TSTP Solution File: COM017+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n006.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 : Fri Sep 1 13:49:28 EDT 2023
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 179
% Syntax : Number of formulae : 572 ( 85 unt; 0 def)
% Number of atoms : 2522 ( 21 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 3404 (1454 ~;1535 |; 216 &)
% ( 170 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 164 ( 162 usr; 145 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 813 (; 752 !; 61 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1180,plain,
$false,
inference(avatar_sat_refutation,[],[f170,f175,f180,f185,f190,f195,f200,f205,f209,f214,f219,f224,f229,f234,f239,f244,f248,f252,f258,f264,f268,f272,f276,f280,f284,f288,f292,f296,f300,f305,f309,f313,f317,f321,f326,f330,f334,f338,f342,f346,f350,f354,f359,f367,f371,f375,f385,f389,f393,f397,f401,f415,f419,f423,f432,f436,f440,f444,f456,f460,f469,f478,f482,f486,f490,f506,f514,f518,f523,f536,f540,f552,f556,f560,f564,f586,f590,f594,f603,f636,f640,f644,f649,f663,f668,f681,f685,f689,f720,f733,f741,f745,f759,f763,f773,f785,f792,f797,f802,f808,f814,f840,f849,f857,f865,f869,f873,f897,f901,f906,f915,f931,f937,f941,f945,f949,f999,f1001,f1005,f1009,f1034,f1053,f1054,f1055,f1059,f1063,f1088,f1113,f1114,f1119,f1133,f1151,f1154,f1158,f1164,f1174,f1179]) ).
fof(f1179,plain,
( ~ spl22_10
| ~ spl22_4
| ~ spl22_139
| spl22_141 ),
inference(avatar_split_clause,[],[f1153,f1148,f1131,f182,f211]) ).
fof(f211,plain,
( spl22_10
<=> aReductOfIn0(xv,xa,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_10])]) ).
fof(f182,plain,
( spl22_4
<=> aElement0(xv) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_4])]) ).
fof(f1131,plain,
( spl22_139
<=> ! [X1] :
( sdtmndtasgtdt0(xu,xR,sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_139])]) ).
fof(f1148,plain,
( spl22_141
<=> sdtmndtasgtdt0(xu,xR,sK16(xR,xv,xu)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_141])]) ).
fof(f1153,plain,
( ~ aElement0(xv)
| ~ aReductOfIn0(xv,xa,xR)
| ~ spl22_139
| spl22_141 ),
inference(resolution,[],[f1150,f1132]) ).
fof(f1132,plain,
( ! [X1] :
( sdtmndtasgtdt0(xu,xR,sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) )
| ~ spl22_139 ),
inference(avatar_component_clause,[],[f1131]) ).
fof(f1150,plain,
( ~ sdtmndtasgtdt0(xu,xR,sK16(xR,xv,xu))
| spl22_141 ),
inference(avatar_component_clause,[],[f1148]) ).
fof(f1174,plain,
( spl22_144
| ~ spl22_42
| ~ spl22_100 ),
inference(avatar_split_clause,[],[f1169,f770,f352,f1171]) ).
fof(f1171,plain,
( spl22_144
<=> sP6(sK20(xR,xc),xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_144])]) ).
fof(f352,plain,
( spl22_42
<=> ! [X2,X0,X1] :
( sP6(X0,X1,X2)
| ~ aReductOfIn0(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_42])]) ).
fof(f770,plain,
( spl22_100
<=> aReductOfIn0(sK20(xR,xc),xc,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_100])]) ).
fof(f1169,plain,
( sP6(sK20(xR,xc),xR,xc)
| ~ spl22_42
| ~ spl22_100 ),
inference(resolution,[],[f772,f353]) ).
fof(f353,plain,
( ! [X2,X0,X1] :
( ~ aReductOfIn0(X0,X2,X1)
| sP6(X0,X1,X2) )
| ~ spl22_42 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f772,plain,
( aReductOfIn0(sK20(xR,xc),xc,xR)
| ~ spl22_100 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f1164,plain,
( ~ spl22_4
| ~ spl22_1
| spl22_143
| ~ spl22_49
| ~ spl22_99 ),
inference(avatar_split_clause,[],[f774,f766,f391,f1162,f167,f182]) ).
fof(f167,plain,
( spl22_1
<=> aRewritingSystem0(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_1])]) ).
fof(f1162,plain,
( spl22_143
<=> ! [X0] : ~ aReductOfIn0(X0,xc,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_143])]) ).
fof(f391,plain,
( spl22_49
<=> ! [X4,X0,X2,X1] :
( ~ aReductOfIn0(X4,X2,X1)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_49])]) ).
fof(f766,plain,
( spl22_99
<=> aNormalFormOfIn0(xc,xv,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_99])]) ).
fof(f774,plain,
( ! [X0] :
( ~ aReductOfIn0(X0,xc,xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xv) )
| ~ spl22_49
| ~ spl22_99 ),
inference(resolution,[],[f768,f392]) ).
fof(f392,plain,
( ! [X2,X0,X1,X4] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_49 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f768,plain,
( aNormalFormOfIn0(xc,xv,xR)
| ~ spl22_99 ),
inference(avatar_component_clause,[],[f766]) ).
fof(f1158,plain,
( spl22_142
| ~ spl22_9
| ~ spl22_137 ),
inference(avatar_split_clause,[],[f1120,f1111,f207,f1156]) ).
fof(f1156,plain,
( spl22_142
<=> ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtasgtdt0(xu,xR,sK16(xR,X0,xv))
| ~ aElement0(sK16(xR,X0,xv)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_142])]) ).
fof(f207,plain,
( spl22_9
<=> ! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_9])]) ).
fof(f1111,plain,
( spl22_137
<=> ! [X0] :
( sdtmndtasgtdt0(xv,xR,sK16(xR,X0,xv))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_137])]) ).
fof(f1120,plain,
( ! [X0] :
( ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR)
| ~ sdtmndtasgtdt0(xu,xR,sK16(xR,X0,xv))
| ~ aElement0(sK16(xR,X0,xv)) )
| ~ spl22_9
| ~ spl22_137 ),
inference(resolution,[],[f1112,f208]) ).
fof(f208,plain,
( ! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) )
| ~ spl22_9 ),
inference(avatar_component_clause,[],[f207]) ).
fof(f1112,plain,
( ! [X0] :
( sdtmndtasgtdt0(xv,xR,sK16(xR,X0,xv))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) )
| ~ spl22_137 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1154,plain,
( ~ spl22_10
| ~ spl22_4
| ~ spl22_134
| spl22_140 ),
inference(avatar_split_clause,[],[f1152,f1144,f1057,f182,f211]) ).
fof(f1057,plain,
( spl22_134
<=> ! [X1] :
( aElement0(sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_134])]) ).
fof(f1144,plain,
( spl22_140
<=> aElement0(sK16(xR,xv,xu)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_140])]) ).
fof(f1152,plain,
( ~ aElement0(xv)
| ~ aReductOfIn0(xv,xa,xR)
| ~ spl22_134
| spl22_140 ),
inference(resolution,[],[f1146,f1058]) ).
fof(f1058,plain,
( ! [X1] :
( aElement0(sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) )
| ~ spl22_134 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f1146,plain,
( ~ aElement0(sK16(xR,xv,xu))
| spl22_140 ),
inference(avatar_component_clause,[],[f1144]) ).
fof(f1151,plain,
( ~ spl22_140
| ~ spl22_141
| ~ spl22_10
| ~ spl22_4
| ~ spl22_9
| ~ spl22_136 ),
inference(avatar_split_clause,[],[f1089,f1086,f207,f182,f211,f1148,f1144]) ).
fof(f1086,plain,
( spl22_136
<=> ! [X1] :
( sdtmndtasgtdt0(X1,xR,sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_136])]) ).
fof(f1089,plain,
( ~ aElement0(xv)
| ~ aReductOfIn0(xv,xa,xR)
| ~ sdtmndtasgtdt0(xu,xR,sK16(xR,xv,xu))
| ~ aElement0(sK16(xR,xv,xu))
| ~ spl22_9
| ~ spl22_136 ),
inference(resolution,[],[f1087,f208]) ).
fof(f1087,plain,
( ! [X1] :
( sdtmndtasgtdt0(X1,xR,sK16(xR,X1,xu))
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,xa,xR) )
| ~ spl22_136 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f1133,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_5
| spl22_139
| ~ spl22_12
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f579,f562,f221,f1131,f187,f192,f859]) ).
fof(f859,plain,
( spl22_114
<=> sP2(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_114])]) ).
fof(f192,plain,
( spl22_6
<=> aElement0(xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_6])]) ).
fof(f187,plain,
( spl22_5
<=> aElement0(xu) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_5])]) ).
fof(f221,plain,
( spl22_12
<=> aReductOfIn0(xu,xa,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_12])]) ).
fof(f562,plain,
( spl22_75
<=> ! [X5,X0,X6,X7] :
( sdtmndtasgtdt0(X7,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_75])]) ).
fof(f579,plain,
( ! [X1] :
( sdtmndtasgtdt0(xu,xR,sK16(xR,X1,xu))
| ~ aReductOfIn0(X1,xa,xR)
| ~ aElement0(xu)
| ~ aElement0(X1)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_12
| ~ spl22_75 ),
inference(resolution,[],[f563,f223]) ).
fof(f223,plain,
( aReductOfIn0(xu,xa,xR)
| ~ spl22_12 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f563,plain,
( ! [X0,X6,X7,X5] :
( ~ aReductOfIn0(X7,X5,X0)
| sdtmndtasgtdt0(X7,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) )
| ~ spl22_75 ),
inference(avatar_component_clause,[],[f562]) ).
fof(f1119,plain,
( ~ spl22_81
| ~ spl22_6
| ~ spl22_8
| spl22_138
| ~ spl22_15
| ~ spl22_52 ),
inference(avatar_split_clause,[],[f425,f413,f236,f1116,f202,f192,f629]) ).
fof(f629,plain,
( spl22_81
<=> sP4(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_81])]) ).
fof(f202,plain,
( spl22_8
<=> aElement0(xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_8])]) ).
fof(f1116,plain,
( spl22_138
<=> iLess0(xc,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_138])]) ).
fof(f236,plain,
( spl22_15
<=> sdtmndtplgtdt0(xa,xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_15])]) ).
fof(f413,plain,
( spl22_52
<=> ! [X4,X0,X3] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_52])]) ).
fof(f425,plain,
( iLess0(xc,xa)
| ~ aElement0(xc)
| ~ aElement0(xa)
| ~ sP4(xR)
| ~ spl22_15
| ~ spl22_52 ),
inference(resolution,[],[f414,f238]) ).
fof(f238,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| ~ spl22_15 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f414,plain,
( ! [X3,X0,X4] :
( ~ sdtmndtplgtdt0(X3,X0,X4)
| iLess0(X4,X3)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sP4(X0) )
| ~ spl22_52 ),
inference(avatar_component_clause,[],[f413]) ).
fof(f1114,plain,
( spl22_81
| ~ spl22_3
| ~ spl22_33
| ~ spl22_43 ),
inference(avatar_split_clause,[],[f446,f356,f315,f177,f629]) ).
fof(f177,plain,
( spl22_3
<=> isTerminating0(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_3])]) ).
fof(f315,plain,
( spl22_33
<=> ! [X0] :
( sP4(X0)
| ~ isTerminating0(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_33])]) ).
fof(f356,plain,
( spl22_43
<=> sP5(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_43])]) ).
fof(f446,plain,
( ~ isTerminating0(xR)
| sP4(xR)
| ~ spl22_33
| ~ spl22_43 ),
inference(resolution,[],[f358,f316]) ).
fof(f316,plain,
( ! [X0] :
( ~ sP5(X0)
| ~ isTerminating0(X0)
| sP4(X0) )
| ~ spl22_33 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f358,plain,
( sP5(xR)
| ~ spl22_43 ),
inference(avatar_component_clause,[],[f356]) ).
fof(f1113,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_4
| spl22_137
| ~ spl22_10
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f578,f562,f211,f1111,f182,f192,f859]) ).
fof(f578,plain,
( ! [X0] :
( sdtmndtasgtdt0(xv,xR,sK16(xR,X0,xv))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(xv)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_10
| ~ spl22_75 ),
inference(resolution,[],[f563,f213]) ).
fof(f213,plain,
( aReductOfIn0(xv,xa,xR)
| ~ spl22_10 ),
inference(avatar_component_clause,[],[f211]) ).
fof(f1088,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_5
| spl22_136
| ~ spl22_12
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f574,f558,f221,f1086,f187,f192,f859]) ).
fof(f558,plain,
( spl22_74
<=> ! [X5,X0,X6,X7] :
( sdtmndtasgtdt0(X6,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_74])]) ).
fof(f574,plain,
( ! [X1] :
( sdtmndtasgtdt0(X1,xR,sK16(xR,X1,xu))
| ~ aReductOfIn0(X1,xa,xR)
| ~ aElement0(xu)
| ~ aElement0(X1)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_12
| ~ spl22_74 ),
inference(resolution,[],[f559,f223]) ).
fof(f559,plain,
( ! [X0,X6,X7,X5] :
( ~ aReductOfIn0(X7,X5,X0)
| sdtmndtasgtdt0(X6,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) )
| ~ spl22_74 ),
inference(avatar_component_clause,[],[f558]) ).
fof(f1063,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_4
| spl22_135
| ~ spl22_10
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f573,f558,f211,f1061,f182,f192,f859]) ).
fof(f1061,plain,
( spl22_135
<=> ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK16(xR,X0,xv))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_135])]) ).
fof(f573,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,sK16(xR,X0,xv))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(xv)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_10
| ~ spl22_74 ),
inference(resolution,[],[f559,f213]) ).
fof(f1059,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_5
| spl22_134
| ~ spl22_12
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f529,f516,f221,f1057,f187,f192,f859]) ).
fof(f516,plain,
( spl22_68
<=> ! [X5,X0,X6,X7] :
( aElement0(sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_68])]) ).
fof(f529,plain,
( ! [X1] :
( aElement0(sK16(xR,X1,xu))
| ~ aReductOfIn0(X1,xa,xR)
| ~ aElement0(xu)
| ~ aElement0(X1)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_12
| ~ spl22_68 ),
inference(resolution,[],[f517,f223]) ).
fof(f517,plain,
( ! [X0,X6,X7,X5] :
( ~ aReductOfIn0(X7,X5,X0)
| aElement0(sK16(X0,X6,X7))
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) )
| ~ spl22_68 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1055,plain,
( spl22_114
| ~ spl22_2
| ~ spl22_31
| ~ spl22_35 ),
inference(avatar_split_clause,[],[f411,f323,f307,f172,f859]) ).
fof(f172,plain,
( spl22_2
<=> isLocallyConfluent0(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_2])]) ).
fof(f307,plain,
( spl22_31
<=> ! [X0] :
( sP2(X0)
| ~ isLocallyConfluent0(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_31])]) ).
fof(f323,plain,
( spl22_35
<=> sP3(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_35])]) ).
fof(f411,plain,
( ~ isLocallyConfluent0(xR)
| sP2(xR)
| ~ spl22_31
| ~ spl22_35 ),
inference(resolution,[],[f325,f308]) ).
fof(f308,plain,
( ! [X0] :
( ~ sP3(X0)
| ~ isLocallyConfluent0(X0)
| sP2(X0) )
| ~ spl22_31 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f325,plain,
( sP3(xR)
| ~ spl22_35 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f1054,plain,
( spl22_80
| ~ spl22_21
| spl22_123 ),
inference(avatar_split_clause,[],[f933,f921,f266,f600]) ).
fof(f600,plain,
( spl22_80
<=> sP0(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_80])]) ).
fof(f266,plain,
( spl22_21
<=> ! [X0] :
( sP0(X0)
| aElement0(sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_21])]) ).
fof(f921,plain,
( spl22_123
<=> aElement0(sK10(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_123])]) ).
fof(f933,plain,
( sP0(xR)
| ~ spl22_21
| spl22_123 ),
inference(resolution,[],[f923,f267]) ).
fof(f267,plain,
( ! [X0] :
( aElement0(sK10(X0))
| sP0(X0) )
| ~ spl22_21 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f923,plain,
( ~ aElement0(sK10(xR))
| spl22_123 ),
inference(avatar_component_clause,[],[f921]) ).
fof(f1053,plain,
( spl22_80
| ~ spl22_20
| spl22_122 ),
inference(avatar_split_clause,[],[f932,f917,f262,f600]) ).
fof(f262,plain,
( spl22_20
<=> ! [X0] :
( sP0(X0)
| aElement0(sK9(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_20])]) ).
fof(f917,plain,
( spl22_122
<=> aElement0(sK9(xR)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_122])]) ).
fof(f932,plain,
( sP0(xR)
| ~ spl22_20
| spl22_122 ),
inference(resolution,[],[f919,f263]) ).
fof(f263,plain,
( ! [X0] :
( aElement0(sK9(X0))
| sP0(X0) )
| ~ spl22_20 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f919,plain,
( ~ aElement0(sK9(xR))
| spl22_122 ),
inference(avatar_component_clause,[],[f917]) ).
fof(f1034,plain,
( spl22_133
| ~ spl22_59
| ~ spl22_75 ),
inference(avatar_split_clause,[],[f582,f562,f454,f1032]) ).
fof(f1032,plain,
( spl22_133
<=> ! [X9,X7,X6,X8] :
( sdtmndtasgtdt0(sK21(X6,X7,X8),X7,sK16(X7,X9,sK21(X6,X7,X8)))
| ~ aReductOfIn0(X9,X8,X7)
| ~ aElement0(sK21(X6,X7,X8))
| ~ aElement0(X9)
| ~ aElement0(X8)
| ~ sP2(X7)
| aReductOfIn0(X6,X8,X7)
| ~ sP6(X6,X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_133])]) ).
fof(f454,plain,
( spl22_59
<=> ! [X2,X0,X1] :
( aReductOfIn0(sK21(X0,X1,X2),X2,X1)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_59])]) ).
fof(f582,plain,
( ! [X8,X6,X9,X7] :
( sdtmndtasgtdt0(sK21(X6,X7,X8),X7,sK16(X7,X9,sK21(X6,X7,X8)))
| ~ aReductOfIn0(X9,X8,X7)
| ~ aElement0(sK21(X6,X7,X8))
| ~ aElement0(X9)
| ~ aElement0(X8)
| ~ sP2(X7)
| aReductOfIn0(X6,X8,X7)
| ~ sP6(X6,X7,X8) )
| ~ spl22_59
| ~ spl22_75 ),
inference(resolution,[],[f563,f455]) ).
fof(f455,plain,
( ! [X2,X0,X1] :
( aReductOfIn0(sK21(X0,X1,X2),X2,X1)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) )
| ~ spl22_59 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f1009,plain,
( spl22_132
| ~ spl22_59
| ~ spl22_74 ),
inference(avatar_split_clause,[],[f577,f558,f454,f1007]) ).
fof(f1007,plain,
( spl22_132
<=> ! [X9,X7,X6,X8] :
( sdtmndtasgtdt0(X6,X7,sK16(X7,X6,sK21(X8,X7,X9)))
| ~ aReductOfIn0(X6,X9,X7)
| ~ aElement0(sK21(X8,X7,X9))
| ~ aElement0(X6)
| ~ aElement0(X9)
| ~ sP2(X7)
| aReductOfIn0(X8,X9,X7)
| ~ sP6(X8,X7,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_132])]) ).
fof(f577,plain,
( ! [X8,X6,X9,X7] :
( sdtmndtasgtdt0(X6,X7,sK16(X7,X6,sK21(X8,X7,X9)))
| ~ aReductOfIn0(X6,X9,X7)
| ~ aElement0(sK21(X8,X7,X9))
| ~ aElement0(X6)
| ~ aElement0(X9)
| ~ sP2(X7)
| aReductOfIn0(X8,X9,X7)
| ~ sP6(X8,X7,X9) )
| ~ spl22_59
| ~ spl22_74 ),
inference(resolution,[],[f559,f455]) ).
fof(f1005,plain,
( spl22_131
| ~ spl22_59
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f532,f516,f454,f1003]) ).
fof(f1003,plain,
( spl22_131
<=> ! [X9,X7,X6,X8] :
( aElement0(sK16(X6,X7,sK21(X8,X6,X9)))
| ~ aReductOfIn0(X7,X9,X6)
| ~ aElement0(sK21(X8,X6,X9))
| ~ aElement0(X7)
| ~ aElement0(X9)
| ~ sP2(X6)
| aReductOfIn0(X8,X9,X6)
| ~ sP6(X8,X6,X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_131])]) ).
fof(f532,plain,
( ! [X8,X6,X9,X7] :
( aElement0(sK16(X6,X7,sK21(X8,X6,X9)))
| ~ aReductOfIn0(X7,X9,X6)
| ~ aElement0(sK21(X8,X6,X9))
| ~ aElement0(X7)
| ~ aElement0(X9)
| ~ sP2(X6)
| aReductOfIn0(X8,X9,X6)
| ~ sP6(X8,X6,X9) )
| ~ spl22_59
| ~ spl22_68 ),
inference(resolution,[],[f517,f455]) ).
fof(f1001,plain,
( ~ spl22_4
| ~ spl22_1
| ~ spl22_3
| ~ spl22_88
| spl22_110 ),
inference(avatar_split_clause,[],[f902,f842,f679,f177,f167,f182]) ).
fof(f679,plain,
( spl22_88
<=> ! [X0,X1] :
( ~ aElement0(X0)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| aElement0(sK19(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_88])]) ).
fof(f842,plain,
( spl22_110
<=> aElement0(sK19(xR,xv)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_110])]) ).
fof(f902,plain,
( ~ isTerminating0(xR)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xv)
| ~ spl22_88
| spl22_110 ),
inference(resolution,[],[f844,f680]) ).
fof(f680,plain,
( ! [X0,X1] :
( aElement0(sK19(X1,X0))
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_88 ),
inference(avatar_component_clause,[],[f679]) ).
fof(f844,plain,
( ~ aElement0(sK19(xR,xv))
| spl22_110 ),
inference(avatar_component_clause,[],[f842]) ).
fof(f999,plain,
( spl22_130
| ~ spl22_60
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f498,f484,f458,f997]) ).
fof(f997,plain,
( spl22_130
<=> ! [X5,X4,X7,X6] :
( sdtmndtplgtdt0(X4,X5,X6)
| ~ sdtmndtplgtdt0(X4,X5,sK21(X6,X5,X7))
| ~ aElement0(X6)
| ~ aElement0(sK21(X6,X5,X7))
| ~ aRewritingSystem0(X5)
| ~ aElement0(X4)
| aReductOfIn0(X6,X7,X5)
| ~ sP6(X6,X5,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_130])]) ).
fof(f458,plain,
( spl22_60
<=> ! [X2,X0,X1] :
( sdtmndtplgtdt0(sK21(X0,X1,X2),X1,X0)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_60])]) ).
fof(f484,plain,
( spl22_64
<=> ! [X0,X3,X2,X1] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_64])]) ).
fof(f498,plain,
( ! [X6,X7,X4,X5] :
( sdtmndtplgtdt0(X4,X5,X6)
| ~ sdtmndtplgtdt0(X4,X5,sK21(X6,X5,X7))
| ~ aElement0(X6)
| ~ aElement0(sK21(X6,X5,X7))
| ~ aRewritingSystem0(X5)
| ~ aElement0(X4)
| aReductOfIn0(X6,X7,X5)
| ~ sP6(X6,X5,X7) )
| ~ spl22_60
| ~ spl22_64 ),
inference(resolution,[],[f485,f459]) ).
fof(f459,plain,
( ! [X2,X0,X1] :
( sdtmndtplgtdt0(sK21(X0,X1,X2),X1,X0)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) )
| ~ spl22_60 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f485,plain,
( ! [X2,X3,X0,X1] :
( ~ sdtmndtplgtdt0(X2,X1,X3)
| sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_64 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f949,plain,
( spl22_129
| ~ spl22_38
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f494,f480,f336,f947]) ).
fof(f947,plain,
( spl22_129
<=> ! [X1] :
( aReductOfIn0(sK20(X1,sK11(X1)),sK11(X1),X1)
| aNormalFormOfIn0(sK11(X1),sK9(X1),X1)
| ~ aElement0(sK11(X1))
| ~ aRewritingSystem0(X1)
| ~ aElement0(sK9(X1))
| sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_129])]) ).
fof(f336,plain,
( spl22_38
<=> ! [X0] :
( sP0(X0)
| sdtmndtasgtdt0(sK9(X0),X0,sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_38])]) ).
fof(f480,plain,
( spl22_63
<=> ! [X2,X0,X1] :
( aNormalFormOfIn0(X2,X0,X1)
| aReductOfIn0(sK20(X1,X2),X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_63])]) ).
fof(f494,plain,
( ! [X1] :
( aReductOfIn0(sK20(X1,sK11(X1)),sK11(X1),X1)
| aNormalFormOfIn0(sK11(X1),sK9(X1),X1)
| ~ aElement0(sK11(X1))
| ~ aRewritingSystem0(X1)
| ~ aElement0(sK9(X1))
| sP0(X1) )
| ~ spl22_38
| ~ spl22_63 ),
inference(resolution,[],[f481,f337]) ).
fof(f337,plain,
( ! [X0] :
( sdtmndtasgtdt0(sK9(X0),X0,sK11(X0))
| sP0(X0) )
| ~ spl22_38 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f481,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| aReductOfIn0(sK20(X1,X2),X2,X1)
| aNormalFormOfIn0(X2,X0,X1)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_63 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f945,plain,
( spl22_128
| ~ spl22_37
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f493,f480,f332,f943]) ).
fof(f943,plain,
( spl22_128
<=> ! [X0] :
( aReductOfIn0(sK20(X0,sK10(X0)),sK10(X0),X0)
| aNormalFormOfIn0(sK10(X0),sK9(X0),X0)
| ~ aElement0(sK10(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK9(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_128])]) ).
fof(f332,plain,
( spl22_37
<=> ! [X0] :
( sP0(X0)
| sdtmndtasgtdt0(sK9(X0),X0,sK10(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_37])]) ).
fof(f493,plain,
( ! [X0] :
( aReductOfIn0(sK20(X0,sK10(X0)),sK10(X0),X0)
| aNormalFormOfIn0(sK10(X0),sK9(X0),X0)
| ~ aElement0(sK10(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK9(X0))
| sP0(X0) )
| ~ spl22_37
| ~ spl22_63 ),
inference(resolution,[],[f481,f333]) ).
fof(f333,plain,
( ! [X0] :
( sdtmndtasgtdt0(sK9(X0),X0,sK10(X0))
| sP0(X0) )
| ~ spl22_37 ),
inference(avatar_component_clause,[],[f332]) ).
fof(f941,plain,
( spl22_127
| ~ spl22_57
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f464,f458,f438,f939]) ).
fof(f939,plain,
( spl22_127
<=> ! [X5,X4,X6,X3] :
( aReductOfIn0(X3,X4,X5)
| ~ sP6(X3,X5,X4)
| sP6(X3,X5,X6)
| ~ aReductOfIn0(sK21(X3,X5,X4),X6,X5)
| ~ aElement0(sK21(X3,X5,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_127])]) ).
fof(f438,plain,
( spl22_57
<=> ! [X0,X3,X2,X1] :
( sP6(X0,X1,X2)
| ~ sdtmndtplgtdt0(X3,X1,X0)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aElement0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_57])]) ).
fof(f464,plain,
( ! [X3,X6,X4,X5] :
( aReductOfIn0(X3,X4,X5)
| ~ sP6(X3,X5,X4)
| sP6(X3,X5,X6)
| ~ aReductOfIn0(sK21(X3,X5,X4),X6,X5)
| ~ aElement0(sK21(X3,X5,X4)) )
| ~ spl22_57
| ~ spl22_60 ),
inference(resolution,[],[f459,f439]) ).
fof(f439,plain,
( ! [X2,X3,X0,X1] :
( ~ sdtmndtplgtdt0(X3,X1,X0)
| sP6(X0,X1,X2)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aElement0(X3) )
| ~ spl22_57 ),
inference(avatar_component_clause,[],[f438]) ).
fof(f937,plain,
( spl22_126
| ~ spl22_58
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f463,f458,f442,f935]) ).
fof(f935,plain,
( spl22_126
<=> ! [X2,X0,X1] :
( aReductOfIn0(X0,X1,X2)
| ~ sP6(X0,X2,X1)
| sdtmndtasgtdt0(sK21(X0,X2,X1),X2,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(sK21(X0,X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_126])]) ).
fof(f442,plain,
( spl22_58
<=> ! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_58])]) ).
fof(f463,plain,
( ! [X2,X0,X1] :
( aReductOfIn0(X0,X1,X2)
| ~ sP6(X0,X2,X1)
| sdtmndtasgtdt0(sK21(X0,X2,X1),X2,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X2)
| ~ aElement0(sK21(X0,X2,X1)) )
| ~ spl22_58
| ~ spl22_60 ),
inference(resolution,[],[f459,f443]) ).
fof(f443,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_58 ),
inference(avatar_component_clause,[],[f442]) ).
fof(f931,plain,
( spl22_80
| ~ spl22_122
| ~ spl22_123
| spl22_124
| ~ spl22_125
| ~ spl22_37
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f509,f504,f332,f928,f925,f921,f917,f600]) ).
fof(f925,plain,
( spl22_124
<=> ! [X2] :
( aElement0(sK8(X2,sK10(xR)))
| ~ aElement0(X2)
| ~ sdtmndtasgtdt0(sK9(xR),xR,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_124])]) ).
fof(f928,plain,
( spl22_125
<=> iLess0(sK9(xR),xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_125])]) ).
fof(f504,plain,
( spl22_66
<=> ! [X2,X0,X1] :
( aElement0(sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_66])]) ).
fof(f509,plain,
( ! [X2] :
( ~ iLess0(sK9(xR),xa)
| aElement0(sK8(X2,sK10(xR)))
| ~ sdtmndtasgtdt0(sK9(xR),xR,X2)
| ~ aElement0(sK10(xR))
| ~ aElement0(X2)
| ~ aElement0(sK9(xR))
| sP0(xR) )
| ~ spl22_37
| ~ spl22_66 ),
inference(resolution,[],[f505,f333]) ).
fof(f505,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ iLess0(X0,xa)
| aElement0(sK8(X1,X2))
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) )
| ~ spl22_66 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f915,plain,
( spl22_121
| ~ spl22_52
| ~ spl22_60 ),
inference(avatar_split_clause,[],[f465,f458,f413,f913]) ).
fof(f913,plain,
( spl22_121
<=> ! [X9,X8,X7] :
( aReductOfIn0(X7,X8,X9)
| ~ sP6(X7,X9,X8)
| iLess0(X7,sK21(X7,X9,X8))
| ~ aElement0(X7)
| ~ aElement0(sK21(X7,X9,X8))
| ~ sP4(X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_121])]) ).
fof(f465,plain,
( ! [X8,X9,X7] :
( aReductOfIn0(X7,X8,X9)
| ~ sP6(X7,X9,X8)
| iLess0(X7,sK21(X7,X9,X8))
| ~ aElement0(X7)
| ~ aElement0(sK21(X7,X9,X8))
| ~ sP4(X9) )
| ~ spl22_52
| ~ spl22_60 ),
inference(resolution,[],[f459,f414]) ).
fof(f906,plain,
( spl22_120
| ~ spl22_38
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f502,f488,f336,f904]) ).
fof(f904,plain,
( spl22_120
<=> ! [X4,X5] :
( sdtmndtasgtdt0(X4,X5,sK11(X5))
| ~ sdtmndtasgtdt0(X4,X5,sK9(X5))
| ~ aElement0(sK11(X5))
| ~ aElement0(sK9(X5))
| ~ aRewritingSystem0(X5)
| ~ aElement0(X4)
| sP0(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_120])]) ).
fof(f488,plain,
( spl22_65
<=> ! [X0,X3,X2,X1] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_65])]) ).
fof(f502,plain,
( ! [X4,X5] :
( sdtmndtasgtdt0(X4,X5,sK11(X5))
| ~ sdtmndtasgtdt0(X4,X5,sK9(X5))
| ~ aElement0(sK11(X5))
| ~ aElement0(sK9(X5))
| ~ aRewritingSystem0(X5)
| ~ aElement0(X4)
| sP0(X5) )
| ~ spl22_38
| ~ spl22_65 ),
inference(resolution,[],[f489,f337]) ).
fof(f489,plain,
( ! [X2,X3,X0,X1] :
( ~ sdtmndtasgtdt0(X2,X1,X3)
| sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_65 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f901,plain,
( spl22_119
| ~ spl22_37
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f501,f488,f332,f899]) ).
fof(f899,plain,
( spl22_119
<=> ! [X2,X3] :
( sdtmndtasgtdt0(X2,X3,sK10(X3))
| ~ sdtmndtasgtdt0(X2,X3,sK9(X3))
| ~ aElement0(sK10(X3))
| ~ aElement0(sK9(X3))
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2)
| sP0(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_119])]) ).
fof(f501,plain,
( ! [X2,X3] :
( sdtmndtasgtdt0(X2,X3,sK10(X3))
| ~ sdtmndtasgtdt0(X2,X3,sK9(X3))
| ~ aElement0(sK10(X3))
| ~ aElement0(sK9(X3))
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2)
| sP0(X3) )
| ~ spl22_37
| ~ spl22_65 ),
inference(resolution,[],[f489,f333]) ).
fof(f897,plain,
( spl22_118
| ~ spl22_41
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f497,f484,f348,f895]) ).
fof(f895,plain,
( spl22_118
<=> ! [X2,X3] :
( sdtmndtplgtdt0(X2,X3,sK18(X3))
| ~ sdtmndtplgtdt0(X2,X3,sK17(X3))
| ~ aElement0(sK18(X3))
| ~ aElement0(sK17(X3))
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2)
| sP4(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_118])]) ).
fof(f348,plain,
( spl22_41
<=> ! [X0] :
( sP4(X0)
| sdtmndtplgtdt0(sK17(X0),X0,sK18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_41])]) ).
fof(f497,plain,
( ! [X2,X3] :
( sdtmndtplgtdt0(X2,X3,sK18(X3))
| ~ sdtmndtplgtdt0(X2,X3,sK17(X3))
| ~ aElement0(sK18(X3))
| ~ aElement0(sK17(X3))
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2)
| sP4(X3) )
| ~ spl22_41
| ~ spl22_64 ),
inference(resolution,[],[f485,f349]) ).
fof(f349,plain,
( ! [X0] :
( sdtmndtplgtdt0(sK17(X0),X0,sK18(X0))
| sP4(X0) )
| ~ spl22_41 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f873,plain,
( spl22_117
| ~ spl22_38
| ~ spl22_61 ),
inference(avatar_split_clause,[],[f473,f467,f336,f871]) ).
fof(f871,plain,
( spl22_117
<=> ! [X1] :
( sK9(X1) = sK11(X1)
| sdtmndtplgtdt0(sK9(X1),X1,sK11(X1))
| ~ aElement0(sK11(X1))
| ~ aRewritingSystem0(X1)
| ~ aElement0(sK9(X1))
| sP0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_117])]) ).
fof(f467,plain,
( spl22_61
<=> ! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_61])]) ).
fof(f473,plain,
( ! [X1] :
( sK9(X1) = sK11(X1)
| sdtmndtplgtdt0(sK9(X1),X1,sK11(X1))
| ~ aElement0(sK11(X1))
| ~ aRewritingSystem0(X1)
| ~ aElement0(sK9(X1))
| sP0(X1) )
| ~ spl22_38
| ~ spl22_61 ),
inference(resolution,[],[f468,f337]) ).
fof(f468,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtasgtdt0(X0,X1,X2)
| X0 = X2
| sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_61 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f869,plain,
( spl22_116
| ~ spl22_37
| ~ spl22_61 ),
inference(avatar_split_clause,[],[f472,f467,f332,f867]) ).
fof(f867,plain,
( spl22_116
<=> ! [X0] :
( sK9(X0) = sK10(X0)
| sdtmndtplgtdt0(sK9(X0),X0,sK10(X0))
| ~ aElement0(sK10(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK9(X0))
| sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_116])]) ).
fof(f472,plain,
( ! [X0] :
( sK9(X0) = sK10(X0)
| sdtmndtplgtdt0(sK9(X0),X0,sK10(X0))
| ~ aElement0(sK10(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK9(X0))
| sP0(X0) )
| ~ spl22_37
| ~ spl22_61 ),
inference(resolution,[],[f468,f333]) ).
fof(f865,plain,
( ~ spl22_114
| ~ spl22_6
| ~ spl22_4
| spl22_115
| ~ spl22_10
| ~ spl22_68 ),
inference(avatar_split_clause,[],[f528,f516,f211,f863,f182,f192,f859]) ).
fof(f863,plain,
( spl22_115
<=> ! [X0] :
( aElement0(sK16(xR,X0,xv))
| ~ aElement0(X0)
| ~ aReductOfIn0(X0,xa,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_115])]) ).
fof(f528,plain,
( ! [X0] :
( aElement0(sK16(xR,X0,xv))
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(xv)
| ~ aElement0(X0)
| ~ aElement0(xa)
| ~ sP2(xR) )
| ~ spl22_10
| ~ spl22_68 ),
inference(resolution,[],[f517,f213]) ).
fof(f857,plain,
( ~ spl22_5
| ~ spl22_7
| spl22_112
| ~ spl22_113
| ~ spl22_13
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f508,f504,f226,f854,f851,f197,f187]) ).
fof(f197,plain,
( spl22_7
<=> aElement0(xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_7])]) ).
fof(f851,plain,
( spl22_112
<=> ! [X1] :
( aElement0(sK8(X1,xb))
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xu,xR,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_112])]) ).
fof(f854,plain,
( spl22_113
<=> iLess0(xu,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_113])]) ).
fof(f226,plain,
( spl22_13
<=> sdtmndtasgtdt0(xu,xR,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_13])]) ).
fof(f508,plain,
( ! [X1] :
( ~ iLess0(xu,xa)
| aElement0(sK8(X1,xb))
| ~ sdtmndtasgtdt0(xu,xR,X1)
| ~ aElement0(xb)
| ~ aElement0(X1)
| ~ aElement0(xu) )
| ~ spl22_13
| ~ spl22_66 ),
inference(resolution,[],[f505,f228]) ).
fof(f228,plain,
( sdtmndtasgtdt0(xu,xR,xb)
| ~ spl22_13 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f849,plain,
( ~ spl22_110
| ~ spl22_111
| ~ spl22_3
| ~ spl22_4
| ~ spl22_1
| ~ spl22_9
| ~ spl22_89 ),
inference(avatar_split_clause,[],[f690,f683,f207,f167,f182,f177,f846,f842]) ).
fof(f846,plain,
( spl22_111
<=> sdtmndtasgtdt0(xu,xR,sK19(xR,xv)) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_111])]) ).
fof(f683,plain,
( spl22_89
<=> ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,sK19(X1,X0))
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ isTerminating0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_89])]) ).
fof(f690,plain,
( ~ aRewritingSystem0(xR)
| ~ aElement0(xv)
| ~ isTerminating0(xR)
| ~ sdtmndtasgtdt0(xu,xR,sK19(xR,xv))
| ~ aElement0(sK19(xR,xv))
| ~ spl22_9
| ~ spl22_89 ),
inference(resolution,[],[f684,f208]) ).
fof(f684,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,sK19(X1,X0))
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ isTerminating0(X1) )
| ~ spl22_89 ),
inference(avatar_component_clause,[],[f683]) ).
fof(f840,plain,
( ~ spl22_4
| ~ spl22_8
| spl22_108
| ~ spl22_109
| ~ spl22_11
| ~ spl22_66 ),
inference(avatar_split_clause,[],[f507,f504,f216,f837,f834,f202,f182]) ).
fof(f834,plain,
( spl22_108
<=> ! [X0] :
( aElement0(sK8(X0,xc))
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(xv,xR,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_108])]) ).
fof(f837,plain,
( spl22_109
<=> iLess0(xv,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_109])]) ).
fof(f216,plain,
( spl22_11
<=> sdtmndtasgtdt0(xv,xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_11])]) ).
fof(f507,plain,
( ! [X0] :
( ~ iLess0(xv,xa)
| aElement0(sK8(X0,xc))
| ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ aElement0(xc)
| ~ aElement0(X0)
| ~ aElement0(xv) )
| ~ spl22_11
| ~ spl22_66 ),
inference(resolution,[],[f505,f218]) ).
fof(f218,plain,
( sdtmndtasgtdt0(xv,xR,xc)
| ~ spl22_11 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f814,plain,
( spl22_107
| ~ spl22_41
| ~ spl22_58 ),
inference(avatar_split_clause,[],[f452,f442,f348,f812]) ).
fof(f812,plain,
( spl22_107
<=> ! [X0] :
( sdtmndtasgtdt0(sK17(X0),X0,sK18(X0))
| ~ aElement0(sK18(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK17(X0))
| sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_107])]) ).
fof(f452,plain,
( ! [X0] :
( sdtmndtasgtdt0(sK17(X0),X0,sK18(X0))
| ~ aElement0(sK18(X0))
| ~ aRewritingSystem0(X0)
| ~ aElement0(sK17(X0))
| sP4(X0) )
| ~ spl22_41
| ~ spl22_58 ),
inference(resolution,[],[f443,f349]) ).
fof(f808,plain,
( ~ spl22_1
| ~ spl22_5
| ~ spl22_7
| spl22_106
| ~ spl22_13
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f500,f488,f226,f806,f197,f187,f167]) ).
fof(f806,plain,
( spl22_106
<=> ! [X1] :
( sdtmndtasgtdt0(X1,xR,xb)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X1,xR,xu) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_106])]) ).
fof(f500,plain,
( ! [X1] :
( sdtmndtasgtdt0(X1,xR,xb)
| ~ sdtmndtasgtdt0(X1,xR,xu)
| ~ aElement0(xb)
| ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X1) )
| ~ spl22_13
| ~ spl22_65 ),
inference(resolution,[],[f489,f228]) ).
fof(f802,plain,
( ~ spl22_1
| ~ spl22_4
| ~ spl22_8
| spl22_105
| ~ spl22_11
| ~ spl22_65 ),
inference(avatar_split_clause,[],[f499,f488,f216,f800,f202,f182,f167]) ).
fof(f800,plain,
( spl22_105
<=> ! [X0] :
( sdtmndtasgtdt0(X0,xR,xc)
| ~ aElement0(X0)
| ~ sdtmndtasgtdt0(X0,xR,xv) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_105])]) ).
fof(f499,plain,
( ! [X0] :
( sdtmndtasgtdt0(X0,xR,xc)
| ~ sdtmndtasgtdt0(X0,xR,xv)
| ~ aElement0(xc)
| ~ aElement0(xv)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) )
| ~ spl22_11
| ~ spl22_65 ),
inference(resolution,[],[f489,f218]) ).
fof(f797,plain,
( ~ spl22_1
| ~ spl22_6
| ~ spl22_8
| spl22_104
| ~ spl22_15
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f496,f484,f236,f795,f202,f192,f167]) ).
fof(f795,plain,
( spl22_104
<=> ! [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
| ~ aElement0(X1)
| ~ sdtmndtplgtdt0(X1,xR,xa) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_104])]) ).
fof(f496,plain,
( ! [X1] :
( sdtmndtplgtdt0(X1,xR,xc)
| ~ sdtmndtplgtdt0(X1,xR,xa)
| ~ aElement0(xc)
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X1) )
| ~ spl22_15
| ~ spl22_64 ),
inference(resolution,[],[f485,f238]) ).
fof(f792,plain,
( ~ spl22_1
| ~ spl22_6
| ~ spl22_7
| spl22_103
| ~ spl22_14
| ~ spl22_64 ),
inference(avatar_split_clause,[],[f495,f484,f231,f790,f197,f192,f167]) ).
fof(f790,plain,
( spl22_103
<=> ! [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
| ~ aElement0(X0)
| ~ sdtmndtplgtdt0(X0,xR,xa) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_103])]) ).
fof(f231,plain,
( spl22_14
<=> sdtmndtplgtdt0(xa,xR,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_14])]) ).
fof(f495,plain,
( ! [X0] :
( sdtmndtplgtdt0(X0,xR,xb)
| ~ sdtmndtplgtdt0(X0,xR,xa)
| ~ aElement0(xb)
| ~ aElement0(xa)
| ~ aRewritingSystem0(xR)
| ~ aElement0(X0) )
| ~ spl22_14
| ~ spl22_64 ),
inference(resolution,[],[f485,f233]) ).
fof(f233,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| ~ spl22_14 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f785,plain,
( ~ spl22_5
| ~ spl22_1
| ~ spl22_7
| spl22_101
| spl22_102
| ~ spl22_13
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f492,f480,f226,f782,f778,f197,f167,f187]) ).
fof(f778,plain,
( spl22_101
<=> aNormalFormOfIn0(xb,xu,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_101])]) ).
fof(f782,plain,
( spl22_102
<=> aReductOfIn0(sK20(xR,xb),xb,xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_102])]) ).
fof(f492,plain,
( aReductOfIn0(sK20(xR,xb),xb,xR)
| aNormalFormOfIn0(xb,xu,xR)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xu)
| ~ spl22_13
| ~ spl22_63 ),
inference(resolution,[],[f481,f228]) ).
fof(f773,plain,
( ~ spl22_4
| ~ spl22_1
| ~ spl22_8
| spl22_99
| spl22_100
| ~ spl22_11
| ~ spl22_63 ),
inference(avatar_split_clause,[],[f491,f480,f216,f770,f766,f202,f167,f182]) ).
fof(f491,plain,
( aReductOfIn0(sK20(xR,xc),xc,xR)
| aNormalFormOfIn0(xc,xv,xR)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xv)
| ~ spl22_11
| ~ spl22_63 ),
inference(resolution,[],[f481,f218]) ).
fof(f763,plain,
( spl22_98
| ~ spl22_42
| ~ spl22_59 ),
inference(avatar_split_clause,[],[f462,f454,f352,f761]) ).
fof(f761,plain,
( spl22_98
<=> ! [X4,X5,X3] :
( aReductOfIn0(X3,X4,X5)
| ~ sP6(X3,X5,X4)
| sP6(sK21(X3,X5,X4),X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_98])]) ).
fof(f462,plain,
( ! [X3,X4,X5] :
( aReductOfIn0(X3,X4,X5)
| ~ sP6(X3,X5,X4)
| sP6(sK21(X3,X5,X4),X5,X4) )
| ~ spl22_42
| ~ spl22_59 ),
inference(resolution,[],[f455,f353]) ).
fof(f759,plain,
( spl22_97
| ~ spl22_41
| ~ spl22_57 ),
inference(avatar_split_clause,[],[f449,f438,f348,f757]) ).
fof(f757,plain,
( spl22_97
<=> ! [X2,X3] :
( sP6(sK18(X2),X2,X3)
| ~ aReductOfIn0(sK17(X2),X3,X2)
| ~ aElement0(sK17(X2))
| sP4(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_97])]) ).
fof(f449,plain,
( ! [X2,X3] :
( sP6(sK18(X2),X2,X3)
| ~ aReductOfIn0(sK17(X2),X3,X2)
| ~ aElement0(sK17(X2))
| sP4(X2) )
| ~ spl22_41
| ~ spl22_57 ),
inference(resolution,[],[f439,f349]) ).
fof(f745,plain,
( spl22_96
| ~ spl22_46
| ~ spl22_51 ),
inference(avatar_split_clause,[],[f409,f399,f373,f743]) ).
fof(f743,plain,
( spl22_96
<=> ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| sdtmndtplgtdt0(X2,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_96])]) ).
fof(f373,plain,
( spl22_46
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_46])]) ).
fof(f399,plain,
( spl22_51
<=> ! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ sP6(X2,X1,X0)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_51])]) ).
fof(f409,plain,
( ! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| sdtmndtplgtdt0(X2,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2) )
| ~ spl22_46
| ~ spl22_51 ),
inference(resolution,[],[f400,f374]) ).
fof(f374,plain,
( ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_46 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f400,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| ~ sP6(X2,X1,X0)
| sdtmndtplgtdt0(X0,X1,X2) )
| ~ spl22_51 ),
inference(avatar_component_clause,[],[f399]) ).
fof(f741,plain,
( spl22_95
| ~ spl22_46
| ~ spl22_50 ),
inference(avatar_split_clause,[],[f408,f395,f373,f739]) ).
fof(f739,plain,
( spl22_95
<=> ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sP6(X2,X1,X0)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_95])]) ).
fof(f395,plain,
( spl22_50
<=> ! [X2,X0,X1] :
( sP6(X2,X1,X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_50])]) ).
fof(f408,plain,
( ! [X2,X0,X1] :
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sP6(X2,X1,X0)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_46
| ~ spl22_50 ),
inference(resolution,[],[f396,f374]) ).
fof(f396,plain,
( ! [X2,X0,X1] :
( ~ sP7(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| sP6(X2,X1,X0) )
| ~ spl22_50 ),
inference(avatar_component_clause,[],[f395]) ).
fof(f733,plain,
( ~ spl22_5
| ~ spl22_1
| ~ spl22_7
| spl22_93
| spl22_94
| ~ spl22_13
| ~ spl22_61 ),
inference(avatar_split_clause,[],[f471,f467,f226,f730,f726,f197,f167,f187]) ).
fof(f726,plain,
( spl22_93
<=> sdtmndtplgtdt0(xu,xR,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_93])]) ).
fof(f730,plain,
( spl22_94
<=> xb = xu ),
introduced(avatar_definition,[new_symbols(naming,[spl22_94])]) ).
fof(f471,plain,
( xb = xu
| sdtmndtplgtdt0(xu,xR,xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xu)
| ~ spl22_13
| ~ spl22_61 ),
inference(resolution,[],[f468,f228]) ).
fof(f720,plain,
( ~ spl22_4
| ~ spl22_1
| ~ spl22_8
| spl22_91
| spl22_92
| ~ spl22_11
| ~ spl22_61 ),
inference(avatar_split_clause,[],[f470,f467,f216,f717,f713,f202,f167,f182]) ).
fof(f713,plain,
( spl22_91
<=> sdtmndtplgtdt0(xv,xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_91])]) ).
fof(f717,plain,
( spl22_92
<=> xc = xv ),
introduced(avatar_definition,[new_symbols(naming,[spl22_92])]) ).
fof(f470,plain,
( xc = xv
| sdtmndtplgtdt0(xv,xR,xc)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xv)
| ~ spl22_11
| ~ spl22_61 ),
inference(resolution,[],[f468,f218]) ).
fof(f689,plain,
( spl22_90
| ~ spl22_47
| ~ spl22_49 ),
inference(avatar_split_clause,[],[f407,f391,f383,f687]) ).
fof(f687,plain,
( spl22_90
<=> ! [X2,X0,X1] :
( ~ aReductOfIn0(X0,sK19(X1,X2),X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ isTerminating0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_90])]) ).
fof(f383,plain,
( spl22_47
<=> ! [X0,X1] :
( aNormalFormOfIn0(sK19(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_47])]) ).
fof(f407,plain,
( ! [X2,X0,X1] :
( ~ aReductOfIn0(X0,sK19(X1,X2),X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ isTerminating0(X1) )
| ~ spl22_47
| ~ spl22_49 ),
inference(duplicate_literal_removal,[],[f406]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( ~ aReductOfIn0(X0,sK19(X1,X2),X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X2)
| ~ aElement0(X2)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1) )
| ~ spl22_47
| ~ spl22_49 ),
inference(resolution,[],[f392,f384]) ).
fof(f384,plain,
( ! [X0,X1] :
( aNormalFormOfIn0(sK19(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) )
| ~ spl22_47 ),
inference(avatar_component_clause,[],[f383]) ).
fof(f685,plain,
( spl22_89
| ~ spl22_47
| ~ spl22_48 ),
inference(avatar_split_clause,[],[f405,f387,f383,f683]) ).
fof(f387,plain,
( spl22_48
<=> ! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_48])]) ).
fof(f405,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,sK19(X1,X0))
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ isTerminating0(X1) )
| ~ spl22_47
| ~ spl22_48 ),
inference(duplicate_literal_removal,[],[f404]) ).
fof(f404,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,sK19(X1,X0))
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0)
| ~ aElement0(X0)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1) )
| ~ spl22_47
| ~ spl22_48 ),
inference(resolution,[],[f388,f384]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_48 ),
inference(avatar_component_clause,[],[f387]) ).
fof(f681,plain,
( spl22_88
| ~ spl22_45
| ~ spl22_47 ),
inference(avatar_split_clause,[],[f403,f383,f369,f679]) ).
fof(f369,plain,
( spl22_45
<=> ! [X2,X0,X1] :
( aElement0(X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_45])]) ).
fof(f403,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| aElement0(sK19(X1,X0)) )
| ~ spl22_45
| ~ spl22_47 ),
inference(duplicate_literal_removal,[],[f402]) ).
fof(f402,plain,
( ! [X0,X1] :
( ~ aElement0(X0)
| ~ isTerminating0(X1)
| ~ aRewritingSystem0(X1)
| aElement0(sK19(X1,X0))
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_45
| ~ spl22_47 ),
inference(resolution,[],[f384,f370]) ).
fof(f370,plain,
( ! [X2,X0,X1] :
( ~ aNormalFormOfIn0(X2,X0,X1)
| aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_45 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f668,plain,
( ~ spl22_6
| ~ spl22_1
| ~ spl22_8
| spl22_87
| ~ spl22_15
| ~ spl22_58 ),
inference(avatar_split_clause,[],[f451,f442,f236,f665,f202,f167,f192]) ).
fof(f665,plain,
( spl22_87
<=> sdtmndtasgtdt0(xa,xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_87])]) ).
fof(f451,plain,
( sdtmndtasgtdt0(xa,xR,xc)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ spl22_15
| ~ spl22_58 ),
inference(resolution,[],[f443,f238]) ).
fof(f663,plain,
( ~ spl22_86
| ~ spl22_1
| ~ spl22_4
| ~ spl22_9
| ~ spl22_78 ),
inference(avatar_split_clause,[],[f627,f592,f207,f182,f167,f660]) ).
fof(f660,plain,
( spl22_86
<=> sdtmndtasgtdt0(xu,xR,xv) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_86])]) ).
fof(f592,plain,
( spl22_78
<=> ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_78])]) ).
fof(f627,plain,
( ~ aElement0(xv)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xu,xR,xv)
| ~ spl22_9
| ~ spl22_78 ),
inference(duplicate_literal_removal,[],[f604]) ).
fof(f604,plain,
( ~ aElement0(xv)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xu,xR,xv)
| ~ aElement0(xv)
| ~ spl22_9
| ~ spl22_78 ),
inference(resolution,[],[f593,f208]) ).
fof(f593,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) )
| ~ spl22_78 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f649,plain,
( ~ spl22_6
| ~ spl22_1
| ~ spl22_7
| spl22_85
| ~ spl22_14
| ~ spl22_58 ),
inference(avatar_split_clause,[],[f450,f442,f231,f646,f197,f167,f192]) ).
fof(f646,plain,
( spl22_85
<=> sdtmndtasgtdt0(xa,xR,xb) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_85])]) ).
fof(f450,plain,
( sdtmndtasgtdt0(xa,xR,xb)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ aElement0(xa)
| ~ spl22_14
| ~ spl22_58 ),
inference(resolution,[],[f443,f233]) ).
fof(f644,plain,
( ~ spl22_6
| spl22_84
| ~ spl22_15
| ~ spl22_57 ),
inference(avatar_split_clause,[],[f448,f438,f236,f642,f192]) ).
fof(f642,plain,
( spl22_84
<=> ! [X1] :
( sP6(xc,xR,X1)
| ~ aReductOfIn0(xa,X1,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_84])]) ).
fof(f448,plain,
( ! [X1] :
( sP6(xc,xR,X1)
| ~ aReductOfIn0(xa,X1,xR)
| ~ aElement0(xa) )
| ~ spl22_15
| ~ spl22_57 ),
inference(resolution,[],[f439,f238]) ).
fof(f640,plain,
( ~ spl22_6
| spl22_83
| ~ spl22_14
| ~ spl22_57 ),
inference(avatar_split_clause,[],[f447,f438,f231,f638,f192]) ).
fof(f638,plain,
( spl22_83
<=> ! [X0] :
( sP6(xb,xR,X0)
| ~ aReductOfIn0(xa,X0,xR) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_83])]) ).
fof(f447,plain,
( ! [X0] :
( sP6(xb,xR,X0)
| ~ aReductOfIn0(xa,X0,xR)
| ~ aElement0(xa) )
| ~ spl22_14
| ~ spl22_57 ),
inference(resolution,[],[f439,f233]) ).
fof(f636,plain,
( ~ spl22_81
| ~ spl22_6
| ~ spl22_7
| spl22_82
| ~ spl22_14
| ~ spl22_52 ),
inference(avatar_split_clause,[],[f424,f413,f231,f633,f197,f192,f629]) ).
fof(f633,plain,
( spl22_82
<=> iLess0(xb,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_82])]) ).
fof(f424,plain,
( iLess0(xb,xa)
| ~ aElement0(xb)
| ~ aElement0(xa)
| ~ sP4(xR)
| ~ spl22_14
| ~ spl22_52 ),
inference(resolution,[],[f414,f233]) ).
fof(f603,plain,
( spl22_79
| ~ spl22_80
| ~ spl22_29
| ~ spl22_30 ),
inference(avatar_split_clause,[],[f380,f302,f298,f600,f596]) ).
fof(f596,plain,
( spl22_79
<=> isConfluent0(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_79])]) ).
fof(f298,plain,
( spl22_29
<=> ! [X0] :
( isConfluent0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_29])]) ).
fof(f302,plain,
( spl22_30
<=> sP1(xR) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_30])]) ).
fof(f380,plain,
( ~ sP0(xR)
| isConfluent0(xR)
| ~ spl22_29
| ~ spl22_30 ),
inference(resolution,[],[f304,f299]) ).
fof(f299,plain,
( ! [X0] :
( ~ sP1(X0)
| ~ sP0(X0)
| isConfluent0(X0) )
| ~ spl22_29 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f304,plain,
( sP1(xR)
| ~ spl22_30 ),
inference(avatar_component_clause,[],[f302]) ).
fof(f594,plain,
( spl22_78
| ~ spl22_54 ),
inference(avatar_split_clause,[],[f428,f421,f592]) ).
fof(f421,plain,
( spl22_54
<=> ! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_54])]) ).
fof(f428,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1) )
| ~ spl22_54 ),
inference(duplicate_literal_removal,[],[f427]) ).
fof(f427,plain,
( ! [X0,X1] :
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_54 ),
inference(equality_resolution,[],[f422]) ).
fof(f422,plain,
( ! [X2,X0,X1] :
( X0 != X2
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) )
| ~ spl22_54 ),
inference(avatar_component_clause,[],[f421]) ).
fof(f590,plain,
( spl22_77
| ~ spl22_40
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f363,f352,f344,f588]) ).
fof(f588,plain,
( spl22_77
<=> ! [X1] :
( sP6(sK15(X1),X1,sK13(X1))
| sP2(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_77])]) ).
fof(f344,plain,
( spl22_40
<=> ! [X0] :
( sP2(X0)
| aReductOfIn0(sK15(X0),sK13(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_40])]) ).
fof(f363,plain,
( ! [X1] :
( sP6(sK15(X1),X1,sK13(X1))
| sP2(X1) )
| ~ spl22_40
| ~ spl22_42 ),
inference(resolution,[],[f353,f345]) ).
fof(f345,plain,
( ! [X0] :
( aReductOfIn0(sK15(X0),sK13(X0),X0)
| sP2(X0) )
| ~ spl22_40 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f586,plain,
( spl22_76
| ~ spl22_39
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f362,f352,f340,f584]) ).
fof(f584,plain,
( spl22_76
<=> ! [X0] :
( sP6(sK14(X0),X0,sK13(X0))
| sP2(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_76])]) ).
fof(f340,plain,
( spl22_39
<=> ! [X0] :
( sP2(X0)
| aReductOfIn0(sK14(X0),sK13(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_39])]) ).
fof(f362,plain,
( ! [X0] :
( sP6(sK14(X0),X0,sK13(X0))
| sP2(X0) )
| ~ spl22_39
| ~ spl22_42 ),
inference(resolution,[],[f353,f341]) ).
fof(f341,plain,
( ! [X0] :
( aReductOfIn0(sK14(X0),sK13(X0),X0)
| sP2(X0) )
| ~ spl22_39 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f564,plain,
spl22_75,
inference(avatar_split_clause,[],[f131,f562]) ).
fof(f131,plain,
! [X0,X6,X7,X5] :
( sdtmndtasgtdt0(X7,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ( sP2(X0)
| ( ! [X4] :
( ~ sdtmndtasgtdt0(sK15(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK14(X0),X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(sK15(X0),sK13(X0),X0)
& aReductOfIn0(sK14(X0),sK13(X0),X0)
& aElement0(sK15(X0))
& aElement0(sK14(X0))
& aElement0(sK13(X0)) ) )
& ( ! [X5,X6,X7] :
( ( sdtmndtasgtdt0(X7,X0,sK16(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK16(X0,X6,X7))
& aElement0(sK16(X0,X6,X7)) )
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP2(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16])],[f73,f75,f74]) ).
fof(f74,plain,
! [X0] :
( ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( ! [X4] :
( ~ sdtmndtasgtdt0(sK15(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK14(X0),X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(sK15(X0),sK13(X0),X0)
& aReductOfIn0(sK14(X0),sK13(X0),X0)
& aElement0(sK15(X0))
& aElement0(sK14(X0))
& aElement0(sK13(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
=> ( sdtmndtasgtdt0(X7,X0,sK16(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK16(X0,X6,X7))
& aElement0(sK16(X0,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0] :
( ( sP2(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X5,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP2(X0) ) ),
inference(rectify,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( sP2(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP2(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( sP2(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f560,plain,
spl22_74,
inference(avatar_split_clause,[],[f130,f558]) ).
fof(f130,plain,
! [X0,X6,X7,X5] :
( sdtmndtasgtdt0(X6,X0,sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f556,plain,
spl22_73,
inference(avatar_split_clause,[],[f119,f554]) ).
fof(f554,plain,
( spl22_73
<=> ! [X5,X0,X6,X7] :
( sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_73])]) ).
fof(f119,plain,
! [X0,X6,X7,X5] :
( sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0] :
( ( sP0(X0)
| ( ! [X4] :
( ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK10(X0),X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(sK9(X0),X0,sK11(X0))
& sdtmndtasgtdt0(sK9(X0),X0,sK10(X0))
& aElement0(sK11(X0))
& aElement0(sK10(X0))
& aElement0(sK9(X0)) ) )
& ( ! [X5,X6,X7] :
( ( sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7))
& aElement0(sK12(X0,X6,X7)) )
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP0(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12])],[f67,f69,f68]) ).
fof(f68,plain,
! [X0] :
( ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ( ! [X4] :
( ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK10(X0),X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(sK9(X0),X0,sK11(X0))
& sdtmndtasgtdt0(sK9(X0),X0,sK10(X0))
& aElement0(sK11(X0))
& aElement0(sK10(X0))
& aElement0(sK9(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
=> ( sdtmndtasgtdt0(X7,X0,sK12(X0,X6,X7))
& sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7))
& aElement0(sK12(X0,X6,X7)) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X5,X6,X7] :
( ? [X8] :
( sdtmndtasgtdt0(X7,X0,X8)
& sdtmndtasgtdt0(X6,X0,X8)
& aElement0(X8) )
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5) )
| ~ sP0(X0) ) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X0] :
( ( sP0(X0)
| ? [X1,X2,X3] :
( ! [X4] :
( ~ sdtmndtasgtdt0(X3,X0,X4)
| ~ sdtmndtasgtdt0(X2,X0,X4)
| ~ aElement0(X4) )
& sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP0(X0) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( sP0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f552,plain,
spl22_72,
inference(avatar_split_clause,[],[f118,f550]) ).
fof(f550,plain,
( spl22_72
<=> ! [X5,X0,X6,X7] :
( sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_72])]) ).
fof(f118,plain,
! [X0,X6,X7,X5] :
( sdtmndtasgtdt0(X6,X0,sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f540,plain,
spl22_71,
inference(avatar_split_clause,[],[f114,f538]) ).
fof(f538,plain,
( spl22_71
<=> ! [X2,X0,X1] :
( sdtmndtasgtdt0(X2,xR,sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_71])]) ).
fof(f114,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X2,xR,sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X2,xR,sK8(X1,X2))
& sdtmndtasgtdt0(X1,xR,sK8(X1,X2))
& aElement0(sK8(X1,X2)) )
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f30,f63]) ).
fof(f63,plain,
! [X1,X2] :
( ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) )
=> ( sdtmndtasgtdt0(X2,xR,sK8(X1,X2))
& sdtmndtasgtdt0(X1,xR,sK8(X1,X2))
& aElement0(sK8(X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) )
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) )
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,xR,X2)
& sdtmndtasgtdt0(X0,xR,X1)
& aElement0(X2)
& aElement0(X1)
& aElement0(X0) )
=> ( iLess0(X0,xa)
=> ? [X3] :
( sdtmndtasgtdt0(X2,xR,X3)
& sdtmndtasgtdt0(X1,xR,X3)
& aElement0(X3) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__715) ).
fof(f536,plain,
spl22_70,
inference(avatar_split_clause,[],[f113,f534]) ).
fof(f534,plain,
( spl22_70
<=> ! [X2,X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_70])]) ).
fof(f113,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X1,xR,sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f523,plain,
( spl22_69
| ~ spl22_12
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f361,f352,f221,f520]) ).
fof(f520,plain,
( spl22_69
<=> sP6(xu,xR,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_69])]) ).
fof(f361,plain,
( sP6(xu,xR,xa)
| ~ spl22_12
| ~ spl22_42 ),
inference(resolution,[],[f353,f223]) ).
fof(f518,plain,
spl22_68,
inference(avatar_split_clause,[],[f129,f516]) ).
fof(f129,plain,
! [X0,X6,X7,X5] :
( aElement0(sK16(X0,X6,X7))
| ~ aReductOfIn0(X7,X5,X0)
| ~ aReductOfIn0(X6,X5,X0)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP2(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f514,plain,
spl22_67,
inference(avatar_split_clause,[],[f117,f512]) ).
fof(f512,plain,
( spl22_67
<=> ! [X5,X0,X6,X7] :
( aElement0(sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_67])]) ).
fof(f117,plain,
! [X0,X6,X7,X5] :
( aElement0(sK12(X0,X6,X7))
| ~ sdtmndtasgtdt0(X5,X0,X7)
| ~ sdtmndtasgtdt0(X5,X0,X6)
| ~ aElement0(X7)
| ~ aElement0(X6)
| ~ aElement0(X5)
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f506,plain,
spl22_66,
inference(avatar_split_clause,[],[f112,f504]) ).
fof(f112,plain,
! [X2,X0,X1] :
( aElement0(sK8(X1,X2))
| ~ iLess0(X0,xa)
| ~ sdtmndtasgtdt0(X0,xR,X2)
| ~ sdtmndtasgtdt0(X0,xR,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f64]) ).
fof(f490,plain,
spl22_65,
inference(avatar_split_clause,[],[f165,f488]) ).
fof(f165,plain,
! [X2,X3,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( sdtmndtasgtdt0(X0,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtasgtdt0(X2,X1,X3)
& sdtmndtasgtdt0(X0,X1,X2) )
=> sdtmndtasgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTCRTrans) ).
fof(f486,plain,
spl22_64,
inference(avatar_split_clause,[],[f164,f484]) ).
fof(f164,plain,
! [X2,X3,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2,X3] :
( ( aElement0(X3)
& aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( ( sdtmndtplgtdt0(X2,X1,X3)
& sdtmndtplgtdt0(X0,X1,X2) )
=> sdtmndtplgtdt0(X0,X1,X3) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTCTrans) ).
fof(f482,plain,
spl22_63,
inference(avatar_split_clause,[],[f152,f480]) ).
fof(f152,plain,
! [X2,X0,X1] :
( aNormalFormOfIn0(X2,X0,X1)
| aReductOfIn0(sK20(X1,X2),X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| aReductOfIn0(sK20(X1,X2),X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2) )
& ( ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f86,f87]) ).
fof(f87,plain,
! [X1,X2] :
( ? [X3] : aReductOfIn0(X3,X2,X1)
=> aReductOfIn0(sK20(X1,X2),X2,X1) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2) )
& ( ( ! [X4] : ~ aReductOfIn0(X4,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2) )
& ( ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( ! [X2] :
( ( aNormalFormOfIn0(X2,X0,X1)
| ? [X3] : aReductOfIn0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2) )
& ( ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) )
| ~ aNormalFormOfIn0(X2,X0,X1) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
! [X0,X1] :
( ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ! [X3] : ~ aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aNormalFormOfIn0(X2,X0,X1)
<=> ( ~ ? [X3] : aReductOfIn0(X3,X2,X1)
& sdtmndtasgtdt0(X0,X1,X2)
& aElement0(X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mNFRDef) ).
fof(f478,plain,
( spl22_62
| ~ spl22_10
| ~ spl22_42 ),
inference(avatar_split_clause,[],[f360,f352,f211,f475]) ).
fof(f475,plain,
( spl22_62
<=> sP6(xv,xR,xa) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_62])]) ).
fof(f360,plain,
( sP6(xv,xR,xa)
| ~ spl22_10
| ~ spl22_42 ),
inference(resolution,[],[f353,f213]) ).
fof(f469,plain,
spl22_61,
inference(avatar_split_clause,[],[f161,f467]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( ( sdtmndtasgtdt0(X0,X1,X2)
| ( ~ sdtmndtplgtdt0(X0,X1,X2)
& X0 != X2 ) )
& ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtasgtdt0(X0,X1,X2)
<=> ( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTCRDef) ).
fof(f460,plain,
spl22_60,
inference(avatar_split_clause,[],[f157,f458]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(sK21(X0,X1,X2),X1,X0)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X0)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X0,X2,X1) ) )
& ( ( sdtmndtplgtdt0(sK21(X0,X1,X2),X1,X0)
& aReductOfIn0(sK21(X0,X1,X2),X2,X1)
& aElement0(sK21(X0,X1,X2)) )
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f92,f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ? [X4] :
( sdtmndtplgtdt0(X4,X1,X0)
& aReductOfIn0(X4,X2,X1)
& aElement0(X4) )
=> ( sdtmndtplgtdt0(sK21(X0,X1,X2),X1,X0)
& aReductOfIn0(sK21(X0,X1,X2),X2,X1)
& aElement0(sK21(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( sP6(X0,X1,X2)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X0)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X0,X2,X1) ) )
& ( ? [X4] :
( sdtmndtplgtdt0(X4,X1,X0)
& aReductOfIn0(X4,X2,X1)
& aElement0(X4) )
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
inference(rectify,[],[f91]) ).
fof(f91,plain,
! [X2,X1,X0] :
( ( sP6(X2,X1,X0)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1)
| ~ sP6(X2,X1,X0) ) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X2,X1,X0] :
( ( sP6(X2,X1,X0)
| ( ! [X3] :
( ~ sdtmndtplgtdt0(X3,X1,X2)
| ~ aReductOfIn0(X3,X0,X1)
| ~ aElement0(X3) )
& ~ aReductOfIn0(X2,X0,X1) ) )
& ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1)
| ~ sP6(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X2,X1,X0] :
( sP6(X2,X1,X0)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f456,plain,
spl22_59,
inference(avatar_split_clause,[],[f156,f454]) ).
fof(f156,plain,
! [X2,X0,X1] :
( aReductOfIn0(sK21(X0,X1,X2),X2,X1)
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f444,plain,
spl22_58,
inference(avatar_split_clause,[],[f163,f442]) ).
fof(f163,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f440,plain,
spl22_57,
inference(avatar_split_clause,[],[f159,f438]) ).
fof(f159,plain,
! [X2,X3,X0,X1] :
( sP6(X0,X1,X2)
| ~ sdtmndtplgtdt0(X3,X1,X0)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aElement0(X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f436,plain,
spl22_56,
inference(avatar_split_clause,[],[f137,f434]) ).
fof(f434,plain,
( spl22_56
<=> ! [X4,X0] :
( sP2(X0)
| ~ sdtmndtasgtdt0(sK15(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK14(X0),X0,X4)
| ~ aElement0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_56])]) ).
fof(f137,plain,
! [X0,X4] :
( sP2(X0)
| ~ sdtmndtasgtdt0(sK15(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK14(X0),X0,X4)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f76]) ).
fof(f432,plain,
spl22_55,
inference(avatar_split_clause,[],[f125,f430]) ).
fof(f430,plain,
( spl22_55
<=> ! [X4,X0] :
( sP0(X0)
| ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK10(X0),X0,X4)
| ~ aElement0(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_55])]) ).
fof(f125,plain,
! [X0,X4] :
( sP0(X0)
| ~ sdtmndtasgtdt0(sK11(X0),X0,X4)
| ~ sdtmndtasgtdt0(sK10(X0),X0,X4)
| ~ aElement0(X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f423,plain,
spl22_54,
inference(avatar_split_clause,[],[f162,f421]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| X0 != X2
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f419,plain,
spl22_53,
inference(avatar_split_clause,[],[f155,f417]) ).
fof(f417,plain,
( spl22_53
<=> ! [X2,X0,X1] :
( aElement0(sK21(X0,X1,X2))
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_53])]) ).
fof(f155,plain,
! [X2,X0,X1] :
( aElement0(sK21(X0,X1,X2))
| aReductOfIn0(X0,X2,X1)
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f415,plain,
spl22_52,
inference(avatar_split_clause,[],[f141,f413]) ).
fof(f141,plain,
! [X3,X0,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3)
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0] :
( ( sP4(X0)
| ( ~ iLess0(sK18(X0),sK17(X0))
& sdtmndtplgtdt0(sK17(X0),X0,sK18(X0))
& aElement0(sK18(X0))
& aElement0(sK17(X0)) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17,sK18])],[f79,f80]) ).
fof(f80,plain,
! [X0] :
( ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) )
=> ( ~ iLess0(sK18(X0),sK17(X0))
& sdtmndtplgtdt0(sK17(X0),X0,sK18(X0))
& aElement0(sK18(X0))
& aElement0(sK17(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0] :
( ( sP4(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X3,X4] :
( iLess0(X4,X3)
| ~ sdtmndtplgtdt0(X3,X0,X4)
| ~ aElement0(X4)
| ~ aElement0(X3) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X0] :
( ( sP4(X0)
| ? [X1,X2] :
( ~ iLess0(X2,X1)
& sdtmndtplgtdt0(X1,X0,X2)
& aElement0(X2)
& aElement0(X1) ) )
& ( ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( sP4(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f401,plain,
spl22_51,
inference(avatar_split_clause,[],[f154,f399]) ).
fof(f154,plain,
! [X2,X0,X1] :
( sdtmndtplgtdt0(X0,X1,X2)
| ~ sP6(X2,X1,X0)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( ( sdtmndtplgtdt0(X0,X1,X2)
| ~ sP6(X2,X1,X0) )
& ( sP6(X2,X1,X0)
| ~ sdtmndtplgtdt0(X0,X1,X2) ) )
| ~ sP7(X0,X1,X2) ),
inference(nnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> sP6(X2,X1,X0) )
| ~ sP7(X0,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f397,plain,
spl22_50,
inference(avatar_split_clause,[],[f153,f395]) ).
fof(f153,plain,
! [X2,X0,X1] :
( sP6(X2,X1,X0)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f393,plain,
spl22_49,
inference(avatar_split_clause,[],[f151,f391]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( ~ aReductOfIn0(X4,X2,X1)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f389,plain,
spl22_48,
inference(avatar_split_clause,[],[f150,f387]) ).
fof(f150,plain,
! [X2,X0,X1] :
( sdtmndtasgtdt0(X0,X1,X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f385,plain,
spl22_47,
inference(avatar_split_clause,[],[f147,f383]) ).
fof(f147,plain,
! [X0,X1] :
( aNormalFormOfIn0(sK19(X0,X1),X1,X0)
| ~ aElement0(X1)
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( aNormalFormOfIn0(sK19(X0,X1),X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f38,f82]) ).
fof(f82,plain,
! [X0,X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
=> aNormalFormOfIn0(sK19(X0,X1),X1,X0) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f37]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ? [X2] : aNormalFormOfIn0(X2,X1,X0)
| ~ aElement0(X1) )
| ~ isTerminating0(X0)
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ( isTerminating0(X0)
& aRewritingSystem0(X0) )
=> ! [X1] :
( aElement0(X1)
=> ? [X2] : aNormalFormOfIn0(X2,X1,X0) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTermNF) ).
fof(f375,plain,
spl22_46,
inference(avatar_split_clause,[],[f160,f373]) ).
fof(f160,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( sP7(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(definition_folding,[],[f44,f61,f60]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) )
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( aElement0(X2)
& aRewritingSystem0(X1)
& aElement0(X0) )
=> ( sdtmndtplgtdt0(X0,X1,X2)
<=> ( ? [X3] :
( sdtmndtplgtdt0(X3,X1,X2)
& aReductOfIn0(X3,X0,X1)
& aElement0(X3) )
| aReductOfIn0(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTCDef) ).
fof(f371,plain,
spl22_45,
inference(avatar_split_clause,[],[f149,f369]) ).
fof(f149,plain,
! [X2,X0,X1] :
( aElement0(X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f367,plain,
spl22_44,
inference(avatar_split_clause,[],[f148,f365]) ).
fof(f365,plain,
( spl22_44
<=> ! [X2,X0,X1] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_44])]) ).
fof(f148,plain,
! [X2,X0,X1] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ! [X2] :
( aElement0(X2)
| ~ aReductOfIn0(X2,X0,X1) )
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0,X1] :
( ( aRewritingSystem0(X1)
& aElement0(X0) )
=> ! [X2] :
( aReductOfIn0(X2,X0,X1)
=> aElement0(X2) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mReduct) ).
fof(f359,plain,
( spl22_43
| ~ spl22_1
| ~ spl22_18 ),
inference(avatar_split_clause,[],[f260,f250,f167,f356]) ).
fof(f250,plain,
( spl22_18
<=> ! [X0] :
( sP5(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_18])]) ).
fof(f260,plain,
( sP5(xR)
| ~ spl22_1
| ~ spl22_18 ),
inference(resolution,[],[f251,f169]) ).
fof(f169,plain,
( aRewritingSystem0(xR)
| ~ spl22_1 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f251,plain,
( ! [X0] :
( ~ aRewritingSystem0(X0)
| sP5(X0) )
| ~ spl22_18 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f354,plain,
spl22_42,
inference(avatar_split_clause,[],[f158,f352]) ).
fof(f158,plain,
! [X2,X0,X1] :
( sP6(X0,X1,X2)
| ~ aReductOfIn0(X0,X2,X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f350,plain,
spl22_41,
inference(avatar_split_clause,[],[f144,f348]) ).
fof(f144,plain,
! [X0] :
( sP4(X0)
| sdtmndtplgtdt0(sK17(X0),X0,sK18(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f346,plain,
spl22_40,
inference(avatar_split_clause,[],[f136,f344]) ).
fof(f136,plain,
! [X0] :
( sP2(X0)
| aReductOfIn0(sK15(X0),sK13(X0),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f342,plain,
spl22_39,
inference(avatar_split_clause,[],[f135,f340]) ).
fof(f135,plain,
! [X0] :
( sP2(X0)
| aReductOfIn0(sK14(X0),sK13(X0),X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f338,plain,
spl22_38,
inference(avatar_split_clause,[],[f124,f336]) ).
fof(f124,plain,
! [X0] :
( sP0(X0)
| sdtmndtasgtdt0(sK9(X0),X0,sK11(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f334,plain,
spl22_37,
inference(avatar_split_clause,[],[f123,f332]) ).
fof(f123,plain,
! [X0] :
( sP0(X0)
| sdtmndtasgtdt0(sK9(X0),X0,sK10(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f330,plain,
spl22_36,
inference(avatar_split_clause,[],[f145,f328]) ).
fof(f328,plain,
( spl22_36
<=> ! [X0] :
( sP4(X0)
| ~ iLess0(sK18(X0),sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_36])]) ).
fof(f145,plain,
! [X0] :
( sP4(X0)
| ~ iLess0(sK18(X0),sK17(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f326,plain,
( spl22_35
| ~ spl22_1
| ~ spl22_17 ),
inference(avatar_split_clause,[],[f259,f246,f167,f323]) ).
fof(f246,plain,
( spl22_17
<=> ! [X0] :
( sP3(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_17])]) ).
fof(f259,plain,
( sP3(xR)
| ~ spl22_1
| ~ spl22_17 ),
inference(resolution,[],[f247,f169]) ).
fof(f247,plain,
( ! [X0] :
( ~ aRewritingSystem0(X0)
| sP3(X0) )
| ~ spl22_17 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f321,plain,
spl22_34,
inference(avatar_split_clause,[],[f140,f319]) ).
fof(f319,plain,
( spl22_34
<=> ! [X0] :
( isTerminating0(X0)
| ~ sP4(X0)
| ~ sP5(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_34])]) ).
fof(f140,plain,
! [X0] :
( isTerminating0(X0)
| ~ sP4(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0] :
( ( ( isTerminating0(X0)
| ~ sP4(X0) )
& ( sP4(X0)
| ~ isTerminating0(X0) ) )
| ~ sP5(X0) ),
inference(nnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ( isTerminating0(X0)
<=> sP4(X0) )
| ~ sP5(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f317,plain,
spl22_33,
inference(avatar_split_clause,[],[f139,f315]) ).
fof(f139,plain,
! [X0] :
( sP4(X0)
| ~ isTerminating0(X0)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f313,plain,
spl22_32,
inference(avatar_split_clause,[],[f128,f311]) ).
fof(f311,plain,
( spl22_32
<=> ! [X0] :
( isLocallyConfluent0(X0)
| ~ sP2(X0)
| ~ sP3(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_32])]) ).
fof(f128,plain,
! [X0] :
( isLocallyConfluent0(X0)
| ~ sP2(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ( ( isLocallyConfluent0(X0)
| ~ sP2(X0) )
& ( sP2(X0)
| ~ isLocallyConfluent0(X0) ) )
| ~ sP3(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ( isLocallyConfluent0(X0)
<=> sP2(X0) )
| ~ sP3(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f309,plain,
spl22_31,
inference(avatar_split_clause,[],[f127,f307]) ).
fof(f127,plain,
! [X0] :
( sP2(X0)
| ~ isLocallyConfluent0(X0)
| ~ sP3(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f305,plain,
( spl22_30
| ~ spl22_1
| ~ spl22_16 ),
inference(avatar_split_clause,[],[f253,f242,f167,f302]) ).
fof(f242,plain,
( spl22_16
<=> ! [X0] :
( sP1(X0)
| ~ aRewritingSystem0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_16])]) ).
fof(f253,plain,
( sP1(xR)
| ~ spl22_1
| ~ spl22_16 ),
inference(resolution,[],[f243,f169]) ).
fof(f243,plain,
( ! [X0] :
( ~ aRewritingSystem0(X0)
| sP1(X0) )
| ~ spl22_16 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f300,plain,
spl22_29,
inference(avatar_split_clause,[],[f116,f298]) ).
fof(f116,plain,
! [X0] :
( isConfluent0(X0)
| ~ sP0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ( ( isConfluent0(X0)
| ~ sP0(X0) )
& ( sP0(X0)
| ~ isConfluent0(X0) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ( isConfluent0(X0)
<=> sP0(X0) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f296,plain,
spl22_28,
inference(avatar_split_clause,[],[f115,f294]) ).
fof(f294,plain,
( spl22_28
<=> ! [X0] :
( sP0(X0)
| ~ isConfluent0(X0)
| ~ sP1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_28])]) ).
fof(f115,plain,
! [X0] :
( sP0(X0)
| ~ isConfluent0(X0)
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f292,plain,
spl22_27,
inference(avatar_split_clause,[],[f143,f290]) ).
fof(f290,plain,
( spl22_27
<=> ! [X0] :
( sP4(X0)
| aElement0(sK18(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_27])]) ).
fof(f143,plain,
! [X0] :
( sP4(X0)
| aElement0(sK18(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f288,plain,
spl22_26,
inference(avatar_split_clause,[],[f142,f286]) ).
fof(f286,plain,
( spl22_26
<=> ! [X0] :
( sP4(X0)
| aElement0(sK17(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_26])]) ).
fof(f142,plain,
! [X0] :
( sP4(X0)
| aElement0(sK17(X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f284,plain,
spl22_25,
inference(avatar_split_clause,[],[f134,f282]) ).
fof(f282,plain,
( spl22_25
<=> ! [X0] :
( sP2(X0)
| aElement0(sK15(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_25])]) ).
fof(f134,plain,
! [X0] :
( sP2(X0)
| aElement0(sK15(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f280,plain,
spl22_24,
inference(avatar_split_clause,[],[f133,f278]) ).
fof(f278,plain,
( spl22_24
<=> ! [X0] :
( sP2(X0)
| aElement0(sK14(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_24])]) ).
fof(f133,plain,
! [X0] :
( sP2(X0)
| aElement0(sK14(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f276,plain,
spl22_23,
inference(avatar_split_clause,[],[f132,f274]) ).
fof(f274,plain,
( spl22_23
<=> ! [X0] :
( sP2(X0)
| aElement0(sK13(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_23])]) ).
fof(f132,plain,
! [X0] :
( sP2(X0)
| aElement0(sK13(X0)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f272,plain,
spl22_22,
inference(avatar_split_clause,[],[f122,f270]) ).
fof(f270,plain,
( spl22_22
<=> ! [X0] :
( sP0(X0)
| aElement0(sK11(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_22])]) ).
fof(f122,plain,
! [X0] :
( sP0(X0)
| aElement0(sK11(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f268,plain,
spl22_21,
inference(avatar_split_clause,[],[f121,f266]) ).
fof(f121,plain,
! [X0] :
( sP0(X0)
| aElement0(sK10(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f264,plain,
spl22_20,
inference(avatar_split_clause,[],[f120,f262]) ).
fof(f120,plain,
! [X0] :
( sP0(X0)
| aElement0(sK9(X0)) ),
inference(cnf_transformation,[],[f70]) ).
fof(f258,plain,
( ~ spl22_8
| ~ spl22_19
| ~ spl22_9
| ~ spl22_11 ),
inference(avatar_split_clause,[],[f240,f216,f207,f255,f202]) ).
fof(f255,plain,
( spl22_19
<=> sdtmndtasgtdt0(xu,xR,xc) ),
introduced(avatar_definition,[new_symbols(naming,[spl22_19])]) ).
fof(f240,plain,
( ~ sdtmndtasgtdt0(xu,xR,xc)
| ~ aElement0(xc)
| ~ spl22_9
| ~ spl22_11 ),
inference(resolution,[],[f218,f208]) ).
fof(f252,plain,
spl22_18,
inference(avatar_split_clause,[],[f146,f250]) ).
fof(f146,plain,
! [X0] :
( sP5(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0] :
( sP5(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f36,f58,f57]) ).
fof(f36,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ( isTerminating0(X0)
<=> ! [X1,X2] :
( iLess0(X2,X1)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isTerminating0(X0)
<=> ! [X1,X2] :
( ( aElement0(X2)
& aElement0(X1) )
=> ( sdtmndtplgtdt0(X1,X0,X2)
=> iLess0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mTermin) ).
fof(f248,plain,
spl22_17,
inference(avatar_split_clause,[],[f138,f246]) ).
fof(f138,plain,
! [X0] :
( sP3(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0] :
( sP3(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f34,f55,f54]) ).
fof(f34,plain,
! [X0] :
( ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ aReductOfIn0(X3,X1,X0)
| ~ aReductOfIn0(X2,X1,X0)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isLocallyConfluent0(X0)
<=> ! [X1,X2,X3] :
( ( aReductOfIn0(X3,X1,X0)
& aReductOfIn0(X2,X1,X0)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mWCRDef) ).
fof(f244,plain,
spl22_16,
inference(avatar_split_clause,[],[f126,f242]) ).
fof(f126,plain,
! [X0] :
( sP1(X0)
| ~ aRewritingSystem0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( sP1(X0)
| ~ aRewritingSystem0(X0) ),
inference(definition_folding,[],[f32,f52,f51]) ).
fof(f32,plain,
! [X0] :
( ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X0] :
( ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) )
| ~ sdtmndtasgtdt0(X1,X0,X3)
| ~ sdtmndtasgtdt0(X1,X0,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ) )
| ~ aRewritingSystem0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( aRewritingSystem0(X0)
=> ( isConfluent0(X0)
<=> ! [X1,X2,X3] :
( ( sdtmndtasgtdt0(X1,X0,X3)
& sdtmndtasgtdt0(X1,X0,X2)
& aElement0(X3)
& aElement0(X2)
& aElement0(X1) )
=> ? [X4] :
( sdtmndtasgtdt0(X3,X0,X4)
& sdtmndtasgtdt0(X2,X0,X4)
& aElement0(X4) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',mCRDef) ).
fof(f239,plain,
spl22_15,
inference(avatar_split_clause,[],[f111,f236]) ).
fof(f111,plain,
sdtmndtplgtdt0(xa,xR,xc),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__731_02) ).
fof(f234,plain,
spl22_14,
inference(avatar_split_clause,[],[f110,f231]) ).
fof(f110,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(cnf_transformation,[],[f19]) ).
fof(f229,plain,
spl22_13,
inference(avatar_split_clause,[],[f106,f226]) ).
fof(f106,plain,
sdtmndtasgtdt0(xu,xR,xb),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
( sdtmndtasgtdt0(xu,xR,xb)
& aReductOfIn0(xu,xa,xR)
& aElement0(xu) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__755) ).
fof(f224,plain,
spl22_12,
inference(avatar_split_clause,[],[f105,f221]) ).
fof(f105,plain,
aReductOfIn0(xu,xa,xR),
inference(cnf_transformation,[],[f20]) ).
fof(f219,plain,
spl22_11,
inference(avatar_split_clause,[],[f103,f216]) ).
fof(f103,plain,
sdtmndtasgtdt0(xv,xR,xc),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
( sdtmndtasgtdt0(xv,xR,xc)
& aReductOfIn0(xv,xa,xR)
& aElement0(xv) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__779) ).
fof(f214,plain,
spl22_10,
inference(avatar_split_clause,[],[f102,f211]) ).
fof(f102,plain,
aReductOfIn0(xv,xa,xR),
inference(cnf_transformation,[],[f21]) ).
fof(f209,plain,
spl22_9,
inference(avatar_split_clause,[],[f97,f207]) ).
fof(f97,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0] :
( ~ sdtmndtasgtdt0(xv,xR,X0)
| ~ sdtmndtasgtdt0(xu,xR,X0)
| ~ aElement0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,negated_conjecture,
~ ? [X0] :
( sdtmndtasgtdt0(xv,xR,X0)
& sdtmndtasgtdt0(xu,xR,X0)
& aElement0(X0) ),
inference(negated_conjecture,[],[f22]) ).
fof(f22,conjecture,
? [X0] :
( sdtmndtasgtdt0(xv,xR,X0)
& sdtmndtasgtdt0(xu,xR,X0)
& aElement0(X0) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__) ).
fof(f205,plain,
spl22_8,
inference(avatar_split_clause,[],[f109,f202]) ).
fof(f109,plain,
aElement0(xc),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__731) ).
fof(f200,plain,
spl22_7,
inference(avatar_split_clause,[],[f108,f197]) ).
fof(f108,plain,
aElement0(xb),
inference(cnf_transformation,[],[f17]) ).
fof(f195,plain,
spl22_6,
inference(avatar_split_clause,[],[f107,f192]) ).
fof(f107,plain,
aElement0(xa),
inference(cnf_transformation,[],[f17]) ).
fof(f190,plain,
spl22_5,
inference(avatar_split_clause,[],[f104,f187]) ).
fof(f104,plain,
aElement0(xu),
inference(cnf_transformation,[],[f20]) ).
fof(f185,plain,
spl22_4,
inference(avatar_split_clause,[],[f101,f182]) ).
fof(f101,plain,
aElement0(xv),
inference(cnf_transformation,[],[f21]) ).
fof(f180,plain,
spl22_3,
inference(avatar_split_clause,[],[f100,f177]) ).
fof(f100,plain,
isTerminating0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
( isTerminating0(xR)
& isLocallyConfluent0(xR) ),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__656_01) ).
fof(f175,plain,
spl22_2,
inference(avatar_split_clause,[],[f99,f172]) ).
fof(f99,plain,
isLocallyConfluent0(xR),
inference(cnf_transformation,[],[f16]) ).
fof(f170,plain,
spl22_1,
inference(avatar_split_clause,[],[f98,f167]) ).
fof(f98,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[],[f15]) ).
fof(f15,axiom,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/tmp/tmp.PmOWgqRCpp/Vampire---4.8_9900',m__656) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : COM017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.15/0.36 % Computer : n006.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 30 17:44:50 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.42 % (10126)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.43 % (10186)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.21/0.43 % (10188)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.21/0.43 % (10192)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.21/0.43 % (10191)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 Vampire---4 for (569ds/0Mi)
% 0.21/0.43 % (10194)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 Vampire---4 for (531ds/0Mi)
% 0.21/0.43 % (10197)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 Vampire---4 for (497ds/0Mi)
% 0.21/0.43 % (10195)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 Vampire---4 for (522ds/0Mi)
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 TRYING [3]
% 0.21/0.43 TRYING [3]
% 0.21/0.44 TRYING [4]
% 0.21/0.44 TRYING [4]
% 0.21/0.45 TRYING [5]
% 0.21/0.45 % (10194)First to succeed.
% 0.21/0.45 TRYING [5]
% 0.21/0.46 % (10194)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for Vampire---4
% 0.21/0.46 % SZS output start Proof for Vampire---4
% See solution above
% 0.21/0.47 % (10194)------------------------------
% 0.21/0.47 % (10194)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.21/0.47 % (10194)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.21/0.47 % (10194)Termination reason: Refutation
% 0.21/0.47
% 0.21/0.47 % (10194)Memory used [KB]: 6396
% 0.21/0.47 % (10194)Time elapsed: 0.035 s
% 0.21/0.47 % (10194)------------------------------
% 0.21/0.47 % (10194)------------------------------
% 0.21/0.47 % (10126)Success in time 0.101 s
% 0.21/0.47 % Vampire---4.8 exiting
%------------------------------------------------------------------------------