TSTP Solution File: SEU044+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.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 15:22:01 EDT 2024
% Result : Theorem 0.16s 0.36s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 171
% Syntax : Number of formulae : 556 ( 87 unt; 0 def)
% Number of atoms : 1839 ( 92 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2230 ( 947 ~; 976 |; 132 &)
% ( 138 <=>; 35 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 135 ( 133 usr; 125 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-3 aty)
% Number of variables : 625 ( 577 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1177,plain,
$false,
inference(avatar_sat_refutation,[],[f173,f178,f183,f188,f193,f198,f203,f208,f213,f218,f223,f228,f233,f238,f243,f248,f253,f258,f267,f272,f276,f280,f284,f288,f292,f296,f310,f314,f319,f323,f327,f331,f335,f353,f357,f361,f365,f373,f377,f381,f385,f400,f404,f414,f425,f429,f439,f443,f447,f451,f455,f468,f479,f485,f491,f501,f505,f512,f518,f524,f529,f538,f543,f553,f558,f564,f569,f573,f578,f584,f589,f594,f606,f611,f617,f621,f628,f634,f635,f636,f637,f638,f661,f699,f702,f706,f710,f729,f733,f742,f746,f750,f779,f783,f794,f799,f803,f819,f829,f833,f837,f847,f851,f867,f884,f885,f889,f893,f897,f915,f919,f923,f940,f945,f955,f959,f986,f1005,f1024,f1028,f1049,f1053,f1073,f1092,f1107,f1114,f1116,f1126,f1127,f1133,f1138,f1165,f1172,f1175,f1176]) ).
fof(f1176,plain,
( ~ spl17_80
| ~ spl17_81
| ~ spl17_1
| ~ spl17_2
| spl17_19
| ~ spl17_52
| ~ spl17_109 ),
inference(avatar_split_clause,[],[f1174,f943,f453,f260,f175,f170,f692,f688]) ).
fof(f688,plain,
( spl17_80
<=> relation(relation_rng_restriction(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_80])]) ).
fof(f692,plain,
( spl17_81
<=> function(relation_rng_restriction(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_81])]) ).
fof(f170,plain,
( spl17_1
<=> relation(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f175,plain,
( spl17_2
<=> function(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f260,plain,
( spl17_19
<=> in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f453,plain,
( spl17_52
<=> ! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_52])]) ).
fof(f943,plain,
( spl17_109
<=> ! [X0] :
( in(sK2,relation_dom(X0))
| ~ sP0(sK1,sK3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_109])]) ).
fof(f1174,plain,
( in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ function(sK3)
| ~ relation(sK3)
| ~ function(relation_rng_restriction(sK1,sK3))
| ~ relation(relation_rng_restriction(sK1,sK3))
| ~ spl17_52
| ~ spl17_109 ),
inference(resolution,[],[f944,f454]) ).
fof(f454,plain,
( ! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) )
| ~ spl17_52 ),
inference(avatar_component_clause,[],[f453]) ).
fof(f944,plain,
( ! [X0] :
( ~ sP0(sK1,sK3,X0)
| in(sK2,relation_dom(X0)) )
| ~ spl17_109 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f1175,plain,
( spl17_19
| spl17_60
| ~ spl17_43
| ~ spl17_62 ),
inference(avatar_split_clause,[],[f548,f526,f398,f515,f260]) ).
fof(f515,plain,
( spl17_60
<=> empty(relation_dom(relation_rng_restriction(sK1,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_60])]) ).
fof(f398,plain,
( spl17_43
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_43])]) ).
fof(f526,plain,
( spl17_62
<=> element(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_62])]) ).
fof(f548,plain,
( empty(relation_dom(relation_rng_restriction(sK1,sK3)))
| in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ spl17_43
| ~ spl17_62 ),
inference(resolution,[],[f528,f399]) ).
fof(f399,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl17_43 ),
inference(avatar_component_clause,[],[f398]) ).
fof(f528,plain,
( element(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ spl17_62 ),
inference(avatar_component_clause,[],[f526]) ).
fof(f1172,plain,
( ~ spl17_19
| ~ spl17_20
| ~ spl17_21 ),
inference(avatar_split_clause,[],[f111,f269,f264,f260]) ).
fof(f264,plain,
( spl17_20
<=> in(sK2,relation_dom(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f269,plain,
( spl17_21
<=> in(apply(sK3,sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_21])]) ).
fof(f111,plain,
( ~ in(apply(sK3,sK2),sK1)
| ~ in(sK2,relation_dom(sK3))
| ~ in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ( ~ in(apply(sK3,sK2),sK1)
| ~ in(sK2,relation_dom(sK3))
| ~ in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) )
& ( ( in(apply(sK3,sK2),sK1)
& in(sK2,relation_dom(sK3)) )
| in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) )
& function(sK3)
& relation(sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f72,f73]) ).
fof(f73,plain,
( ? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& function(X2)
& relation(X2) )
=> ( ( ~ in(apply(sK3,sK2),sK1)
| ~ in(sK2,relation_dom(sK3))
| ~ in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) )
& ( ( in(apply(sK3,sK2),sK1)
& in(sK2,relation_dom(sK3)) )
| in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) )
& function(sK3)
& relation(sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f72,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
? [X0,X1,X2] :
( ( ~ in(apply(X2,X1),X0)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& ( ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) )
| in(X1,relation_dom(relation_rng_restriction(X0,X2))) )
& function(X2)
& relation(X2) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
? [X0,X1,X2] :
( ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<~> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) )
& function(X2)
& relation(X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( in(X1,relation_dom(relation_rng_restriction(X0,X2)))
<=> ( in(apply(X2,X1),X0)
& in(X1,relation_dom(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_funct_1) ).
fof(f1165,plain,
( spl17_21
| ~ spl17_2
| ~ spl17_80
| ~ spl17_81
| ~ spl17_1
| ~ spl17_19
| ~ spl17_113 ),
inference(avatar_split_clause,[],[f1016,f1003,f260,f170,f692,f688,f175,f269]) ).
fof(f1003,plain,
( spl17_113
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(apply(X0,X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_113])]) ).
fof(f1016,plain,
( ~ relation(sK3)
| ~ function(relation_rng_restriction(sK1,sK3))
| ~ relation(relation_rng_restriction(sK1,sK3))
| ~ function(sK3)
| in(apply(sK3,sK2),sK1)
| ~ spl17_19
| ~ spl17_113 ),
inference(resolution,[],[f1004,f262]) ).
fof(f262,plain,
( in(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f1004,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(apply(X0,X2),X1) )
| ~ spl17_113 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1138,plain,
( spl17_124
| ~ spl17_3
| ~ spl17_71
| ~ spl17_83 ),
inference(avatar_split_clause,[],[f717,f704,f581,f180,f1135]) ).
fof(f1135,plain,
( spl17_124
<=> sK10 = relation_dom(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_124])]) ).
fof(f180,plain,
( spl17_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f581,plain,
( spl17_71
<=> empty_set = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_71])]) ).
fof(f704,plain,
( spl17_83
<=> ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_83])]) ).
fof(f717,plain,
( sK10 = relation_dom(sK10)
| ~ spl17_3
| ~ spl17_71
| ~ spl17_83 ),
inference(forward_demodulation,[],[f711,f583]) ).
fof(f583,plain,
( empty_set = sK10
| ~ spl17_71 ),
inference(avatar_component_clause,[],[f581]) ).
fof(f711,plain,
( sK10 = relation_dom(empty_set)
| ~ spl17_3
| ~ spl17_83 ),
inference(resolution,[],[f705,f182]) ).
fof(f182,plain,
( empty(empty_set)
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f705,plain,
( ! [X0] :
( ~ empty(X0)
| relation_dom(X0) = sK10 )
| ~ spl17_83 ),
inference(avatar_component_clause,[],[f704]) ).
fof(f1133,plain,
( spl17_123
| ~ spl17_33
| ~ spl17_75 ),
inference(avatar_split_clause,[],[f612,f609,f329,f1131]) ).
fof(f1131,plain,
( spl17_123
<=> ! [X0] : element(sK10,powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_123])]) ).
fof(f329,plain,
( spl17_33
<=> ! [X0] : element(sK6(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_33])]) ).
fof(f609,plain,
( spl17_75
<=> ! [X0] : sK6(X0) = sK10 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_75])]) ).
fof(f612,plain,
( ! [X0] : element(sK10,powerset(X0))
| ~ spl17_33
| ~ spl17_75 ),
inference(superposition,[],[f330,f610]) ).
fof(f610,plain,
( ! [X0] : sK6(X0) = sK10
| ~ spl17_75 ),
inference(avatar_component_clause,[],[f609]) ).
fof(f330,plain,
( ! [X0] : element(sK6(X0),powerset(X0))
| ~ spl17_33 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f1127,plain,
( spl17_21
| spl17_63
| ~ spl17_43
| ~ spl17_64 ),
inference(avatar_split_clause,[],[f941,f540,f398,f535,f269]) ).
fof(f535,plain,
( spl17_63
<=> empty(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_63])]) ).
fof(f540,plain,
( spl17_64
<=> element(apply(sK3,sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_64])]) ).
fof(f941,plain,
( empty(sK1)
| in(apply(sK3,sK2),sK1)
| ~ spl17_43
| ~ spl17_64 ),
inference(resolution,[],[f542,f399]) ).
fof(f542,plain,
( element(apply(sK3,sK2),sK1)
| ~ spl17_64 ),
inference(avatar_component_clause,[],[f540]) ).
fof(f1126,plain,
( spl17_122
| ~ spl17_20
| ~ spl17_90 ),
inference(avatar_split_clause,[],[f787,f777,f264,f1124]) ).
fof(f1124,plain,
( spl17_122
<=> ! [X0] :
( element(sK2,X0)
| ~ subset(relation_dom(sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_122])]) ).
fof(f777,plain,
( spl17_90
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_90])]) ).
fof(f787,plain,
( ! [X0] :
( element(sK2,X0)
| ~ subset(relation_dom(sK3),X0) )
| ~ spl17_20
| ~ spl17_90 ),
inference(resolution,[],[f778,f266]) ).
fof(f266,plain,
( in(sK2,relation_dom(sK3))
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f778,plain,
( ! [X2,X0,X1] :
( ~ in(X0,X2)
| element(X0,X1)
| ~ subset(X2,X1) )
| ~ spl17_90 ),
inference(avatar_component_clause,[],[f777]) ).
fof(f1116,plain,
( spl17_20
| ~ spl17_2
| ~ spl17_80
| ~ spl17_81
| ~ spl17_1
| ~ spl17_19
| ~ spl17_112 ),
inference(avatar_split_clause,[],[f997,f984,f260,f170,f692,f688,f175,f264]) ).
fof(f984,plain,
( spl17_112
<=> ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(X2,relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_112])]) ).
fof(f997,plain,
( ~ relation(sK3)
| ~ function(relation_rng_restriction(sK1,sK3))
| ~ relation(relation_rng_restriction(sK1,sK3))
| ~ function(sK3)
| in(sK2,relation_dom(sK3))
| ~ spl17_19
| ~ spl17_112 ),
inference(resolution,[],[f985,f262]) ).
fof(f985,plain,
( ! [X2,X0,X1] :
( ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ function(X0)
| in(X2,relation_dom(X0)) )
| ~ spl17_112 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1114,plain,
( spl17_121
| ~ spl17_19
| ~ spl17_90 ),
inference(avatar_split_clause,[],[f788,f777,f260,f1112]) ).
fof(f1112,plain,
( spl17_121
<=> ! [X0] :
( element(sK2,X0)
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK3)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_121])]) ).
fof(f788,plain,
( ! [X0] :
( element(sK2,X0)
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK3)),X0) )
| ~ spl17_19
| ~ spl17_90 ),
inference(resolution,[],[f778,f262]) ).
fof(f1107,plain,
( spl17_120
| ~ spl17_21
| ~ spl17_90 ),
inference(avatar_split_clause,[],[f930,f777,f269,f1105]) ).
fof(f1105,plain,
( spl17_120
<=> ! [X0] :
( element(apply(sK3,sK2),X0)
| ~ subset(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_120])]) ).
fof(f930,plain,
( ! [X0] :
( element(apply(sK3,sK2),X0)
| ~ subset(sK1,X0) )
| ~ spl17_21
| ~ spl17_90 ),
inference(resolution,[],[f271,f778]) ).
fof(f271,plain,
( in(apply(sK3,sK2),sK1)
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f269]) ).
fof(f1092,plain,
( spl17_119
| ~ spl17_53
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f496,f489,f466,f1090]) ).
fof(f1090,plain,
( spl17_119
<=> ! [X0,X3,X2,X1] :
( apply(X0,apply(X1,sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3))) = apply(relation_rng_restriction(X2,X0),apply(X1,sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X2,X0)),X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_119])]) ).
fof(f466,plain,
( spl17_53
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK7(X0,X1,X2)),X0)
| in(sK7(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_53])]) ).
fof(f489,plain,
( spl17_56
<=> ! [X4,X0,X2] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_56])]) ).
fof(f496,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,apply(X1,sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3))) = apply(relation_rng_restriction(X2,X0),apply(X1,sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK7(relation_dom(relation_rng_restriction(X2,X0)),X1,X3),relation_dom(X3))
| sP0(relation_dom(relation_rng_restriction(X2,X0)),X1,X3) )
| ~ spl17_53
| ~ spl17_56 ),
inference(resolution,[],[f490,f467]) ).
fof(f467,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2) )
| ~ spl17_53 ),
inference(avatar_component_clause,[],[f466]) ).
fof(f490,plain,
( ! [X2,X0,X4] :
( ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) )
| ~ spl17_56 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f1073,plain,
( spl17_118
| ~ spl17_53
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f493,f489,f466,f1071]) ).
fof(f1071,plain,
( spl17_118
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK7(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK7(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(apply(X2,sK7(X1,X2,relation_rng_restriction(X3,X0))),X1)
| sP0(X1,X2,relation_rng_restriction(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_118])]) ).
fof(f493,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK7(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK7(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(apply(X2,sK7(X1,X2,relation_rng_restriction(X3,X0))),X1)
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_53
| ~ spl17_56 ),
inference(resolution,[],[f490,f467]) ).
fof(f1053,plain,
( spl17_117
| ~ spl17_51
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f495,f489,f449,f1051]) ).
fof(f1051,plain,
( spl17_117
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK7(X1,relation_rng_restriction(X2,X0),X3)) = apply(relation_rng_restriction(X2,X0),sK7(X1,relation_rng_restriction(X2,X0),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK7(X1,relation_rng_restriction(X2,X0),X3),relation_dom(X3))
| sP0(X1,relation_rng_restriction(X2,X0),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_117])]) ).
fof(f449,plain,
( spl17_51
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK7(X0,X1,X2),relation_dom(X1))
| in(sK7(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_51])]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK7(X1,relation_rng_restriction(X2,X0),X3)) = apply(relation_rng_restriction(X2,X0),sK7(X1,relation_rng_restriction(X2,X0),X3))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X2,X0))
| ~ relation(relation_rng_restriction(X2,X0))
| in(sK7(X1,relation_rng_restriction(X2,X0),X3),relation_dom(X3))
| sP0(X1,relation_rng_restriction(X2,X0),X3) )
| ~ spl17_51
| ~ spl17_56 ),
inference(resolution,[],[f490,f450]) ).
fof(f450,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2) )
| ~ spl17_51 ),
inference(avatar_component_clause,[],[f449]) ).
fof(f1049,plain,
( spl17_116
| ~ spl17_51
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f494,f489,f449,f1047]) ).
fof(f1047,plain,
( spl17_116
<=> ! [X0,X3,X2,X1] :
( apply(X0,sK7(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK7(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(sK7(X1,X2,relation_rng_restriction(X3,X0)),relation_dom(X2))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_116])]) ).
fof(f494,plain,
( ! [X2,X3,X0,X1] :
( apply(X0,sK7(X1,X2,relation_rng_restriction(X3,X0))) = apply(relation_rng_restriction(X3,X0),sK7(X1,X2,relation_rng_restriction(X3,X0)))
| ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X3,X0))
| ~ relation(relation_rng_restriction(X3,X0))
| in(sK7(X1,X2,relation_rng_restriction(X3,X0)),relation_dom(X2))
| sP0(X1,X2,relation_rng_restriction(X3,X0)) )
| ~ spl17_51
| ~ spl17_56 ),
inference(resolution,[],[f490,f450]) ).
fof(f1028,plain,
( spl17_115
| ~ spl17_50
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f469,f466,f445,f1026]) ).
fof(f1026,plain,
( spl17_115
<=> ! [X0,X3,X2,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| in(sK7(X1,X0,X2),relation_dom(X3))
| ~ in(sK7(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_115])]) ).
fof(f445,plain,
( spl17_50
<=> ! [X4,X0,X2,X1] :
( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_50])]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| in(sK7(X1,X0,X2),relation_dom(X3))
| ~ in(sK7(X1,X0,X2),relation_dom(X0))
| ~ sP0(X1,X0,X3) )
| ~ spl17_50
| ~ spl17_53 ),
inference(resolution,[],[f467,f446]) ).
fof(f446,plain,
( ! [X2,X0,X1,X4] :
( ~ in(apply(X1,X4),X0)
| in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) )
| ~ spl17_50 ),
inference(avatar_component_clause,[],[f445]) ).
fof(f1024,plain,
( spl17_114
| ~ spl17_21
| ~ spl17_88 ),
inference(avatar_split_clause,[],[f931,f744,f269,f1022]) ).
fof(f1022,plain,
( spl17_114
<=> ! [X0] :
( ~ empty(X0)
| ~ subset(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_114])]) ).
fof(f744,plain,
( spl17_88
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_88])]) ).
fof(f931,plain,
( ! [X0] :
( ~ empty(X0)
| ~ subset(sK1,X0) )
| ~ spl17_21
| ~ spl17_88 ),
inference(resolution,[],[f271,f745]) ).
fof(f745,plain,
( ! [X2,X0,X1] :
( ~ in(X1,X2)
| ~ empty(X0)
| ~ subset(X2,X0) )
| ~ spl17_88 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f1005,plain,
( spl17_113
| ~ spl17_49
| ~ spl17_52 ),
inference(avatar_split_clause,[],[f463,f453,f441,f1003]) ).
fof(f441,plain,
( spl17_49
<=> ! [X2,X4,X0,X1] :
( in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_49])]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(apply(X0,X2),X1) )
| ~ spl17_49
| ~ spl17_52 ),
inference(resolution,[],[f454,f442]) ).
fof(f442,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,relation_dom(X2))
| in(apply(X1,X4),X0) )
| ~ spl17_49 ),
inference(avatar_component_clause,[],[f441]) ).
fof(f986,plain,
( spl17_112
| ~ spl17_48
| ~ spl17_52 ),
inference(avatar_split_clause,[],[f464,f453,f437,f984]) ).
fof(f437,plain,
( spl17_48
<=> ! [X4,X0,X1,X2] :
( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_48])]) ).
fof(f464,plain,
( ! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ function(relation_rng_restriction(X1,X0))
| ~ relation(relation_rng_restriction(X1,X0))
| ~ in(X2,relation_dom(relation_rng_restriction(X1,X0)))
| in(X2,relation_dom(X0)) )
| ~ spl17_48
| ~ spl17_52 ),
inference(resolution,[],[f454,f438]) ).
fof(f438,plain,
( ! [X2,X0,X1,X4] :
( ~ sP0(X0,X1,X2)
| ~ in(X4,relation_dom(X2))
| in(X4,relation_dom(X1)) )
| ~ spl17_48 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f959,plain,
( spl17_111
| ~ spl17_37
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f474,f466,f359,f957]) ).
fof(f957,plain,
( spl17_111
<=> ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK7(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_111])]) ).
fof(f359,plain,
( spl17_37
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_37])]) ).
fof(f474,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK7(X0,X1,X2)) )
| ~ spl17_37
| ~ spl17_53 ),
inference(resolution,[],[f467,f360]) ).
fof(f360,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl17_37 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f955,plain,
( spl17_110
| ~ spl17_38
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f473,f466,f363,f953]) ).
fof(f953,plain,
( spl17_110
<=> ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_110])]) ).
fof(f363,plain,
( spl17_38
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_38])]) ).
fof(f473,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_38
| ~ spl17_53 ),
inference(resolution,[],[f467,f364]) ).
fof(f364,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl17_38 ),
inference(avatar_component_clause,[],[f363]) ).
fof(f945,plain,
( ~ spl17_20
| spl17_109
| ~ spl17_21
| ~ spl17_50 ),
inference(avatar_split_clause,[],[f530,f445,f269,f943,f264]) ).
fof(f530,plain,
( ! [X0] :
( in(sK2,relation_dom(X0))
| ~ in(sK2,relation_dom(sK3))
| ~ sP0(sK1,sK3,X0) )
| ~ spl17_21
| ~ spl17_50 ),
inference(resolution,[],[f271,f446]) ).
fof(f940,plain,
( ~ spl17_108
| ~ spl17_21
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f532,f359,f269,f937]) ).
fof(f937,plain,
( spl17_108
<=> in(sK1,apply(sK3,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_108])]) ).
fof(f532,plain,
( ~ in(sK1,apply(sK3,sK2))
| ~ spl17_21
| ~ spl17_37 ),
inference(resolution,[],[f271,f360]) ).
fof(f923,plain,
( spl17_107
| ~ spl17_19
| ~ spl17_88 ),
inference(avatar_split_clause,[],[f770,f744,f260,f921]) ).
fof(f921,plain,
( spl17_107
<=> ! [X0] :
( ~ empty(X0)
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK3)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_107])]) ).
fof(f770,plain,
( ! [X0] :
( ~ empty(X0)
| ~ subset(relation_dom(relation_rng_restriction(sK1,sK3)),X0) )
| ~ spl17_19
| ~ spl17_88 ),
inference(resolution,[],[f745,f262]) ).
fof(f919,plain,
( spl17_106
| ~ spl17_37
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f471,f466,f359,f917]) ).
fof(f917,plain,
( spl17_106
<=> ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK7(X1,X0,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_106])]) ).
fof(f471,plain,
( ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ in(X1,apply(X0,sK7(X1,X0,X2))) )
| ~ spl17_37
| ~ spl17_53 ),
inference(resolution,[],[f467,f360]) ).
fof(f915,plain,
( spl17_105
| ~ spl17_38
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f470,f466,f363,f913]) ).
fof(f913,plain,
( spl17_105
<=> ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| element(apply(X0,sK7(X1,X0,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_105])]) ).
fof(f470,plain,
( ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| element(apply(X0,sK7(X1,X0,X2)),X1) )
| ~ spl17_38
| ~ spl17_53 ),
inference(resolution,[],[f467,f364]) ).
fof(f897,plain,
( spl17_104
| ~ spl17_37
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f460,f449,f359,f895]) ).
fof(f895,plain,
( spl17_104
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK7(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_104])]) ).
fof(f460,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X1),sK7(X0,X1,X2)) )
| ~ spl17_37
| ~ spl17_51 ),
inference(resolution,[],[f450,f360]) ).
fof(f893,plain,
( spl17_103
| ~ spl17_38
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f459,f449,f363,f891]) ).
fof(f891,plain,
( spl17_103
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_103])]) ).
fof(f459,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X1)) )
| ~ spl17_38
| ~ spl17_51 ),
inference(resolution,[],[f450,f364]) ).
fof(f889,plain,
( spl17_102
| ~ spl17_37
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f457,f449,f359,f887]) ).
fof(f887,plain,
( spl17_102
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK7(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_102])]) ).
fof(f457,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ in(relation_dom(X2),sK7(X0,X1,X2)) )
| ~ spl17_37
| ~ spl17_51 ),
inference(resolution,[],[f450,f360]) ).
fof(f885,plain,
( spl17_20
| spl17_35
| ~ spl17_43
| ~ spl17_59 ),
inference(avatar_split_clause,[],[f513,f509,f398,f350,f264]) ).
fof(f350,plain,
( spl17_35
<=> empty(relation_dom(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_35])]) ).
fof(f509,plain,
( spl17_59
<=> element(sK2,relation_dom(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_59])]) ).
fof(f513,plain,
( empty(relation_dom(sK3))
| in(sK2,relation_dom(sK3))
| ~ spl17_43
| ~ spl17_59 ),
inference(resolution,[],[f511,f399]) ).
fof(f511,plain,
( element(sK2,relation_dom(sK3))
| ~ spl17_59 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f884,plain,
( spl17_101
| ~ spl17_38
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f456,f449,f363,f882]) ).
fof(f882,plain,
( spl17_101
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_101])]) ).
fof(f456,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| element(sK7(X0,X1,X2),relation_dom(X2)) )
| ~ spl17_38
| ~ spl17_51 ),
inference(resolution,[],[f450,f364]) ).
fof(f867,plain,
( spl17_100
| ~ spl17_34
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f475,f466,f333,f865]) ).
fof(f865,plain,
( spl17_100
<=> ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_100])]) ).
fof(f333,plain,
( spl17_34
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_34])]) ).
fof(f475,plain,
( ! [X2,X0,X1] :
( in(apply(X1,sK7(X0,X1,X2)),X0)
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_34
| ~ spl17_53 ),
inference(resolution,[],[f467,f334]) ).
fof(f334,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl17_34 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f851,plain,
( spl17_99
| ~ spl17_34
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f461,f449,f333,f849]) ).
fof(f849,plain,
( spl17_99
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_99])]) ).
fof(f461,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X2))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X1)) )
| ~ spl17_34
| ~ spl17_51 ),
inference(resolution,[],[f450,f334]) ).
fof(f847,plain,
( spl17_98
| ~ spl17_34
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f458,f449,f333,f845]) ).
fof(f845,plain,
( spl17_98
<=> ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_98])]) ).
fof(f458,plain,
( ! [X2,X0,X1] :
( in(sK7(X0,X1,X2),relation_dom(X1))
| sP0(X0,X1,X2)
| ~ empty(relation_dom(X2)) )
| ~ spl17_34
| ~ spl17_51 ),
inference(resolution,[],[f450,f334]) ).
fof(f837,plain,
( spl17_97
| ~ spl17_20
| ~ spl17_88 ),
inference(avatar_split_clause,[],[f769,f744,f264,f835]) ).
fof(f835,plain,
( spl17_97
<=> ! [X0] :
( ~ empty(X0)
| ~ subset(relation_dom(sK3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_97])]) ).
fof(f769,plain,
( ! [X0] :
( ~ empty(X0)
| ~ subset(relation_dom(sK3),X0) )
| ~ spl17_20
| ~ spl17_88 ),
inference(resolution,[],[f745,f266]) ).
fof(f833,plain,
( spl17_96
| ~ spl17_58 ),
inference(avatar_split_clause,[],[f507,f503,f831]) ).
fof(f831,plain,
( spl17_96
<=> ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_96])]) ).
fof(f503,plain,
( spl17_58
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_58])]) ).
fof(f507,plain,
( ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_58 ),
inference(duplicate_literal_removal,[],[f506]) ).
fof(f506,plain,
( ! [X0,X1] :
( relation_rng_restriction(X0,X1) = X1
| ~ sP0(X0,X1,X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_58 ),
inference(equality_resolution,[],[f504]) ).
fof(f504,plain,
( ! [X2,X0,X1] :
( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
| relation_rng_restriction(X0,X2) = X1
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_58 ),
inference(avatar_component_clause,[],[f503]) ).
fof(f829,plain,
( spl17_95
| ~ spl17_34
| ~ spl17_53 ),
inference(avatar_split_clause,[],[f472,f466,f333,f827]) ).
fof(f827,plain,
( spl17_95
<=> ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_95])]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( in(sK7(X1,X0,X2),relation_dom(X2))
| sP0(X1,X0,X2)
| ~ empty(X1) )
| ~ spl17_34
| ~ spl17_53 ),
inference(resolution,[],[f467,f334]) ).
fof(f819,plain,
( spl17_94
| ~ spl17_51 ),
inference(avatar_split_clause,[],[f462,f449,f817]) ).
fof(f817,plain,
( spl17_94
<=> ! [X0,X1] :
( in(sK7(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_94])]) ).
fof(f462,plain,
( ! [X0,X1] :
( in(sK7(X0,X1,X1),relation_dom(X1))
| sP0(X0,X1,X1) )
| ~ spl17_51 ),
inference(factoring,[],[f450]) ).
fof(f803,plain,
( spl17_93
| ~ spl17_39
| ~ spl17_43 ),
inference(avatar_split_clause,[],[f406,f398,f371,f801]) ).
fof(f801,plain,
( spl17_93
<=> ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_93])]) ).
fof(f371,plain,
( spl17_39
<=> ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_39])]) ).
fof(f406,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl17_39
| ~ spl17_43 ),
inference(resolution,[],[f399,f372]) ).
fof(f372,plain,
( ! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) )
| ~ spl17_39 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f799,plain,
( spl17_92
| ~ spl17_41
| ~ spl17_43 ),
inference(avatar_split_clause,[],[f405,f398,f379,f797]) ).
fof(f797,plain,
( spl17_92
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_92])]) ).
fof(f379,plain,
( spl17_41
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_41])]) ).
fof(f405,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl17_41
| ~ spl17_43 ),
inference(resolution,[],[f399,f380]) ).
fof(f380,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl17_41 ),
inference(avatar_component_clause,[],[f379]) ).
fof(f794,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_44
| spl17_81 ),
inference(avatar_split_clause,[],[f701,f692,f402,f175,f170]) ).
fof(f402,plain,
( spl17_44
<=> ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_44])]) ).
fof(f701,plain,
( ~ function(sK3)
| ~ relation(sK3)
| ~ spl17_44
| spl17_81 ),
inference(resolution,[],[f694,f403]) ).
fof(f403,plain,
( ! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) )
| ~ spl17_44 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f694,plain,
( ~ function(relation_rng_restriction(sK1,sK3))
| spl17_81 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f783,plain,
( spl17_91
| ~ spl17_39
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f431,f427,f371,f781]) ).
fof(f781,plain,
( spl17_91
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_91])]) ).
fof(f427,plain,
( spl17_47
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_47])]) ).
fof(f431,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(X1))
| empty(X1) )
| ~ spl17_39
| ~ spl17_47 ),
inference(resolution,[],[f428,f372]) ).
fof(f428,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl17_47 ),
inference(avatar_component_clause,[],[f427]) ).
fof(f779,plain,
( spl17_90
| ~ spl17_41
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f430,f427,f379,f777]) ).
fof(f430,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl17_41
| ~ spl17_47 ),
inference(resolution,[],[f428,f380]) ).
fof(f750,plain,
( spl17_89
| ~ spl17_27
| ~ spl17_47 ),
inference(avatar_split_clause,[],[f432,f427,f294,f748]) ).
fof(f748,plain,
( spl17_89
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_89])]) ).
fof(f294,plain,
( spl17_27
<=> ! [X0] : element(sK5(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_27])]) ).
fof(f432,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK5(powerset(X1))) )
| ~ spl17_27
| ~ spl17_47 ),
inference(resolution,[],[f428,f295]) ).
fof(f295,plain,
( ! [X0] : element(sK5(X0),X0)
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f746,plain,
( spl17_88
| ~ spl17_41
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f415,f412,f379,f744]) ).
fof(f412,plain,
( spl17_45
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_45])]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl17_41
| ~ spl17_45 ),
inference(resolution,[],[f413,f380]) ).
fof(f413,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl17_45 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f742,plain,
( spl17_87
| ~ spl17_31
| ~ spl17_42 ),
inference(avatar_split_clause,[],[f389,f383,f321,f740]) ).
fof(f740,plain,
( spl17_87
<=> ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_87])]) ).
fof(f321,plain,
( spl17_31
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_31])]) ).
fof(f383,plain,
( spl17_42
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_42])]) ).
fof(f389,plain,
( ! [X0,X1] :
( relation_dom(X1) = X0
| ~ empty(X0)
| ~ empty(X1) )
| ~ spl17_31
| ~ spl17_42 ),
inference(resolution,[],[f384,f322]) ).
fof(f322,plain,
( ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) )
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f321]) ).
fof(f384,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl17_42 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f733,plain,
( spl17_86
| ~ spl17_27
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f417,f412,f294,f731]) ).
fof(f731,plain,
( spl17_86
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_86])]) ).
fof(f417,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK5(powerset(X0))) )
| ~ spl17_27
| ~ spl17_45 ),
inference(resolution,[],[f413,f295]) ).
fof(f729,plain,
( spl17_85
| ~ spl17_6
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_43 ),
inference(avatar_split_clause,[],[f410,f398,f329,f312,f278,f195,f727]) ).
fof(f727,plain,
( spl17_85
<=> ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_85])]) ).
fof(f195,plain,
( spl17_6
<=> empty(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f278,plain,
( spl17_23
<=> ! [X0] : empty(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_23])]) ).
fof(f312,plain,
( spl17_29
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_29])]) ).
fof(f410,plain,
( ! [X0] :
( in(sK10,powerset(X0))
| empty(powerset(X0)) )
| ~ spl17_6
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_43 ),
inference(forward_demodulation,[],[f409,f338]) ).
fof(f338,plain,
( empty_set = sK10
| ~ spl17_6
| ~ spl17_29 ),
inference(resolution,[],[f313,f197]) ).
fof(f197,plain,
( empty(sK10)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f195]) ).
fof(f313,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl17_29 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f409,plain,
( ! [X0] :
( in(empty_set,powerset(X0))
| empty(powerset(X0)) )
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_43 ),
inference(forward_demodulation,[],[f408,f337]) ).
fof(f337,plain,
( ! [X0] : empty_set = sK6(X0)
| ~ spl17_23
| ~ spl17_29 ),
inference(resolution,[],[f313,f279]) ).
fof(f279,plain,
( ! [X0] : empty(sK6(X0))
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f408,plain,
( ! [X0] :
( empty(powerset(X0))
| in(sK6(X0),powerset(X0)) )
| ~ spl17_33
| ~ spl17_43 ),
inference(resolution,[],[f399,f330]) ).
fof(f710,plain,
( spl17_84
| ~ spl17_27
| ~ spl17_43 ),
inference(avatar_split_clause,[],[f407,f398,f294,f708]) ).
fof(f708,plain,
( spl17_84
<=> ! [X0] :
( empty(X0)
| in(sK5(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_84])]) ).
fof(f407,plain,
( ! [X0] :
( empty(X0)
| in(sK5(X0),X0) )
| ~ spl17_27
| ~ spl17_43 ),
inference(resolution,[],[f399,f295]) ).
fof(f706,plain,
( spl17_83
| ~ spl17_6
| ~ spl17_29
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f346,f321,f312,f195,f704]) ).
fof(f346,plain,
( ! [X0] :
( relation_dom(X0) = sK10
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_29
| ~ spl17_31 ),
inference(forward_demodulation,[],[f343,f338]) ).
fof(f343,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = relation_dom(X0) )
| ~ spl17_29
| ~ spl17_31 ),
inference(resolution,[],[f322,f313]) ).
fof(f702,plain,
( ~ spl17_1
| ~ spl17_36
| spl17_80 ),
inference(avatar_split_clause,[],[f700,f688,f355,f170]) ).
fof(f355,plain,
( spl17_36
<=> ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_36])]) ).
fof(f700,plain,
( ~ relation(sK3)
| ~ spl17_36
| spl17_80 ),
inference(resolution,[],[f690,f356]) ).
fof(f356,plain,
( ! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) )
| ~ spl17_36 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f690,plain,
( ~ relation(relation_rng_restriction(sK1,sK3))
| spl17_80 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f699,plain,
( ~ spl17_80
| ~ spl17_81
| ~ spl17_1
| ~ spl17_2
| spl17_82
| ~ spl17_19
| ~ spl17_56 ),
inference(avatar_split_clause,[],[f492,f489,f260,f696,f175,f170,f692,f688]) ).
fof(f696,plain,
( spl17_82
<=> apply(sK3,sK2) = apply(relation_rng_restriction(sK1,sK3),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_82])]) ).
fof(f492,plain,
( apply(sK3,sK2) = apply(relation_rng_restriction(sK1,sK3),sK2)
| ~ function(sK3)
| ~ relation(sK3)
| ~ function(relation_rng_restriction(sK1,sK3))
| ~ relation(relation_rng_restriction(sK1,sK3))
| ~ spl17_19
| ~ spl17_56 ),
inference(resolution,[],[f490,f262]) ).
fof(f661,plain,
( spl17_77
| ~ spl17_29
| ~ spl17_71 ),
inference(avatar_split_clause,[],[f639,f581,f312,f619]) ).
fof(f619,plain,
( spl17_77
<=> ! [X0] :
( sK10 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_77])]) ).
fof(f639,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl17_29
| ~ spl17_71 ),
inference(forward_demodulation,[],[f313,f583]) ).
fof(f638,plain,
( ~ spl17_3
| ~ spl17_78 ),
inference(avatar_contradiction_clause,[],[f629]) ).
fof(f629,plain,
( $false
| ~ spl17_3
| ~ spl17_78 ),
inference(resolution,[],[f624,f182]) ).
fof(f624,plain,
( ! [X0] : ~ empty(X0)
| ~ spl17_78 ),
inference(avatar_component_clause,[],[f623]) ).
fof(f623,plain,
( spl17_78
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_78])]) ).
fof(f637,plain,
( ~ spl17_23
| ~ spl17_78 ),
inference(avatar_contradiction_clause,[],[f630]) ).
fof(f630,plain,
( $false
| ~ spl17_23
| ~ spl17_78 ),
inference(resolution,[],[f624,f279]) ).
fof(f636,plain,
( ~ spl17_6
| ~ spl17_78 ),
inference(avatar_contradiction_clause,[],[f631]) ).
fof(f631,plain,
( $false
| ~ spl17_6
| ~ spl17_78 ),
inference(resolution,[],[f624,f197]) ).
fof(f635,plain,
( ~ spl17_9
| ~ spl17_78 ),
inference(avatar_contradiction_clause,[],[f632]) ).
fof(f632,plain,
( $false
| ~ spl17_9
| ~ spl17_78 ),
inference(resolution,[],[f624,f212]) ).
fof(f212,plain,
( empty(sK12)
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f210,plain,
( spl17_9
<=> empty(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f634,plain,
( ~ spl17_17
| ~ spl17_78 ),
inference(avatar_contradiction_clause,[],[f633]) ).
fof(f633,plain,
( $false
| ~ spl17_17
| ~ spl17_78 ),
inference(resolution,[],[f624,f252]) ).
fof(f252,plain,
( empty(sK16)
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f250,plain,
( spl17_17
<=> empty(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f628,plain,
( spl17_78
| spl17_79
| ~ spl17_6
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_45 ),
inference(avatar_split_clause,[],[f420,f412,f329,f312,f278,f195,f626,f623]) ).
fof(f626,plain,
( spl17_79
<=> ! [X1] : ~ in(X1,sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_79])]) ).
fof(f420,plain,
( ! [X0,X1] :
( ~ in(X1,sK10)
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_45 ),
inference(forward_demodulation,[],[f419,f338]) ).
fof(f419,plain,
( ! [X0,X1] :
( ~ in(X1,empty_set)
| ~ empty(X0) )
| ~ spl17_23
| ~ spl17_29
| ~ spl17_33
| ~ spl17_45 ),
inference(forward_demodulation,[],[f418,f337]) ).
fof(f418,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK6(X0)) )
| ~ spl17_33
| ~ spl17_45 ),
inference(resolution,[],[f413,f330]) ).
fof(f621,plain,
( spl17_77
| ~ spl17_6
| ~ spl17_42 ),
inference(avatar_split_clause,[],[f391,f383,f195,f619]) ).
fof(f391,plain,
( ! [X0] :
( sK10 = X0
| ~ empty(X0) )
| ~ spl17_6
| ~ spl17_42 ),
inference(resolution,[],[f384,f197]) ).
fof(f617,plain,
( spl17_76
| ~ spl17_25
| ~ spl17_31 ),
inference(avatar_split_clause,[],[f345,f321,f286,f615]) ).
fof(f615,plain,
( spl17_76
<=> ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_76])]) ).
fof(f286,plain,
( spl17_25
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_25])]) ).
fof(f345,plain,
( ! [X0] :
( ~ empty(X0)
| function(relation_dom(X0)) )
| ~ spl17_25
| ~ spl17_31 ),
inference(resolution,[],[f322,f287]) ).
fof(f287,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f611,plain,
( spl17_75
| ~ spl17_71
| ~ spl17_74 ),
inference(avatar_split_clause,[],[f607,f604,f581,f609]) ).
fof(f604,plain,
( spl17_74
<=> ! [X0] : empty_set = sK6(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_74])]) ).
fof(f607,plain,
( ! [X0] : sK6(X0) = sK10
| ~ spl17_71
| ~ spl17_74 ),
inference(forward_demodulation,[],[f605,f583]) ).
fof(f605,plain,
( ! [X0] : empty_set = sK6(X0)
| ~ spl17_74 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f606,plain,
( spl17_74
| ~ spl17_23
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f337,f312,f278,f604]) ).
fof(f594,plain,
( spl17_73
| ~ spl17_6
| ~ spl17_17
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f342,f312,f250,f195,f591]) ).
fof(f591,plain,
( spl17_73
<=> sK10 = sK16 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_73])]) ).
fof(f342,plain,
( sK10 = sK16
| ~ spl17_6
| ~ spl17_17
| ~ spl17_29 ),
inference(forward_demodulation,[],[f340,f338]) ).
fof(f340,plain,
( empty_set = sK16
| ~ spl17_17
| ~ spl17_29 ),
inference(resolution,[],[f313,f252]) ).
fof(f589,plain,
( spl17_72
| ~ spl17_6
| ~ spl17_9
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f341,f312,f210,f195,f586]) ).
fof(f586,plain,
( spl17_72
<=> sK10 = sK12 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_72])]) ).
fof(f341,plain,
( sK10 = sK12
| ~ spl17_6
| ~ spl17_9
| ~ spl17_29 ),
inference(forward_demodulation,[],[f339,f338]) ).
fof(f339,plain,
( empty_set = sK12
| ~ spl17_9
| ~ spl17_29 ),
inference(resolution,[],[f313,f212]) ).
fof(f584,plain,
( spl17_71
| ~ spl17_6
| ~ spl17_29 ),
inference(avatar_split_clause,[],[f338,f312,f195,f581]) ).
fof(f578,plain,
( spl17_70
| ~ spl17_23
| ~ spl17_26 ),
inference(avatar_split_clause,[],[f303,f290,f278,f576]) ).
fof(f576,plain,
( spl17_70
<=> ! [X0] : relation(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_70])]) ).
fof(f290,plain,
( spl17_26
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_26])]) ).
fof(f303,plain,
( ! [X0] : relation(sK6(X0))
| ~ spl17_23
| ~ spl17_26 ),
inference(resolution,[],[f291,f279]) ).
fof(f291,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f573,plain,
( spl17_69
| ~ spl17_23
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f298,f286,f278,f571]) ).
fof(f571,plain,
( spl17_69
<=> ! [X0] : function(sK6(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_69])]) ).
fof(f298,plain,
( ! [X0] : function(sK6(X0))
| ~ spl17_23
| ~ spl17_25 ),
inference(resolution,[],[f287,f279]) ).
fof(f569,plain,
( spl17_68
| ~ spl17_6
| ~ spl17_26 ),
inference(avatar_split_clause,[],[f304,f290,f195,f566]) ).
fof(f566,plain,
( spl17_68
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_68])]) ).
fof(f304,plain,
( relation(sK10)
| ~ spl17_6
| ~ spl17_26 ),
inference(resolution,[],[f291,f197]) ).
fof(f564,plain,
( ~ spl17_67
| ~ spl17_31
| spl17_60 ),
inference(avatar_split_clause,[],[f519,f515,f321,f561]) ).
fof(f561,plain,
( spl17_67
<=> empty(relation_rng_restriction(sK1,sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_67])]) ).
fof(f519,plain,
( ~ empty(relation_rng_restriction(sK1,sK3))
| ~ spl17_31
| spl17_60 ),
inference(resolution,[],[f517,f322]) ).
fof(f517,plain,
( ~ empty(relation_dom(relation_rng_restriction(sK1,sK3)))
| spl17_60 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f558,plain,
( spl17_66
| ~ spl17_9
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f300,f286,f210,f555]) ).
fof(f555,plain,
( spl17_66
<=> function(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_66])]) ).
fof(f300,plain,
( function(sK12)
| ~ spl17_9
| ~ spl17_25 ),
inference(resolution,[],[f287,f212]) ).
fof(f553,plain,
( spl17_65
| ~ spl17_6
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f299,f286,f195,f550]) ).
fof(f550,plain,
( spl17_65
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_65])]) ).
fof(f299,plain,
( function(sK10)
| ~ spl17_6
| ~ spl17_25 ),
inference(resolution,[],[f287,f197]) ).
fof(f543,plain,
( spl17_64
| ~ spl17_21
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f531,f363,f269,f540]) ).
fof(f531,plain,
( element(apply(sK3,sK2),sK1)
| ~ spl17_21
| ~ spl17_38 ),
inference(resolution,[],[f271,f364]) ).
fof(f538,plain,
( ~ spl17_63
| ~ spl17_21
| ~ spl17_34 ),
inference(avatar_split_clause,[],[f533,f333,f269,f535]) ).
fof(f533,plain,
( ~ empty(sK1)
| ~ spl17_21
| ~ spl17_34 ),
inference(resolution,[],[f271,f334]) ).
fof(f529,plain,
( spl17_62
| ~ spl17_19
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f369,f363,f260,f526]) ).
fof(f369,plain,
( element(sK2,relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ spl17_19
| ~ spl17_38 ),
inference(resolution,[],[f364,f262]) ).
fof(f524,plain,
( ~ spl17_61
| ~ spl17_19
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f367,f359,f260,f521]) ).
fof(f521,plain,
( spl17_61
<=> in(relation_dom(relation_rng_restriction(sK1,sK3)),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_61])]) ).
fof(f367,plain,
( ~ in(relation_dom(relation_rng_restriction(sK1,sK3)),sK2)
| ~ spl17_19
| ~ spl17_37 ),
inference(resolution,[],[f360,f262]) ).
fof(f518,plain,
( ~ spl17_60
| ~ spl17_19
| ~ spl17_34 ),
inference(avatar_split_clause,[],[f348,f333,f260,f515]) ).
fof(f348,plain,
( ~ empty(relation_dom(relation_rng_restriction(sK1,sK3)))
| ~ spl17_19
| ~ spl17_34 ),
inference(resolution,[],[f334,f262]) ).
fof(f512,plain,
( spl17_59
| ~ spl17_20
| ~ spl17_38 ),
inference(avatar_split_clause,[],[f368,f363,f264,f509]) ).
fof(f368,plain,
( element(sK2,relation_dom(sK3))
| ~ spl17_20
| ~ spl17_38 ),
inference(resolution,[],[f364,f266]) ).
fof(f505,plain,
spl17_58,
inference(avatar_split_clause,[],[f147,f503]) ).
fof(f147,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
& in(sK8(X1,X2),relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f88,f89]) ).
fof(f89,plain,
! [X1,X2] :
( ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
=> ( apply(X2,sK8(X1,X2)) != apply(X1,sK8(X1,X2))
& in(sK8(X1,X2),relation_dom(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( ( ( relation_rng_restriction(X0,X2) = X1
| ? [X3] :
( apply(X2,X3) != apply(X1,X3)
& in(X3,relation_dom(X1)) )
| ~ sP0(X0,X2,X1) )
& ( ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) )
| relation_rng_restriction(X0,X2) != X1 ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& sP0(X0,X2,X1) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(definition_folding,[],[f62,f69]) ).
fof(f69,plain,
! [X0,X2,X1] :
( sP0(X0,X2,X1)
<=> ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f62,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ! [X2] :
( ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( apply(X2,X3) = apply(X1,X3)
| ~ in(X3,relation_dom(X1)) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) )
| ~ function(X2)
| ~ relation(X2) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X4] :
( in(X4,relation_dom(X1))
<=> ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) ) ) ) ) ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ! [X2] :
( ( function(X2)
& relation(X2) )
=> ( relation_rng_restriction(X0,X2) = X1
<=> ( ! [X3] :
( in(X3,relation_dom(X1))
=> apply(X2,X3) = apply(X1,X3) )
& ! [X3] :
( in(X3,relation_dom(X1))
<=> ( in(apply(X2,X3),X0)
& in(X3,relation_dom(X2)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t85_funct_1) ).
fof(f501,plain,
( ~ spl17_57
| ~ spl17_20
| ~ spl17_37 ),
inference(avatar_split_clause,[],[f366,f359,f264,f498]) ).
fof(f498,plain,
( spl17_57
<=> in(relation_dom(sK3),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_57])]) ).
fof(f366,plain,
( ~ in(relation_dom(sK3),sK2)
| ~ spl17_20
| ~ spl17_37 ),
inference(resolution,[],[f360,f266]) ).
fof(f491,plain,
spl17_56,
inference(avatar_split_clause,[],[f167,f489]) ).
fof(f167,plain,
! [X2,X0,X4] :
( apply(X2,X4) = apply(relation_rng_restriction(X0,X2),X4)
| ~ in(X4,relation_dom(relation_rng_restriction(X0,X2)))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(equality_resolution,[],[f145]) ).
fof(f145,plain,
! [X2,X0,X1,X4] :
( apply(X2,X4) = apply(X1,X4)
| ~ in(X4,relation_dom(X1))
| relation_rng_restriction(X0,X2) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f485,plain,
spl17_55,
inference(avatar_split_clause,[],[f143,f483]) ).
fof(f483,plain,
( spl17_55
<=> ! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK7(X0,X1,X2)),X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X1))
| ~ in(sK7(X0,X1,X2),relation_dom(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_55])]) ).
fof(f143,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| ~ in(apply(X1,sK7(X0,X1,X2)),X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X1))
| ~ in(sK7(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ( ( ~ in(apply(X1,sK7(X0,X1,X2)),X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X1))
| ~ in(sK7(X0,X1,X2),relation_dom(X2)) )
& ( ( in(apply(X1,sK7(X0,X1,X2)),X0)
& in(sK7(X0,X1,X2),relation_dom(X1)) )
| in(sK7(X0,X1,X2),relation_dom(X2)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f83,f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2)) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,relation_dom(X2)) ) )
=> ( ( ~ in(apply(X1,sK7(X0,X1,X2)),X0)
| ~ in(sK7(X0,X1,X2),relation_dom(X1))
| ~ in(sK7(X0,X1,X2),relation_dom(X2)) )
& ( ( in(apply(X1,sK7(X0,X1,X2)),X0)
& in(sK7(X0,X1,X2),relation_dom(X1)) )
| in(sK7(X0,X1,X2),relation_dom(X2)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ? [X3] :
( ( ~ in(apply(X1,X3),X0)
| ~ in(X3,relation_dom(X1))
| ~ in(X3,relation_dom(X2)) )
& ( ( in(apply(X1,X3),X0)
& in(X3,relation_dom(X1)) )
| in(X3,relation_dom(X2)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X1,X4),X0)
& in(X4,relation_dom(X1)) )
| ~ in(X4,relation_dom(X2)) ) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X0,X2,X1] :
( ( sP0(X0,X2,X1)
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X0,X2,X1) ) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X2,X1] :
( ( sP0(X0,X2,X1)
| ? [X4] :
( ( ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ in(X4,relation_dom(X1)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| in(X4,relation_dom(X1)) ) ) )
& ( ! [X4] :
( ( in(X4,relation_dom(X1))
| ~ in(apply(X2,X4),X0)
| ~ in(X4,relation_dom(X2)) )
& ( ( in(apply(X2,X4),X0)
& in(X4,relation_dom(X2)) )
| ~ in(X4,relation_dom(X1)) ) )
| ~ sP0(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f479,plain,
spl17_54,
inference(avatar_split_clause,[],[f146,f477]) ).
fof(f477,plain,
( spl17_54
<=> ! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| in(sK8(X1,X2),relation_dom(X1))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_54])]) ).
fof(f146,plain,
! [X2,X0,X1] :
( relation_rng_restriction(X0,X2) = X1
| in(sK8(X1,X2),relation_dom(X1))
| ~ sP0(X0,X2,X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f468,plain,
spl17_53,
inference(avatar_split_clause,[],[f142,f466]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(apply(X1,sK7(X0,X1,X2)),X0)
| in(sK7(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f455,plain,
spl17_52,
inference(avatar_split_clause,[],[f168,f453]) ).
fof(f168,plain,
! [X2,X0] :
( sP0(X0,X2,relation_rng_restriction(X0,X2))
| ~ function(X2)
| ~ relation(X2)
| ~ function(relation_rng_restriction(X0,X2))
| ~ relation(relation_rng_restriction(X0,X2)) ),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X2,X0,X1] :
( sP0(X0,X2,X1)
| relation_rng_restriction(X0,X2) != X1
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f451,plain,
spl17_51,
inference(avatar_split_clause,[],[f141,f449]) ).
fof(f141,plain,
! [X2,X0,X1] :
( sP0(X0,X1,X2)
| in(sK7(X0,X1,X2),relation_dom(X1))
| in(sK7(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f85]) ).
fof(f447,plain,
spl17_50,
inference(avatar_split_clause,[],[f140,f445]) ).
fof(f140,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X2))
| ~ in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X1))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f443,plain,
spl17_49,
inference(avatar_split_clause,[],[f139,f441]) ).
fof(f139,plain,
! [X2,X0,X1,X4] :
( in(apply(X1,X4),X0)
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f439,plain,
spl17_48,
inference(avatar_split_clause,[],[f138,f437]) ).
fof(f138,plain,
! [X2,X0,X1,X4] :
( in(X4,relation_dom(X1))
| ~ in(X4,relation_dom(X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f429,plain,
spl17_47,
inference(avatar_split_clause,[],[f151,f427]) ).
fof(f151,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f425,plain,
( ~ spl17_46
| ~ spl17_31
| spl17_35 ),
inference(avatar_split_clause,[],[f386,f350,f321,f422]) ).
fof(f422,plain,
( spl17_46
<=> empty(sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_46])]) ).
fof(f386,plain,
( ~ empty(sK3)
| ~ spl17_31
| spl17_35 ),
inference(resolution,[],[f352,f322]) ).
fof(f352,plain,
( ~ empty(relation_dom(sK3))
| spl17_35 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f414,plain,
spl17_45,
inference(avatar_split_clause,[],[f152,f412]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f404,plain,
spl17_44,
inference(avatar_split_clause,[],[f137,f402]) ).
fof(f137,plain,
! [X0,X1] :
( function(relation_rng_restriction(X0,X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( function(relation_rng_restriction(X0,X1))
& relation(relation_rng_restriction(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_funct_1) ).
fof(f400,plain,
spl17_43,
inference(avatar_split_clause,[],[f135,f398]) ).
fof(f135,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f385,plain,
spl17_42,
inference(avatar_split_clause,[],[f149,f383]) ).
fof(f149,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f381,plain,
spl17_41,
inference(avatar_split_clause,[],[f148,f379]) ).
fof(f148,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f377,plain,
spl17_40,
inference(avatar_split_clause,[],[f125,f375]) ).
fof(f375,plain,
( spl17_40
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_40])]) ).
fof(f125,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f373,plain,
spl17_39,
inference(avatar_split_clause,[],[f118,f371]) ).
fof(f118,plain,
! [X0] :
( element(sK4(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f45,f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f45,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f365,plain,
spl17_38,
inference(avatar_split_clause,[],[f134,f363]) ).
fof(f134,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f361,plain,
spl17_37,
inference(avatar_split_clause,[],[f133,f359]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f357,plain,
spl17_36,
inference(avatar_split_clause,[],[f132,f355]) ).
fof(f132,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_rng_restriction(X0,X1))
| ~ relation(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( relation(X1)
=> relation(relation_rng_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k8_relat_1) ).
fof(f353,plain,
( ~ spl17_35
| ~ spl17_20
| ~ spl17_34 ),
inference(avatar_split_clause,[],[f347,f333,f264,f350]) ).
fof(f347,plain,
( ~ empty(relation_dom(sK3))
| ~ spl17_20
| ~ spl17_34 ),
inference(resolution,[],[f334,f266]) ).
fof(f335,plain,
spl17_34,
inference(avatar_split_clause,[],[f150,f333]) ).
fof(f150,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f331,plain,
spl17_33,
inference(avatar_split_clause,[],[f129,f329]) ).
fof(f129,plain,
! [X0] : element(sK6(X0),powerset(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0] :
( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f25,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK6(X0))
& element(sK6(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f327,plain,
spl17_32,
inference(avatar_split_clause,[],[f124,f325]) ).
fof(f325,plain,
( spl17_32
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_32])]) ).
fof(f124,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f323,plain,
spl17_31,
inference(avatar_split_clause,[],[f123,f321]) ).
fof(f123,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f319,plain,
( spl17_30
| ~ spl17_3
| ~ spl17_25 ),
inference(avatar_split_clause,[],[f297,f286,f180,f316]) ).
fof(f316,plain,
( spl17_30
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_30])]) ).
fof(f297,plain,
( function(empty_set)
| ~ spl17_3
| ~ spl17_25 ),
inference(resolution,[],[f287,f182]) ).
fof(f314,plain,
spl17_29,
inference(avatar_split_clause,[],[f122,f312]) ).
fof(f122,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f310,plain,
spl17_28,
inference(avatar_split_clause,[],[f119,f308]) ).
fof(f308,plain,
( spl17_28
<=> ! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_28])]) ).
fof(f119,plain,
! [X0] :
( ~ empty(sK4(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f296,plain,
spl17_27,
inference(avatar_split_clause,[],[f128,f294]) ).
fof(f128,plain,
! [X0] : element(sK5(X0),X0),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0] : element(sK5(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f5,f77]) ).
fof(f77,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK5(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f5,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f292,plain,
spl17_26,
inference(avatar_split_clause,[],[f121,f290]) ).
fof(f121,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f288,plain,
spl17_25,
inference(avatar_split_clause,[],[f120,f286]) ).
fof(f120,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f284,plain,
spl17_24,
inference(avatar_split_clause,[],[f131,f282]) ).
fof(f282,plain,
( spl17_24
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_24])]) ).
fof(f131,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f280,plain,
spl17_23,
inference(avatar_split_clause,[],[f130,f278]) ).
fof(f130,plain,
! [X0] : empty(sK6(X0)),
inference(cnf_transformation,[],[f80]) ).
fof(f276,plain,
spl17_22,
inference(avatar_split_clause,[],[f117,f274]) ).
fof(f274,plain,
( spl17_22
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_22])]) ).
fof(f117,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f272,plain,
( spl17_19
| spl17_21 ),
inference(avatar_split_clause,[],[f110,f269,f260]) ).
fof(f110,plain,
( in(apply(sK3,sK2),sK1)
| in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) ),
inference(cnf_transformation,[],[f74]) ).
fof(f267,plain,
( spl17_19
| spl17_20 ),
inference(avatar_split_clause,[],[f109,f264,f260]) ).
fof(f109,plain,
( in(sK2,relation_dom(sK3))
| in(sK2,relation_dom(relation_rng_restriction(sK1,sK3))) ),
inference(cnf_transformation,[],[f74]) ).
fof(f258,plain,
spl17_18,
inference(avatar_split_clause,[],[f166,f255]) ).
fof(f255,plain,
( spl17_18
<=> function(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f166,plain,
function(sK16),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
( function(sK16)
& empty(sK16)
& relation(sK16) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f22,f105]) ).
fof(f105,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK16)
& empty(sK16)
& relation(sK16) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f253,plain,
spl17_17,
inference(avatar_split_clause,[],[f165,f250]) ).
fof(f165,plain,
empty(sK16),
inference(cnf_transformation,[],[f106]) ).
fof(f248,plain,
spl17_16,
inference(avatar_split_clause,[],[f164,f245]) ).
fof(f245,plain,
( spl17_16
<=> relation(sK16) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f164,plain,
relation(sK16),
inference(cnf_transformation,[],[f106]) ).
fof(f243,plain,
spl17_15,
inference(avatar_split_clause,[],[f163,f240]) ).
fof(f240,plain,
( spl17_15
<=> function(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f163,plain,
function(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( function(sK15)
& relation(sK15) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f40,f103]) ).
fof(f103,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK15)
& relation(sK15) ) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f23]) ).
fof(f23,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f238,plain,
spl17_14,
inference(avatar_split_clause,[],[f162,f235]) ).
fof(f235,plain,
( spl17_14
<=> relation(sK15) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f162,plain,
relation(sK15),
inference(cnf_transformation,[],[f104]) ).
fof(f233,plain,
spl17_13,
inference(avatar_split_clause,[],[f161,f230]) ).
fof(f230,plain,
( spl17_13
<=> function(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f161,plain,
function(sK14),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
( function(sK14)
& relation(sK14) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f21,f101]) ).
fof(f101,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK14)
& relation(sK14) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f228,plain,
spl17_12,
inference(avatar_split_clause,[],[f160,f225]) ).
fof(f225,plain,
( spl17_12
<=> relation(sK14) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f160,plain,
relation(sK14),
inference(cnf_transformation,[],[f102]) ).
fof(f223,plain,
spl17_11,
inference(avatar_split_clause,[],[f159,f220]) ).
fof(f220,plain,
( spl17_11
<=> relation(sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f159,plain,
relation(sK13),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
relation(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f42,f99]) ).
fof(f99,plain,
( ? [X0] : relation(X0)
=> relation(sK13) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f28]) ).
fof(f28,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f218,plain,
spl17_10,
inference(avatar_split_clause,[],[f158,f215]) ).
fof(f215,plain,
( spl17_10
<=> relation(sK12) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f158,plain,
relation(sK12),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( relation(sK12)
& empty(sK12) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f26,f97]) ).
fof(f97,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK12)
& empty(sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f213,plain,
spl17_9,
inference(avatar_split_clause,[],[f157,f210]) ).
fof(f157,plain,
empty(sK12),
inference(cnf_transformation,[],[f98]) ).
fof(f208,plain,
spl17_8,
inference(avatar_split_clause,[],[f156,f205]) ).
fof(f205,plain,
( spl17_8
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f156,plain,
relation(sK11),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
( relation(sK11)
& ~ empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f27,f95]) ).
fof(f95,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK11)
& ~ empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f203,plain,
~ spl17_7,
inference(avatar_split_clause,[],[f155,f200]) ).
fof(f200,plain,
( spl17_7
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f155,plain,
~ empty(sK11),
inference(cnf_transformation,[],[f96]) ).
fof(f198,plain,
spl17_6,
inference(avatar_split_clause,[],[f154,f195]) ).
fof(f154,plain,
empty(sK10),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
empty(sK10),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f29,f93]) ).
fof(f93,plain,
( ? [X0] : empty(X0)
=> empty(sK10) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f193,plain,
~ spl17_5,
inference(avatar_split_clause,[],[f153,f190]) ).
fof(f190,plain,
( spl17_5
<=> empty(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f153,plain,
~ empty(sK9),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
~ empty(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f30,f91]) ).
fof(f91,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK9) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f188,plain,
spl17_4,
inference(avatar_split_clause,[],[f114,f185]) ).
fof(f185,plain,
( spl17_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f114,plain,
relation(empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f183,plain,
spl17_3,
inference(avatar_split_clause,[],[f112,f180]) ).
fof(f112,plain,
empty(empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f178,plain,
spl17_2,
inference(avatar_split_clause,[],[f108,f175]) ).
fof(f108,plain,
function(sK3),
inference(cnf_transformation,[],[f74]) ).
fof(f173,plain,
spl17_1,
inference(avatar_split_clause,[],[f107,f170]) ).
fof(f107,plain,
relation(sK3),
inference(cnf_transformation,[],[f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU044+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.31 % Computer : n026.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 29 20:34:19 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.11/0.31 % (6216)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (6217)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.32 % (6219)WARNING: value z3 for option sas not known
% 0.16/0.32 % (6219)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)
% 0.16/0.32 % (6220)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (6218)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (6221)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)
% 0.16/0.33 % (6222)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)
% 0.16/0.33 % (6223)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [1]
% 0.16/0.34 TRYING [2]
% 0.16/0.34 TRYING [3]
% 0.16/0.35 % (6221)First to succeed.
% 0.16/0.35 TRYING [4]
% 0.16/0.36 TRYING [4]
% 0.16/0.36 % (6221)Refutation found. Thanks to Tanya!
% 0.16/0.36 % SZS status Theorem for theBenchmark
% 0.16/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.37 % (6221)------------------------------
% 0.16/0.37 % (6221)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.37 % (6221)Termination reason: Refutation
% 0.16/0.37
% 0.16/0.37 % (6221)Memory used [KB]: 1349
% 0.16/0.37 % (6221)Time elapsed: 0.035 s
% 0.16/0.37 % (6221)Instructions burned: 60 (million)
% 0.16/0.37 % (6221)------------------------------
% 0.16/0.37 % (6221)------------------------------
% 0.16/0.37 % (6216)Success in time 0.051 s
%------------------------------------------------------------------------------