain,
( spl0_54
<=> ! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f602,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| universal_class = X0 )
| ~ spl0_4
| ~ spl0_54 ),
inference(resolution,[],[f558,f301]) ).
fof(f558,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 )
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f729,plain,
spl0_78,
inference(avatar_split_clause,[],[f216,f727]) ).
fof(f727,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(f216,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/sandbox/benchmark/theBenchmark.p',member_exists4) ).
fof(f725,plain,
spl0_77,
inference(avatar_split_clause,[],[f215,f723]) ).
fof(f723,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(f215,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/sandbox/benchmark/theBenchmark.p',member_of_non_singleton_unique2) ).
fof(f721,plain,
spl0_76,
inference(avatar_split_clause,[],[f190,f719]) ).
fof(f190,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/sandbox/benchmark/theBenchmark.p',single_valued_class2) ).
fof(f717,plain,
spl0_75,
inference(avatar_split_clause,[],[f189,f715]) ).
fof(f189,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/sandbox/benchmark/theBenchmark.p',function2) ).
fof(f713,plain,
spl0_74,
inference(avatar_split_clause,[],[f185,f711]) ).
fof(f711,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(f185,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/sandbox/benchmark/theBenchmark.p',single_valued_class1) ).
fof(f709,plain,
spl0_73,
inference(avatar_split_clause,[],[f183,f707]) ).
fof(f707,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(f705,plain,
spl0_72,
inference(avatar_split_clause,[],[f119,f703]) ).
fof(f703,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/sandbox/benchmark/theBenchmark.p',unordered_pair_is_subset) ).
fof(f701,plain,
spl0_71,
inference(avatar_split_clause,[],[f113,f699]) ).
fof(f699,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/sandbox/benchmark/theBenchmark.p',null_unordered_pair) ).
fof(f697,plain,
spl0_70,
inference(avatar_split_clause,[],[f23,f695]) ).
fof(f695,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/sandbox/benchmark/theBenchmark.p',intersection3) ).
fof(f693,plain,
spl0_69,
inference(avatar_split_clause,[],[f8,f691]) ).
fof(f691,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/sandbox/benchmark/theBenchmark.p',unordered_pair_member) ).
fof(f689,plain,
( spl0_68
| ~ spl0_5
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f592,f553,f304,f687]) ).
fof(f687,plain,
( spl0_68
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f304,plain,
( spl0_5
<=> member(omega,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f553,plain,
( spl0_53
<=> ! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f592,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(omega,X0) )
| ~ spl0_5
| ~ spl0_53 ),
inference(resolution,[],[f554,f306]) ).
fof(f306,plain,
( member(omega,universal_class)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f554,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X0)
| ~ subclass(X0,X1)
| member(X2,X1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f553]) ).
fof(f675,plain,
spl0_67,
inference(avatar_split_clause,[],[f229,f673]) ).
fof(f673,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(f229,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/sandbox/benchmark/theBenchmark.p',one_to_one3) ).
fof(f671,plain,
spl0_66,
inference(avatar_split_clause,[],[f206,f669]) ).
fof(f669,plain,
( spl0_66
<=> ! [X0,X1] :
( member(X1,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f206,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/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
fof(f667,plain,
spl0_65,
inference(avatar_split_clause,[],[f205,f665]) ).
fof(f665,plain,
( spl0_65
<=> ! [X0,X1] :
( member(X0,universal_class)
| unordered_pair(X0,X1) = unordered_pair(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f205,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/sandbox/benchmark/theBenchmark.p',unordered_pair_equals_singleton2) ).
fof(f663,plain,
spl0_64,
inference(avatar_split_clause,[],[f204,f661]) ).
fof(f661,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(f204,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/sandbox/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
fof(f659,plain,
( spl0_63
| ~ spl0_9
| ~ spl0_53 ),
inference(avatar_split_clause,[],[f591,f553,f321,f657]) ).
fof(f657,plain,
( spl0_63
<=> ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f591,plain,
( ! [X0] :
( ~ subclass(universal_class,X0)
| member(null_class,X0) )
| ~ spl0_9
| ~ spl0_53 ),
inference(resolution,[],[f554,f323]) ).
fof(f323,plain,
( member(null_class,universal_class)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f655,plain,
spl0_62,
inference(avatar_split_clause,[],[f83,f653]) ).
fof(f653,plain,
( spl0_62
<=> ! [X9,X11,X10] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f83,axiom,
! [X10,X11,X9] :
( ~ compatible(X9,X10,X11)
| domain_of(domain_of(X10)) = domain_of(X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compatible2) ).
fof(f651,plain,
spl0_61,
inference(avatar_split_clause,[],[f25,f649]) ).
fof(f649,plain,
( spl0_61
<=> ! [X4,X0] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f25,axiom,
! [X0,X4] :
( ~ member(X4,universal_class)
| member(X4,X0)
| member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
fof(f584,plain,
spl0_60,
inference(avatar_split_clause,[],[f197,f582]) ).
fof(f582,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(f197,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/sandbox/benchmark/theBenchmark.p',member_exists1) ).
fof(f580,plain,
spl0_59,
inference(avatar_split_clause,[],[f196,f578]) ).
fof(f578,plain,
( spl0_59
<=> ! [X2] :
( ~ member(X2,universal_class)
| member_of(unordered_pair(X2,X2)) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f196,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/sandbox/benchmark/theBenchmark.p',member_of_singleton_is_unique) ).
fof(f576,plain,
spl0_58,
inference(avatar_split_clause,[],[f181,f574]) ).
fof(f574,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(f181,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/sandbox/benchmark/theBenchmark.p',corollary_1_to_singletons_are_sets) ).
fof(f572,plain,
spl0_57,
inference(avatar_split_clause,[],[f177,f569]) ).
fof(f177,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/sandbox/benchmark/theBenchmark.p',identity_relation) ).
fof(f567,plain,
spl0_56,
inference(avatar_split_clause,[],[f97,f565]) ).
fof(f97,axiom,
! [X0,X1,X4] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X4)
| subclass(X0,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_subclass) ).
fof(f563,plain,
spl0_55,
inference(avatar_split_clause,[],[f67,f561]) ).
fof(f561,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/sandbox/benchmark/theBenchmark.p',regularity2) ).
fof(f559,plain,
spl0_54,
inference(avatar_split_clause,[],[f7,f557]) ).
fof(f7,axiom,
! [X0,X1] :
( ~ subclass(X0,X1)
| ~ subclass(X1,X0)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_implies_equal) ).
fof(f555,plain,
spl0_53,
inference(avatar_split_clause,[],[f1,f553]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ subclass(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subclass_members) ).
fof(f532,plain,
( spl0_52
| ~ spl0_23
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f429,f408,f384,f530]) ).
fof(f530,plain,
( spl0_52
<=> ! [X0] : null_class = intersection(complement(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f384,plain,
( spl0_23
<=> ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f408,plain,
( spl0_28
<=> ! [X0] :
( null_class = X0
| member(regular(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f429,plain,
( ! [X0] : null_class = intersection(complement(X0),X0)
| ~ spl0_23
| ~ spl0_28 ),
inference(resolution,[],[f409,f385]) ).
fof(f385,plain,
( ! [X0,X1] : ~ member(X1,intersection(complement(X0),X0))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f409,plain,
( ! [X0] :
( member(regular(X0),X0)
| null_class = X0 )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f512,plain,
spl0_51,
inference(avatar_split_clause,[],[f203,f510]) ).
fof(f510,plain,
( spl0_51
<=> ! [X0] :
( member(X0,universal_class)
| unordered_pair(X0,X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f203,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/sandbox/benchmark/theBenchmark.p',singleton_is_null_class) ).
fof(f508,plain,
spl0_50,
inference(avatar_split_clause,[],[f199,f506]) ).
fof(f506,plain,
( spl0_50
<=> ! [X0,X1] :
( X0 = X1
| ~ member(X1,unordered_pair(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f199,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/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
fof(f504,plain,
spl0_49,
inference(avatar_split_clause,[],[f191,f502]) ).
fof(f502,plain,
( spl0_49
<=> ! [X0,X1] :
( ~ member(X0,X1)
| subclass(unordered_pair(X0,X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f191,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/sandbox/benchmark/theBenchmark.p',property_of_singletons2) ).
fof(f500,plain,
spl0_48,
inference(avatar_split_clause,[],[f186,f498]) ).
fof(f498,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(f186,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/sandbox/benchmark/theBenchmark.p',one_to_one2) ).
fof(f496,plain,
( spl0_47
| ~ spl0_16
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f423,f396,f353,f494]) ).
fof(f494,plain,
( spl0_47
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f353,plain,
( spl0_16
<=> ! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f396,plain,
( spl0_25
<=> ! [X4,X0] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f423,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl0_16
| ~ spl0_25 ),
inference(resolution,[],[f397,f354]) ).
fof(f354,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f397,plain,
( ! [X0,X4] :
( ~ member(X4,complement(X0))
| ~ member(X4,X0) )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f396]) ).
fof(f492,plain,
spl0_46,
inference(avatar_split_clause,[],[f135,f490]) ).
fof(f490,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/sandbox/benchmark/theBenchmark.p',member_of_non_singleton_unique1) ).
fof(f488,plain,
spl0_45,
inference(avatar_split_clause,[],[f132,f486]) ).
fof(f486,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/sandbox/benchmark/theBenchmark.p',member_exists3) ).
fof(f484,plain,
spl0_44,
inference(avatar_split_clause,[],[f117,f482]) ).
fof(f482,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/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom2) ).
fof(f480,plain,
spl0_43,
inference(avatar_split_clause,[],[f116,f478]) ).
fof(f478,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/sandbox/benchmark/theBenchmark.p',corollary_to_unordered_pair_axiom1) ).
fof(f476,plain,
spl0_42,
inference(avatar_split_clause,[],[f106,f474]) ).
fof(f474,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/sandbox/benchmark/theBenchmark.p',null_class_is_unique) ).
fof(f472,plain,
spl0_41,
inference(avatar_split_clause,[],[f88,f470]) ).
fof(f470,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/sandbox/benchmark/theBenchmark.p',homomorphism3) ).
fof(f468,plain,
spl0_40,
inference(avatar_split_clause,[],[f35,f466]) ).
fof(f466,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/sandbox/benchmark/theBenchmark.p',flip1) ).
fof(f464,plain,
spl0_39,
inference(avatar_split_clause,[],[f32,f462]) ).
fof(f462,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/sandbox/benchmark/theBenchmark.p',rotate1) ).
fof(f460,plain,
spl0_38,
inference(avatar_split_clause,[],[f22,f458]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,X1)
| ~ member(X4,intersection(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
fof(f456,plain,
spl0_37,
inference(avatar_split_clause,[],[f21,f454]) ).
fof(f454,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/sandbox/benchmark/theBenchmark.p',intersection1) ).
fof(f452,plain,
spl0_36,
inference(avatar_split_clause,[],[f10,f450]) ).
fof(f450,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/sandbox/benchmark/theBenchmark.p',unordered_pair3) ).
fof(f448,plain,
spl0_35,
inference(avatar_split_clause,[],[f9,f446]) ).
fof(f446,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/sandbox/benchmark/theBenchmark.p',unordered_pair2) ).
fof(f444,plain,
spl0_34,
inference(avatar_split_clause,[],[f3,f442]) ).
fof(f442,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/sandbox/benchmark/theBenchmark.p',not_subclass_members2) ).
fof(f440,plain,
spl0_33,
inference(avatar_split_clause,[],[f2,f438]) ).
fof(f438,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/sandbox/benchmark/theBenchmark.p',not_subclass_members1) ).
fof(f427,plain,
( spl0_32
| ~ spl0_16
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f391,f384,f353,f425]) ).
fof(f425,plain,
( spl0_32
<=> ! [X0] : ~ inductive(intersection(complement(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f391,plain,
( ! [X0] : ~ inductive(intersection(complement(X0),X0))
| ~ spl0_16
| ~ spl0_23 ),
inference(resolution,[],[f385,f354]) ).
fof(f422,plain,
spl0_31,
inference(avatar_split_clause,[],[f179,f420]) ).
fof(f420,plain,
( spl0_31
<=> ! [X0,X1] : subclass(unordered_pair(X0,X0),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f179,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/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair1) ).
fof(f418,plain,
spl0_30,
inference(avatar_split_clause,[],[f178,f416]) ).
fof(f416,plain,
( spl0_30
<=> ! [X0,X1] : subclass(unordered_pair(X1,X1),unordered_pair(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f178,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/sandbox/benchmark/theBenchmark.p',singleton_in_unordered_pair2) ).
fof(f414,plain,
spl0_29,
inference(avatar_split_clause,[],[f108,f412]) ).
fof(f412,plain,
( spl0_29
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f108,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
fof(f410,plain,
spl0_28,
inference(avatar_split_clause,[],[f66,f408]) ).
fof(f66,axiom,
! [X0] :
( null_class = X0
| member(regular(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',regularity1) ).
fof(f406,plain,
spl0_27,
inference(avatar_split_clause,[],[f62,f404]) ).
fof(f404,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/sandbox/benchmark/theBenchmark.p',function1) ).
fof(f402,plain,
spl0_26,
inference(avatar_split_clause,[],[f57,f400]) ).
fof(f400,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/sandbox/benchmark/theBenchmark.p',compose1) ).
fof(f398,plain,
spl0_25,
inference(avatar_split_clause,[],[f24,f396]) ).
fof(f24,axiom,
! [X0,X4] :
( ~ member(X4,X0)
| ~ member(X4,complement(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
fof(f390,plain,
spl0_24,
inference(avatar_split_clause,[],[f105,f388]) ).
fof(f388,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/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(f386,plain,
spl0_23,
inference(avatar_split_clause,[],[f102,f384]) ).
fof(f102,axiom,
! [X0,X1] : ~ member(X1,intersection(complement(X0),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',special_classes_lemma) ).
fof(f382,plain,
spl0_22,
inference(avatar_split_clause,[],[f87,f380]) ).
fof(f380,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/sandbox/benchmark/theBenchmark.p',homomorphism2) ).
fof(f378,plain,
spl0_21,
inference(avatar_split_clause,[],[f86,f376]) ).
fof(f376,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/sandbox/benchmark/theBenchmark.p',homomorphism1) ).
fof(f374,plain,
spl0_20,
inference(avatar_split_clause,[],[f82,f372]) ).
fof(f372,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/sandbox/benchmark/theBenchmark.p',compatible1) ).
fof(f370,plain,
( ~ spl0_19
| ~ spl0_7
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f365,f353,f313,f367]) ).
fof(f367,plain,
( spl0_19
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f313,plain,
( spl0_7
<=> ! [X4] : ~ member(X4,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f365,plain,
( ~ inductive(null_class)
| ~ spl0_7
| ~ spl0_16 ),
inference(resolution,[],[f354,f314]) ).
fof(f314,plain,
( ! [X4] : ~ member(X4,null_class)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f364,plain,
spl0_18,
inference(avatar_split_clause,[],[f174,f361]) ).
fof(f361,plain,
( spl0_18
<=> member(null_class,unordered_pair(null_class,null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f174,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/sandbox/benchmark/theBenchmark.p',null_class_in_its_singleton) ).
fof(f359,plain,
spl0_17,
inference(avatar_split_clause,[],[f51,f357]) ).
fof(f357,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/sandbox/benchmark/theBenchmark.p',omega_is_inductive2) ).
fof(f355,plain,
spl0_16,
inference(avatar_split_clause,[],[f47,f353]) ).
fof(f47,axiom,
! [X0] :
( ~ inductive(X0)
| member(null_class,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inductive1) ).
fof(f351,plain,
spl0_15,
inference(avatar_split_clause,[],[f44,f348]) ).
fof(f348,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/sandbox/benchmark/theBenchmark.p',successor_relation1) ).
fof(f346,plain,
spl0_14,
inference(avatar_split_clause,[],[f18,f343]) ).
fof(f343,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/sandbox/benchmark/theBenchmark.p',element_relation1) ).
fof(f341,plain,
spl0_13,
inference(avatar_split_clause,[],[f11,f339]) ).
fof(f339,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/sandbox/benchmark/theBenchmark.p',unordered_pairs_in_universal) ).
fof(f337,plain,
spl0_12,
inference(avatar_split_clause,[],[f78,f335]) ).
fof(f335,plain,
( spl0_12
<=> ! [X8] :
( ~ operation(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f78,axiom,
! [X8] :
( ~ operation(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',operation1) ).
fof(f333,plain,
spl0_11,
inference(avatar_split_clause,[],[f71,f331]) ).
fof(f331,plain,
( spl0_11
<=> ! [X8] :
( ~ one_to_one(X8)
| function(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f71,axiom,
! [X8] :
( ~ one_to_one(X8)
| function(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_to_one1) ).
fof(f329,plain,
~ spl0_10,
inference(avatar_split_clause,[],[f173,f326]) ).
fof(f173,plain,
x != unordered_pair(unordered_pair(first(x),first(x)),unordered_pair(first(x),unordered_pair(second(x),second(x)))),
inference(definition_unfolding,[],[f160,f166]) ).
fof(f160,axiom,
x != ordered_pair(first(x),second(x)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets4_1) ).
fof(f324,plain,
spl0_9,
inference(avatar_split_clause,[],[f107,f321]) ).
fof(f107,axiom,
member(null_class,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).
fof(f319,plain,
spl0_8,
inference(avatar_split_clause,[],[f104,f317]) ).
fof(f104,axiom,
! [X0] : subclass(null_class,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_subclass) ).
fof(f315,plain,
spl0_7,
inference(avatar_split_clause,[],[f103,f313]) ).
fof(f103,axiom,
! [X4] : ~ member(X4,null_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_null_class) ).
fof(f311,plain,
spl0_6,
inference(avatar_split_clause,[],[f96,f309]) ).
fof(f309,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/sandbox/benchmark/theBenchmark.p',subclass_is_reflexive) ).
fof(f307,plain,
spl0_5,
inference(avatar_split_clause,[],[f52,f304]) ).
fof(f52,axiom,
member(omega,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_in_universal) ).
fof(f302,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f300]) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f298,plain,
spl0_3,
inference(avatar_split_clause,[],[f69,f295]) ).
fof(f69,axiom,
function(choice),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',choice1) ).
fof(f293,plain,
spl0_2,
inference(avatar_split_clause,[],[f50,f290]) ).
fof(f290,plain,
( spl0_2
<=> inductive(omega) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f50,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega_is_inductive1) ).
fof(f288,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f161,f285]) ).
fof(f161,axiom,
x != second(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_unique_2nd_in_pair_of_non_sets) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SET116-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.08/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.31 % Computer : n025.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Apr 30 01:43:41 EDT 2024
% 0.17/0.31 % CPUTime :
% 0.17/0.31 % (12115)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.33 % (12118)WARNING: value z3 for option sas not known
% 0.17/0.33 % (12118)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)
% 0.17/0.33 % (12117)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.33 % (12119)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.33 % (12120)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)
% 0.17/0.33 % (12122)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)
% 0.17/0.34 % (12116)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.34 % (12121)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)
% 0.17/0.37 TRYING [1]
% 0.17/0.37 TRYING [2]
% 0.17/0.37 % (12120)First to succeed.
% 0.17/0.38 % (12120)Refutation found. Thanks to Tanya!
% 0.17/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.38 % (12120)------------------------------
% 0.17/0.38 % (12120)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.17/0.38 % (12120)Termination reason: Refutation
% 0.17/0.38
% 0.17/0.38 % (12120)Memory used [KB]: 1579
% 0.17/0.38 % (12120)Time elapsed: 0.045 s
% 0.17/0.38 % (12120)Instructions burned: 86 (million)
% 0.17/0.38 % (12120)------------------------------
% 0.17/0.38 % (12120)------------------------------
% 0.17/0.38 % (12115)Success in time 0.065 s
%------------------------------------------------------------------------------