TSTP Solution File: SET020+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:04:23 EDT 2024
% Result : Theorem 0.13s 0.40s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 180
% Syntax : Number of formulae : 617 ( 133 unt; 0 def)
% Number of atoms : 1732 ( 194 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1861 ( 746 ~; 750 |; 178 &)
% ( 162 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 136 ( 134 usr; 130 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 10 con; 0-3 aty)
% Number of variables : 924 ( 890 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1245,plain,
$false,
inference(avatar_sat_refutation,[],[f276,f281,f290,f295,f300,f305,f309,f313,f318,f322,f327,f332,f336,f340,f344,f350,f354,f358,f363,f367,f371,f375,f379,f383,f387,f391,f395,f399,f403,f413,f423,f427,f431,f435,f439,f443,f447,f451,f455,f459,f463,f481,f495,f499,f503,f507,f511,f515,f556,f560,f564,f600,f604,f608,f612,f635,f644,f648,f652,f656,f660,f664,f668,f679,f683,f687,f691,f695,f708,f712,f716,f730,f735,f739,f743,f776,f780,f794,f798,f825,f834,f839,f849,f853,f857,f863,f867,f873,f877,f883,f894,f904,f908,f918,f922,f926,f935,f937,f949,f956,f971,f973,f980,f984,f988,f992,f996,f1000,f1073,f1084,f1085,f1089,f1093,f1097,f1107,f1111,f1123,f1132,f1136,f1140,f1147,f1151,f1152,f1156,f1221,f1225,f1229,f1244]) ).
fof(f1244,plain,
( spl9_3
| ~ spl9_1
| ~ spl9_7
| ~ spl9_112 ),
inference(avatar_split_clause,[],[f1069,f998,f302,f273,f283]) ).
fof(f283,plain,
( spl9_3
<=> sK0 = first(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f273,plain,
( spl9_1
<=> member(sK0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f302,plain,
( spl9_7
<=> sK2 = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f998,plain,
( spl9_112
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_112])]) ).
fof(f1069,plain,
( sK0 = first(sK2)
| ~ spl9_1
| ~ spl9_7
| ~ spl9_112 ),
inference(forward_demodulation,[],[f1058,f304]) ).
fof(f304,plain,
( sK2 = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1)))
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f1058,plain,
( sK0 = first(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))))
| ~ spl9_1
| ~ spl9_112 ),
inference(resolution,[],[f999,f275]) ).
fof(f275,plain,
( member(sK0,universal_class)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f273]) ).
fof(f999,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1)))) = X0 )
| ~ spl9_112 ),
inference(avatar_component_clause,[],[f998]) ).
fof(f1229,plain,
( spl9_129
| ~ spl9_15
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f581,f562,f338,f1227]) ).
fof(f1227,plain,
( spl9_129
<=> ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_129])]) ).
fof(f338,plain,
( spl9_15
<=> ! [X0,X1] : member(unordered_pair(X0,X1),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f562,plain,
( spl9_52
<=> ! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
fof(f581,plain,
( ! [X2,X0,X1] :
( member(X0,sum_class(universal_class))
| ~ member(X0,unordered_pair(X1,X2)) )
| ~ spl9_15
| ~ spl9_52 ),
inference(resolution,[],[f563,f339]) ).
fof(f339,plain,
( ! [X0,X1] : member(unordered_pair(X0,X1),universal_class)
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f563,plain,
( ! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X0,sum_class(X1))
| ~ member(X0,X2) )
| ~ spl9_52 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f1225,plain,
( spl9_128
| ~ spl9_18
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f417,f397,f352,f1223]) ).
fof(f1223,plain,
( spl9_128
<=> ! [X0] :
( subclass(sK3(power_class(X0)),X0)
| null_class = power_class(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_128])]) ).
fof(f352,plain,
( spl9_18
<=> ! [X0] :
( member(sK3(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f397,plain,
( spl9_29
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f417,plain,
( ! [X0] :
( subclass(sK3(power_class(X0)),X0)
| null_class = power_class(X0) )
| ~ spl9_18
| ~ spl9_29 ),
inference(resolution,[],[f398,f353]) ).
fof(f353,plain,
( ! [X0] :
( member(sK3(X0),X0)
| null_class = X0 )
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f398,plain,
( ! [X0,X1] :
( ~ member(X0,power_class(X1))
| subclass(X0,X1) )
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f1221,plain,
( spl9_127
| ~ spl9_18
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f408,f389,f352,f1219]) ).
fof(f1219,plain,
( spl9_127
<=> ! [X0] :
( ~ member(sK3(complement(X0)),X0)
| complement(X0) = null_class ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_127])]) ).
fof(f389,plain,
( spl9_27
<=> ! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f408,plain,
( ! [X0] :
( ~ member(sK3(complement(X0)),X0)
| complement(X0) = null_class )
| ~ spl9_18
| ~ spl9_27 ),
inference(resolution,[],[f390,f353]) ).
fof(f390,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| ~ member(X1,X0) )
| ~ spl9_27 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f1156,plain,
( spl9_126
| ~ spl9_15
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f529,f501,f338,f1154]) ).
fof(f1154,plain,
( spl9_126
<=> ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_126])]) ).
fof(f501,plain,
( spl9_46
<=> ! [X0,X1,X3] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
fof(f529,plain,
( ! [X2,X0,X1] :
( member(unordered_pair(X0,X1),X2)
| ~ subclass(universal_class,X2) )
| ~ spl9_15
| ~ spl9_46 ),
inference(resolution,[],[f502,f339]) ).
fof(f502,plain,
( ! [X3,X0,X1] :
( ~ member(X3,X0)
| member(X3,X1)
| ~ subclass(X0,X1) )
| ~ spl9_46 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f1152,plain,
( spl9_4
| ~ spl9_1
| ~ spl9_7
| ~ spl9_109 ),
inference(avatar_split_clause,[],[f1038,f986,f302,f273,f287]) ).
fof(f287,plain,
( spl9_4
<=> sK1 = second(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f986,plain,
( spl9_109
<=> ! [X0] :
( sK1 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_109])]) ).
fof(f1038,plain,
( sK1 = second(sK2)
| ~ spl9_1
| ~ spl9_7
| ~ spl9_109 ),
inference(forward_demodulation,[],[f1027,f304]) ).
fof(f1027,plain,
( sK1 = second(unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))))
| ~ spl9_1
| ~ spl9_109 ),
inference(resolution,[],[f987,f275]) ).
fof(f987,plain,
( ! [X0] :
( ~ member(X0,universal_class)
| sK1 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1)))) )
| ~ spl9_109 ),
inference(avatar_component_clause,[],[f986]) ).
fof(f1151,plain,
( spl9_125
| ~ spl9_14
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f526,f501,f334,f1149]) ).
fof(f1149,plain,
( spl9_125
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_125])]) ).
fof(f334,plain,
( spl9_14
<=> ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f526,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ subclass(X1,X0)
| ~ inductive(X1) )
| ~ spl9_14
| ~ spl9_46 ),
inference(resolution,[],[f502,f335]) ).
fof(f335,plain,
( ! [X0] :
( member(null_class,X0)
| ~ inductive(X0) )
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f1147,plain,
( spl9_124
| ~ spl9_16
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f524,f493,f342,f1145]) ).
fof(f1145,plain,
( spl9_124
<=> ! [X0] :
( sK8 = X0
| ~ subclass(X0,sK8)
| ~ inductive(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_124])]) ).
fof(f342,plain,
( spl9_16
<=> ! [X1] :
( subclass(sK8,X1)
| ~ inductive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f493,plain,
( spl9_44
<=> ! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
fof(f524,plain,
( ! [X0] :
( sK8 = X0
| ~ subclass(X0,sK8)
| ~ inductive(X0) )
| ~ spl9_16
| ~ spl9_44 ),
inference(resolution,[],[f494,f343]) ).
fof(f343,plain,
( ! [X1] :
( subclass(sK8,X1)
| ~ inductive(X1) )
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f494,plain,
( ! [X0,X1] :
( ~ subclass(X1,X0)
| X0 = X1
| ~ subclass(X0,X1) )
| ~ spl9_44 ),
inference(avatar_component_clause,[],[f493]) ).
fof(f1140,plain,
( spl9_123
| ~ spl9_10
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f589,f562,f315,f1138]) ).
fof(f1138,plain,
( spl9_123
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_123])]) ).
fof(f315,plain,
( spl9_10
<=> member(sK8,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f589,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK8) )
| ~ spl9_10
| ~ spl9_52 ),
inference(resolution,[],[f563,f317]) ).
fof(f317,plain,
( member(sK8,universal_class)
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f1136,plain,
( spl9_122
| ~ spl9_14
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f475,f441,f334,f1134]) ).
fof(f1134,plain,
( spl9_122
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_122])]) ).
fof(f441,plain,
( spl9_37
<=> ! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
fof(f475,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X1,X0)) )
| ~ spl9_14
| ~ spl9_37 ),
inference(resolution,[],[f442,f335]) ).
fof(f442,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) )
| ~ spl9_37 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f1132,plain,
( spl9_121
| ~ spl9_14
| ~ spl9_36 ),
inference(avatar_split_clause,[],[f472,f437,f334,f1130]) ).
fof(f1130,plain,
( spl9_121
<=> ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_121])]) ).
fof(f437,plain,
( spl9_36
<=> ! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
fof(f472,plain,
( ! [X0,X1] :
( member(null_class,X0)
| ~ inductive(intersection(X0,X1)) )
| ~ spl9_14
| ~ spl9_36 ),
inference(resolution,[],[f438,f335]) ).
fof(f438,plain,
( ! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) )
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f1123,plain,
( spl9_120
| ~ spl9_7
| ~ spl9_83 ),
inference(avatar_split_clause,[],[f835,f832,f302,f1121]) ).
fof(f1121,plain,
( spl9_120
<=> ! [X0,X1] :
( ~ member(sK2,compose(X0,X1))
| member(sK1,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(sK0,sK0),universal_class)),universal_class)))),universal_class)),universal_class))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_120])]) ).
fof(f832,plain,
( spl9_83
<=> ! [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,[spl9_83])]) ).
fof(f835,plain,
( ! [X0,X1] :
( ~ member(sK2,compose(X0,X1))
| member(sK1,domain_of(domain_of(flip(cross_product(intersection(X0,cross_product(domain_of(domain_of(flip(cross_product(intersection(X1,cross_product(unordered_pair(sK0,sK0),universal_class)),universal_class)))),universal_class)),universal_class))))) )
| ~ spl9_7
| ~ spl9_83 ),
inference(superposition,[],[f833,f304]) ).
fof(f833,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))))) )
| ~ spl9_83 ),
inference(avatar_component_clause,[],[f832]) ).
fof(f1111,plain,
( spl9_119
| ~ spl9_7
| ~ spl9_89 ),
inference(avatar_split_clause,[],[f869,f865,f302,f1109]) ).
fof(f1109,plain,
( spl9_119
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),flip(X1))
| member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_119])]) ).
fof(f865,plain,
( spl9_89
<=> ! [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,[spl9_89])]) ).
fof(f869,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),flip(X1))
| member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl9_7
| ~ spl9_89 ),
inference(superposition,[],[f866,f304]) ).
fof(f866,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(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)) )
| ~ spl9_89 ),
inference(avatar_component_clause,[],[f865]) ).
fof(f1107,plain,
( spl9_118
| ~ spl9_7
| ~ spl9_88 ),
inference(avatar_split_clause,[],[f868,f861,f302,f1105]) ).
fof(f1105,plain,
( spl9_118
<=> ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),rotate(X1))
| member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_118])]) ).
fof(f861,plain,
( spl9_88
<=> ! [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,[spl9_88])]) ).
fof(f868,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),rotate(X1))
| member(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,unordered_pair(X0,X0))),cross_product(cross_product(universal_class,universal_class),universal_class)) )
| ~ spl9_7
| ~ spl9_88 ),
inference(superposition,[],[f862,f304]) ).
fof(f862,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(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)) )
| ~ spl9_88 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f1097,plain,
( spl9_117
| ~ spl9_10
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f537,f501,f315,f1095]) ).
fof(f1095,plain,
( spl9_117
<=> ! [X0] :
( member(sK8,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_117])]) ).
fof(f537,plain,
( ! [X0] :
( member(sK8,X0)
| ~ subclass(universal_class,X0) )
| ~ spl9_10
| ~ spl9_46 ),
inference(resolution,[],[f502,f317]) ).
fof(f1093,plain,
( spl9_116
| ~ spl9_9
| ~ spl9_44 ),
inference(avatar_split_clause,[],[f516,f493,f311,f1091]) ).
fof(f1091,plain,
( spl9_116
<=> ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_116])]) ).
fof(f311,plain,
( spl9_9
<=> ! [X0] : subclass(X0,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f516,plain,
( ! [X0] :
( universal_class = X0
| ~ subclass(universal_class,X0) )
| ~ spl9_9
| ~ spl9_44 ),
inference(resolution,[],[f494,f312]) ).
fof(f312,plain,
( ! [X0] : subclass(X0,universal_class)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f1089,plain,
( spl9_115
| ~ spl9_14
| ~ spl9_27 ),
inference(avatar_split_clause,[],[f407,f389,f334,f1087]) ).
fof(f1087,plain,
( spl9_115
<=> ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_115])]) ).
fof(f407,plain,
( ! [X0] :
( ~ member(null_class,X0)
| ~ inductive(complement(X0)) )
| ~ spl9_14
| ~ spl9_27 ),
inference(resolution,[],[f390,f335]) ).
fof(f1085,plain,
( ~ spl9_59
| spl9_75
| ~ spl9_9
| ~ spl9_71 ),
inference(avatar_split_clause,[],[f718,f706,f311,f732,f641]) ).
fof(f641,plain,
( spl9_59
<=> member(null_class,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_59])]) ).
fof(f732,plain,
( spl9_75
<=> inductive(universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_75])]) ).
fof(f706,plain,
( spl9_71
<=> ! [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,[spl9_71])]) ).
fof(f718,plain,
( inductive(universal_class)
| ~ member(null_class,universal_class)
| ~ spl9_9
| ~ spl9_71 ),
inference(resolution,[],[f707,f312]) ).
fof(f707,plain,
( ! [X0] :
( ~ subclass(domain_of(domain_of(flip(cross_product(intersection(successor_relation,cross_product(X0,universal_class)),universal_class)))),X0)
| inductive(X0)
| ~ member(null_class,X0) )
| ~ spl9_71 ),
inference(avatar_component_clause,[],[f706]) ).
fof(f1084,plain,
( spl9_114
| spl9_59
| ~ spl9_14
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f405,f385,f334,f641,f1082]) ).
fof(f1082,plain,
( spl9_114
<=> ! [X0] : ~ inductive(complement(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_114])]) ).
fof(f385,plain,
( spl9_26
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f405,plain,
( ! [X0] :
( member(null_class,universal_class)
| ~ inductive(complement(X0)) )
| ~ spl9_14
| ~ spl9_26 ),
inference(resolution,[],[f386,f335]) ).
fof(f386,plain,
( ! [X0,X1] :
( ~ member(X1,complement(X0))
| member(X1,universal_class) )
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f1073,plain,
( spl9_113
| ~ spl9_8
| ~ spl9_48 ),
inference(avatar_split_clause,[],[f549,f509,f307,f1071]) ).
fof(f1071,plain,
( spl9_113
<=> ! [X0] : ~ member(X0,sum_class(null_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_113])]) ).
fof(f307,plain,
( spl9_8
<=> ! [X0] : ~ member(X0,null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f509,plain,
( spl9_48
<=> ! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
fof(f549,plain,
( ! [X0] : ~ member(X0,sum_class(null_class))
| ~ spl9_8
| ~ spl9_48 ),
inference(resolution,[],[f510,f308]) ).
fof(f308,plain,
( ! [X0] : ~ member(X0,null_class)
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f510,plain,
( ! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ member(X0,sum_class(X1)) )
| ~ spl9_48 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f1000,plain,
( spl9_112
| ~ spl9_2
| ~ spl9_76 ),
inference(avatar_split_clause,[],[f763,f737,f278,f998]) ).
fof(f278,plain,
( spl9_2
<=> member(sK1,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f737,plain,
( spl9_76
<=> ! [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,[spl9_76])]) ).
fof(f763,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1)))) = X0
| ~ member(X0,universal_class) )
| ~ spl9_2
| ~ spl9_76 ),
inference(resolution,[],[f738,f280]) ).
fof(f280,plain,
( member(sK1,universal_class)
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f738,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X0
| ~ member(X0,universal_class) )
| ~ spl9_76 ),
inference(avatar_component_clause,[],[f737]) ).
fof(f996,plain,
( spl9_111
| ~ spl9_20
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f586,f562,f360,f994]) ).
fof(f994,plain,
( spl9_111
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_111])]) ).
fof(f360,plain,
( spl9_20
<=> member(sK2,universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
fof(f586,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK2) )
| ~ spl9_20
| ~ spl9_52 ),
inference(resolution,[],[f563,f362]) ).
fof(f362,plain,
( member(sK2,universal_class)
| ~ spl9_20 ),
inference(avatar_component_clause,[],[f360]) ).
fof(f992,plain,
( spl9_110
| ~ spl9_1
| ~ spl9_76 ),
inference(avatar_split_clause,[],[f762,f737,f273,f990]) ).
fof(f990,plain,
( spl9_110
<=> ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_110])]) ).
fof(f762,plain,
( ! [X0] :
( first(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0)))) = X0
| ~ member(X0,universal_class) )
| ~ spl9_1
| ~ spl9_76 ),
inference(resolution,[],[f738,f275]) ).
fof(f988,plain,
( spl9_109
| ~ spl9_2
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f749,f728,f278,f986]) ).
fof(f728,plain,
( spl9_74
<=> ! [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,[spl9_74])]) ).
fof(f749,plain,
( ! [X0] :
( sK1 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK1,sK1))))
| ~ member(X0,universal_class) )
| ~ spl9_2
| ~ spl9_74 ),
inference(resolution,[],[f729,f280]) ).
fof(f729,plain,
( ! [X0,X1] :
( ~ member(X1,universal_class)
| second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1)))) = X1
| ~ member(X0,universal_class) )
| ~ spl9_74 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f984,plain,
( spl9_108
| ~ spl9_1
| ~ spl9_74 ),
inference(avatar_split_clause,[],[f748,f728,f273,f982]) ).
fof(f982,plain,
( spl9_108
<=> ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_108])]) ).
fof(f748,plain,
( ! [X0] :
( sK0 = second(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(sK0,sK0))))
| ~ member(X0,universal_class) )
| ~ spl9_1
| ~ spl9_74 ),
inference(resolution,[],[f729,f275]) ).
fof(f980,plain,
( spl9_107
| ~ spl9_7
| ~ spl9_55 ),
inference(avatar_split_clause,[],[f630,f606,f302,f978]) ).
fof(f978,plain,
( spl9_107
<=> ! [X0] :
( ~ member(X0,sK2)
| unordered_pair(sK0,sK0) = X0
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_107])]) ).
fof(f606,plain,
( spl9_55
<=> ! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
fof(f630,plain,
( ! [X0] :
( ~ member(X0,sK2)
| unordered_pair(sK0,sK0) = X0
| unordered_pair(sK0,unordered_pair(sK1,sK1)) = X0 )
| ~ spl9_7
| ~ spl9_55 ),
inference(superposition,[],[f607,f304]) ).
fof(f607,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 )
| ~ spl9_55 ),
inference(avatar_component_clause,[],[f606]) ).
fof(f973,plain,
( ~ spl9_15
| spl9_105 ),
inference(avatar_contradiction_clause,[],[f972]) ).
fof(f972,plain,
( $false
| ~ spl9_15
| spl9_105 ),
inference(resolution,[],[f966,f339]) ).
fof(f966,plain,
( ~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class)
| spl9_105 ),
inference(avatar_component_clause,[],[f964]) ).
fof(f964,plain,
( spl9_105
<=> member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_105])]) ).
fof(f971,plain,
( ~ spl9_105
| spl9_106
| ~ spl9_7
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f489,f457,f302,f968,f964]) ).
fof(f968,plain,
( spl9_106
<=> member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_106])]) ).
fof(f457,plain,
( spl9_41
<=> ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
fof(f489,plain,
( member(unordered_pair(sK0,unordered_pair(sK1,sK1)),sK2)
| ~ member(unordered_pair(sK0,unordered_pair(sK1,sK1)),universal_class)
| ~ spl9_7
| ~ spl9_41 ),
inference(superposition,[],[f458,f304]) ).
fof(f458,plain,
( ! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) )
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f457]) ).
fof(f956,plain,
( spl9_104
| ~ spl9_7
| ~ spl9_79 ),
inference(avatar_split_clause,[],[f790,f778,f302,f954]) ).
fof(f954,plain,
( spl9_104
<=> ! [X0,X1] :
( member(sK2,cross_product(X0,X1))
| ~ member(sK1,X1)
| ~ member(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_104])]) ).
fof(f778,plain,
( spl9_79
<=> ! [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,[spl9_79])]) ).
fof(f790,plain,
( ! [X0,X1] :
( member(sK2,cross_product(X0,X1))
| ~ member(sK1,X1)
| ~ member(sK0,X0) )
| ~ spl9_7
| ~ spl9_79 ),
inference(superposition,[],[f779,f304]) ).
fof(f779,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) )
| ~ spl9_79 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f949,plain,
( spl9_102
| ~ spl9_103
| ~ spl9_7
| ~ spl9_77 ),
inference(avatar_split_clause,[],[f772,f741,f302,f946,f942]) ).
fof(f942,plain,
( spl9_102
<=> sK1 = union(sK0,unordered_pair(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_102])]) ).
fof(f946,plain,
( spl9_103
<=> member(sK2,successor_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_103])]) ).
fof(f741,plain,
( spl9_77
<=> ! [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,[spl9_77])]) ).
fof(f772,plain,
( ~ member(sK2,successor_relation)
| sK1 = union(sK0,unordered_pair(sK0,sK0))
| ~ spl9_7
| ~ spl9_77 ),
inference(superposition,[],[f742,f304]) ).
fof(f742,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 )
| ~ spl9_77 ),
inference(avatar_component_clause,[],[f741]) ).
fof(f937,plain,
( ~ spl9_15
| spl9_100 ),
inference(avatar_contradiction_clause,[],[f936]) ).
fof(f936,plain,
( $false
| ~ spl9_15
| spl9_100 ),
inference(resolution,[],[f930,f339]) ).
fof(f930,plain,
( ~ member(unordered_pair(sK0,sK0),universal_class)
| spl9_100 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f928,plain,
( spl9_100
<=> member(unordered_pair(sK0,sK0),universal_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_100])]) ).
fof(f935,plain,
( ~ spl9_100
| spl9_101
| ~ spl9_7
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f491,f461,f302,f932,f928]) ).
fof(f932,plain,
( spl9_101
<=> member(unordered_pair(sK0,sK0),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_101])]) ).
fof(f461,plain,
( spl9_42
<=> ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f491,plain,
( member(unordered_pair(sK0,sK0),sK2)
| ~ member(unordered_pair(sK0,sK0),universal_class)
| ~ spl9_7
| ~ spl9_42 ),
inference(superposition,[],[f462,f304]) ).
fof(f462,plain,
( ! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) )
| ~ spl9_42 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f926,plain,
( spl9_99
| ~ spl9_7
| ~ spl9_70 ),
inference(avatar_split_clause,[],[f704,f693,f302,f924]) ).
fof(f924,plain,
( spl9_99
<=> ! [X0,X1] :
( ~ member(sK2,cross_product(X0,X1))
| member(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_99])]) ).
fof(f693,plain,
( spl9_70
<=> ! [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,[spl9_70])]) ).
fof(f704,plain,
( ! [X0,X1] :
( ~ member(sK2,cross_product(X0,X1))
| member(sK0,X0) )
| ~ spl9_7
| ~ spl9_70 ),
inference(superposition,[],[f694,f304]) ).
fof(f694,plain,
( ! [X2,X3,X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),cross_product(X2,X3))
| member(X0,X2) )
| ~ spl9_70 ),
inference(avatar_component_clause,[],[f693]) ).
fof(f922,plain,
( spl9_98
| ~ spl9_7
| ~ spl9_69 ),
inference(avatar_split_clause,[],[f703,f689,f302,f920]) ).
fof(f920,plain,
( spl9_98
<=> ! [X0,X1] :
( ~ member(sK2,cross_product(X0,X1))
| member(sK1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_98])]) ).
fof(f689,plain,
( spl9_69
<=> ! [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,[spl9_69])]) ).
fof(f703,plain,
( ! [X0,X1] :
( ~ member(sK2,cross_product(X0,X1))
| member(sK1,X1) )
| ~ spl9_7
| ~ spl9_69 ),
inference(superposition,[],[f690,f304]) ).
fof(f690,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) )
| ~ spl9_69 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f918,plain,
( spl9_97
| ~ spl9_20
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f534,f501,f360,f916]) ).
fof(f916,plain,
( spl9_97
<=> ! [X0] :
( member(sK2,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_97])]) ).
fof(f534,plain,
( ! [X0] :
( member(sK2,X0)
| ~ subclass(universal_class,X0) )
| ~ spl9_20
| ~ spl9_46 ),
inference(resolution,[],[f502,f362]) ).
fof(f908,plain,
( spl9_96
| ~ spl9_2
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f585,f562,f278,f906]) ).
fof(f906,plain,
( spl9_96
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_96])]) ).
fof(f585,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK1) )
| ~ spl9_2
| ~ spl9_52 ),
inference(resolution,[],[f563,f280]) ).
fof(f904,plain,
( spl9_95
| ~ spl9_1
| ~ spl9_52 ),
inference(avatar_split_clause,[],[f584,f562,f273,f902]) ).
fof(f902,plain,
( spl9_95
<=> ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_95])]) ).
fof(f584,plain,
( ! [X0] :
( member(X0,sum_class(universal_class))
| ~ member(X0,sK0) )
| ~ spl9_1
| ~ spl9_52 ),
inference(resolution,[],[f563,f275]) ).
fof(f894,plain,
( spl9_93
| ~ spl9_94
| ~ spl9_7
| ~ spl9_61 ),
inference(avatar_split_clause,[],[f670,f650,f302,f891,f887]) ).
fof(f887,plain,
( spl9_93
<=> member(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_93])]) ).
fof(f891,plain,
( spl9_94
<=> member(sK2,element_relation) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_94])]) ).
fof(f650,plain,
( spl9_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,[spl9_61])]) ).
fof(f670,plain,
( ~ member(sK2,element_relation)
| member(sK0,sK1)
| ~ spl9_7
| ~ spl9_61 ),
inference(superposition,[],[f651,f304]) ).
fof(f651,plain,
( ! [X0,X1] :
( ~ member(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),element_relation)
| member(X0,X1) )
| ~ spl9_61 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f883,plain,
( spl9_92
| ~ spl9_2
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f533,f501,f278,f881]) ).
fof(f881,plain,
( spl9_92
<=> ! [X0] :
( member(sK1,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_92])]) ).
fof(f533,plain,
( ! [X0] :
( member(sK1,X0)
| ~ subclass(universal_class,X0) )
| ~ spl9_2
| ~ spl9_46 ),
inference(resolution,[],[f502,f280]) ).
fof(f877,plain,
spl9_91,
inference(avatar_split_clause,[],[f262,f875]) ).
fof(f875,plain,
( spl9_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))),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,[spl9_91])]) ).
fof(f262,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,[],[f222,f231,f231,f231,f231,f231,f231]) ).
fof(f231,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f169,f146,f146]) ).
fof(f146,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(f169,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(f222,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,[],[f132]) ).
fof(f132,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,[],[f131]) ).
fof(f131,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,[],[f69]) ).
fof(f69,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(f873,plain,
spl9_90,
inference(avatar_split_clause,[],[f259,f871]) ).
fof(f871,plain,
( spl9_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))),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,[spl9_90])]) ).
fof(f259,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,[],[f219,f231,f231,f231,f231,f231,f231]) ).
fof(f219,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,[],[f130]) ).
fof(f130,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,[],[f129]) ).
fof(f129,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,[],[f68]) ).
fof(f68,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(f867,plain,
spl9_89,
inference(avatar_split_clause,[],[f264,f865]) ).
fof(f264,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,[],[f220,f231,f231,f231,f231]) ).
fof(f220,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,[],[f132]) ).
fof(f863,plain,
spl9_88,
inference(avatar_split_clause,[],[f261,f861]) ).
fof(f261,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,[],[f217,f231,f231,f231,f231]) ).
fof(f217,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,[],[f130]) ).
fof(f857,plain,
spl9_87,
inference(avatar_split_clause,[],[f263,f855]) ).
fof(f855,plain,
( spl9_87
<=> ! [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,[spl9_87])]) ).
fof(f263,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,[],[f221,f231,f231,f231,f231]) ).
fof(f221,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,[],[f132]) ).
fof(f853,plain,
( spl9_86
| ~ spl9_1
| ~ spl9_46 ),
inference(avatar_split_clause,[],[f532,f501,f273,f851]) ).
fof(f851,plain,
( spl9_86
<=> ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_86])]) ).
fof(f532,plain,
( ! [X0] :
( member(sK0,X0)
| ~ subclass(universal_class,X0) )
| ~ spl9_1
| ~ spl9_46 ),
inference(resolution,[],[f502,f275]) ).
fof(f849,plain,
spl9_85,
inference(avatar_split_clause,[],[f260,f847]) ).
fof(f847,plain,
( spl9_85
<=> ! [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,[spl9_85])]) ).
fof(f260,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,[],[f218,f231,f231,f231,f231]) ).
fof(f218,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,[],[f130]) ).
fof(f839,plain,
spl9_84,
inference(avatar_split_clause,[],[f253,f837]) ).
fof(f837,plain,
( spl9_84
<=> ! [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,[spl9_84])]) ).
fof(f253,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,[],[f213,f231,f230,f230,f146]) ).
fof(f230,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,[],[f168,f229,f199]) ).
fof(f199,plain,
! [X2,X0,X1] : restrict(X1,X0,X2) = intersection(X1,cross_product(X0,X2)),
inference(cnf_transformation,[],[f61]) ).
fof(f61,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(f229,plain,
! [X0] : range_of(X0) = domain_of(domain_of(flip(cross_product(X0,universal_class)))),
inference(definition_unfolding,[],[f145,f148]) ).
fof(f148,plain,
! [X0] : inverse(X0) = domain_of(flip(cross_product(X0,universal_class))),
inference(cnf_transformation,[],[f48]) ).
fof(f48,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(f145,plain,
! [X0] : range_of(X0) = domain_of(inverse(X0)),
inference(cnf_transformation,[],[f47]) ).
fof(f47,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(f168,plain,
! [X0,X1] : image(X1,X0) = range_of(restrict(X1,X0,universal_class)),
inference(cnf_transformation,[],[f55]) ).
fof(f55,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(f213,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,[],[f126]) ).
fof(f126,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,[],[f125]) ).
fof(f125,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,[],[f66]) ).
fof(f66,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(f834,plain,
spl9_83,
inference(avatar_split_clause,[],[f254,f832]) ).
fof(f254,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,[],[f212,f230,f230,f146,f231]) ).
fof(f212,plain,
! [X2,X3,X0,X1] :
( member(X3,image(X1,image(X0,singleton(X2))))
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f825,plain,
spl9_82,
inference(avatar_split_clause,[],[f269,f823]) ).
fof(f823,plain,
( spl9_82
<=> ! [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,[spl9_82])]) ).
fof(f269,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,[],[f248]) ).
fof(f248,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,[],[f198,f231,f228]) ).
fof(f228,plain,
! [X0] : successor(X0) = union(X0,unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f147,f146]) ).
fof(f147,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(f198,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),successor_relation)
| successor(X0) != X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,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,[],[f117]) ).
fof(f117,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(f798,plain,
spl9_81,
inference(avatar_split_clause,[],[f265,f796]) ).
fof(f796,plain,
( spl9_81
<=> ! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK7,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_81])]) ).
fof(f265,plain,
! [X1] :
( member(sum_class(domain_of(domain_of(flip(cross_product(intersection(sK7,cross_product(unordered_pair(X1,X1),universal_class)),universal_class))))),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f224,f232]) ).
fof(f232,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,[],[f167,f230,f146]) ).
fof(f167,plain,
! [X0,X1] : apply(X0,X1) = sum_class(image(X0,singleton(X1))),
inference(cnf_transformation,[],[f54]) ).
fof(f54,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(f224,plain,
! [X1] :
( member(apply(sK7,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
( ! [X1] :
( member(apply(sK7,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f85,f133]) ).
fof(f133,plain,
( ? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) )
=> ( ! [X1] :
( member(apply(sK7,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
? [X0] :
( ! [X1] :
( member(apply(X0,X1),X1)
| null_class = X1
| ~ member(X1,universal_class) )
& function(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,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(f794,plain,
spl9_80,
inference(avatar_split_clause,[],[f252,f792]) ).
fof(f792,plain,
( spl9_80
<=> ! [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,[spl9_80])]) ).
fof(f252,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,[],[f200,f231]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ordered_pair(first(X2),second(X2)) = X2
| ~ member(X2,cross_product(X0,X1)) ),
inference(ennf_transformation,[],[f62]) ).
fof(f62,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(f780,plain,
spl9_79,
inference(avatar_split_clause,[],[f256,f778]) ).
fof(f256,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,[],[f216,f231]) ).
fof(f216,plain,
! [X2,X3,X0,X1] :
( member(ordered_pair(X0,X1),cross_product(X2,X3))
| ~ member(X1,X3)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,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,[],[f127]) ).
fof(f127,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,[],[f67]) ).
fof(f67,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(f776,plain,
spl9_78,
inference(avatar_split_clause,[],[f239,f774]) ).
fof(f774,plain,
( spl9_78
<=> ! [X0] :
( unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK4(X0),sK4(X0)))) = X0
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_78])]) ).
fof(f239,plain,
! [X0] :
( unordered_pair(unordered_pair(sK4(X0),sK4(X0)),unordered_pair(sK4(X0),unordered_pair(sK4(X0),sK4(X0)))) = X0
| ~ member(X0,identity_relation) ),
inference(definition_unfolding,[],[f163,f231]) ).
fof(f163,plain,
! [X0] :
( ordered_pair(sK4(X0),sK4(X0)) = X0
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0] :
( ( member(X0,identity_relation)
| ! [X1] :
( ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ) )
& ( ( ordered_pair(sK4(X0),sK4(X0)) = X0
& member(sK4(X0),universal_class) )
| ~ member(X0,identity_relation) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f96,f97]) ).
fof(f97,plain,
! [X0] :
( ? [X2] :
( ordered_pair(X2,X2) = X0
& member(X2,universal_class) )
=> ( ordered_pair(sK4(X0),sK4(X0)) = X0
& member(sK4(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f96,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,[],[f95]) ).
fof(f95,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,[],[f52]) ).
fof(f52,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(f743,plain,
spl9_77,
inference(avatar_split_clause,[],[f249,f741]) ).
fof(f249,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,[],[f197,f228,f231]) ).
fof(f197,plain,
! [X0,X1] :
( successor(X0) = X1
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f739,plain,
spl9_76,
inference(avatar_split_clause,[],[f242,f737]) ).
fof(f242,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,[],[f171,f231]) ).
fof(f171,plain,
! [X0,X1] :
( first(ordered_pair(X0,X1)) = X0
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,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,[],[f79]) ).
fof(f79,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(f735,plain,
( ~ spl9_75
| ~ spl9_14
| spl9_59 ),
inference(avatar_split_clause,[],[f701,f641,f334,f732]) ).
fof(f701,plain,
( ~ inductive(universal_class)
| ~ spl9_14
| spl9_59 ),
inference(resolution,[],[f642,f335]) ).
fof(f642,plain,
( ~ member(null_class,universal_class)
| spl9_59 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f730,plain,
spl9_74,
inference(avatar_split_clause,[],[f241,f728]) ).
fof(f241,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,[],[f172,f231]) ).
fof(f172,plain,
! [X0,X1] :
( second(ordered_pair(X0,X1)) = X1
| ~ member(X1,universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f80]) ).
fof(f716,plain,
spl9_73,
inference(avatar_split_clause,[],[f245,f714]) ).
fof(f714,plain,
( spl9_73
<=> ! [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,[spl9_73])]) ).
fof(f245,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,[],[f194,f231]) ).
fof(f194,plain,
! [X0,X1] :
( member(ordered_pair(X0,X1),element_relation)
| ~ member(X0,X1)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,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,[],[f115]) ).
fof(f115,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(f712,plain,
spl9_72,
inference(avatar_split_clause,[],[f240,f710]) ).
fof(f710,plain,
( spl9_72
<=> ! [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,[spl9_72])]) ).
fof(f240,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,[],[f170,f230]) ).
fof(f170,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( member(image(X1,X0),universal_class)
| ~ function(X1)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,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(f708,plain,
spl9_71,
inference(avatar_split_clause,[],[f234,f706]) ).
fof(f234,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,[],[f158,f230]) ).
fof(f158,plain,
! [X0] :
( inductive(X0)
| ~ subclass(image(successor_relation,X0),X0)
| ~ member(null_class,X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,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,[],[f91]) ).
fof(f91,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(f695,plain,
spl9_70,
inference(avatar_split_clause,[],[f258,f693]) ).
fof(f258,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,[],[f214,f231]) ).
fof(f214,plain,
! [X2,X3,X0,X1] :
( member(X0,X2)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f691,plain,
spl9_69,
inference(avatar_split_clause,[],[f257,f689]) ).
fof(f257,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,[],[f215,f231]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( member(X1,X3)
| ~ member(ordered_pair(X0,X1),cross_product(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f687,plain,
spl9_68,
inference(avatar_split_clause,[],[f255,f685]) ).
fof(f685,plain,
( spl9_68
<=> ! [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,[spl9_68])]) ).
fof(f255,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,[],[f211,f231]) ).
fof(f211,plain,
! [X2,X3,X0,X1] :
( member(X2,universal_class)
| ~ member(ordered_pair(X2,X3),compose(X1,X0)) ),
inference(cnf_transformation,[],[f126]) ).
fof(f683,plain,
spl9_67,
inference(avatar_split_clause,[],[f243,f681]) ).
fof(f681,plain,
( spl9_67
<=> ! [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,[spl9_67])]) ).
fof(f243,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,[],[f188,f199,f146]) ).
fof(f188,plain,
! [X0,X1] :
( member(X1,domain_of(X0))
| null_class = restrict(X0,singleton(X1),universal_class)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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,[],[f109]) ).
fof(f109,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,[],[f59]) ).
fof(f59,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(f679,plain,
spl9_66,
inference(avatar_split_clause,[],[f236,f677]) ).
fof(f677,plain,
( spl9_66
<=> ! [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,[spl9_66])]) ).
fof(f236,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,[],[f161,f148]) ).
fof(f161,plain,
! [X0] :
( function(X0)
| ~ subclass(compose(X0,inverse(X0)),identity_relation)
| ~ subclass(X0,cross_product(universal_class,universal_class)) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,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,[],[f93]) ).
fof(f93,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,[],[f51]) ).
fof(f51,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(f668,plain,
spl9_65,
inference(avatar_split_clause,[],[f266,f666]) ).
fof(f666,plain,
( spl9_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,[spl9_65])]) ).
fof(f266,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,[],[f238]) ).
fof(f238,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,[],[f164,f231]) ).
fof(f164,plain,
! [X0,X1] :
( member(X0,identity_relation)
| ordered_pair(X1,X1) != X0
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f98]) ).
fof(f664,plain,
spl9_64,
inference(avatar_split_clause,[],[f251,f662]) ).
fof(f662,plain,
( spl9_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,[spl9_64])]) ).
fof(f251,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,[],[f195,f231]) ).
fof(f195,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f660,plain,
spl9_63,
inference(avatar_split_clause,[],[f250,f658]) ).
fof(f658,plain,
( spl9_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,[spl9_63])]) ).
fof(f250,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,[],[f196,f231]) ).
fof(f196,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),successor_relation) ),
inference(cnf_transformation,[],[f118]) ).
fof(f656,plain,
spl9_62,
inference(avatar_split_clause,[],[f247,f654]) ).
fof(f654,plain,
( spl9_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,[spl9_62])]) ).
fof(f247,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,[],[f192,f231]) ).
fof(f192,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f116]) ).
fof(f652,plain,
spl9_61,
inference(avatar_split_clause,[],[f246,f650]) ).
fof(f246,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,[],[f193,f231]) ).
fof(f193,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(ordered_pair(X0,X1),element_relation) ),
inference(cnf_transformation,[],[f116]) ).
fof(f648,plain,
spl9_60,
inference(avatar_split_clause,[],[f235,f646]) ).
fof(f646,plain,
( spl9_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,[spl9_60])]) ).
fof(f235,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,[],[f157,f230]) ).
fof(f157,plain,
! [X0] :
( subclass(image(successor_relation,X0),X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f644,plain,
( ~ spl9_58
| spl9_59
| ~ spl9_14
| ~ spl9_49 ),
inference(avatar_split_clause,[],[f573,f513,f334,f641,f637]) ).
fof(f637,plain,
( spl9_58
<=> inductive(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_58])]) ).
fof(f513,plain,
( spl9_49
<=> ! [X0] :
( ~ member(X0,sK2)
| member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
fof(f573,plain,
( member(null_class,universal_class)
| ~ inductive(sK2)
| ~ spl9_14
| ~ spl9_49 ),
inference(resolution,[],[f514,f335]) ).
fof(f514,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,universal_class) )
| ~ spl9_49 ),
inference(avatar_component_clause,[],[f513]) ).
fof(f635,plain,
spl9_57,
inference(avatar_split_clause,[],[f244,f633]) ).
fof(f633,plain,
( spl9_57
<=> ! [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,[spl9_57])]) ).
fof(f244,plain,
! [X0,X1] :
( null_class != intersection(X0,cross_product(unordered_pair(X1,X1),universal_class))
| ~ member(X1,domain_of(X0)) ),
inference(definition_unfolding,[],[f187,f199,f146]) ).
fof(f187,plain,
! [X0,X1] :
( null_class != restrict(X0,singleton(X1),universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f612,plain,
spl9_56,
inference(avatar_split_clause,[],[f237,f610]) ).
fof(f610,plain,
( spl9_56
<=> ! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
fof(f237,plain,
! [X0] :
( subclass(compose(X0,domain_of(flip(cross_product(X0,universal_class)))),identity_relation)
| ~ function(X0) ),
inference(definition_unfolding,[],[f160,f148]) ).
fof(f160,plain,
! [X0] :
( subclass(compose(X0,inverse(X0)),identity_relation)
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f608,plain,
spl9_55,
inference(avatar_split_clause,[],[f208,f606]) ).
fof(f208,plain,
! [X2,X0,X1] :
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f124,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,[],[f123]) ).
fof(f123,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,[],[f65]) ).
fof(f65,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(f604,plain,
spl9_54,
inference(avatar_split_clause,[],[f204,f602]) ).
fof(f602,plain,
( spl9_54
<=> ! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
fof(f204,plain,
! [X2,X0,X1] :
( member(X2,X1)
| member(X2,X0)
| ~ member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,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,[],[f121]) ).
fof(f121,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,[],[f64]) ).
fof(f64,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(f600,plain,
spl9_53,
inference(avatar_split_clause,[],[f203,f598]) ).
fof(f598,plain,
( spl9_53
<=> ! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
fof(f203,plain,
! [X2,X0,X1] :
( member(X2,intersection(X0,X1))
| ~ member(X2,X1)
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,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,[],[f119]) ).
fof(f119,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,[],[f63]) ).
fof(f63,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(f564,plain,
spl9_52,
inference(avatar_split_clause,[],[f191,f562]) ).
fof(f191,plain,
! [X2,X0,X1] :
( member(X0,sum_class(X1))
| ~ member(X2,X1)
| ~ member(X0,X2) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1] :
( ( member(X0,sum_class(X1))
| ! [X2] :
( ~ member(X2,X1)
| ~ member(X0,X2) ) )
& ( ( member(sK6(X0,X1),X1)
& member(X0,sK6(X0,X1)) )
| ~ member(X0,sum_class(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f112,f113]) ).
fof(f113,plain,
! [X0,X1] :
( ? [X3] :
( member(X3,X1)
& member(X0,X3) )
=> ( member(sK6(X0,X1),X1)
& member(X0,sK6(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f112,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,[],[f111]) ).
fof(f111,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,[],[f60]) ).
fof(f60,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(f560,plain,
spl9_51,
inference(avatar_split_clause,[],[f185,f558]) ).
fof(f558,plain,
( spl9_51
<=> ! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
fof(f185,plain,
! [X0,X1] :
( member(X0,power_class(X1))
| ~ subclass(X0,X1)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,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,[],[f107]) ).
fof(f107,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,[],[f58]) ).
fof(f58,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(f556,plain,
spl9_50,
inference(avatar_split_clause,[],[f182,f554]) ).
fof(f554,plain,
( spl9_50
<=> ! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f182,plain,
! [X0,X1] :
( member(X1,complement(X0))
| member(X1,X0)
| ~ member(X1,universal_class) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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,[],[f105]) ).
fof(f105,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,[],[f57]) ).
fof(f57,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(f515,plain,
( spl9_49
| ~ spl9_7
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f487,f453,f302,f513]) ).
fof(f453,plain,
( spl9_40
<=> ! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
fof(f487,plain,
( ! [X0] :
( ~ member(X0,sK2)
| member(X0,universal_class) )
| ~ spl9_7
| ~ spl9_40 ),
inference(superposition,[],[f454,f304]) ).
fof(f454,plain,
( ! [X2,X0,X1] :
( ~ member(X0,unordered_pair(X1,X2))
| member(X0,universal_class) )
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f511,plain,
spl9_48,
inference(avatar_split_clause,[],[f190,f509]) ).
fof(f190,plain,
! [X0,X1] :
( member(sK6(X0,X1),X1)
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f507,plain,
spl9_47,
inference(avatar_split_clause,[],[f189,f505]) ).
fof(f505,plain,
( spl9_47
<=> ! [X0,X1] :
( member(X0,sK6(X0,X1))
| ~ member(X0,sum_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
fof(f189,plain,
! [X0,X1] :
( member(X0,sK6(X0,X1))
| ~ member(X0,sum_class(X1)) ),
inference(cnf_transformation,[],[f114]) ).
fof(f503,plain,
spl9_46,
inference(avatar_split_clause,[],[f177,f501]) ).
fof(f177,plain,
! [X3,X0,X1] :
( member(X3,X1)
| ~ member(X3,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f102,f103]) ).
fof(f103,plain,
! [X0,X1] :
( ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) )
=> ( ~ member(sK5(X0,X1),X1)
& member(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f102,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,[],[f101]) ).
fof(f101,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,[],[f82]) ).
fof(f82,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(f499,plain,
spl9_45,
inference(avatar_split_clause,[],[f176,f497]) ).
fof(f497,plain,
( spl9_45
<=> ! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
fof(f176,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| ~ disjoint(X0,X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,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(f495,plain,
spl9_44,
inference(avatar_split_clause,[],[f175,f493]) ).
fof(f175,plain,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) )
& ( ( subclass(X1,X0)
& subclass(X0,X1) )
| X0 != X1 ) ),
inference(flattening,[],[f99]) ).
fof(f99,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(f481,plain,
( spl9_43
| ~ spl9_8
| ~ spl9_34 ),
inference(avatar_split_clause,[],[f466,f429,f307,f479]) ).
fof(f479,plain,
( spl9_43
<=> ! [X0] : subclass(null_class,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
fof(f429,plain,
( spl9_34
<=> ! [X0,X1] :
( subclass(X0,X1)
| member(sK5(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
fof(f466,plain,
( ! [X0] : subclass(null_class,X0)
| ~ spl9_8
| ~ spl9_34 ),
inference(resolution,[],[f430,f308]) ).
fof(f430,plain,
( ! [X0,X1] :
( member(sK5(X0,X1),X0)
| subclass(X0,X1) )
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f429]) ).
fof(f463,plain,
spl9_42,
inference(avatar_split_clause,[],[f271,f461]) ).
fof(f271,plain,
! [X2,X1] :
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(equality_resolution,[],[f209]) ).
fof(f209,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X1
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f459,plain,
spl9_41,
inference(avatar_split_clause,[],[f270,f457]) ).
fof(f270,plain,
! [X2,X1] :
( member(X2,unordered_pair(X1,X2))
| ~ member(X2,universal_class) ),
inference(equality_resolution,[],[f210]) ).
fof(f210,plain,
! [X2,X0,X1] :
( member(X0,unordered_pair(X1,X2))
| X0 != X2
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f124]) ).
fof(f455,plain,
spl9_40,
inference(avatar_split_clause,[],[f207,f453]) ).
fof(f207,plain,
! [X2,X0,X1] :
( member(X0,universal_class)
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f451,plain,
spl9_39,
inference(avatar_split_clause,[],[f206,f449]) ).
fof(f449,plain,
( spl9_39
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
fof(f206,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f447,plain,
spl9_38,
inference(avatar_split_clause,[],[f205,f445]) ).
fof(f445,plain,
( spl9_38
<=> ! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
fof(f205,plain,
! [X2,X0,X1] :
( member(X2,union(X0,X1))
| ~ member(X2,X0) ),
inference(cnf_transformation,[],[f122]) ).
fof(f443,plain,
spl9_37,
inference(avatar_split_clause,[],[f202,f441]) ).
fof(f202,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f439,plain,
spl9_36,
inference(avatar_split_clause,[],[f201,f437]) ).
fof(f201,plain,
! [X2,X0,X1] :
( member(X2,X0)
| ~ member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f435,plain,
spl9_35,
inference(avatar_split_clause,[],[f179,f433]) ).
fof(f433,plain,
( spl9_35
<=> ! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK5(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
fof(f179,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f104]) ).
fof(f431,plain,
spl9_34,
inference(avatar_split_clause,[],[f178,f429]) ).
fof(f178,plain,
! [X0,X1] :
( subclass(X0,X1)
| member(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f427,plain,
spl9_33,
inference(avatar_split_clause,[],[f150,f425]) ).
fof(f425,plain,
( spl9_33
<=> ! [X0] : subclass(flip(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
fof(f150,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(f423,plain,
spl9_32,
inference(avatar_split_clause,[],[f149,f421]) ).
fof(f421,plain,
( spl9_32
<=> ! [X0] : subclass(rotate(X0),cross_product(cross_product(universal_class,universal_class),universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
fof(f149,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(f413,plain,
( ~ spl9_31
| ~ spl9_8
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f345,f334,f307,f410]) ).
fof(f410,plain,
( spl9_31
<=> inductive(null_class) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
fof(f345,plain,
( ~ inductive(null_class)
| ~ spl9_8
| ~ spl9_14 ),
inference(resolution,[],[f335,f308]) ).
fof(f403,plain,
spl9_30,
inference(avatar_split_clause,[],[f186,f401]) ).
fof(f401,plain,
( spl9_30
<=> ! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f186,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,domain_of(X0)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f399,plain,
spl9_29,
inference(avatar_split_clause,[],[f184,f397]) ).
fof(f184,plain,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f395,plain,
spl9_28,
inference(avatar_split_clause,[],[f183,f393]) ).
fof(f393,plain,
( spl9_28
<=> ! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f183,plain,
! [X0,X1] :
( member(X0,universal_class)
| ~ member(X0,power_class(X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f391,plain,
spl9_27,
inference(avatar_split_clause,[],[f181,f389]) ).
fof(f181,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f387,plain,
spl9_26,
inference(avatar_split_clause,[],[f180,f385]) ).
fof(f180,plain,
! [X0,X1] :
( member(X1,universal_class)
| ~ member(X1,complement(X0)) ),
inference(cnf_transformation,[],[f106]) ).
fof(f383,plain,
spl9_25,
inference(avatar_split_clause,[],[f166,f381]) ).
fof(f381,plain,
( spl9_25
<=> ! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f166,plain,
! [X0,X1] : subclass(compose(X1,X0),cross_product(universal_class,universal_class)),
inference(cnf_transformation,[],[f53]) ).
fof(f53,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(f379,plain,
spl9_24,
inference(avatar_split_clause,[],[f162,f377]) ).
fof(f377,plain,
( spl9_24
<=> ! [X0] :
( member(sK4(X0),universal_class)
| ~ member(X0,identity_relation) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f162,plain,
! [X0] :
( member(sK4(X0),universal_class)
| ~ member(X0,identity_relation) ),
inference(cnf_transformation,[],[f98]) ).
fof(f375,plain,
spl9_23,
inference(avatar_split_clause,[],[f159,f373]) ).
fof(f373,plain,
( spl9_23
<=> ! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f159,plain,
! [X0] :
( subclass(X0,cross_product(universal_class,universal_class))
| ~ function(X0) ),
inference(cnf_transformation,[],[f94]) ).
fof(f371,plain,
spl9_22,
inference(avatar_split_clause,[],[f155,f369]) ).
fof(f369,plain,
( spl9_22
<=> ! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f155,plain,
! [X0] :
( member(sum_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,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(f367,plain,
spl9_21,
inference(avatar_split_clause,[],[f154,f365]) ).
fof(f365,plain,
( spl9_21
<=> ! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f154,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0] :
( member(power_class(X0),universal_class)
| ~ member(X0,universal_class) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,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(f363,plain,
( spl9_20
| ~ spl9_7
| ~ spl9_15 ),
inference(avatar_split_clause,[],[f346,f338,f302,f360]) ).
fof(f346,plain,
( member(sK2,universal_class)
| ~ spl9_7
| ~ spl9_15 ),
inference(superposition,[],[f339,f304]) ).
fof(f358,plain,
spl9_19,
inference(avatar_split_clause,[],[f153,f356]) ).
fof(f356,plain,
( spl9_19
<=> ! [X0] :
( disjoint(sK3(X0),X0)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f153,plain,
! [X0] :
( disjoint(sK3(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0] :
( ( disjoint(sK3(X0),X0)
& member(sK3(X0),X0)
& member(sK3(X0),universal_class) )
| null_class = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f74,f89]) ).
fof(f89,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
=> ( disjoint(sK3(X0),X0)
& member(sK3(X0),X0)
& member(sK3(X0),universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0] :
( ? [X1] :
( disjoint(X1,X0)
& member(X1,X0)
& member(X1,universal_class) )
| null_class = X0 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,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(f354,plain,
spl9_18,
inference(avatar_split_clause,[],[f152,f352]) ).
fof(f152,plain,
! [X0] :
( member(sK3(X0),X0)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f350,plain,
spl9_17,
inference(avatar_split_clause,[],[f151,f348]) ).
fof(f348,plain,
( spl9_17
<=> ! [X0] :
( member(sK3(X0),universal_class)
| null_class = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f151,plain,
! [X0] :
( member(sK3(X0),universal_class)
| null_class = X0 ),
inference(cnf_transformation,[],[f90]) ).
fof(f344,plain,
spl9_16,
inference(avatar_split_clause,[],[f227,f342]) ).
fof(f227,plain,
! [X1] :
( subclass(sK8,X1)
| ~ inductive(X1) ),
inference(cnf_transformation,[],[f136]) ).
fof(f136,plain,
( ! [X1] :
( subclass(sK8,X1)
| ~ inductive(X1) )
& inductive(sK8)
& member(sK8,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f86,f135]) ).
fof(f135,plain,
( ? [X0] :
( ! [X1] :
( subclass(X0,X1)
| ~ inductive(X1) )
& inductive(X0)
& member(X0,universal_class) )
=> ( ! [X1] :
( subclass(sK8,X1)
| ~ inductive(X1) )
& inductive(sK8)
& member(sK8,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f86,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(f340,plain,
spl9_15,
inference(avatar_split_clause,[],[f165,f338]) ).
fof(f165,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(f336,plain,
spl9_14,
inference(avatar_split_clause,[],[f156,f334]) ).
fof(f156,plain,
! [X0] :
( member(null_class,X0)
| ~ inductive(X0) ),
inference(cnf_transformation,[],[f92]) ).
fof(f332,plain,
spl9_13,
inference(avatar_split_clause,[],[f142,f329]) ).
fof(f329,plain,
( spl9_13
<=> subclass(successor_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f142,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(f327,plain,
spl9_12,
inference(avatar_split_clause,[],[f141,f324]) ).
fof(f324,plain,
( spl9_12
<=> subclass(element_relation,cross_product(universal_class,universal_class)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f141,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(f322,plain,
spl9_11,
inference(avatar_split_clause,[],[f267,f320]) ).
fof(f320,plain,
( spl9_11
<=> ! [X1] : subclass(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f267,plain,
! [X1] : subclass(X1,X1),
inference(equality_resolution,[],[f174]) ).
fof(f174,plain,
! [X0,X1] :
( subclass(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f100]) ).
fof(f318,plain,
spl9_10,
inference(avatar_split_clause,[],[f225,f315]) ).
fof(f225,plain,
member(sK8,universal_class),
inference(cnf_transformation,[],[f136]) ).
fof(f313,plain,
spl9_9,
inference(avatar_split_clause,[],[f144,f311]) ).
fof(f144,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(f309,plain,
spl9_8,
inference(avatar_split_clause,[],[f143,f307]) ).
fof(f143,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(f305,plain,
spl9_7,
inference(avatar_split_clause,[],[f233,f302]) ).
fof(f233,plain,
sK2 = unordered_pair(unordered_pair(sK0,sK0),unordered_pair(sK0,unordered_pair(sK1,sK1))),
inference(definition_unfolding,[],[f139,f231]) ).
fof(f139,plain,
sK2 = ordered_pair(sK0,sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( ( sK1 != second(sK2)
| sK0 != first(sK2) )
& sK2 = ordered_pair(sK0,sK1)
& member(sK1,universal_class)
& member(sK0,universal_class) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f73,f87]) ).
fof(f87,plain,
( ? [X0,X1,X2] :
( ( second(X2) != X1
| first(X2) != X0 )
& ordered_pair(X0,X1) = X2
& member(X1,universal_class)
& member(X0,universal_class) )
=> ( ( sK1 != second(sK2)
| sK0 != first(sK2) )
& sK2 = ordered_pair(sK0,sK1)
& member(sK1,universal_class)
& member(sK0,universal_class) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
? [X0,X1,X2] :
( ( second(X2) != X1
| first(X2) != X0 )
& ordered_pair(X0,X1) = X2
& member(X1,universal_class)
& member(X0,universal_class) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
? [X0,X1,X2] :
( ( second(X2) != X1
| first(X2) != X0 )
& ordered_pair(X0,X1) = X2
& member(X1,universal_class)
& member(X0,universal_class) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,plain,
~ ! [X0,X1,X2] :
( ( ordered_pair(X0,X1) = X2
& member(X1,universal_class)
& member(X0,universal_class) )
=> ( second(X2) = X1
& first(X2) = X0 ) ),
inference(rectify,[],[f45]) ).
fof(f45,negated_conjecture,
~ ! [X2,X3,X0] :
( ( ordered_pair(X2,X3) = X0
& member(X3,universal_class)
& member(X2,universal_class) )
=> ( second(X0) = X3
& first(X0) = X2 ) ),
inference(negated_conjecture,[],[f44]) ).
fof(f44,conjecture,
! [X2,X3,X0] :
( ( ordered_pair(X2,X3) = X0
& member(X3,universal_class)
& member(X2,universal_class) )
=> ( second(X0) = X3
& first(X0) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(f300,plain,
spl9_6,
inference(avatar_split_clause,[],[f226,f297]) ).
fof(f297,plain,
( spl9_6
<=> inductive(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f226,plain,
inductive(sK8),
inference(cnf_transformation,[],[f136]) ).
fof(f295,plain,
spl9_5,
inference(avatar_split_clause,[],[f223,f292]) ).
fof(f292,plain,
( spl9_5
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f223,plain,
function(sK7),
inference(cnf_transformation,[],[f134]) ).
fof(f290,plain,
( ~ spl9_3
| ~ spl9_4 ),
inference(avatar_split_clause,[],[f140,f287,f283]) ).
fof(f140,plain,
( sK1 != second(sK2)
| sK0 != first(sK2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f281,plain,
spl9_2,
inference(avatar_split_clause,[],[f138,f278]) ).
fof(f138,plain,
member(sK1,universal_class),
inference(cnf_transformation,[],[f88]) ).
fof(f276,plain,
spl9_1,
inference(avatar_split_clause,[],[f137,f273]) ).
fof(f137,plain,
member(sK0,universal_class),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 01:35:44 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (5981)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (5985)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (5983)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (5984)WARNING: value z3 for option sas not known
% 0.13/0.36 % (5984)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)
% 0.13/0.36 % (5986)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)
% 0.13/0.37 % (5988)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)
% 0.13/0.37 % (5987)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)
% 0.13/0.37 % (5982)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 TRYING [2]
% 0.13/0.39 % (5986)First to succeed.
% 0.13/0.39 TRYING [1]
% 0.13/0.40 TRYING [3]
% 0.13/0.40 TRYING [2]
% 0.13/0.40 % (5986)Refutation found. Thanks to Tanya!
% 0.13/0.40 % SZS status Theorem for theBenchmark
% 0.13/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.41 % (5986)------------------------------
% 0.13/0.41 % (5986)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.41 % (5986)Termination reason: Refutation
% 0.13/0.41
% 0.13/0.41 % (5986)Memory used [KB]: 1535
% 0.13/0.41 % (5986)Time elapsed: 0.038 s
% 0.13/0.41 % (5986)Instructions burned: 70 (million)
% 0.13/0.41 % (5986)------------------------------
% 0.13/0.41 % (5986)------------------------------
% 0.13/0.41 % (5981)Success in time 0.056 s
%------------------------------------------------------------------------------