TSTP Solution File: SET094+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET094+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:16:03 EDT 2024
% Result : Theorem 0.21s 0.43s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 158
% Syntax : Number of formulae : 531 ( 137 unt; 0 def)
% Number of atoms : 1411 ( 178 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1425 ( 545 ~; 550 |; 166 &)
% ( 136 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 110 ( 108 usr; 104 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 813 ( 782 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1074,plain,
$false,
inference(avatar_sat_refutation,[],[f289,f294,f299,f304,f309,f313,f317,f322,f326,f331,f336,f340,f344,f348,f354,f358,f362,f366,f370,f374,f379,f383,f387,f391,f395,f399,f403,f407,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f467,f471,f490,f503,f507,f511,f515,f519,f523,f527,f570,f574,f578,f616,f620,f624,f628,f632,f656,f668,f674,f678,f682,f686,f690,f694,f721,f725,f729,f733,f742,f746,f750,f785,f789,f793,f811,f815,f819,f858,f862,f879,f883,f913,f925,f929,f937,f949,f953,f969,f973,f989,f993,f1011,f1018,f1022,f1026,f1047,f1050,f1052,f1057,f1062,f1066,f1071,f1073]) ).
fof(f1073,plain,
( spl8_2
| ~ spl8_1
| ~ spl8_96 ),
inference(avatar_split_clause,[],[f1032,f1020,f286,f291]) ).
fof(f291,plain,
( spl8_2
<=> sK1 = member_of(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_2])]) ).
fof(f286,plain,
( spl8_1
<=> member(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_1])]) ).
fof(f1020,plain,
( spl8_96
<=> ! [X0] :
( ~ member(X0,sK0)
| member_of(sK0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_96])]) ).
fof(f1032,plain,
( sK1 = member_of(sK0)
| ~ spl8_1
| ~ spl8_96 ),
inference(resolution,[],[f1021,f288]) ).
fof(f288,plain,
( member(sK1,sK0)
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f1021,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member_of(sK0) = X0 )
| ~ spl8_96 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1071,plain,
( ~ spl8_98
| spl8_103
| ~ spl8_3
| ~ spl8_65 ),
inference(avatar_split_clause,[],[f716,f692,f296,f1068,f1040]) ).
fof(f1040,plain,
( spl8_98
<=> member(member_of(sK0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_98])]) ).
fof(f1068,plain,
( spl8_103
<=> member(unordered_pair(sK0,unordered_pair(member_of(sK0),sK0)),identity_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_103])]) ).
fof(f296,plain,
( spl8_3
<=> sK0 = unordered_pair(member_of(sK0),member_of(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_3])]) ).
fof(f692,plain,
( spl8_65
<=> ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_65])]) ).
fof(f716,plain,
( member(unordered_pair(sK0,unordered_pair(member_of(sK0),sK0)),identity_relation)
| ~ member(member_of(sK0),universal_class)
| ~ spl8_3
| ~ spl8_65 ),
inference(superposition,[],[f693,f298]) ).
fof(f298,plain,
( sK0 = unordered_pair(member_of(sK0),member_of(sK0))
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f296]) ).
fof(f693,plain,
( ! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) )
| ~ spl8_65 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f1066,plain,
( spl8_102
| ~ spl8_3
| ~ spl8_64 ),
inference(avatar_split_clause,[],[f712,f688,f296,f1064]) ).
fof(f1064,plain,
( spl8_102
<=> ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK0)),successor_relation)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_102])]) ).
fof(f688,plain,
( spl8_64
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_64])]) ).
fof(f712,plain,
( ! [X0] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,sK0)),successor_relation)
| member(X0,universal_class) )
| ~ spl8_3
| ~ spl8_64 ),
inference(superposition,[],[f689,f298]) ).
fof(f689,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| member(X0,universal_class) )
| ~ spl8_64 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1062,plain,
( spl8_101
| ~ spl8_1
| ~ spl8_96
| ~ spl8_100 ),
inference(avatar_split_clause,[],[f1058,f1055,f1020,f286,f1060]) ).
fof(f1060,plain,
( spl8_101
<=> ! [X0] :
( ~ member(sK1,domain_of(X0))
| null_class != intersection(X0,cross_product(sK0,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_101])]) ).
fof(f1055,plain,
( spl8_100
<=> ! [X0] :
( null_class != intersection(X0,cross_product(sK0,universal_class))
| ~ member(member_of(sK0),domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_100])]) ).
fof(f1058,plain,
( ! [X0] :
( ~ member(sK1,domain_of(X0))
| null_class != intersection(X0,cross_product(sK0,universal_class)) )
| ~ spl8_1
| ~ spl8_96
| ~ spl8_100 ),
inference(forward_demodulation,[],[f1056,f1032]) ).
fof(f1056,plain,
( ! [X0] :
( null_class != intersection(X0,cross_product(sK0,universal_class))
| ~ member(member_of(sK0),domain_of(X0)) )
| ~ spl8_100 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f1057,plain,
( spl8_100
| ~ spl8_3
| ~ spl8_59 ),
inference(avatar_split_clause,[],[f669,f666,f296,f1055]) ).
fof(f666,plain,
( spl8_59
<=> ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_59])]) ).
fof(f669,plain,
( ! [X0] :
( null_class != intersection(X0,cross_product(sK0,universal_class))
| ~ member(member_of(sK0),domain_of(X0)) )
| ~ spl8_3
| ~ spl8_59 ),
inference(superposition,[],[f667,f298]) ).
fof(f667,plain,
( ! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) )
| ~ spl8_59 ),
inference(avatar_component_clause,[],[f666]) ).
fof(f1052,plain,
( ~ spl8_58
| ~ spl8_1
| ~ spl8_96
| spl8_98 ),
inference(avatar_split_clause,[],[f1049,f1040,f1020,f286,f653]) ).
fof(f653,plain,
( spl8_58
<=> member(sK1,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_58])]) ).
fof(f1049,plain,
( ~ member(sK1,universal_class)
| ~ spl8_1
| ~ spl8_96
| spl8_98 ),
inference(forward_demodulation,[],[f1042,f1032]) ).
fof(f1042,plain,
( ~ member(member_of(sK0),universal_class)
| spl8_98 ),
inference(avatar_component_clause,[],[f1040]) ).
fof(f1050,plain,
( ~ spl8_1
| ~ spl8_1
| ~ spl8_96
| spl8_99 ),
inference(avatar_split_clause,[],[f1048,f1044,f1020,f286,f286]) ).
fof(f1044,plain,
( spl8_99
<=> member(member_of(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_99])]) ).
fof(f1048,plain,
( ~ member(sK1,sK0)
| ~ spl8_1
| ~ spl8_96
| spl8_99 ),
inference(forward_demodulation,[],[f1045,f1032]) ).
fof(f1045,plain,
( ~ member(member_of(sK0),sK0)
| spl8_99 ),
inference(avatar_component_clause,[],[f1044]) ).
fof(f1047,plain,
( ~ spl8_98
| spl8_99
| ~ spl8_3
| ~ spl8_40 ),
inference(avatar_split_clause,[],[f497,f465,f296,f1044,f1040]) ).
fof(f465,plain,
( spl8_40
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_40])]) ).
fof(f497,plain,
( member(member_of(sK0),sK0)
| ~ member(member_of(sK0),universal_class)
| ~ spl8_3
| ~ spl8_40 ),
inference(superposition,[],[f466,f298]) ).
fof(f466,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl8_40 ),
inference(avatar_component_clause,[],[f465]) ).
fof(f1026,plain,
( spl8_97
| ~ spl8_21
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f547,f509,f376,f1024]) ).
fof(f1024,plain,
( spl8_97
<=> ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_97])]) ).
fof(f376,plain,
( spl8_21
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_21])]) ).
fof(f509,plain,
( spl8_45
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_45])]) ).
fof(f547,plain,
( ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) )
| ~ spl8_21
| ~ spl8_45 ),
inference(resolution,[],[f510,f378]) ).
fof(f378,plain,
( member(sK0,universal_class)
| ~ spl8_21 ),
inference(avatar_component_clause,[],[f376]) ).
fof(f510,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl8_45 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f1022,plain,
( spl8_96
| ~ spl8_3
| ~ spl8_55 ),
inference(avatar_split_clause,[],[f651,f622,f296,f1020]) ).
fof(f622,plain,
( spl8_55
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_55])]) ).
fof(f651,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member_of(sK0) = X0 )
| ~ spl8_3
| ~ spl8_55 ),
inference(duplicate_literal_removal,[],[f650]) ).
fof(f650,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member_of(sK0) = X0
| member_of(sK0) = X0 )
| ~ spl8_3
| ~ spl8_55 ),
inference(superposition,[],[f623,f298]) ).
fof(f623,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl8_55 ),
inference(avatar_component_clause,[],[f622]) ).
fof(f1018,plain,
( spl8_95
| ~ spl8_1
| ~ spl8_52 ),
inference(avatar_split_clause,[],[f606,f576,f286,f1016]) ).
fof(f1016,plain,
( spl8_95
<=> ! [X0] :
( member(X0,sum_class(sK0))
| ~ member(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_95])]) ).
fof(f576,plain,
( spl8_52
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_52])]) ).
fof(f606,plain,
( ! [X0] :
( member(X0,sum_class(sK0))
| ~ member(X0,sK1) )
| ~ spl8_1
| ~ spl8_52 ),
inference(resolution,[],[f577,f288]) ).
fof(f577,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum_class(X1))
| ~ member(X0,X2) )
| ~ spl8_52 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f1011,plain,
( spl8_94
| ~ spl8_1
| ~ spl8_45 ),
inference(avatar_split_clause,[],[f548,f509,f286,f1009]) ).
fof(f1009,plain,
( spl8_94
<=> ! [X0] :
( member(sK1,X0)
| ~ subclass(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_94])]) ).
fof(f548,plain,
( ! [X0] :
( member(sK1,X0)
| ~ subclass(sK0,X0) )
| ~ spl8_1
| ~ spl8_45 ),
inference(resolution,[],[f510,f288]) ).
fof(f993,plain,
spl8_93,
inference(avatar_split_clause,[],[f275,f991]) ).
fof(f991,plain,
( spl8_93
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_93])]) ).
fof(f275,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f232,f241,f241,f241,f241,f241,f241]) ).
fof(f241,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f179,f152,f152]) ).
fof(f152,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_set_defn) ).
fof(f179,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_defn) ).
fof(f232,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f139,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(flattening,[],[f138]) ).
fof(f138,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
| ~ member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ) ),
inference(nnf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3))
<=> ( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
& member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X2,X3,X6,X0] :
( member(ordered_pair(ordered_pair(X2,X3),X6),flip(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X2),X6),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip_defn) ).
fof(f989,plain,
spl8_92,
inference(avatar_split_clause,[],[f272,f987]) ).
fof(f987,plain,
( spl8_92
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_92])]) ).
fof(f272,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(definition_unfolding,[],[f229,f241,f241,f241,f241,f241,f241]) ).
fof(f229,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(flattening,[],[f136]) ).
fof(f136,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
| ~ member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
& ( ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
& member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X0,X2,X3,X6] :
( member(ordered_pair(ordered_pair(X2,X3),X6),rotate(X0))
<=> ( member(ordered_pair(ordered_pair(X3,X6),X2),X0)
& member(ordered_pair(ordered_pair(X2,X3),X6),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate_defn) ).
fof(f973,plain,
spl8_91,
inference(avatar_split_clause,[],[f277,f971]) ).
fof(f971,plain,
( spl8_91
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_91])]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f230,f241,f241,f241,f241]) ).
fof(f230,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X0,X1),X2),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f969,plain,
spl8_90,
inference(avatar_split_clause,[],[f274,f967]) ).
fof(f967,plain,
( spl8_90
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_90])]) ).
fof(f274,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f227,f241,f241,f241,f241]) ).
fof(f227,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X2),X3),cross_product(cross_product(universal_class,universal_class),universal_class))
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f953,plain,
spl8_89,
inference(avatar_split_clause,[],[f276,f951]) ).
fof(f951,plain,
( spl8_89
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_89])]) ).
fof(f276,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X0,X0))),unordered_pair(X2,X2))),X3)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))),unordered_pair(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),unordered_pair(X2,X2))),flip(X3)) ),
inference(definition_unfolding,[],[f231,f241,f241,f241,f241]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X1,X0),X2),X3)
| ~ member(ordered_pair(ordered_pair(X0,X1),X2),flip(X3)) ),
inference(cnf_transformation,[],[f139]) ).
fof(f949,plain,
spl8_88,
inference(avatar_split_clause,[],[f273,f947]) ).
fof(f947,plain,
( spl8_88
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_88])]) ).
fof(f273,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3)))),unordered_pair(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),unordered_pair(X1,X1))),X0)
| ~ member(unordered_pair(unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),unordered_pair(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),unordered_pair(X3,X3))),rotate(X0)) ),
inference(definition_unfolding,[],[f228,f241,f241,f241,f241]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(ordered_pair(X2,X3),X1),X0)
| ~ member(ordered_pair(ordered_pair(X1,X2),X3),rotate(X0)) ),
inference(cnf_transformation,[],[f137]) ).
fof(f937,plain,
spl8_87,
inference(avatar_split_clause,[],[f266,f935]) ).
fof(f935,plain,
( spl8_87
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_87])]) ).
fof(f266,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0))
| ~ member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(X2,universal_class) ),
inference(definition_unfolding,[],[f223,f241,f240,f240,f152]) ).
fof(f240,plain,
! [X0,X1] : image(X1,X0) = domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),
inference(definition_unfolding,[],[f178,f239,f209]) ).
fof(f209,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X5,X1] : restrict(X5,X0,X1) = intersection(X5,cross_product(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',restrict_defn) ).
fof(f239,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f151,f154]) ).
fof(f154,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X1] : inverse(X1) = domain_of(flip(cross_product(X1,universal_class))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_defn) ).
fof(f151,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X4] : range_of(X4) = domain_of(inverse(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',range_of_defn) ).
fof(f178,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X0,X5] : image(X5,X0) = range_of(restrict(X5,X0,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',image_defn) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X2,X3),compose(X1,X0))
| ~ member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(X2,universal_class) )
& ( ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) )
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ) ),
inference(nnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X2,X3),compose(X1,X0))
<=> ( member(X3,image(X1,image(X0,singleton(X2))))
& member(X2,universal_class) ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X5,X7,X2,X3] :
( member(ordered_pair(X2,X3),compose(X7,X5))
<=> ( member(X3,image(X7,image(X5,singleton(X2))))
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn2) ).
fof(f929,plain,
spl8_86,
inference(avatar_split_clause,[],[f267,f927]) ).
fof(f927,plain,
( spl8_86
<=> ! [X0,X3,X2,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_86])]) ).
fof(f267,plain,
! [X2,X3,X0,X1] :
( member(X3,domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X2,X2),universal_class)),universal_class)))),universal_class)),universal_class)))))
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f222,f240,f240,f152,f241]) ).
fof(f222,plain,
! [X2,X3,X0,X1] :
( member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f925,plain,
( ~ spl8_85
| ~ spl8_12
| spl8_71 ),
inference(avatar_split_clause,[],[f854,f739,f338,f922]) ).
fof(f922,plain,
( spl8_85
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_85])]) ).
fof(f338,plain,
( spl8_12
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_12])]) ).
fof(f739,plain,
( spl8_71
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_71])]) ).
fof(f854,plain,
( ~ inductive(universal_class)
| ~ spl8_12
| spl8_71 ),
inference(resolution,[],[f740,f339]) ).
fof(f339,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl8_12 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f740,plain,
( ~ member(null_class,universal_class)
| spl8_71 ),
inference(avatar_component_clause,[],[f739]) ).
fof(f913,plain,
spl8_84,
inference(avatar_split_clause,[],[f282,f911]) ).
fof(f911,plain,
( spl8_84
<=> ! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_84])]) ).
fof(f282,plain,
! [X0] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(union(X0,unordered_pair(X0,X0)),union(X0,unordered_pair(X0,X0))))),successor_relation)
| ~ member(union(X0,unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(equality_resolution,[],[f261]) ).
fof(f261,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation)
| union(X0,unordered_pair(X0,X0)) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f208,f241,f238]) ).
fof(f238,plain,
! [X0] : successor(X0) = union(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f153,f152]) ).
fof(f153,plain,
! [X0] : successor(X0) = union(X0,singleton(X0)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] : successor(X0) = union(X0,singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_defn) ).
fof(f208,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) )
& ( ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) )
| ~ member(ordered_pair(X0,X1),successor_relation) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
<=> ( successor(X0) = X1
& member(X1,universal_class)
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn2) ).
fof(f883,plain,
spl8_83,
inference(avatar_split_clause,[],[f278,f881]) ).
fof(f881,plain,
( spl8_83
<=> ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_83])]) ).
fof(f278,plain,
! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK6,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f234,f242]) ).
fof(f242,plain,
! [X0,X1] : apply(X0,X1) = sum_class(domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),
inference(definition_unfolding,[],[f177,f240,f152]) ).
fof(f177,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X8,X1] : apply(X8,X1) = sum_class(image(X8,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_defn) ).
fof(f234,plain,
! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f92,f140]) ).
fof(f140,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK6,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,plain,
? [X0] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X0,X1),X1)
| null_class = X1 ) )
& function(X0) ),
inference(rectify,[],[f43]) ).
fof(f43,axiom,
? [X8] :
( ! [X1] :
( member(X1,universal_class)
=> ( member(apply(X8,X1),X1)
| null_class = X1 ) )
& function(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choice) ).
fof(f879,plain,
spl8_82,
inference(avatar_split_clause,[],[f265,f877]) ).
fof(f877,plain,
( spl8_82
<=> ! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_82])]) ).
fof(f265,plain,
! [X2,X0,X1] :
( unordered_pair(unordered_pair(first(X2),first(X2)),unordered_pair(first(X2),unordered_pair(second(X2),second(X2)))) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(definition_unfolding,[],[f210,f241]) ).
fof(f210,plain,
! [X2,X0,X1] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( member(X2,cross_product(X0,X1))
=> ordered_pair(first(X2),second(X2)) = X2 ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X4] :
( member(X4,cross_product(X0,X1))
=> ordered_pair(first(X4),second(X4)) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product) ).
fof(f862,plain,
spl8_81,
inference(avatar_split_clause,[],[f269,f860]) ).
fof(f860,plain,
( spl8_81
<=> ! [X0,X3,X2,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_81])]) ).
fof(f269,plain,
! [X2,X3,X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(definition_unfolding,[],[f226,f241]) ).
fof(f226,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0,X1,X2,X3] :
( ( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) )
& ( ( member(X1,X3)
& member(X0,X2) )
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ) ),
inference(nnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
<=> ( member(X1,X3)
& member(X0,X2) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( member(ordered_pair(X2,X3),cross_product(X0,X1))
<=> ( member(X3,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cross_product_defn) ).
fof(f858,plain,
spl8_80,
inference(avatar_split_clause,[],[f252,f856]) ).
fof(f856,plain,
( spl8_80
<=> ! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_80])]) ).
fof(f252,plain,
! [X0] :
( unordered_pair(unordered_pair(sK3(X0),sK3(X0)),unordered_pair(sK3(X0),unordered_pair(sK3(X0),sK3(X0)))) = X0
| ~ member(X0,identity_relation) ),
inference(definition_unfolding,[],[f173,f241]) ).
fof(f173,plain,
! [X0] :
( ordered_pair(sK3(X0),sK3(X0)) = X0
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f103,f104]) ).
fof(f104,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK3(X0),sK3(X0)) = X0
& member(sK3(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f103,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(rectify,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( member(X0,identity_relation)
<=> ? [X1] :
( ordered_pair(X1,X1) = X0
& member(X1,universal_class) ) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X4] :
( member(X4,identity_relation)
<=> ? [X0] :
( ordered_pair(X0,X0) = X4
& member(X0,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_relation) ).
fof(f819,plain,
spl8_79,
inference(avatar_split_clause,[],[f262,f817]) ).
fof(f817,plain,
( spl8_79
<=> ! [X0,X1] :
( union(X0,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,[spl8_79])]) ).
fof(f262,plain,
! [X0,X1] :
( union(X0,unordered_pair(X0,X0)) = X1
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f207,f238,f241]) ).
fof(f207,plain,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f125]) ).
fof(f815,plain,
spl8_78,
inference(avatar_split_clause,[],[f255,f813]) ).
fof(f813,plain,
( spl8_78
<=> ! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_78])]) ).
fof(f255,plain,
! [X0,X1] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f181,f241]) ).
fof(f181,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 )
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( member(X1,universal_class)
& member(X0,universal_class) )
=> ( second(ordered_pair(X0,X1)) = X1
& first(ordered_pair(X0,X1)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_second) ).
fof(f811,plain,
spl8_77,
inference(avatar_split_clause,[],[f254,f809]) ).
fof(f809,plain,
( spl8_77
<=> ! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_77])]) ).
fof(f254,plain,
! [X0,X1] :
( second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f182,f241]) ).
fof(f182,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f87]) ).
fof(f793,plain,
spl8_76,
inference(avatar_split_clause,[],[f258,f791]) ).
fof(f791,plain,
( spl8_76
<=> ! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_76])]) ).
fof(f258,plain,
! [X0,X1] :
( member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f204,f241]) ).
fof(f204,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0,X1] :
( ( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) )
& ( ( member(X0,X1)
& member(X1,universal_class) )
| ~ member(ordered_pair(X0,X1),element_relation) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
<=> ( member(X0,X1)
& member(X1,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation_defn) ).
fof(f789,plain,
spl8_75,
inference(avatar_split_clause,[],[f253,f787]) ).
fof(f787,plain,
( spl8_75
<=> ! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_75])]) ).
fof(f253,plain,
! [X0,X1] :
( member(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(X0,universal_class)),universal_class)))),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f180,f240]) ).
fof(f180,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( function(X1)
& member(X0,universal_class) )
=> member(image(X1,X0),universal_class) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X8] :
( ( function(X8)
& member(X0,universal_class) )
=> member(image(X8,X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replacement) ).
fof(f785,plain,
spl8_74,
inference(avatar_split_clause,[],[f247,f783]) ).
fof(f783,plain,
( spl8_74
<=> ! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_74])]) ).
fof(f247,plain,
! [X0] :
( inductive(X0)
| ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ member(null_class,X0) ),
inference(definition_unfolding,[],[f168,f240]) ).
fof(f168,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(flattening,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) )
& ( ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) )
| ~ inductive(X0) ) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( inductive(X0)
<=> ( subclass(image(successor_relation,X0),X0)
& member(null_class,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inductive_defn) ).
fof(f750,plain,
spl8_73,
inference(avatar_split_clause,[],[f271,f748]) ).
fof(f748,plain,
( spl8_73
<=> ! [X0,X3,X2,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_73])]) ).
fof(f271,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f224,f241]) ).
fof(f224,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f135]) ).
fof(f746,plain,
spl8_72,
inference(avatar_split_clause,[],[f270,f744]) ).
fof(f744,plain,
( spl8_72
<=> ! [X0,X3,X2,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_72])]) ).
fof(f270,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3)) ),
inference(definition_unfolding,[],[f225,f241]) ).
fof(f225,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f135]) ).
fof(f742,plain,
( ~ spl8_70
| spl8_71
| ~ spl8_12
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f583,f525,f338,f739,f735]) ).
fof(f735,plain,
( spl8_70
<=> inductive(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_70])]) ).
fof(f525,plain,
( spl8_49
<=> ! [X0] :
( ~ member(X0,sK0)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_49])]) ).
fof(f583,plain,
( member(null_class,universal_class)
| ~ inductive(sK0)
| ~ spl8_12
| ~ spl8_49 ),
inference(resolution,[],[f526,f339]) ).
fof(f526,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member(X0,universal_class) )
| ~ spl8_49 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f733,plain,
spl8_69,
inference(avatar_split_clause,[],[f268,f731]) ).
fof(f731,plain,
( spl8_69
<=> ! [X0,X3,X2,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_69])]) ).
fof(f268,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,unordered_pair(X3,X3))),compose(X1,X0)) ),
inference(definition_unfolding,[],[f221,f241]) ).
fof(f221,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f133]) ).
fof(f729,plain,
spl8_68,
inference(avatar_split_clause,[],[f256,f727]) ).
fof(f727,plain,
( spl8_68
<=> ! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_68])]) ).
fof(f256,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f198,f209,f152]) ).
fof(f198,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0,X1] :
( ( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) )
& ( ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) )
| ~ member(X1,domain_of(X0)) ) ),
inference(nnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X1),universal_class)
& member(X1,universal_class) ) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X0,X4] :
( member(X4,domain_of(X0))
<=> ( null_class != restrict(X0,singleton(X4),universal_class)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_of) ).
fof(f725,plain,
spl8_67,
inference(avatar_split_clause,[],[f249,f723]) ).
fof(f723,plain,
( spl8_67
<=> ! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_67])]) ).
fof(f249,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(definition_unfolding,[],[f171,f154]) ).
fof(f171,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0] :
( ( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) )
& ( ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( function(X0)
<=> ( subclass(compose(X0,inverse(X0)),identity_relation)
& subclass(X0,cross_product(universal_class,universal_class)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X8] :
( function(X8)
<=> ( subclass(compose(X8,inverse(X8)),identity_relation)
& subclass(X8,cross_product(universal_class,universal_class)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',function_defn) ).
fof(f721,plain,
spl8_66,
inference(avatar_split_clause,[],[f246,f719]) ).
fof(f719,plain,
( spl8_66
<=> ! [X0] :
( unordered_pair(X0,X0) = unordered_pair(member_of(unordered_pair(X0,X0)),member_of(unordered_pair(X0,X0)))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_66])]) ).
fof(f246,plain,
! [X0] :
( unordered_pair(X0,X0) = unordered_pair(member_of(unordered_pair(X0,X0)),member_of(unordered_pair(X0,X0)))
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f165,f152,f152,f152]) ).
fof(f165,plain,
! [X0] :
( singleton(X0) = singleton(member_of(singleton(X0)))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( singleton(X0) = singleton(member_of(singleton(X0)))
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( member(X0,universal_class)
=> singleton(X0) = singleton(member_of(singleton(X0))) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X1] :
( member(X1,universal_class)
=> singleton(X1) = singleton(member_of(singleton(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_singleton) ).
fof(f694,plain,
spl8_65,
inference(avatar_split_clause,[],[f279,f692]) ).
fof(f279,plain,
! [X1] :
( member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))),identity_relation)
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f251]) ).
fof(f251,plain,
! [X0,X1] :
( member(X0,identity_relation)
| unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X1,X1))) != X0
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f174,f241]) ).
fof(f174,plain,
! [X0,X1] :
( member(X0,identity_relation)
| ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f105]) ).
fof(f690,plain,
spl8_64,
inference(avatar_split_clause,[],[f264,f688]) ).
fof(f264,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f205,f241]) ).
fof(f205,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f125]) ).
fof(f686,plain,
spl8_63,
inference(avatar_split_clause,[],[f263,f684]) ).
fof(f684,plain,
( spl8_63
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_63])]) ).
fof(f263,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),successor_relation) ),
inference(definition_unfolding,[],[f206,f241]) ).
fof(f206,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f125]) ).
fof(f682,plain,
spl8_62,
inference(avatar_split_clause,[],[f260,f680]) ).
fof(f680,plain,
( spl8_62
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_62])]) ).
fof(f260,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ),
inference(definition_unfolding,[],[f202,f241]) ).
fof(f202,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f123]) ).
fof(f678,plain,
spl8_61,
inference(avatar_split_clause,[],[f259,f676]) ).
fof(f676,plain,
( spl8_61
<=> ! [X0,X1] :
( member(X0,X1)
| ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_61])]) ).
fof(f259,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,[],[f203,f241]) ).
fof(f203,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f123]) ).
fof(f674,plain,
spl8_60,
inference(avatar_split_clause,[],[f248,f672]) ).
fof(f672,plain,
( spl8_60
<=> ! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_60])]) ).
fof(f248,plain,
! [X0] :
( subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| ~ inductive(X0) ),
inference(definition_unfolding,[],[f167,f240]) ).
fof(f167,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f668,plain,
spl8_59,
inference(avatar_split_clause,[],[f257,f666]) ).
fof(f257,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f197,f209,f152]) ).
fof(f197,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(X1),universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f656,plain,
( spl8_58
| ~ spl8_1
| ~ spl8_49 ),
inference(avatar_split_clause,[],[f584,f525,f286,f653]) ).
fof(f584,plain,
( member(sK1,universal_class)
| ~ spl8_1
| ~ spl8_49 ),
inference(resolution,[],[f526,f288]) ).
fof(f632,plain,
spl8_57,
inference(avatar_split_clause,[],[f250,f630]) ).
fof(f630,plain,
( spl8_57
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_57])]) ).
fof(f250,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f170,f154]) ).
fof(f170,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f628,plain,
spl8_56,
inference(avatar_split_clause,[],[f244,f626]) ).
fof(f626,plain,
( spl8_56
<=> ! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_56])]) ).
fof(f244,plain,
! [X0] :
( member_of(X0) = X0
| unordered_pair(member_of(X0),member_of(X0)) = X0 ),
inference(definition_unfolding,[],[f158,f152]) ).
fof(f158,plain,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( member_of(X0) = X0
| singleton(member_of(X0)) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_self) ).
fof(f624,plain,
spl8_55,
inference(avatar_split_clause,[],[f218,f622]) ).
fof(f218,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0,X1,X2] :
( ( member(X0,unordered_pair(X1,X2))
| ( X0 != X2
& X0 != X1 )
| ~ member(X0,universal_class) )
& ( ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) )
| ~ member(X0,unordered_pair(X1,X2)) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( member(X0,unordered_pair(X1,X2))
<=> ( ( X0 = X2
| X0 = X1 )
& member(X0,universal_class) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X2,X0,X1] :
( member(X2,unordered_pair(X0,X1))
<=> ( ( X1 = X2
| X0 = X2 )
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_defn) ).
fof(f620,plain,
spl8_54,
inference(avatar_split_clause,[],[f214,f618]) ).
fof(f618,plain,
( spl8_54
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_54])]) ).
fof(f214,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0,X1,X2] :
( ( member(X2,union(X0,X1))
| ( ~ member(X2,X1)
& ~ member(X2,X0) ) )
& ( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X4] :
( member(X4,union(X0,X1))
<=> ( member(X4,X1)
| member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f616,plain,
spl8_53,
inference(avatar_split_clause,[],[f213,f614]) ).
fof(f614,plain,
( spl8_53
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_53])]) ).
fof(f213,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0,X1,X2] :
( ( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) )
& ( ( member(X2,X1)
& member(X2,X0) )
| ~ member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X4] :
( member(X4,intersection(X0,X1))
<=> ( member(X4,X1)
& member(X4,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection) ).
fof(f578,plain,
spl8_52,
inference(avatar_split_clause,[],[f201,f576]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f119,f120]) ).
fof(f120,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK5(X0,X1),X1)
& member(X0,sK5(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f119,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
| ~ member(X0,sum_class(X1)) ) ),
inference(rectify,[],[f118]) ).
fof(f118,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& member(X0,X2) )
| ~ member(X0,sum_class(X1)) ) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( member(X0,sum_class(X1))
<=> ? [X2] :
( member(X2,X1)
& member(X0,X2) ) ),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X2,X0] :
( member(X2,sum_class(X0))
<=> ? [X1] :
( member(X1,X0)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class_defn) ).
fof(f574,plain,
spl8_51,
inference(avatar_split_clause,[],[f195,f572]) ).
fof(f572,plain,
( spl8_51
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_51])]) ).
fof(f195,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) )
& ( ( subclass(X0,X1)
& member(X0,universal_class) )
| ~ member(X0,power_class(X1)) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( member(X0,power_class(X1))
<=> ( subclass(X0,X1)
& member(X0,universal_class) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X2,X0] :
( member(X2,power_class(X0))
<=> ( subclass(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class_defn) ).
fof(f570,plain,
spl8_50,
inference(avatar_split_clause,[],[f192,f568]) ).
fof(f568,plain,
( spl8_50
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_50])]) ).
fof(f192,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0,X1] :
( ( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) )
& ( ( ~ member(X1,X0)
& member(X1,universal_class) )
| ~ member(X1,complement(X0)) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( member(X1,complement(X0))
<=> ( ~ member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X4] :
( member(X4,complement(X0))
<=> ( ~ member(X4,X0)
& member(X4,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement) ).
fof(f527,plain,
( spl8_49
| ~ spl8_3
| ~ spl8_39 ),
inference(avatar_split_clause,[],[f495,f461,f296,f525]) ).
fof(f461,plain,
( spl8_39
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_39])]) ).
fof(f495,plain,
( ! [X0] :
( ~ member(X0,sK0)
| member(X0,universal_class) )
| ~ spl8_3
| ~ spl8_39 ),
inference(superposition,[],[f462,f298]) ).
fof(f462,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) )
| ~ spl8_39 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f523,plain,
spl8_48,
inference(avatar_split_clause,[],[f245,f521]) ).
fof(f521,plain,
( spl8_48
<=> ! [X0] :
( member(member_of(unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_48])]) ).
fof(f245,plain,
! [X0] :
( member(member_of(unordered_pair(X0,X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(definition_unfolding,[],[f164,f152]) ).
fof(f164,plain,
! [X0] :
( member(member_of(singleton(X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0] :
( member(member_of(singleton(X0)),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( member(X0,universal_class)
=> member(member_of(singleton(X0)),universal_class) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X1] :
( member(X1,universal_class)
=> member(member_of(singleton(X1)),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_singleton_universal) ).
fof(f519,plain,
spl8_47,
inference(avatar_split_clause,[],[f200,f517]) ).
fof(f517,plain,
( spl8_47
<=> ! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_47])]) ).
fof(f200,plain,
! [X0,X1] :
( member(sK5(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f515,plain,
spl8_46,
inference(avatar_split_clause,[],[f199,f513]) ).
fof(f513,plain,
( spl8_46
<=> ! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_46])]) ).
fof(f199,plain,
! [X0,X1] :
( member(X0,sK5(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f121]) ).
fof(f511,plain,
spl8_45,
inference(avatar_split_clause,[],[f187,f509]) ).
fof(f187,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK4(X0,X1),X1)
& member(sK4(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_defn) ).
fof(f507,plain,
spl8_44,
inference(avatar_split_clause,[],[f186,f505]) ).
fof(f505,plain,
( spl8_44
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_44])]) ).
fof(f186,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( disjoint(X0,X1)
=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ! [X2] :
~ ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f503,plain,
spl8_43,
inference(avatar_split_clause,[],[f185,f501]) ).
fof(f501,plain,
( spl8_43
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_43])]) ).
fof(f185,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f106]) ).
fof(f106,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X1,X0)
& subclass(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality) ).
fof(f490,plain,
( spl8_42
| ~ spl8_6
| ~ spl8_33 ),
inference(avatar_split_clause,[],[f474,f437,f311,f488]) ).
fof(f488,plain,
( spl8_42
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_42])]) ).
fof(f311,plain,
( spl8_6
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_6])]) ).
fof(f437,plain,
( spl8_33
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_33])]) ).
fof(f474,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl8_6
| ~ spl8_33 ),
inference(resolution,[],[f438,f312]) ).
fof(f312,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f438,plain,
( ! [X0,X1] :
( member(sK4(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl8_33 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f471,plain,
spl8_41,
inference(avatar_split_clause,[],[f284,f469]) ).
fof(f469,plain,
( spl8_41
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_41])]) ).
fof(f284,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f219]) ).
fof(f219,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f131]) ).
fof(f467,plain,
spl8_40,
inference(avatar_split_clause,[],[f283,f465]) ).
fof(f283,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f220]) ).
fof(f220,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f131]) ).
fof(f463,plain,
spl8_39,
inference(avatar_split_clause,[],[f217,f461]) ).
fof(f217,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f131]) ).
fof(f459,plain,
spl8_38,
inference(avatar_split_clause,[],[f216,f457]) ).
fof(f457,plain,
( spl8_38
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_38])]) ).
fof(f216,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f129]) ).
fof(f455,plain,
spl8_37,
inference(avatar_split_clause,[],[f215,f453]) ).
fof(f453,plain,
( spl8_37
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_37])]) ).
fof(f215,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f451,plain,
spl8_36,
inference(avatar_split_clause,[],[f212,f449]) ).
fof(f449,plain,
( spl8_36
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_36])]) ).
fof(f212,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f447,plain,
spl8_35,
inference(avatar_split_clause,[],[f211,f445]) ).
fof(f445,plain,
( spl8_35
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_35])]) ).
fof(f211,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f443,plain,
spl8_34,
inference(avatar_split_clause,[],[f189,f441]) ).
fof(f441,plain,
( spl8_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_34])]) ).
fof(f189,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK4(X0,X1),X1) ),
inference(cnf_transformation,[],[f111]) ).
fof(f439,plain,
spl8_33,
inference(avatar_split_clause,[],[f188,f437]) ).
fof(f188,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f435,plain,
spl8_32,
inference(avatar_split_clause,[],[f157,f433]) ).
fof(f433,plain,
( spl8_32
<=> ! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_32])]) ).
fof(f157,plain,
! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( member_of(X0) = X0
| member(member_of(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_universal_self) ).
fof(f431,plain,
spl8_31,
inference(avatar_split_clause,[],[f156,f429]) ).
fof(f429,plain,
( spl8_31
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_31])]) ).
fof(f156,plain,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',flip) ).
fof(f427,plain,
spl8_30,
inference(avatar_split_clause,[],[f155,f425]) ).
fof(f425,plain,
( spl8_30
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_30])]) ).
fof(f155,plain,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rotate) ).
fof(f423,plain,
( ~ spl8_29
| ~ spl8_6
| ~ spl8_12 ),
inference(avatar_split_clause,[],[f349,f338,f311,f420]) ).
fof(f420,plain,
( spl8_29
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_29])]) ).
fof(f349,plain,
( ~ inductive(null_class)
| ~ spl8_6
| ~ spl8_12 ),
inference(resolution,[],[f339,f312]) ).
fof(f407,plain,
spl8_28,
inference(avatar_split_clause,[],[f196,f405]) ).
fof(f405,plain,
( spl8_28
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_28])]) ).
fof(f196,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f403,plain,
spl8_27,
inference(avatar_split_clause,[],[f194,f401]) ).
fof(f401,plain,
( spl8_27
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_27])]) ).
fof(f194,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f399,plain,
spl8_26,
inference(avatar_split_clause,[],[f193,f397]) ).
fof(f397,plain,
( spl8_26
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_26])]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f115]) ).
fof(f395,plain,
spl8_25,
inference(avatar_split_clause,[],[f191,f393]) ).
fof(f393,plain,
( spl8_25
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_25])]) ).
fof(f191,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f391,plain,
spl8_24,
inference(avatar_split_clause,[],[f190,f389]) ).
fof(f389,plain,
( spl8_24
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_24])]) ).
fof(f190,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f113]) ).
fof(f387,plain,
spl8_23,
inference(avatar_split_clause,[],[f176,f385]) ).
fof(f385,plain,
( spl8_23
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_23])]) ).
fof(f176,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X5,X7] : subclass(compose(X7,X5),cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_defn1) ).
fof(f383,plain,
spl8_22,
inference(avatar_split_clause,[],[f172,f381]) ).
fof(f381,plain,
( spl8_22
<=> ! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_22])]) ).
fof(f172,plain,
! [X0] :
( member(sK3(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f105]) ).
fof(f379,plain,
( spl8_21
| ~ spl8_3
| ~ spl8_13 ),
inference(avatar_split_clause,[],[f350,f342,f296,f376]) ).
fof(f342,plain,
( spl8_13
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_13])]) ).
fof(f350,plain,
( member(sK0,universal_class)
| ~ spl8_3
| ~ spl8_13 ),
inference(superposition,[],[f343,f298]) ).
fof(f343,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl8_13 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f374,plain,
spl8_20,
inference(avatar_split_clause,[],[f169,f372]) ).
fof(f372,plain,
( spl8_20
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_20])]) ).
fof(f169,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f370,plain,
spl8_19,
inference(avatar_split_clause,[],[f163,f368]) ).
fof(f368,plain,
( spl8_19
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_19])]) ).
fof(f163,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( member(X0,universal_class)
=> member(sum_class(X0),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_class) ).
fof(f366,plain,
spl8_18,
inference(avatar_split_clause,[],[f162,f364]) ).
fof(f364,plain,
( spl8_18
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_18])]) ).
fof(f162,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( member(X0,universal_class)
=> member(power_class(X0),universal_class) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X2] :
( member(X2,universal_class)
=> member(power_class(X2),universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',power_class) ).
fof(f362,plain,
spl8_17,
inference(avatar_split_clause,[],[f161,f360]) ).
fof(f360,plain,
( spl8_17
<=> ! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_17])]) ).
fof(f161,plain,
! [X0] :
( disjoint(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0] :
( ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f79,f96]) ).
fof(f96,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK2(X0),X0)
& member(sK2(X0),X0)
& member(sK2(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( null_class != X0
=> ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) ) ),
inference(rectify,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( null_class != X0
=> ? [X2] :
( disjoint(X2,X0)
& member(X2,X0)
& member(X2,universal_class) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',regularity) ).
fof(f358,plain,
spl8_16,
inference(avatar_split_clause,[],[f160,f356]) ).
fof(f356,plain,
( spl8_16
<=> ! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_16])]) ).
fof(f160,plain,
! [X0] :
( member(sK2(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f97]) ).
fof(f354,plain,
spl8_15,
inference(avatar_split_clause,[],[f159,f352]) ).
fof(f352,plain,
( spl8_15
<=> ! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_15])]) ).
fof(f159,plain,
! [X0] :
( member(sK2(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f97]) ).
fof(f348,plain,
spl8_14,
inference(avatar_split_clause,[],[f237,f346]) ).
fof(f346,plain,
( spl8_14
<=> ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_14])]) ).
fof(f237,plain,
! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f93,f142]) ).
fof(f142,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK7,X1)
| ~ inductive(X1) )
& inductive(sK7)
& member(sK7,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
? [X0] :
( ! [X1] :
( inductive(X1)
=> subclass(X0,X1) )
& inductive(X0)
& member(X0,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infinity) ).
fof(f344,plain,
spl8_13,
inference(avatar_split_clause,[],[f175,f342]) ).
fof(f175,plain,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : member(unordered_pair(X0,X1),universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair) ).
fof(f340,plain,
spl8_12,
inference(avatar_split_clause,[],[f166,f338]) ).
fof(f166,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f336,plain,
spl8_11,
inference(avatar_split_clause,[],[f148,f333]) ).
fof(f333,plain,
( spl8_11
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_11])]) ).
fof(f148,plain,
subclass(successor_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
subclass(successor_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_relation_defn1) ).
fof(f331,plain,
spl8_10,
inference(avatar_split_clause,[],[f147,f328]) ).
fof(f328,plain,
( spl8_10
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_10])]) ).
fof(f147,plain,
subclass(element_relation,cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
subclass(element_relation,cross_product(universal_class,universal_class)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_relation) ).
fof(f326,plain,
spl8_9,
inference(avatar_split_clause,[],[f280,f324]) ).
fof(f324,plain,
( spl8_9
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_9])]) ).
fof(f280,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f107]) ).
fof(f322,plain,
spl8_8,
inference(avatar_split_clause,[],[f235,f319]) ).
fof(f319,plain,
( spl8_8
<=> member(sK7,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_8])]) ).
fof(f235,plain,
member(sK7,universal_class),
inference(cnf_transformation,[],[f143]) ).
fof(f317,plain,
spl8_7,
inference(avatar_split_clause,[],[f150,f315]) ).
fof(f315,plain,
( spl8_7
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_7])]) ).
fof(f150,plain,
! [X0] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).
fof(f313,plain,
spl8_6,
inference(avatar_split_clause,[],[f149,f311]) ).
fof(f149,plain,
! [X0] : ~ member(X0,null_class),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : ~ member(X0,null_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_defn) ).
fof(f309,plain,
spl8_5,
inference(avatar_split_clause,[],[f236,f306]) ).
fof(f306,plain,
( spl8_5
<=> inductive(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_5])]) ).
fof(f236,plain,
inductive(sK7),
inference(cnf_transformation,[],[f143]) ).
fof(f304,plain,
spl8_4,
inference(avatar_split_clause,[],[f233,f301]) ).
fof(f301,plain,
( spl8_4
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl8_4])]) ).
fof(f233,plain,
function(sK6),
inference(cnf_transformation,[],[f141]) ).
fof(f299,plain,
spl8_3,
inference(avatar_split_clause,[],[f243,f296]) ).
fof(f243,plain,
sK0 = unordered_pair(member_of(sK0),member_of(sK0)),
inference(definition_unfolding,[],[f144,f152]) ).
fof(f144,plain,
sK0 = singleton(member_of(sK0)),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( sK1 != member_of(sK0)
& member(sK1,sK0)
& sK0 = singleton(member_of(sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f78,f94]) ).
fof(f94,plain,
( ? [X0,X1] :
( member_of(X0) != X1
& member(X1,X0)
& singleton(member_of(X0)) = X0 )
=> ( sK1 != member_of(sK0)
& member(sK1,sK0)
& sK0 = singleton(member_of(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0,X1] :
( member_of(X0) != X1
& member(X1,X0)
& singleton(member_of(X0)) = X0 ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
? [X0,X1] :
( member_of(X0) != X1
& member(X1,X0)
& singleton(member_of(X0)) = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,negated_conjecture,
~ ! [X0,X1] :
( ( member(X1,X0)
& singleton(member_of(X0)) = X0 )
=> member_of(X0) = X1 ),
inference(negated_conjecture,[],[f48]) ).
fof(f48,conjecture,
! [X0,X1] :
( ( member(X1,X0)
& singleton(member_of(X0)) = X0 )
=> member_of(X0) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_singletons1_1) ).
fof(f294,plain,
~ spl8_2,
inference(avatar_split_clause,[],[f146,f291]) ).
fof(f146,plain,
sK1 != member_of(sK0),
inference(cnf_transformation,[],[f95]) ).
fof(f289,plain,
spl8_1,
inference(avatar_split_clause,[],[f145,f286]) ).
fof(f145,plain,
member(sK1,sK0),
inference(cnf_transformation,[],[f95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET094+1 : TPTP v8.2.0. Bugfixed v7.3.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n029.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:15:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.35 % (16211)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.36 % (16218)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.37 % (16216)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.37 % (16217)WARNING: value z3 for option sas not known
% 0.21/0.37 % (16215)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.37 % (16217)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)
% 0.21/0.37 % (16219)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)
% 0.21/0.37 % (16220)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)
% 0.21/0.37 % (16221)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)
% 0.21/0.38 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [2]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 TRYING [3]
% 0.21/0.41 % (16219)First to succeed.
% 0.21/0.42 % (16219)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16211"
% 0.21/0.43 % (16219)Refutation found. Thanks to Tanya!
% 0.21/0.43 % SZS status Theorem for theBenchmark
% 0.21/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.43 % (16219)------------------------------
% 0.21/0.43 % (16219)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.43 % (16219)Termination reason: Refutation
% 0.21/0.43
% 0.21/0.43 % (16219)Memory used [KB]: 1507
% 0.21/0.43 % (16219)Time elapsed: 0.056 s
% 0.21/0.43 % (16219)Instructions burned: 67 (million)
% 0.21/0.43 % (16211)Success in time 0.072 s
%------------------------------------------------------------------------------