TSTP Solution File: NUM469+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM469+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.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 : Sun May 5 08:29:06 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 153
% Syntax : Number of formulae : 517 ( 73 unt; 0 def)
% Number of atoms : 1852 ( 480 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 2305 ( 970 ~;1008 |; 153 &)
% ( 127 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 121 ( 119 usr; 117 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 499 ( 479 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1287,plain,
$false,
inference(avatar_sat_refutation,[],[f197,f202,f207,f212,f217,f222,f227,f232,f236,f241,f246,f251,f260,f265,f270,f277,f282,f287,f291,f295,f299,f303,f307,f311,f315,f374,f380,f387,f391,f395,f422,f428,f433,f439,f443,f447,f451,f455,f482,f510,f514,f518,f526,f531,f535,f539,f560,f569,f573,f577,f582,f586,f626,f630,f634,f664,f668,f676,f680,f684,f715,f734,f739,f753,f758,f786,f790,f794,f798,f846,f851,f865,f870,f886,f891,f907,f912,f923,f928,f933,f939,f945,f951,f957,f963,f969,f976,f1034,f1041,f1072,f1080,f1088,f1096,f1104,f1112,f1118,f1124,f1132,f1141,f1149,f1157,f1163,f1168,f1174,f1179,f1184,f1190,f1196,f1201,f1207,f1212,f1262,f1269,f1276,f1283,f1286]) ).
fof(f1286,plain,
( ~ spl5_3
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(avatar_split_clause,[],[f1239,f1069,f1038,f973,f479,f253,f234,f204]) ).
fof(f204,plain,
( spl5_3
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f234,plain,
( spl5_9
<=> ! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f253,plain,
( spl5_13
<=> sz00 = xl ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f479,plain,
( spl5_40
<=> sz00 = sdtasdt0(xl,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
fof(f973,plain,
( spl5_87
<=> xl = xn ),
introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).
fof(f1038,plain,
( spl5_89
<=> xl = xm ),
introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).
fof(f1069,plain,
( spl5_90
<=> xl = sdtpldt0(xl,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).
fof(f1239,plain,
( ~ aNaturalNumber0(xm)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1238,f1042]) ).
fof(f1042,plain,
( xm = xn
| ~ spl5_87
| ~ spl5_89 ),
inference(superposition,[],[f1040,f975]) ).
fof(f975,plain,
( xl = xn
| ~ spl5_87 ),
inference(avatar_component_clause,[],[f973]) ).
fof(f1040,plain,
( xl = xm
| ~ spl5_89 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1238,plain,
( ~ aNaturalNumber0(xn)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1237,f975]) ).
fof(f1237,plain,
( ~ aNaturalNumber0(xl)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1236,f255]) ).
fof(f255,plain,
( sz00 = xl
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f253]) ).
fof(f1236,plain,
( ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(trivial_inequality_removal,[],[f1235]) ).
fof(f1235,plain,
( xm != xm
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1234,f1042]) ).
fof(f1234,plain,
( xm != xn
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1233,f975]) ).
fof(f1233,plain,
( xl != xm
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1232,f255]) ).
fof(f1232,plain,
( sz00 != xm
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_13
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1231,f1075]) ).
fof(f1075,plain,
( xm = sdtpldt0(xm,xm)
| ~ spl5_13
| ~ spl5_87
| ~ spl5_89
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1074,f1042]) ).
fof(f1074,plain,
( xn = sdtpldt0(xn,xn)
| ~ spl5_13
| ~ spl5_87
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1073,f975]) ).
fof(f1073,plain,
( xl = sdtpldt0(xl,xl)
| ~ spl5_13
| ~ spl5_90 ),
inference(forward_demodulation,[],[f1071,f255]) ).
fof(f1071,plain,
( xl = sdtpldt0(xl,sz00)
| ~ spl5_90 ),
inference(avatar_component_clause,[],[f1069]) ).
fof(f1231,plain,
( sz00 != sdtpldt0(xm,xm)
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_40
| ~ spl5_87
| ~ spl5_89 ),
inference(forward_demodulation,[],[f1216,f1042]) ).
fof(f1216,plain,
( sz00 != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sz00)
| ~ spl5_9
| ~ spl5_40 ),
inference(superposition,[],[f235,f481]) ).
fof(f481,plain,
( sz00 = sdtasdt0(xl,sz00)
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f235,plain,
( ! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f1283,plain,
( spl5_115
| ~ spl5_13
| ~ spl5_83 ),
inference(avatar_split_clause,[],[f952,f948,f253,f1280]) ).
fof(f1280,plain,
( spl5_115
<=> xl = sdtasdt0(xl,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_115])]) ).
fof(f948,plain,
( spl5_83
<=> sz00 = sdtasdt0(sz00,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).
fof(f952,plain,
( xl = sdtasdt0(xl,xl)
| ~ spl5_13
| ~ spl5_83 ),
inference(forward_demodulation,[],[f950,f255]) ).
fof(f950,plain,
( sz00 = sdtasdt0(sz00,xl)
| ~ spl5_83 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f1276,plain,
( spl5_114
| ~ spl5_13
| ~ spl5_82 ),
inference(avatar_split_clause,[],[f946,f942,f253,f1273]) ).
fof(f1273,plain,
( spl5_114
<=> xl = sdtasdt0(sK2,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_114])]) ).
fof(f942,plain,
( spl5_82
<=> sz00 = sdtasdt0(sK2,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).
fof(f946,plain,
( xl = sdtasdt0(sK2,xl)
| ~ spl5_13
| ~ spl5_82 ),
inference(forward_demodulation,[],[f944,f255]) ).
fof(f944,plain,
( sz00 = sdtasdt0(sK2,sz00)
| ~ spl5_82 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1269,plain,
( spl5_113
| ~ spl5_13
| ~ spl5_81 ),
inference(avatar_split_clause,[],[f940,f936,f253,f1266]) ).
fof(f1266,plain,
( spl5_113
<=> xl = sdtasdt0(sK1,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_113])]) ).
fof(f936,plain,
( spl5_81
<=> sz00 = sdtasdt0(sK1,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).
fof(f940,plain,
( xl = sdtasdt0(sK1,xl)
| ~ spl5_13
| ~ spl5_81 ),
inference(forward_demodulation,[],[f938,f255]) ).
fof(f938,plain,
( sz00 = sdtasdt0(sK1,sz00)
| ~ spl5_81 ),
inference(avatar_component_clause,[],[f936]) ).
fof(f1262,plain,
( spl5_112
| ~ spl5_13
| ~ spl5_80 ),
inference(avatar_split_clause,[],[f934,f930,f253,f1259]) ).
fof(f1259,plain,
( spl5_112
<=> xl = sdtasdt0(xn,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_112])]) ).
fof(f930,plain,
( spl5_80
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).
fof(f934,plain,
( xl = sdtasdt0(xn,xl)
| ~ spl5_13
| ~ spl5_80 ),
inference(forward_demodulation,[],[f932,f255]) ).
fof(f932,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl5_80 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f1212,plain,
( spl5_111
| ~ spl5_5
| ~ spl5_26 ),
inference(avatar_split_clause,[],[f369,f313,f214,f1209]) ).
fof(f1209,plain,
( spl5_111
<=> sK2 = sdtasdt0(sz10,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_111])]) ).
fof(f214,plain,
( spl5_5
<=> aNaturalNumber0(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f313,plain,
( spl5_26
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
fof(f369,plain,
( sK2 = sdtasdt0(sz10,sK2)
| ~ spl5_5
| ~ spl5_26 ),
inference(resolution,[],[f314,f216]) ).
fof(f216,plain,
( aNaturalNumber0(sK2)
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f314,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(sz10,X0) = X0 )
| ~ spl5_26 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f1207,plain,
( spl5_110
| ~ spl5_6
| ~ spl5_26 ),
inference(avatar_split_clause,[],[f368,f313,f219,f1204]) ).
fof(f1204,plain,
( spl5_110
<=> sK1 = sdtasdt0(sz10,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_110])]) ).
fof(f219,plain,
( spl5_6
<=> aNaturalNumber0(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f368,plain,
( sK1 = sdtasdt0(sz10,sK1)
| ~ spl5_6
| ~ spl5_26 ),
inference(resolution,[],[f314,f221]) ).
fof(f221,plain,
( aNaturalNumber0(sK1)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f1201,plain,
( spl5_109
| ~ spl5_4
| ~ spl5_26 ),
inference(avatar_split_clause,[],[f367,f313,f209,f1198]) ).
fof(f1198,plain,
( spl5_109
<=> xn = sdtasdt0(sz10,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).
fof(f209,plain,
( spl5_4
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f367,plain,
( xn = sdtasdt0(sz10,xn)
| ~ spl5_4
| ~ spl5_26 ),
inference(resolution,[],[f314,f211]) ).
fof(f211,plain,
( aNaturalNumber0(xn)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f209]) ).
fof(f1196,plain,
( spl5_108
| ~ spl5_3
| ~ spl5_26 ),
inference(avatar_split_clause,[],[f366,f313,f204,f1193]) ).
fof(f1193,plain,
( spl5_108
<=> xm = sdtasdt0(sz10,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_108])]) ).
fof(f366,plain,
( xm = sdtasdt0(sz10,xm)
| ~ spl5_3
| ~ spl5_26 ),
inference(resolution,[],[f314,f206]) ).
fof(f206,plain,
( aNaturalNumber0(xm)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f1190,plain,
( ~ spl5_107
| spl5_1
| ~ spl5_87
| ~ spl5_89 ),
inference(avatar_split_clause,[],[f1059,f1038,f973,f194,f1187]) ).
fof(f1187,plain,
( spl5_107
<=> doDivides0(xm,sdtpldt0(xm,xm)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_107])]) ).
fof(f194,plain,
( spl5_1
<=> doDivides0(xl,sdtpldt0(xm,xn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f1059,plain,
( ~ doDivides0(xm,sdtpldt0(xm,xm))
| spl5_1
| ~ spl5_87
| ~ spl5_89 ),
inference(forward_demodulation,[],[f1043,f1042]) ).
fof(f1043,plain,
( ~ doDivides0(xm,sdtpldt0(xm,xn))
| spl5_1
| ~ spl5_89 ),
inference(superposition,[],[f196,f1040]) ).
fof(f196,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
| spl5_1 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f1184,plain,
( spl5_106
| ~ spl5_2
| ~ spl5_26 ),
inference(avatar_split_clause,[],[f365,f313,f199,f1181]) ).
fof(f1181,plain,
( spl5_106
<=> xl = sdtasdt0(sz10,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_106])]) ).
fof(f199,plain,
( spl5_2
<=> aNaturalNumber0(xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f365,plain,
( xl = sdtasdt0(sz10,xl)
| ~ spl5_2
| ~ spl5_26 ),
inference(resolution,[],[f314,f201]) ).
fof(f201,plain,
( aNaturalNumber0(xl)
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f199]) ).
fof(f1179,plain,
( spl5_105
| ~ spl5_5
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f360,f309,f214,f1176]) ).
fof(f1176,plain,
( spl5_105
<=> sK2 = sdtasdt0(sK2,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_105])]) ).
fof(f309,plain,
( spl5_25
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
fof(f360,plain,
( sK2 = sdtasdt0(sK2,sz10)
| ~ spl5_5
| ~ spl5_25 ),
inference(resolution,[],[f310,f216]) ).
fof(f310,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtasdt0(X0,sz10) = X0 )
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f1174,plain,
( spl5_104
| ~ spl5_6
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f359,f309,f219,f1171]) ).
fof(f1171,plain,
( spl5_104
<=> sK1 = sdtasdt0(sK1,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_104])]) ).
fof(f359,plain,
( sK1 = sdtasdt0(sK1,sz10)
| ~ spl5_6
| ~ spl5_25 ),
inference(resolution,[],[f310,f221]) ).
fof(f1168,plain,
( spl5_103
| ~ spl5_4
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f358,f309,f209,f1165]) ).
fof(f1165,plain,
( spl5_103
<=> xn = sdtasdt0(xn,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_103])]) ).
fof(f358,plain,
( xn = sdtasdt0(xn,sz10)
| ~ spl5_4
| ~ spl5_25 ),
inference(resolution,[],[f310,f211]) ).
fof(f1163,plain,
( spl5_102
| ~ spl5_3
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f357,f309,f204,f1160]) ).
fof(f1160,plain,
( spl5_102
<=> xm = sdtasdt0(xm,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_102])]) ).
fof(f357,plain,
( xm = sdtasdt0(xm,sz10)
| ~ spl5_3
| ~ spl5_25 ),
inference(resolution,[],[f310,f206]) ).
fof(f1157,plain,
( spl5_101
| ~ spl5_2
| ~ spl5_25 ),
inference(avatar_split_clause,[],[f356,f309,f199,f1154]) ).
fof(f1154,plain,
( spl5_101
<=> xl = sdtasdt0(xl,sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).
fof(f356,plain,
( xl = sdtasdt0(xl,sz10)
| ~ spl5_2
| ~ spl5_25 ),
inference(resolution,[],[f310,f201]) ).
fof(f1149,plain,
( spl5_100
| ~ spl5_5
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f351,f305,f214,f1146]) ).
fof(f1146,plain,
( spl5_100
<=> sK2 = sdtpldt0(sz00,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_100])]) ).
fof(f305,plain,
( spl5_24
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f351,plain,
( sK2 = sdtpldt0(sz00,sK2)
| ~ spl5_5
| ~ spl5_24 ),
inference(resolution,[],[f306,f216]) ).
fof(f306,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(sz00,X0) = X0 )
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f1141,plain,
( spl5_99
| ~ spl5_6
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f350,f305,f219,f1138]) ).
fof(f1138,plain,
( spl5_99
<=> sK1 = sdtpldt0(sz00,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_99])]) ).
fof(f350,plain,
( sK1 = sdtpldt0(sz00,sK1)
| ~ spl5_6
| ~ spl5_24 ),
inference(resolution,[],[f306,f221]) ).
fof(f1132,plain,
( spl5_98
| ~ spl5_4
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f349,f305,f209,f1129]) ).
fof(f1129,plain,
( spl5_98
<=> xn = sdtpldt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_98])]) ).
fof(f349,plain,
( xn = sdtpldt0(sz00,xn)
| ~ spl5_4
| ~ spl5_24 ),
inference(resolution,[],[f306,f211]) ).
fof(f1124,plain,
( spl5_97
| ~ spl5_3
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f348,f305,f204,f1121]) ).
fof(f1121,plain,
( spl5_97
<=> xm = sdtpldt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).
fof(f348,plain,
( xm = sdtpldt0(sz00,xm)
| ~ spl5_3
| ~ spl5_24 ),
inference(resolution,[],[f306,f206]) ).
fof(f1118,plain,
( ~ spl5_96
| spl5_1
| ~ spl5_87 ),
inference(avatar_split_clause,[],[f1015,f973,f194,f1115]) ).
fof(f1115,plain,
( spl5_96
<=> doDivides0(xn,sdtpldt0(xm,xn)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).
fof(f1015,plain,
( ~ doDivides0(xn,sdtpldt0(xm,xn))
| spl5_1
| ~ spl5_87 ),
inference(superposition,[],[f196,f975]) ).
fof(f1112,plain,
( spl5_95
| ~ spl5_2
| ~ spl5_24 ),
inference(avatar_split_clause,[],[f347,f305,f199,f1109]) ).
fof(f1109,plain,
( spl5_95
<=> xl = sdtpldt0(sz00,xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).
fof(f347,plain,
( xl = sdtpldt0(sz00,xl)
| ~ spl5_2
| ~ spl5_24 ),
inference(resolution,[],[f306,f201]) ).
fof(f1104,plain,
( spl5_94
| ~ spl5_5
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f342,f301,f214,f1101]) ).
fof(f1101,plain,
( spl5_94
<=> sK2 = sdtpldt0(sK2,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).
fof(f301,plain,
( spl5_23
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f342,plain,
( sK2 = sdtpldt0(sK2,sz00)
| ~ spl5_5
| ~ spl5_23 ),
inference(resolution,[],[f302,f216]) ).
fof(f302,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f1096,plain,
( spl5_93
| ~ spl5_6
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f341,f301,f219,f1093]) ).
fof(f1093,plain,
( spl5_93
<=> sK1 = sdtpldt0(sK1,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).
fof(f341,plain,
( sK1 = sdtpldt0(sK1,sz00)
| ~ spl5_6
| ~ spl5_23 ),
inference(resolution,[],[f302,f221]) ).
fof(f1088,plain,
( spl5_92
| ~ spl5_4
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f340,f301,f209,f1085]) ).
fof(f1085,plain,
( spl5_92
<=> xn = sdtpldt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).
fof(f340,plain,
( xn = sdtpldt0(xn,sz00)
| ~ spl5_4
| ~ spl5_23 ),
inference(resolution,[],[f302,f211]) ).
fof(f1080,plain,
( spl5_91
| ~ spl5_3
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f339,f301,f204,f1077]) ).
fof(f1077,plain,
( spl5_91
<=> xm = sdtpldt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).
fof(f339,plain,
( xm = sdtpldt0(xm,sz00)
| ~ spl5_3
| ~ spl5_23 ),
inference(resolution,[],[f302,f206]) ).
fof(f1072,plain,
( spl5_90
| ~ spl5_2
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f338,f301,f199,f1069]) ).
fof(f338,plain,
( xl = sdtpldt0(xl,sz00)
| ~ spl5_2
| ~ spl5_23 ),
inference(resolution,[],[f302,f201]) ).
fof(f1041,plain,
( spl5_89
| ~ spl5_13
| ~ spl5_15
| ~ spl5_88 ),
inference(avatar_split_clause,[],[f1036,f1031,f262,f253,f1038]) ).
fof(f262,plain,
( spl5_15
<=> xm = sdtasdt0(xl,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f1031,plain,
( spl5_88
<=> sz00 = sdtasdt0(sz00,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).
fof(f1036,plain,
( xl = xm
| ~ spl5_13
| ~ spl5_15
| ~ spl5_88 ),
inference(forward_demodulation,[],[f1035,f264]) ).
fof(f264,plain,
( xm = sdtasdt0(xl,sK2)
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f1035,plain,
( xl = sdtasdt0(xl,sK2)
| ~ spl5_13
| ~ spl5_88 ),
inference(forward_demodulation,[],[f1033,f255]) ).
fof(f1033,plain,
( sz00 = sdtasdt0(sz00,sK2)
| ~ spl5_88 ),
inference(avatar_component_clause,[],[f1031]) ).
fof(f1034,plain,
( spl5_88
| ~ spl5_5
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f333,f297,f214,f1031]) ).
fof(f297,plain,
( spl5_22
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f333,plain,
( sz00 = sdtasdt0(sz00,sK2)
| ~ spl5_5
| ~ spl5_22 ),
inference(resolution,[],[f298,f216]) ).
fof(f298,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f976,plain,
( spl5_87
| ~ spl5_13
| ~ spl5_16
| ~ spl5_86 ),
inference(avatar_split_clause,[],[f971,f966,f267,f253,f973]) ).
fof(f267,plain,
( spl5_16
<=> xn = sdtasdt0(xl,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f966,plain,
( spl5_86
<=> sz00 = sdtasdt0(sz00,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).
fof(f971,plain,
( xl = xn
| ~ spl5_13
| ~ spl5_16
| ~ spl5_86 ),
inference(forward_demodulation,[],[f970,f269]) ).
fof(f269,plain,
( xn = sdtasdt0(xl,sK1)
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f267]) ).
fof(f970,plain,
( xl = sdtasdt0(xl,sK1)
| ~ spl5_13
| ~ spl5_86 ),
inference(forward_demodulation,[],[f968,f255]) ).
fof(f968,plain,
( sz00 = sdtasdt0(sz00,sK1)
| ~ spl5_86 ),
inference(avatar_component_clause,[],[f966]) ).
fof(f969,plain,
( spl5_86
| ~ spl5_6
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f332,f297,f219,f966]) ).
fof(f332,plain,
( sz00 = sdtasdt0(sz00,sK1)
| ~ spl5_6
| ~ spl5_22 ),
inference(resolution,[],[f298,f221]) ).
fof(f963,plain,
( spl5_85
| ~ spl5_4
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f331,f297,f209,f960]) ).
fof(f960,plain,
( spl5_85
<=> sz00 = sdtasdt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).
fof(f331,plain,
( sz00 = sdtasdt0(sz00,xn)
| ~ spl5_4
| ~ spl5_22 ),
inference(resolution,[],[f298,f211]) ).
fof(f957,plain,
( spl5_84
| ~ spl5_3
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f330,f297,f204,f954]) ).
fof(f954,plain,
( spl5_84
<=> sz00 = sdtasdt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).
fof(f330,plain,
( sz00 = sdtasdt0(sz00,xm)
| ~ spl5_3
| ~ spl5_22 ),
inference(resolution,[],[f298,f206]) ).
fof(f951,plain,
( spl5_83
| ~ spl5_2
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f329,f297,f199,f948]) ).
fof(f329,plain,
( sz00 = sdtasdt0(sz00,xl)
| ~ spl5_2
| ~ spl5_22 ),
inference(resolution,[],[f298,f201]) ).
fof(f945,plain,
( spl5_82
| ~ spl5_5
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f324,f293,f214,f942]) ).
fof(f293,plain,
( spl5_21
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f324,plain,
( sz00 = sdtasdt0(sK2,sz00)
| ~ spl5_5
| ~ spl5_21 ),
inference(resolution,[],[f294,f216]) ).
fof(f294,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f939,plain,
( spl5_81
| ~ spl5_6
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f323,f293,f219,f936]) ).
fof(f323,plain,
( sz00 = sdtasdt0(sK1,sz00)
| ~ spl5_6
| ~ spl5_21 ),
inference(resolution,[],[f294,f221]) ).
fof(f933,plain,
( spl5_80
| ~ spl5_4
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f322,f293,f209,f930]) ).
fof(f322,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl5_4
| ~ spl5_21 ),
inference(resolution,[],[f294,f211]) ).
fof(f928,plain,
( ~ spl5_79
| spl5_12
| ~ spl5_13 ),
inference(avatar_split_clause,[],[f381,f253,f248,f925]) ).
fof(f925,plain,
( spl5_79
<=> sz10 = xl ),
introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).
fof(f248,plain,
( spl5_12
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f381,plain,
( sz10 != xl
| spl5_12
| ~ spl5_13 ),
inference(superposition,[],[f250,f255]) ).
fof(f250,plain,
( sz00 != sz10
| spl5_12 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f923,plain,
( spl5_78
| ~ spl5_13
| ~ spl5_22
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f770,f579,f297,f253,f920]) ).
fof(f920,plain,
( spl5_78
<=> xl = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).
fof(f579,plain,
( spl5_52
<=> aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).
fof(f770,plain,
( xl = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_13
| ~ spl5_22
| ~ spl5_52 ),
inference(forward_demodulation,[],[f760,f255]) ).
fof(f760,plain,
( sz00 = sdtasdt0(sz00,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_22
| ~ spl5_52 ),
inference(resolution,[],[f580,f298]) ).
fof(f580,plain,
( aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_52 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f912,plain,
( spl5_77
| ~ spl5_13
| ~ spl5_76 ),
inference(avatar_split_clause,[],[f908,f905,f253,f910]) ).
fof(f910,plain,
( spl5_77
<=> ! [X2,X0] :
( xl = X0
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).
fof(f905,plain,
( spl5_76
<=> ! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).
fof(f908,plain,
( ! [X2,X0] :
( xl = X0
| sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_76 ),
inference(forward_demodulation,[],[f906,f255]) ).
fof(f906,plain,
( ! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) )
| ~ spl5_76 ),
inference(avatar_component_clause,[],[f905]) ).
fof(f907,plain,
spl5_76,
inference(avatar_split_clause,[],[f187,f905]) ).
fof(f187,plain,
! [X2,X0] :
( sdtsldt0(sdtasdt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,sdtasdt0(X0,X2))
| sz00 = X0
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f162]) ).
fof(f162,plain,
! [X2,X0,X1] :
( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f102]) ).
fof(f102,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtsldt0(X1,X0) = X2
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtsldt0(X1,X0) != X2 ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1] :
( ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X0,X1)
& sz00 != X0 )
=> ! [X2] :
( sdtsldt0(X1,X0) = X2
<=> ( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefQuot) ).
fof(f891,plain,
( spl5_75
| ~ spl5_13
| ~ spl5_74 ),
inference(avatar_split_clause,[],[f887,f884,f253,f889]) ).
fof(f889,plain,
( spl5_75
<=> ! [X2,X0,X1] :
( xl = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).
fof(f884,plain,
( spl5_74
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).
fof(f887,plain,
( ! [X2,X0,X1] :
( xl = X0
| sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_74 ),
inference(forward_demodulation,[],[f885,f255]) ).
fof(f885,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_74 ),
inference(avatar_component_clause,[],[f884]) ).
fof(f886,plain,
spl5_74,
inference(avatar_split_clause,[],[f177,f884]) ).
fof(f177,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& X1 != X2
& sz00 != X0 )
=> ( sdtlseqdt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul) ).
fof(f870,plain,
( spl5_73
| ~ spl5_13
| ~ spl5_72 ),
inference(avatar_split_clause,[],[f866,f863,f253,f868]) ).
fof(f868,plain,
( spl5_73
<=> ! [X2,X0,X1] :
( xl = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).
fof(f863,plain,
( spl5_72
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).
fof(f866,plain,
( ! [X2,X0,X1] :
( xl = X0
| sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_72 ),
inference(forward_demodulation,[],[f864,f255]) ).
fof(f864,plain,
( ! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_72 ),
inference(avatar_component_clause,[],[f863]) ).
fof(f865,plain,
spl5_72,
inference(avatar_split_clause,[],[f175,f863]) ).
fof(f175,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ sdtlseqdt0(X1,X2)
| X1 = X2
| sz00 = X0
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f87]) ).
fof(f851,plain,
( spl5_71
| ~ spl5_13
| ~ spl5_21
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f769,f579,f293,f253,f848]) ).
fof(f848,plain,
( spl5_71
<=> xl = sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).
fof(f769,plain,
( xl = sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),xl)
| ~ spl5_13
| ~ spl5_21
| ~ spl5_52 ),
inference(forward_demodulation,[],[f759,f255]) ).
fof(f759,plain,
( sz00 = sdtasdt0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)),sz00)
| ~ spl5_21
| ~ spl5_52 ),
inference(resolution,[],[f580,f294]) ).
fof(f846,plain,
spl5_70,
inference(avatar_split_clause,[],[f184,f844]) ).
fof(f844,plain,
( spl5_70
<=> ! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).
fof(f184,plain,
! [X2,X0] :
( sdtmndt0(sdtpldt0(X0,X2),X0) = X2
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f152]) ).
fof(f152,plain,
! [X2,X0,X1] :
( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtmndt0(X1,X0) = X2
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) )
& ( ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| sdtmndt0(X1,X0) != X2 ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
=> ! [X2] :
( sdtmndt0(X1,X0) = X2
<=> ( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
fof(f798,plain,
spl5_69,
inference(avatar_split_clause,[],[f173,f796]) ).
fof(f796,plain,
( spl5_69
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).
fof(f173,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f794,plain,
spl5_68,
inference(avatar_split_clause,[],[f172,f792]) ).
fof(f792,plain,
( spl5_68
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).
fof(f172,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f790,plain,
spl5_67,
inference(avatar_split_clause,[],[f159,f788]) ).
fof(f788,plain,
( spl5_67
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).
fof(f159,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1] :
( ! [X2] :
( ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) )
| ~ aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X0,X1)
& X0 != X1 )
=> ! [X2] :
( aNaturalNumber0(X2)
=> ( sdtlseqdt0(sdtpldt0(X0,X2),sdtpldt0(X1,X2))
& sdtpldt0(X1,X2) != sdtpldt0(X0,X2)
& sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
& sdtpldt0(X2,X0) != sdtpldt0(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonAdd) ).
fof(f786,plain,
spl5_66,
inference(avatar_split_clause,[],[f157,f784]) ).
fof(f784,plain,
( spl5_66
<=> ! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).
fof(f157,plain,
! [X2,X0,X1] :
( sdtlseqdt0(sdtpldt0(X2,X0),sdtpldt0(X2,X1))
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X0,X1)
| X0 = X1
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f758,plain,
( spl5_65
| ~ spl5_13
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f754,f751,f253,f756]) ).
fof(f756,plain,
( spl5_65
<=> ! [X2,X0,X1] :
( xl = X0
| X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).
fof(f751,plain,
( spl5_64
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).
fof(f754,plain,
( ! [X2,X0,X1] :
( xl = X0
| X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_64 ),
inference(forward_demodulation,[],[f752,f255]) ).
fof(f752,plain,
( ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_64 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f753,plain,
spl5_64,
inference(avatar_split_clause,[],[f142,f751]) ).
fof(f142,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f739,plain,
( spl5_63
| ~ spl5_13
| ~ spl5_62 ),
inference(avatar_split_clause,[],[f735,f732,f253,f737]) ).
fof(f737,plain,
( spl5_63
<=> ! [X2,X0,X1] :
( xl = X0
| X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).
fof(f732,plain,
( spl5_62
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).
fof(f735,plain,
( ! [X2,X0,X1] :
( xl = X0
| X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_62 ),
inference(forward_demodulation,[],[f733,f255]) ).
fof(f733,plain,
( ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_62 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f734,plain,
spl5_62,
inference(avatar_split_clause,[],[f141,f732]) ).
fof(f141,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f715,plain,
( ~ spl5_17
| ~ spl5_18
| ~ spl5_30
| spl5_52 ),
inference(avatar_split_clause,[],[f648,f579,f389,f279,f274]) ).
fof(f274,plain,
( spl5_17
<=> aNaturalNumber0(sdtsldt0(xm,xl)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f279,plain,
( spl5_18
<=> aNaturalNumber0(sdtsldt0(xn,xl)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f389,plain,
( spl5_30
<=> ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
fof(f648,plain,
( ~ aNaturalNumber0(sdtsldt0(xn,xl))
| ~ aNaturalNumber0(sdtsldt0(xm,xl))
| ~ spl5_30
| spl5_52 ),
inference(resolution,[],[f581,f390]) ).
fof(f390,plain,
( ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) )
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f389]) ).
fof(f581,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| spl5_52 ),
inference(avatar_component_clause,[],[f579]) ).
fof(f684,plain,
spl5_61,
inference(avatar_split_clause,[],[f188,f682]) ).
fof(f682,plain,
( spl5_61
<=> ! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).
fof(f188,plain,
! [X0,X1] :
( sdtasdt0(X0,sdtsldt0(X1,X0)) = X1
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f161]) ).
fof(f161,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,X2) = X1
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f680,plain,
spl5_60,
inference(avatar_split_clause,[],[f171,f678]) ).
fof(f678,plain,
( spl5_60
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).
fof(f171,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f676,plain,
spl5_59,
inference(avatar_split_clause,[],[f170,f674]) ).
fof(f674,plain,
( spl5_59
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).
fof(f170,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f668,plain,
spl5_58,
inference(avatar_split_clause,[],[f181,f666]) ).
fof(f666,plain,
( spl5_58
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).
fof(f181,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f664,plain,
spl5_57,
inference(avatar_split_clause,[],[f180,f662]) ).
fof(f662,plain,
( spl5_57
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).
fof(f180,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f93]) ).
fof(f634,plain,
spl5_56,
inference(avatar_split_clause,[],[f179,f632]) ).
fof(f632,plain,
( spl5_56
<=> ! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).
fof(f179,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( sdtlseqdt0(X0,X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X0,X1) )
=> sdtlseqdt0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETran) ).
fof(f630,plain,
spl5_55,
inference(avatar_split_clause,[],[f178,f628]) ).
fof(f628,plain,
( spl5_55
<=> ! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).
fof(f178,plain,
! [X2,X0,X1] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( doDivides0(X0,X2)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X0,X1) )
=> doDivides0(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivTrans) ).
fof(f626,plain,
spl5_54,
inference(avatar_split_clause,[],[f155,f624]) ).
fof(f624,plain,
( spl5_54
<=> ! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).
fof(f155,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( sz00 = X1
| sz00 = X0
| sz00 != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtasdt0(X0,X1)
=> ( sz00 = X1
| sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroMul) ).
fof(f586,plain,
spl5_53,
inference(avatar_split_clause,[],[f189,f584]) ).
fof(f584,plain,
( spl5_53
<=> ! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).
fof(f189,plain,
! [X0,X1] :
( aNaturalNumber0(sdtsldt0(X1,X0))
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f160]) ).
fof(f160,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtsldt0(X1,X0) != X2
| ~ doDivides0(X0,X1)
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f582,plain,
( ~ spl5_52
| ~ spl5_9
| ~ spl5_48 ),
inference(avatar_split_clause,[],[f565,f557,f234,f579]) ).
fof(f557,plain,
( spl5_48
<=> sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).
fof(f565,plain,
( ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_9
| ~ spl5_48 ),
inference(trivial_inequality_removal,[],[f561]) ).
fof(f561,plain,
( sdtpldt0(xm,xn) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_9
| ~ spl5_48 ),
inference(superposition,[],[f235,f559]) ).
fof(f559,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ spl5_48 ),
inference(avatar_component_clause,[],[f557]) ).
fof(f577,plain,
spl5_51,
inference(avatar_split_clause,[],[f185,f575]) ).
fof(f575,plain,
( spl5_51
<=> ! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).
fof(f185,plain,
! [X0,X1] :
( sdtpldt0(X0,sdtmndt0(X1,X0)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f151]) ).
fof(f151,plain,
! [X2,X0,X1] :
( sdtpldt0(X0,X2) = X1
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f573,plain,
spl5_50,
inference(avatar_split_clause,[],[f168,f571]) ).
fof(f571,plain,
( spl5_50
<=> ! [X0,X1] :
( sdtpldt0(X0,sK4(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).
fof(f168,plain,
! [X0,X1] :
( sdtpldt0(X0,sK4(X0,X1)) = X1
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtpldt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f109,f110]) ).
fof(f110,plain,
! [X0,X1] :
( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtpldt0(X0,sK4(X0,X1)) = X1
& aNaturalNumber0(sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f109,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtpldt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( ( ( sdtlseqdt0(X0,X1)
| ! [X2] :
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ sdtlseqdt0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtlseqdt0(X0,X1)
<=> ? [X2] :
( sdtpldt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f569,plain,
spl5_49,
inference(avatar_split_clause,[],[f165,f567]) ).
fof(f567,plain,
( spl5_49
<=> ! [X0,X1] :
( sdtasdt0(X0,sK3(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).
fof(f165,plain,
! [X0,X1] :
( sdtasdt0(X0,sK3(X0,X1)) = X1
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f105,f106]) ).
fof(f106,plain,
! [X0,X1] :
( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
=> ( sdtasdt0(X0,sK3(X0,X1)) = X1
& aNaturalNumber0(sK3(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f105,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X3] :
( sdtasdt0(X0,X3) = X1
& aNaturalNumber0(X3) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(rectify,[],[f104]) ).
fof(f104,plain,
! [X0,X1] :
( ( ( doDivides0(X0,X1)
| ! [X2] :
( sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2) ) )
& ( ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) )
| ~ doDivides0(X0,X1) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(nnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1] :
( ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) )
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( doDivides0(X0,X1)
<=> ? [X2] :
( sdtasdt0(X0,X2) = X1
& aNaturalNumber0(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(f560,plain,
( ~ spl5_14
| spl5_48 ),
inference(avatar_split_clause,[],[f127,f557,f257]) ).
fof(f257,plain,
( spl5_14
<=> sP0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f127,plain,
( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
| ~ sP0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
| ~ sP0 ),
inference(nnf_transformation,[],[f94]) ).
fof(f94,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
| ~ sP0 ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f539,plain,
spl5_47,
inference(avatar_split_clause,[],[f191,f537]) ).
fof(f537,plain,
( spl5_47
<=> ! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).
fof(f191,plain,
! [X2,X0] :
( sdtlseqdt0(X0,sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtpldt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f169,plain,
! [X2,X0,X1] :
( sdtlseqdt0(X0,X1)
| sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f535,plain,
spl5_46,
inference(avatar_split_clause,[],[f190,f533]) ).
fof(f533,plain,
( spl5_46
<=> ! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).
fof(f190,plain,
! [X2,X0] :
( doDivides0(X0,sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f166]) ).
fof(f166,plain,
! [X2,X0,X1] :
( doDivides0(X0,X1)
| sdtasdt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f531,plain,
( spl5_45
| ~ spl5_3
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f321,f293,f204,f528]) ).
fof(f528,plain,
( spl5_45
<=> sz00 = sdtasdt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).
fof(f321,plain,
( sz00 = sdtasdt0(xm,sz00)
| ~ spl5_3
| ~ spl5_21 ),
inference(resolution,[],[f294,f206]) ).
fof(f526,plain,
spl5_44,
inference(avatar_split_clause,[],[f163,f524]) ).
fof(f524,plain,
( spl5_44
<=> ! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
fof(f163,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& sdtlseqdt0(X0,X1) )
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLEAsym) ).
fof(f518,plain,
spl5_43,
inference(avatar_split_clause,[],[f154,f516]) ).
fof(f516,plain,
( spl5_43
<=> ! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f154,plain,
! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f514,plain,
spl5_42,
inference(avatar_split_clause,[],[f153,f512]) ).
fof(f512,plain,
( spl5_42
<=> ! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f153,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f510,plain,
spl5_41,
inference(avatar_split_clause,[],[f149,f508]) ).
fof(f508,plain,
( spl5_41
<=> ! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
fof(f149,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1] :
( sdtlseqdt0(X1,sdtasdt0(X1,X0))
| sz00 = X0
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 != X0
=> sdtlseqdt0(X1,sdtasdt0(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
fof(f482,plain,
( spl5_40
| ~ spl5_2
| ~ spl5_21 ),
inference(avatar_split_clause,[],[f320,f293,f199,f479]) ).
fof(f320,plain,
( sz00 = sdtasdt0(xl,sz00)
| ~ spl5_2
| ~ spl5_21 ),
inference(resolution,[],[f294,f201]) ).
fof(f455,plain,
spl5_39,
inference(avatar_split_clause,[],[f186,f453]) ).
fof(f453,plain,
( spl5_39
<=> ! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
fof(f186,plain,
! [X0,X1] :
( aNaturalNumber0(sdtmndt0(X1,X0))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X0,X1] :
( aNaturalNumber0(X2)
| sdtmndt0(X1,X0) != X2
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f451,plain,
spl5_38,
inference(avatar_split_clause,[],[f167,f449]) ).
fof(f449,plain,
( spl5_38
<=> ! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
fof(f167,plain,
! [X0,X1] :
( aNaturalNumber0(sK4(X0,X1))
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f447,plain,
spl5_37,
inference(avatar_split_clause,[],[f164,f445]) ).
fof(f445,plain,
( spl5_37
<=> ! [X0,X1] :
( aNaturalNumber0(sK3(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f164,plain,
! [X0,X1] :
( aNaturalNumber0(sK3(X0,X1))
| ~ doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f443,plain,
spl5_36,
inference(avatar_split_clause,[],[f146,f441]) ).
fof(f441,plain,
( spl5_36
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
fof(f146,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f439,plain,
spl5_35,
inference(avatar_split_clause,[],[f145,f437]) ).
fof(f437,plain,
( spl5_35
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
fof(f145,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f433,plain,
( spl5_34
| ~ spl5_13
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f429,f426,f253,f431]) ).
fof(f431,plain,
( spl5_34
<=> ! [X0] :
( xl = X0
| sdtlseqdt0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f426,plain,
( spl5_33
<=> ! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
fof(f429,plain,
( ! [X0] :
( xl = X0
| sdtlseqdt0(sz10,X0)
| sz10 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_13
| ~ spl5_33 ),
inference(forward_demodulation,[],[f427,f255]) ).
fof(f427,plain,
( ! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f428,plain,
spl5_33,
inference(avatar_split_clause,[],[f140,f426]) ).
fof(f140,plain,
! [X0] :
( sdtlseqdt0(sz10,X0)
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( ( sdtlseqdt0(sz10,X0)
& sz10 != X0 )
| sz10 = X0
| sz00 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLENTr) ).
fof(f422,plain,
spl5_32,
inference(avatar_split_clause,[],[f148,f420]) ).
fof(f420,plain,
( spl5_32
<=> ! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
fof(f148,plain,
! [X0,X1] :
( sdtlseqdt0(X1,X0)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0,X1] :
( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtlseqdt0(X1,X0)
& X0 != X1 )
| sdtlseqdt0(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(f395,plain,
spl5_31,
inference(avatar_split_clause,[],[f144,f393]) ).
fof(f393,plain,
( spl5_31
<=> ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
fof(f144,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f391,plain,
spl5_30,
inference(avatar_split_clause,[],[f143,f389]) ).
fof(f143,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f387,plain,
( ~ spl5_6
| ~ spl5_29
| ~ spl5_9
| ~ spl5_16 ),
inference(avatar_split_clause,[],[f272,f267,f234,f384,f219]) ).
fof(f384,plain,
( spl5_29
<=> xn = sdtpldt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
fof(f272,plain,
( xn != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sK1)
| ~ spl5_9
| ~ spl5_16 ),
inference(superposition,[],[f235,f269]) ).
fof(f380,plain,
( ~ spl5_14
| spl5_28 ),
inference(avatar_split_clause,[],[f126,f377,f257]) ).
fof(f377,plain,
( spl5_28
<=> xn = sdtasdt0(xl,sdtsldt0(xn,xl)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
fof(f126,plain,
( xn = sdtasdt0(xl,sdtsldt0(xn,xl))
| ~ sP0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f374,plain,
( ~ spl5_14
| spl5_27 ),
inference(avatar_split_clause,[],[f124,f371,f257]) ).
fof(f371,plain,
( spl5_27
<=> xm = sdtasdt0(xl,sdtsldt0(xm,xl)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
fof(f124,plain,
( xm = sdtasdt0(xl,sdtsldt0(xm,xl))
| ~ sP0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f315,plain,
spl5_26,
inference(avatar_split_clause,[],[f138,f313]) ).
fof(f138,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f311,plain,
spl5_25,
inference(avatar_split_clause,[],[f137,f309]) ).
fof(f137,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f307,plain,
spl5_24,
inference(avatar_split_clause,[],[f136,f305]) ).
fof(f136,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f303,plain,
spl5_23,
inference(avatar_split_clause,[],[f135,f301]) ).
fof(f135,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f299,plain,
spl5_22,
inference(avatar_split_clause,[],[f134,f297]) ).
fof(f134,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f295,plain,
spl5_21,
inference(avatar_split_clause,[],[f133,f293]) ).
fof(f133,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f291,plain,
spl5_20,
inference(avatar_split_clause,[],[f132,f289]) ).
fof(f289,plain,
( spl5_20
<=> ! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f132,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( sdtlseqdt0(X0,X0)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> sdtlseqdt0(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLERefl) ).
fof(f287,plain,
( ~ spl5_5
| ~ spl5_19
| ~ spl5_9
| ~ spl5_15 ),
inference(avatar_split_clause,[],[f271,f262,f234,f284,f214]) ).
fof(f284,plain,
( spl5_19
<=> xm = sdtpldt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f271,plain,
( xm != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(sK2)
| ~ spl5_9
| ~ spl5_15 ),
inference(superposition,[],[f235,f264]) ).
fof(f282,plain,
( ~ spl5_14
| spl5_18 ),
inference(avatar_split_clause,[],[f125,f279,f257]) ).
fof(f125,plain,
( aNaturalNumber0(sdtsldt0(xn,xl))
| ~ sP0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f277,plain,
( ~ spl5_14
| spl5_17 ),
inference(avatar_split_clause,[],[f123,f274,f257]) ).
fof(f123,plain,
( aNaturalNumber0(sdtsldt0(xm,xl))
| ~ sP0 ),
inference(cnf_transformation,[],[f99]) ).
fof(f270,plain,
spl5_16,
inference(avatar_split_clause,[],[f121,f267]) ).
fof(f121,plain,
xn = sdtasdt0(xl,sK1),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
( doDivides0(xl,xn)
& xn = sdtasdt0(xl,sK1)
& aNaturalNumber0(sK1)
& doDivides0(xl,xm)
& xm = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f38,f97,f96]) ).
fof(f96,plain,
( ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
=> ( xn = sdtasdt0(xl,sK1)
& aNaturalNumber0(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) )
=> ( xm = sdtasdt0(xl,sK2)
& aNaturalNumber0(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
( doDivides0(xl,xn)
& ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X1] :
( xm = sdtasdt0(xl,X1)
& aNaturalNumber0(X1) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
( doDivides0(xl,xn)
& ? [X0] :
( xn = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) )
& doDivides0(xl,xm)
& ? [X0] :
( xm = sdtasdt0(xl,X0)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240_04) ).
fof(f265,plain,
spl5_15,
inference(avatar_split_clause,[],[f118,f262]) ).
fof(f118,plain,
xm = sdtasdt0(xl,sK2),
inference(cnf_transformation,[],[f98]) ).
fof(f260,plain,
( spl5_13
| spl5_14 ),
inference(avatar_split_clause,[],[f128,f257,f253]) ).
fof(f128,plain,
( sP0
| sz00 = xl ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
( sP0
| sz00 = xl ),
inference(definition_folding,[],[f43,f94]) ).
fof(f43,plain,
( ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) )
| sz00 = xl ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
( sz00 != xl
=> ( sdtpldt0(xm,xn) = sdtasdt0(xl,sdtpldt0(sdtsldt0(xm,xl),sdtsldt0(xn,xl)))
& xn = sdtasdt0(xl,sdtsldt0(xn,xl))
& aNaturalNumber0(sdtsldt0(xn,xl))
& xm = sdtasdt0(xl,sdtsldt0(xm,xl))
& aNaturalNumber0(sdtsldt0(xm,xl)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1298) ).
fof(f251,plain,
~ spl5_12,
inference(avatar_split_clause,[],[f131,f248]) ).
fof(f131,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f246,plain,
spl5_11,
inference(avatar_split_clause,[],[f122,f243]) ).
fof(f243,plain,
( spl5_11
<=> doDivides0(xl,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f122,plain,
doDivides0(xl,xn),
inference(cnf_transformation,[],[f98]) ).
fof(f241,plain,
spl5_10,
inference(avatar_split_clause,[],[f119,f238]) ).
fof(f238,plain,
( spl5_10
<=> doDivides0(xl,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f119,plain,
doDivides0(xl,xm),
inference(cnf_transformation,[],[f98]) ).
fof(f236,plain,
spl5_9,
inference(avatar_split_clause,[],[f112,f234]) ).
fof(f112,plain,
! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
( ~ doDivides0(xl,sdtpldt0(xm,xn))
& ! [X0] :
( sdtasdt0(xl,X0) != sdtpldt0(xm,xn)
| ~ aNaturalNumber0(X0) ) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,negated_conjecture,
~ ( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) ),
inference(negated_conjecture,[],[f36]) ).
fof(f36,conjecture,
( doDivides0(xl,sdtpldt0(xm,xn))
| ? [X0] :
( sdtasdt0(xl,X0) = sdtpldt0(xm,xn)
& aNaturalNumber0(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f232,plain,
spl5_8,
inference(avatar_split_clause,[],[f130,f229]) ).
fof(f229,plain,
( spl5_8
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f130,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f227,plain,
spl5_7,
inference(avatar_split_clause,[],[f129,f224]) ).
fof(f224,plain,
( spl5_7
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f129,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f222,plain,
spl5_6,
inference(avatar_split_clause,[],[f120,f219]) ).
fof(f120,plain,
aNaturalNumber0(sK1),
inference(cnf_transformation,[],[f98]) ).
fof(f217,plain,
spl5_5,
inference(avatar_split_clause,[],[f117,f214]) ).
fof(f117,plain,
aNaturalNumber0(sK2),
inference(cnf_transformation,[],[f98]) ).
fof(f212,plain,
spl5_4,
inference(avatar_split_clause,[],[f116,f209]) ).
fof(f116,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1240) ).
fof(f207,plain,
spl5_3,
inference(avatar_split_clause,[],[f115,f204]) ).
fof(f115,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f33]) ).
fof(f202,plain,
spl5_2,
inference(avatar_split_clause,[],[f114,f199]) ).
fof(f114,plain,
aNaturalNumber0(xl),
inference(cnf_transformation,[],[f33]) ).
fof(f197,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f113,f194]) ).
fof(f113,plain,
~ doDivides0(xl,sdtpldt0(xm,xn)),
inference(cnf_transformation,[],[f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : NUM469+2 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 14:02:42 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (12752)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (12757)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (12755)WARNING: value z3 for option sas not known
% 0.14/0.38 % (12753)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (12756)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (12754)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (12755)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (12758)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (12759)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.39 TRYING [3]
% 0.14/0.39 % (12757)First to succeed.
% 0.14/0.40 TRYING [4]
% 0.14/0.40 % (12757)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-12752"
% 0.14/0.40 % (12757)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.40 % (12757)------------------------------
% 0.14/0.40 % (12757)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.40 % (12757)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (12757)Memory used [KB]: 1468
% 0.14/0.40 % (12757)Time elapsed: 0.027 s
% 0.14/0.40 % (12757)Instructions burned: 65 (million)
% 0.14/0.40 % (12752)Success in time 0.04 s
%------------------------------------------------------------------------------