TSTP Solution File: SWV177+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV177+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:13:40 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 377
% Syntax : Number of formulae : 1184 ( 328 unt; 0 def)
% Number of atoms : 4194 ( 806 equ)
% Maximal formula atoms : 37 ( 3 avg)
% Number of connectives : 4723 (1713 ~;1879 |; 722 &)
% ( 263 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 277 ( 275 usr; 261 prp; 0-4 aty)
% Number of functors : 69 ( 69 usr; 24 con; 0-4 aty)
% Number of variables : 2110 (1953 !; 157 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3411,plain,
$false,
inference(avatar_sat_refutation,[],[f484,f489,f494,f499,f504,f509,f514,f519,f523,f530,f538,f543,f548,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f648,f653,f662,f667,f672,f677,f682,f687,f692,f696,f700,f705,f711,f715,f721,f729,f737,f745,f754,f763,f768,f772,f777,f782,f787,f792,f802,f808,f830,f835,f840,f844,f885,f889,f893,f914,f921,f925,f930,f935,f940,f944,f949,f953,f958,f962,f967,f972,f976,f981,f985,f990,f994,f998,f1003,f1007,f1012,f1016,f1021,f1025,f1030,f1034,f1039,f1043,f1048,f1052,f1057,f1061,f1067,f1071,f1075,f1080,f1084,f1089,f1093,f1098,f1102,f1107,f1111,f1116,f1120,f1125,f1129,f1134,f1138,f1143,f1147,f1152,f1156,f1161,f1165,f1169,f1173,f1177,f1181,f1185,f1189,f1193,f1197,f1201,f1209,f1217,f1225,f1233,f1242,f1246,f1254,f1262,f1270,f1278,f1286,f1294,f1302,f1310,f1318,f1327,f1335,f1343,f1351,f1359,f1364,f1372,f1380,f1388,f1396,f1520,f1525,f1529,f1536,f1540,f1544,f1548,f1552,f1556,f1560,f1564,f1568,f1851,f1886,f1890,f1894,f1960,f1965,f1998,f2003,f2035,f2039,f2111,f2117,f2122,f2127,f2131,f2135,f2139,f2143,f2205,f2209,f2215,f2221,f2225,f2333,f2339,f2347,f2384,f2388,f2392,f2396,f2400,f2404,f2408,f2412,f2416,f2420,f2426,f2431,f2435,f2439,f2443,f2452,f2456,f2460,f2532,f2538,f2575,f2580,f2585,f2591,f2628,f2703,f2709,f2715,f2719,f2761,f2800,f2806,f2845,f2851,f2857,f2861,f2948,f2954,f2960,f2964,f3038,f3045,f3084,f3093,f3137,f3156,f3171,f3175,f3177,f3182,f3187,f3192,f3197,f3202,f3211,f3248,f3282,f3376,f3409,f3410]) ).
fof(f3410,plain,
( ~ spl41_7
| spl41_8
| ~ spl41_6
| ~ spl41_49 ),
inference(avatar_split_clause,[],[f732,f727,f506,f516,f511]) ).
fof(f511,plain,
( spl41_7
<=> leq(sK13,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_7])]) ).
fof(f516,plain,
( spl41_8
<=> init = a_select2(rhoold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_8])]) ).
fof(f506,plain,
( spl41_6
<=> leq(n0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_6])]) ).
fof(f727,plain,
( spl41_49
<=> ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_49])]) ).
fof(f732,plain,
( init = a_select2(rhoold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_6
| ~ spl41_49 ),
inference(resolution,[],[f728,f508]) ).
fof(f508,plain,
( leq(n0,sK13)
| ~ spl41_6 ),
inference(avatar_component_clause,[],[f506]) ).
fof(f728,plain,
( ! [X2] :
( ~ leq(n0,X2)
| init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4) )
| ~ spl41_49 ),
inference(avatar_component_clause,[],[f727]) ).
fof(f3409,plain,
( ~ spl41_3
| spl41_260
| ~ spl41_1
| ~ spl41_49 ),
inference(avatar_split_clause,[],[f730,f727,f481,f3406,f491]) ).
fof(f491,plain,
( spl41_3
<=> leq(pv40,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_3])]) ).
fof(f3406,plain,
( spl41_260
<=> init = a_select2(rhoold_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_260])]) ).
fof(f481,plain,
( spl41_1
<=> leq(n0,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_1])]) ).
fof(f730,plain,
( init = a_select2(rhoold_init,pv40)
| ~ leq(pv40,n4)
| ~ spl41_1
| ~ spl41_49 ),
inference(resolution,[],[f728,f483]) ).
fof(f483,plain,
( leq(n0,pv40)
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f3376,plain,
( spl41_259
| ~ spl41_56
| ~ spl41_250 ),
inference(avatar_split_clause,[],[f3206,f3169,f770,f3373]) ).
fof(f3373,plain,
( spl41_259
<=> gt(plus(loopcounter,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_259])]) ).
fof(f770,plain,
( spl41_56
<=> ! [X0] : gt(plus(X0,n1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_56])]) ).
fof(f3169,plain,
( spl41_250
<=> ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_250])]) ).
fof(f3206,plain,
( gt(plus(loopcounter,n1),n1)
| ~ spl41_56
| ~ spl41_250 ),
inference(resolution,[],[f3170,f771]) ).
fof(f771,plain,
( ! [X0] : gt(plus(X0,n1),X0)
| ~ spl41_56 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f3170,plain,
( ! [X0] :
( ~ gt(X0,loopcounter)
| gt(X0,n1) )
| ~ spl41_250 ),
inference(avatar_component_clause,[],[f3169]) ).
fof(f3282,plain,
( spl41_257
| ~ spl41_248
| ~ spl41_253 ),
inference(avatar_split_clause,[],[f3188,f3185,f3149,f3209]) ).
fof(f3209,plain,
( spl41_257
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_257])]) ).
fof(f3149,plain,
( spl41_248
<=> tptp_float_0_0 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_248])]) ).
fof(f3185,plain,
( spl41_253
<=> ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_253])]) ).
fof(f3188,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) )
| ~ spl41_248
| ~ spl41_253 ),
inference(forward_demodulation,[],[f3186,f3151]) ).
fof(f3151,plain,
( tptp_float_0_0 = sK13
| ~ spl41_248 ),
inference(avatar_component_clause,[],[f3149]) ).
fof(f3186,plain,
( ! [X0] :
( ~ leq(X0,sK13)
| leq(X0,n4) )
| ~ spl41_253 ),
inference(avatar_component_clause,[],[f3185]) ).
fof(f3248,plain,
( spl41_258
| ~ spl41_246
| ~ spl41_252 ),
inference(avatar_split_clause,[],[f3183,f3180,f3130,f3246]) ).
fof(f3246,plain,
( spl41_258
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n135299) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_258])]) ).
fof(f3130,plain,
( spl41_246
<=> tptp_float_0_0 = pv45 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_246])]) ).
fof(f3180,plain,
( spl41_252
<=> ! [X0] :
( leq(X0,n135299)
| ~ leq(X0,pv45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_252])]) ).
fof(f3183,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n135299) )
| ~ spl41_246
| ~ spl41_252 ),
inference(forward_demodulation,[],[f3181,f3132]) ).
fof(f3132,plain,
( tptp_float_0_0 = pv45
| ~ spl41_246 ),
inference(avatar_component_clause,[],[f3130]) ).
fof(f3181,plain,
( ! [X0] :
( ~ leq(X0,pv45)
| leq(X0,n135299) )
| ~ spl41_252 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f3211,plain,
( spl41_257
| ~ spl41_230
| ~ spl41_251 ),
inference(avatar_split_clause,[],[f3176,f3173,f2754,f3209]) ).
fof(f2754,plain,
( spl41_230
<=> tptp_float_0_0 = pv40 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_230])]) ).
fof(f3173,plain,
( spl41_251
<=> ! [X0] :
( leq(X0,n4)
| ~ leq(X0,pv40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_251])]) ).
fof(f3176,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) )
| ~ spl41_230
| ~ spl41_251 ),
inference(forward_demodulation,[],[f3174,f2756]) ).
fof(f2756,plain,
( tptp_float_0_0 = pv40
| ~ spl41_230 ),
inference(avatar_component_clause,[],[f2754]) ).
fof(f3174,plain,
( ! [X0] :
( ~ leq(X0,pv40)
| leq(X0,n4) )
| ~ spl41_251 ),
inference(avatar_component_clause,[],[f3173]) ).
fof(f3202,plain,
( spl41_256
| ~ spl41_6
| ~ spl41_62
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1750,f1546,f805,f506,f3200]) ).
fof(f3200,plain,
( spl41_256
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_256])]) ).
fof(f805,plain,
( spl41_62
<=> n0 = tptp_float_0_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_62])]) ).
fof(f1546,plain,
( spl41_166
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_166])]) ).
fof(f1750,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) )
| ~ spl41_6
| ~ spl41_62
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1690,f807]) ).
fof(f807,plain,
( n0 = tptp_float_0_0
| ~ spl41_62 ),
inference(avatar_component_clause,[],[f805]) ).
fof(f1690,plain,
( ! [X0] :
( leq(X0,sK13)
| ~ leq(X0,n0) )
| ~ spl41_6
| ~ spl41_166 ),
inference(resolution,[],[f1547,f508]) ).
fof(f1547,plain,
( ! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1) )
| ~ spl41_166 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f3197,plain,
( spl41_255
| ~ spl41_2
| ~ spl41_62
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1749,f1546,f805,f486,f3195]) ).
fof(f3195,plain,
( spl41_255
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_255])]) ).
fof(f486,plain,
( spl41_2
<=> leq(n0,pv45) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_2])]) ).
fof(f1749,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv45) )
| ~ spl41_2
| ~ spl41_62
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1689,f807]) ).
fof(f1689,plain,
( ! [X0] :
( leq(X0,pv45)
| ~ leq(X0,n0) )
| ~ spl41_2
| ~ spl41_166 ),
inference(resolution,[],[f1547,f488]) ).
fof(f488,plain,
( leq(n0,pv45)
| ~ spl41_2 ),
inference(avatar_component_clause,[],[f486]) ).
fof(f3192,plain,
( spl41_254
| ~ spl41_1
| ~ spl41_62
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1748,f1546,f805,f481,f3190]) ).
fof(f3190,plain,
( spl41_254
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_254])]) ).
fof(f1748,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv40) )
| ~ spl41_1
| ~ spl41_62
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1688,f807]) ).
fof(f1688,plain,
( ! [X0] :
( leq(X0,pv40)
| ~ leq(X0,n0) )
| ~ spl41_1
| ~ spl41_166 ),
inference(resolution,[],[f1547,f483]) ).
fof(f3187,plain,
( spl41_253
| ~ spl41_7
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1723,f1546,f511,f3185]) ).
fof(f1723,plain,
( ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) )
| ~ spl41_7
| ~ spl41_166 ),
inference(resolution,[],[f1547,f513]) ).
fof(f513,plain,
( leq(sK13,n4)
| ~ spl41_7 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f3182,plain,
( spl41_252
| ~ spl41_4
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1722,f1546,f496,f3180]) ).
fof(f496,plain,
( spl41_4
<=> leq(pv45,n135299) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_4])]) ).
fof(f1722,plain,
( ! [X0] :
( leq(X0,n135299)
| ~ leq(X0,pv45) )
| ~ spl41_4
| ~ spl41_166 ),
inference(resolution,[],[f1547,f498]) ).
fof(f498,plain,
( leq(pv45,n135299)
| ~ spl41_4 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f3177,plain,
( spl41_155
| ~ spl41_14
| ~ spl41_230 ),
inference(avatar_split_clause,[],[f2934,f2754,f550,f1361]) ).
fof(f1361,plain,
( spl41_155
<=> init = a_select2(rho_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_155])]) ).
fof(f550,plain,
( spl41_14
<=> init = a_select2(rho_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_14])]) ).
fof(f2934,plain,
( init = a_select2(rho_init,tptp_float_0_0)
| ~ spl41_14
| ~ spl41_230 ),
inference(superposition,[],[f552,f2756]) ).
fof(f552,plain,
( init = a_select2(rho_init,pv40)
| ~ spl41_14 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f3175,plain,
( spl41_251
| ~ spl41_3
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1721,f1546,f491,f3173]) ).
fof(f1721,plain,
( ! [X0] :
( leq(X0,n4)
| ~ leq(X0,pv40) )
| ~ spl41_3
| ~ spl41_166 ),
inference(resolution,[],[f1547,f493]) ).
fof(f493,plain,
( leq(pv40,n4)
| ~ spl41_3 ),
inference(avatar_component_clause,[],[f491]) ).
fof(f3171,plain,
( spl41_250
| ~ spl41_5
| ~ spl41_165 ),
inference(avatar_split_clause,[],[f1677,f1542,f501,f3169]) ).
fof(f501,plain,
( spl41_5
<=> gt(loopcounter,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_5])]) ).
fof(f1542,plain,
( spl41_165
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_165])]) ).
fof(f1677,plain,
( ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) )
| ~ spl41_5
| ~ spl41_165 ),
inference(resolution,[],[f1543,f503]) ).
fof(f503,plain,
( gt(loopcounter,n1)
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f1543,plain,
( ! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) )
| ~ spl41_165 ),
inference(avatar_component_clause,[],[f1542]) ).
fof(f3156,plain,
( spl41_248
| spl41_249
| ~ spl41_6
| ~ spl41_62
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1644,f1538,f805,f506,f3153,f3149]) ).
fof(f3153,plain,
( spl41_249
<=> gt(sK13,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_249])]) ).
fof(f1538,plain,
( spl41_164
<=> ! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_164])]) ).
fof(f1644,plain,
( gt(sK13,tptp_float_0_0)
| tptp_float_0_0 = sK13
| ~ spl41_6
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1643,f807]) ).
fof(f1643,plain,
( tptp_float_0_0 = sK13
| gt(sK13,n0)
| ~ spl41_6
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1581,f807]) ).
fof(f1581,plain,
( n0 = sK13
| gt(sK13,n0)
| ~ spl41_6
| ~ spl41_164 ),
inference(resolution,[],[f1539,f508]) ).
fof(f1539,plain,
( ! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) )
| ~ spl41_164 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f3137,plain,
( spl41_246
| spl41_247
| ~ spl41_2
| ~ spl41_62
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1642,f1538,f805,f486,f3134,f3130]) ).
fof(f3134,plain,
( spl41_247
<=> gt(pv45,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_247])]) ).
fof(f1642,plain,
( gt(pv45,tptp_float_0_0)
| tptp_float_0_0 = pv45
| ~ spl41_2
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1641,f807]) ).
fof(f1641,plain,
( tptp_float_0_0 = pv45
| gt(pv45,n0)
| ~ spl41_2
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1580,f807]) ).
fof(f1580,plain,
( n0 = pv45
| gt(pv45,n0)
| ~ spl41_2
| ~ spl41_164 ),
inference(resolution,[],[f1539,f488]) ).
fof(f3093,plain,
( spl41_245
| ~ spl41_62
| ~ spl41_244 ),
inference(avatar_split_clause,[],[f3086,f3082,f805,f3091]) ).
fof(f3091,plain,
( spl41_245
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ leq(tptp_float_0_0,X8)
| ~ leq(tptp_float_0_0,X9)
| a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(X8,X6)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_245])]) ).
fof(f3082,plain,
( spl41_244
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_244])]) ).
fof(f3086,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ leq(tptp_float_0_0,X8)
| ~ leq(tptp_float_0_0,X9)
| a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(X8,X6)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) )
| ~ spl41_62
| ~ spl41_244 ),
inference(forward_demodulation,[],[f3085,f807]) ).
fof(f3085,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ leq(tptp_float_0_0,X9)
| a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) )
| ~ spl41_62
| ~ spl41_244 ),
inference(forward_demodulation,[],[f3083,f807]) ).
fof(f3083,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) )
| ~ spl41_244 ),
inference(avatar_component_clause,[],[f3082]) ).
fof(f3084,plain,
spl41_244,
inference(avatar_split_clause,[],[f430,f3082]) ).
fof(f430,plain,
! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X8,X9] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8) )
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ),
inference(rectify,[],[f191]) ).
fof(f191,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X14,X15] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X14,X15) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X15,X14)
| ~ leq(X15,X6)
| ~ leq(n0,X15)
| ~ leq(X14,X6)
| ~ leq(n0,X14) )
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ),
inference(definition_folding,[],[f169,f190,f189,f188]) ).
fof(f188,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f189,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f190,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X14,X15] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X14,X15) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X15,X14)
| ~ leq(X15,X6)
| ~ leq(n0,X15)
| ~ leq(X14,X6)
| ~ leq(n0,X14) )
| ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) ) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ! [X14,X15] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X14,X15) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X15,X14)
| ~ leq(X15,X6)
| ~ leq(n0,X15)
| ~ leq(X14,X6)
| ~ leq(n0,X14) )
| ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) ) ),
inference(ennf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( ! [X8,X9] :
( ( leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
=> a_select3(X5,X8,X9) = a_select3(X5,X9,X8) )
& ! [X10,X11] :
( ( leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
=> a_select3(X0,X10,X11) = a_select3(X0,X11,X10) )
& ! [X12,X13] :
( ( leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
=> a_select3(X3,X12,X13) = a_select3(X3,X13,X12) ) )
=> ! [X14,X15] :
( ( leq(X15,X6)
& leq(n0,X15)
& leq(X14,X6)
& leq(n0,X14) )
=> a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X14,X15) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X15,X14) ) ),
inference(rectify,[],[f25]) ).
fof(f25,axiom,
! [X13,X17,X3,X19,X20,X21,X14,X18] :
( ( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X21,X4,X10) = a_select3(X21,X10,X4) )
& ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) )
& ! [X4,X10] :
( ( leq(X10,X18)
& leq(n0,X10)
& leq(X4,X18)
& leq(n0,X4) )
=> a_select3(X19,X4,X10) = a_select3(X19,X10,X4) ) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_madd(X13,tptp_mmul(X17,tptp_mmul(tptp_madd(tptp_mmul(X3,tptp_mmul(X19,trans(X3))),tptp_mmul(X20,tptp_mmul(X21,trans(X20)))),trans(X17)))),X4,X10) = a_select3(tptp_madd(X13,tptp_mmul(X17,tptp_mmul(tptp_madd(tptp_mmul(X3,tptp_mmul(X19,trans(X3))),tptp_mmul(X20,tptp_mmul(X21,trans(X20)))),trans(X17)))),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_joseph_update) ).
fof(f3045,plain,
( spl41_243
| ~ spl41_62
| ~ spl41_242 ),
inference(avatar_split_clause,[],[f3041,f3036,f805,f3043]) ).
fof(f3043,plain,
( spl41_243
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_243])]) ).
fof(f3036,plain,
( spl41_242
<=> ! [X3,X4,X0,X5,X2,X1] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_242])]) ).
fof(f3041,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP2(X0,X1) )
| ~ spl41_62
| ~ spl41_242 ),
inference(forward_demodulation,[],[f3040,f807]) ).
fof(f3040,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) )
| ~ spl41_62
| ~ spl41_242 ),
inference(forward_demodulation,[],[f3039,f807]) ).
fof(f3039,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) )
| ~ spl41_62
| ~ spl41_242 ),
inference(forward_demodulation,[],[f3037,f807]) ).
fof(f3037,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) )
| ~ spl41_242 ),
inference(avatar_component_clause,[],[f3036]) ).
fof(f3038,plain,
spl41_242,
inference(avatar_split_clause,[],[f357,f3036]) ).
fof(f357,plain,
! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0,X1] :
( ! [X2,X3,X4,X5] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2) )
| sP2(X0,X1) ),
inference(rectify,[],[f175]) ).
fof(f175,plain,
! [X0,X1] :
( ! [X4,X5,X6,X7] :
( a_select3(tptp_update3(X0,X6,X6,X7),X4,X5) = a_select3(tptp_update3(X0,X6,X6,X7),X5,X4)
| ~ leq(X6,X1)
| ~ leq(n0,X6)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| sP2(X0,X1) ),
inference(definition_folding,[],[f143,f174]) ).
fof(f174,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f143,plain,
! [X0,X1] :
( ! [X4,X5,X6,X7] :
( a_select3(tptp_update3(X0,X6,X6,X7),X4,X5) = a_select3(tptp_update3(X0,X6,X6,X7),X5,X4)
| ~ leq(X6,X1)
| ~ leq(n0,X6)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(flattening,[],[f142]) ).
fof(f142,plain,
! [X0,X1] :
( ! [X4,X5,X6,X7] :
( a_select3(tptp_update3(X0,X6,X6,X7),X4,X5) = a_select3(tptp_update3(X0,X6,X6,X7),X5,X4)
| ~ leq(X6,X1)
| ~ leq(n0,X6)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(ennf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> a_select3(X0,X2,X3) = a_select3(X0,X3,X2) )
=> ! [X4,X5,X6,X7] :
( ( leq(X6,X1)
& leq(n0,X6)
& leq(X5,X1)
& leq(n0,X5)
& leq(X4,X1)
& leq(n0,X4) )
=> a_select3(tptp_update3(X0,X6,X6,X7),X4,X5) = a_select3(tptp_update3(X0,X6,X6,X7),X5,X4) ) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X13,X14] :
( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) )
=> ! [X4,X10,X15,X16] :
( ( leq(X15,X14)
& leq(n0,X15)
& leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_update3(X13,X15,X15,X16),X4,X10) = a_select3(tptp_update3(X13,X15,X15,X16),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_update_diagonal) ).
fof(f2964,plain,
( spl41_241
| ~ spl41_62
| ~ spl41_239 ),
inference(avatar_split_clause,[],[f2956,f2952,f805,f2962]) ).
fof(f2962,plain,
( spl41_241
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ leq(tptp_float_0_0,X4)
| ~ leq(tptp_float_0_0,X5)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(X4,X2)
| sP8(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_241])]) ).
fof(f2952,plain,
( spl41_239
<=> ! [X2,X3,X4,X0,X5,X1] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_239])]) ).
fof(f2956,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X4)
| ~ leq(tptp_float_0_0,X5)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(X4,X2)
| sP8(X1,X3) )
| ~ spl41_62
| ~ spl41_239 ),
inference(forward_demodulation,[],[f2955,f807]) ).
fof(f2955,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X5)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) )
| ~ spl41_62
| ~ spl41_239 ),
inference(forward_demodulation,[],[f2953,f807]) ).
fof(f2953,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) )
| ~ spl41_239 ),
inference(avatar_component_clause,[],[f2952]) ).
fof(f2960,plain,
( spl41_240
| ~ spl41_62
| ~ spl41_238 ),
inference(avatar_split_clause,[],[f2950,f2946,f805,f2958]) ).
fof(f2958,plain,
( spl41_240
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP7(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_240])]) ).
fof(f2946,plain,
( spl41_238
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_238])]) ).
fof(f2950,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP7(X1,X2) )
| ~ spl41_62
| ~ spl41_238 ),
inference(forward_demodulation,[],[f2949,f807]) ).
fof(f2949,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) )
| ~ spl41_62
| ~ spl41_238 ),
inference(forward_demodulation,[],[f2947,f807]) ).
fof(f2947,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) )
| ~ spl41_238 ),
inference(avatar_component_clause,[],[f2946]) ).
fof(f2954,plain,
spl41_239,
inference(avatar_split_clause,[],[f405,f2952]) ).
fof(f405,plain,
! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) ),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4) )
| sP8(X1,X3) ),
inference(rectify,[],[f185]) ).
fof(f185,plain,
! [X0,X1,X2,X3] :
( ! [X6,X7] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X7) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X7,X6)
| ~ leq(X7,X2)
| ~ leq(n0,X7)
| ~ leq(X6,X2)
| ~ leq(n0,X6) )
| sP8(X1,X3) ),
inference(definition_folding,[],[f159,f184]) ).
fof(f184,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f159,plain,
! [X0,X1,X2,X3] :
( ! [X6,X7] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X7) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X7,X6)
| ~ leq(X7,X2)
| ~ leq(n0,X7)
| ~ leq(X6,X2)
| ~ leq(n0,X6) )
| ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) ) ),
inference(flattening,[],[f158]) ).
fof(f158,plain,
! [X0,X1,X2,X3] :
( ! [X6,X7] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X7) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X7,X6)
| ~ leq(X7,X2)
| ~ leq(n0,X7)
| ~ leq(X6,X2)
| ~ leq(n0,X6) )
| ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) ) ),
inference(ennf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0,X1,X2,X3] :
( ! [X4,X5] :
( ( leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
=> a_select3(X1,X4,X5) = a_select3(X1,X5,X4) )
=> ! [X6,X7] :
( ( leq(X7,X2)
& leq(n0,X7)
& leq(X6,X2)
& leq(n0,X6) )
=> a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X7) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X7,X6) ) ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X13,X17,X14,X18] :
( ! [X4,X10] :
( ( leq(X10,X18)
& leq(n0,X10)
& leq(X4,X18)
& leq(n0,X4) )
=> a_select3(X17,X4,X10) = a_select3(X17,X10,X4) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_mmul(X13,tptp_mmul(X17,trans(X13))),X4,X10) = a_select3(tptp_mmul(X13,tptp_mmul(X17,trans(X13))),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba2) ).
fof(f2948,plain,
spl41_238,
inference(avatar_split_clause,[],[f394,f2946]) ).
fof(f394,plain,
! [X2,X3,X0,X1,X4] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) ),
inference(cnf_transformation,[],[f232]) ).
fof(f232,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3) )
| sP7(X1,X2) ),
inference(rectify,[],[f183]) ).
fof(f183,plain,
! [X0,X1,X2] :
( ! [X5,X6] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X6) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X5)
| ~ leq(X6,X2)
| ~ leq(n0,X6)
| ~ leq(X5,X2)
| ~ leq(n0,X5) )
| sP7(X1,X2) ),
inference(definition_folding,[],[f153,f182]) ).
fof(f182,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f153,plain,
! [X0,X1,X2] :
( ! [X5,X6] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X6) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X5)
| ~ leq(X6,X2)
| ~ leq(n0,X6)
| ~ leq(X5,X2)
| ~ leq(n0,X5) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) ) ),
inference(flattening,[],[f152]) ).
fof(f152,plain,
! [X0,X1,X2] :
( ! [X5,X6] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X6) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X5)
| ~ leq(X6,X2)
| ~ leq(n0,X6)
| ~ leq(X5,X2)
| ~ leq(n0,X5) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) ) ),
inference(ennf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
=> a_select3(X1,X3,X4) = a_select3(X1,X4,X3) )
=> ! [X5,X6] :
( ( leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
=> a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X6) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X6,X5) ) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X13,X17,X14] :
( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X17,X4,X10) = a_select3(X17,X10,X4) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_mmul(X13,tptp_mmul(X17,trans(X13))),X4,X10) = a_select3(tptp_mmul(X13,tptp_mmul(X17,trans(X13))),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_aba1) ).
fof(f2861,plain,
( spl41_237
| ~ spl41_62
| ~ spl41_235 ),
inference(avatar_split_clause,[],[f2853,f2849,f805,f2859]) ).
fof(f2859,plain,
( spl41_237
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP6(X1,X2)
| sP5(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_237])]) ).
fof(f2849,plain,
( spl41_235
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_235])]) ).
fof(f2853,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP6(X1,X2)
| sP5(X0,X2) )
| ~ spl41_62
| ~ spl41_235 ),
inference(forward_demodulation,[],[f2852,f807]) ).
fof(f2852,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) )
| ~ spl41_62
| ~ spl41_235 ),
inference(forward_demodulation,[],[f2850,f807]) ).
fof(f2850,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) )
| ~ spl41_235 ),
inference(avatar_component_clause,[],[f2849]) ).
fof(f2857,plain,
( spl41_236
| ~ spl41_62
| ~ spl41_234 ),
inference(avatar_split_clause,[],[f2847,f2843,f805,f2855]) ).
fof(f2855,plain,
( spl41_236
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP4(X1,X2)
| sP3(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_236])]) ).
fof(f2843,plain,
( spl41_234
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_234])]) ).
fof(f2847,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP4(X1,X2)
| sP3(X0,X2) )
| ~ spl41_62
| ~ spl41_234 ),
inference(forward_demodulation,[],[f2846,f807]) ).
fof(f2846,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) )
| ~ spl41_62
| ~ spl41_234 ),
inference(forward_demodulation,[],[f2844,f807]) ).
fof(f2844,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) )
| ~ spl41_234 ),
inference(avatar_component_clause,[],[f2843]) ).
fof(f2851,plain,
spl41_235,
inference(avatar_split_clause,[],[f388,f2849]) ).
fof(f388,plain,
! [X2,X3,X0,X1,X4] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) ),
inference(cnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3) )
| sP6(X1,X2)
| sP5(X0,X2) ),
inference(rectify,[],[f181]) ).
fof(f181,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_madd(X0,X1),X7,X8) = a_select3(tptp_madd(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| sP6(X1,X2)
| sP5(X0,X2) ),
inference(definition_folding,[],[f151,f180,f179]) ).
fof(f179,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f180,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f151,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_madd(X0,X1),X7,X8) = a_select3(tptp_madd(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) ) ),
inference(flattening,[],[f150]) ).
fof(f150,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_madd(X0,X1),X7,X8) = a_select3(tptp_madd(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) ) ),
inference(ennf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
=> a_select3(X1,X3,X4) = a_select3(X1,X4,X3) )
& ! [X5,X6] :
( ( leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
=> a_select3(X0,X5,X6) = a_select3(X0,X6,X5) ) )
=> ! [X7,X8] :
( ( leq(X8,X2)
& leq(n0,X8)
& leq(X7,X2)
& leq(n0,X7) )
=> a_select3(tptp_madd(X0,X1),X7,X8) = a_select3(tptp_madd(X0,X1),X8,X7) ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X13,X17,X14] :
( ( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X17,X4,X10) = a_select3(X17,X10,X4) )
& ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) ) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_madd(X13,X17),X4,X10) = a_select3(tptp_madd(X13,X17),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_add) ).
fof(f2845,plain,
spl41_234,
inference(avatar_split_clause,[],[f377,f2843]) ).
fof(f377,plain,
! [X2,X3,X0,X1,X4] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3) )
| sP4(X1,X2)
| sP3(X0,X2) ),
inference(rectify,[],[f178]) ).
fof(f178,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_msub(X0,X1),X7,X8) = a_select3(tptp_msub(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| sP4(X1,X2)
| sP3(X0,X2) ),
inference(definition_folding,[],[f149,f177,f176]) ).
fof(f176,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f177,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f149,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_msub(X0,X1),X7,X8) = a_select3(tptp_msub(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) ) ),
inference(flattening,[],[f148]) ).
fof(f148,plain,
! [X0,X1,X2] :
( ! [X7,X8] :
( a_select3(tptp_msub(X0,X1),X7,X8) = a_select3(tptp_msub(X0,X1),X8,X7)
| ~ leq(X8,X2)
| ~ leq(n0,X8)
| ~ leq(X7,X2)
| ~ leq(n0,X7) )
| ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) ) ),
inference(ennf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
=> a_select3(X1,X3,X4) = a_select3(X1,X4,X3) )
& ! [X5,X6] :
( ( leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
=> a_select3(X0,X5,X6) = a_select3(X0,X6,X5) ) )
=> ! [X7,X8] :
( ( leq(X8,X2)
& leq(n0,X8)
& leq(X7,X2)
& leq(n0,X7) )
=> a_select3(tptp_msub(X0,X1),X7,X8) = a_select3(tptp_msub(X0,X1),X8,X7) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X13,X17,X14] :
( ( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X17,X4,X10) = a_select3(X17,X10,X4) )
& ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) ) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(tptp_msub(X13,X17),X4,X10) = a_select3(tptp_msub(X13,X17),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_sub) ).
fof(f2806,plain,
( spl41_233
| ~ spl41_62
| ~ spl41_232 ),
inference(avatar_split_clause,[],[f2802,f2798,f805,f2804]) ).
fof(f2804,plain,
( spl41_233
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(tptp_float_0_0,X1)
| a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(X0,X2)
| sP9(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_233])]) ).
fof(f2798,plain,
( spl41_232
<=> ! [X2,X3,X4,X0,X5,X1] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| sP9(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_232])]) ).
fof(f2802,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(tptp_float_0_0,X1)
| a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(X0,X2)
| sP9(X5,X4,X3,X2) )
| ~ spl41_62
| ~ spl41_232 ),
inference(forward_demodulation,[],[f2801,f807]) ).
fof(f2801,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ leq(tptp_float_0_0,X1)
| a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| sP9(X5,X4,X3,X2) )
| ~ spl41_62
| ~ spl41_232 ),
inference(forward_demodulation,[],[f2799,f807]) ).
fof(f2799,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| sP9(X5,X4,X3,X2) )
| ~ spl41_232 ),
inference(avatar_component_clause,[],[f2798]) ).
fof(f2800,plain,
spl41_232,
inference(avatar_split_clause,[],[f412,f2798]) ).
fof(f412,plain,
! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| sP9(X5,X4,X3,X2) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0,X1,X2,X3,X4,X5] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| sP9(X5,X4,X3,X2) ),
inference(definition_folding,[],[f163,f186]) ).
fof(f186,plain,
! [X5,X4,X3,X2] :
( ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) )
| ~ sP9(X5,X4,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f163,plain,
! [X0,X1,X2,X3,X4,X5] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) ) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4,X5] :
( a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5
| ~ leq(X1,X3)
| ~ leq(n0,X1)
| ~ leq(X0,X2)
| ~ leq(n0,X0)
| ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) ) ),
inference(ennf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( leq(X1,X3)
& leq(n0,X1)
& leq(X0,X2)
& leq(n0,X0)
& ! [X6,X7] :
( ( leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) )
=> a_select3(X4,X6,X7) = X5 ) )
=> a_select3(tptp_update3(X4,X2,X3,X5),X0,X1) = X5 ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X4,X10,X6,X23,X0,X16] :
( ( leq(X10,X23)
& leq(n0,X10)
& leq(X4,X6)
& leq(n0,X4)
& ! [X25,X26] :
( ( leq(X26,X23)
& leq(X25,X6)
& leq(n0,X26)
& leq(n0,X25) )
=> a_select3(X0,X25,X26) = X16 ) )
=> a_select3(tptp_update3(X0,X6,X23,X16),X4,X10) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_3) ).
fof(f2761,plain,
( spl41_230
| spl41_231
| ~ spl41_1
| ~ spl41_62
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1640,f1538,f805,f481,f2758,f2754]) ).
fof(f2758,plain,
( spl41_231
<=> gt(pv40,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_231])]) ).
fof(f1640,plain,
( gt(pv40,tptp_float_0_0)
| tptp_float_0_0 = pv40
| ~ spl41_1
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1639,f807]) ).
fof(f1639,plain,
( tptp_float_0_0 = pv40
| gt(pv40,n0)
| ~ spl41_1
| ~ spl41_62
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1579,f807]) ).
fof(f1579,plain,
( n0 = pv40
| gt(pv40,n0)
| ~ spl41_1
| ~ spl41_164 ),
inference(resolution,[],[f1539,f483]) ).
fof(f2719,plain,
( spl41_229
| ~ spl41_62
| ~ spl41_227 ),
inference(avatar_split_clause,[],[f2711,f2707,f805,f2717]) ).
fof(f2717,plain,
( spl41_229
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_229])]) ).
fof(f2707,plain,
( spl41_227
<=> ! [X0,X3,X2,X1] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_227])]) ).
fof(f2711,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP1(X0,X1) )
| ~ spl41_62
| ~ spl41_227 ),
inference(forward_demodulation,[],[f2710,f807]) ).
fof(f2710,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X3)
| a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) )
| ~ spl41_62
| ~ spl41_227 ),
inference(forward_demodulation,[],[f2708,f807]) ).
fof(f2708,plain,
( ! [X2,X3,X0,X1] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) )
| ~ spl41_227 ),
inference(avatar_component_clause,[],[f2707]) ).
fof(f2715,plain,
( spl41_228
| ~ spl41_62
| ~ spl41_226 ),
inference(avatar_split_clause,[],[f2705,f2701,f805,f2713]) ).
fof(f2713,plain,
( spl41_228
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_228])]) ).
fof(f2701,plain,
( spl41_226
<=> ! [X0,X3,X2,X1] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_226])]) ).
fof(f2705,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP0(X0,X1) )
| ~ spl41_62
| ~ spl41_226 ),
inference(forward_demodulation,[],[f2704,f807]) ).
fof(f2704,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X3)
| a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) )
| ~ spl41_62
| ~ spl41_226 ),
inference(forward_demodulation,[],[f2702,f807]) ).
fof(f2702,plain,
( ! [X2,X3,X0,X1] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) )
| ~ spl41_226 ),
inference(avatar_component_clause,[],[f2701]) ).
fof(f2709,plain,
spl41_227,
inference(avatar_split_clause,[],[f351,f2707]) ).
fof(f351,plain,
! [X2,X3,X0,X1] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) ),
inference(cnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0,X1] :
( ! [X2,X3] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2) )
| sP1(X0,X1) ),
inference(rectify,[],[f173]) ).
fof(f173,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(trans(X0),X4,X5) = a_select3(trans(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| sP1(X0,X1) ),
inference(definition_folding,[],[f141,f172]) ).
fof(f172,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f141,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(trans(X0),X4,X5) = a_select3(trans(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(flattening,[],[f140]) ).
fof(f140,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(trans(X0),X4,X5) = a_select3(trans(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(ennf_transformation,[],[f100]) ).
fof(f100,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> a_select3(X0,X2,X3) = a_select3(X0,X3,X2) )
=> ! [X4,X5] :
( ( leq(X5,X1)
& leq(n0,X5)
& leq(X4,X1)
& leq(n0,X4) )
=> a_select3(trans(X0),X4,X5) = a_select3(trans(X0),X5,X4) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X13,X14] :
( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(trans(X13),X4,X10) = a_select3(trans(X13),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_trans) ).
fof(f2703,plain,
spl41_226,
inference(avatar_split_clause,[],[f345,f2701]) ).
fof(f345,plain,
! [X2,X3,X0,X1] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0,X1] :
( ! [X2,X3] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2) )
| sP0(X0,X1) ),
inference(rectify,[],[f171]) ).
fof(f171,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(inv(X0),X4,X5) = a_select3(inv(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| sP0(X0,X1) ),
inference(definition_folding,[],[f139,f170]) ).
fof(f170,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f139,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(inv(X0),X4,X5) = a_select3(inv(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(flattening,[],[f138]) ).
fof(f138,plain,
! [X0,X1] :
( ! [X4,X5] :
( a_select3(inv(X0),X4,X5) = a_select3(inv(X0),X5,X4)
| ~ leq(X5,X1)
| ~ leq(n0,X5)
| ~ leq(X4,X1)
| ~ leq(n0,X4) )
| ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) ) ),
inference(ennf_transformation,[],[f99]) ).
fof(f99,plain,
! [X0,X1] :
( ! [X2,X3] :
( ( leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> a_select3(X0,X2,X3) = a_select3(X0,X3,X2) )
=> ! [X4,X5] :
( ( leq(X5,X1)
& leq(n0,X5)
& leq(X4,X1)
& leq(n0,X4) )
=> a_select3(inv(X0),X4,X5) = a_select3(inv(X0),X5,X4) ) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X13,X14] :
( ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(X13,X4,X10) = a_select3(X13,X10,X4) )
=> ! [X4,X10] :
( ( leq(X10,X14)
& leq(n0,X10)
& leq(X4,X14)
& leq(n0,X4) )
=> a_select3(inv(X13),X4,X10) = a_select3(inv(X13),X10,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',matrix_symm_inv) ).
fof(f2628,plain,
spl41_225,
inference(avatar_split_clause,[],[f414,f2626]) ).
fof(f2626,plain,
( spl41_225
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6
| ~ leq(X3,X5)
| ~ leq(X4,X3)
| ~ leq(X0,X2)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_225])]) ).
fof(f414,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6
| ~ leq(X3,X5)
| ~ leq(X4,X3)
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f167]) ).
fof(f167,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6
| ~ leq(X3,X5)
| ~ leq(X4,X3)
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6
| ~ leq(X3,X5)
| ~ leq(X4,X3)
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( leq(X3,X5)
& leq(X4,X3)
& leq(X0,X2)
& leq(X1,X0) )
=> a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6 ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X4,X8,X9,X10,X11,X12,X7] :
( ( leq(X10,X12)
& leq(X11,X10)
& leq(X4,X9)
& leq(X8,X4) )
=> a_select3(tptp_const_array2(dim(X8,X9),dim(X11,X12),X7),X4,X10) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array2_select) ).
fof(f2591,plain,
( spl41_224
| ~ spl41_62
| ~ spl41_223 ),
inference(avatar_split_clause,[],[f2587,f2583,f805,f2589]) ).
fof(f2589,plain,
( spl41_224
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_224])]) ).
fof(f2583,plain,
( spl41_223
<=> ! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_223])]) ).
fof(f2587,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n5) )
| ~ spl41_62
| ~ spl41_223 ),
inference(forward_demodulation,[],[f2586,f807]) ).
fof(f2586,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_223 ),
inference(forward_demodulation,[],[f2584,f807]) ).
fof(f2584,plain,
( ! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) )
| ~ spl41_223 ),
inference(avatar_component_clause,[],[f2583]) ).
fof(f2585,plain,
spl41_223,
inference(avatar_split_clause,[],[f326,f2583]) ).
fof(f326,plain,
! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ( leq(X0,n5)
& leq(n0,X0) )
=> ( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_5) ).
fof(f2580,plain,
( spl41_222
| ~ spl41_62
| ~ spl41_221 ),
inference(avatar_split_clause,[],[f2576,f2573,f805,f2578]) ).
fof(f2578,plain,
( spl41_222
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| a_select2(X2,sK30(X1,X2,X3)) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_222])]) ).
fof(f2573,plain,
( spl41_221
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| a_select2(X2,sK30(X1,X2,X3)) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_221])]) ).
fof(f2576,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| a_select2(X2,sK30(X1,X2,X3)) != X3 )
| ~ spl41_62
| ~ spl41_221 ),
inference(forward_demodulation,[],[f2574,f807]) ).
fof(f2574,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| a_select2(X2,sK30(X1,X2,X3)) != X3 )
| ~ spl41_221 ),
inference(avatar_component_clause,[],[f2573]) ).
fof(f2575,plain,
spl41_221,
inference(avatar_split_clause,[],[f399,f2573]) ).
fof(f399,plain,
! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| a_select2(X2,sK30(X1,X2,X3)) != X3 ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| ( a_select2(X2,sK30(X1,X2,X3)) != X3
& leq(sK30(X1,X2,X3),X1)
& leq(n0,sK30(X1,X2,X3)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f157,f233]) ).
fof(f233,plain,
! [X1,X2,X3] :
( ? [X4] :
( a_select2(X2,X4) != X3
& leq(X4,X1)
& leq(n0,X4) )
=> ( a_select2(X2,sK30(X1,X2,X3)) != X3
& leq(sK30(X1,X2,X3),X1)
& leq(n0,sK30(X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| ? [X4] :
( a_select2(X2,X4) != X3
& leq(X4,X1)
& leq(n0,X4) ) ),
inference(flattening,[],[f156]) ).
fof(f156,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| ? [X4] :
( a_select2(X2,X4) != X3
& leq(X4,X1)
& leq(n0,X4) ) ),
inference(ennf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0,X1,X2,X3] :
( ( leq(X0,X1)
& leq(n0,X0)
& ! [X4] :
( ( leq(X4,X1)
& leq(n0,X4) )
=> a_select2(X2,X4) = X3 ) )
=> a_select2(tptp_update2(X2,X1,X3),X0) = X3 ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X4,X6,X0,X16] :
( ( leq(X4,X6)
& leq(n0,X4)
& ! [X25] :
( ( leq(X25,X6)
& leq(n0,X25) )
=> a_select2(X0,X25) = X16 ) )
=> a_select2(tptp_update2(X0,X6,X16),X4) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_3) ).
fof(f2538,plain,
( spl41_220
| ~ spl41_62
| ~ spl41_219 ),
inference(avatar_split_clause,[],[f2534,f2530,f805,f2536]) ).
fof(f2536,plain,
( spl41_220
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_220])]) ).
fof(f2530,plain,
( spl41_219
<=> ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_219])]) ).
fof(f2534,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4) )
| ~ spl41_62
| ~ spl41_219 ),
inference(forward_demodulation,[],[f2533,f807]) ).
fof(f2533,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_219 ),
inference(forward_demodulation,[],[f2531,f807]) ).
fof(f2531,plain,
( ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_219 ),
inference(avatar_component_clause,[],[f2530]) ).
fof(f2532,plain,
spl41_219,
inference(avatar_split_clause,[],[f330,f2530]) ).
fof(f330,plain,
! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ( leq(X0,n4)
& leq(n0,X0) )
=> ( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_4) ).
fof(f2460,plain,
( spl41_218
| ~ spl41_62
| ~ spl41_210 ),
inference(avatar_split_clause,[],[f2427,f2424,f805,f2458]) ).
fof(f2458,plain,
( spl41_218
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| leq(sK30(X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_218])]) ).
fof(f2424,plain,
( spl41_210
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(sK30(X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_210])]) ).
fof(f2427,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| leq(sK30(X1,X2,X3),X1) )
| ~ spl41_62
| ~ spl41_210 ),
inference(forward_demodulation,[],[f2425,f807]) ).
fof(f2425,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(sK30(X1,X2,X3),X1) )
| ~ spl41_210 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f2456,plain,
( spl41_217
| ~ spl41_62
| ~ spl41_209 ),
inference(avatar_split_clause,[],[f2422,f2418,f805,f2454]) ).
fof(f2454,plain,
( spl41_217
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK30(X1,X2,X3))
| ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_217])]) ).
fof(f2418,plain,
( spl41_209
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(n0,sK30(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_209])]) ).
fof(f2422,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK30(X1,X2,X3))
| ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1) )
| ~ spl41_62
| ~ spl41_209 ),
inference(forward_demodulation,[],[f2421,f807]) ).
fof(f2421,plain,
( ! [X2,X3,X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| leq(n0,sK30(X1,X2,X3)) )
| ~ spl41_62
| ~ spl41_209 ),
inference(forward_demodulation,[],[f2419,f807]) ).
fof(f2419,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(n0,sK30(X1,X2,X3)) )
| ~ spl41_209 ),
inference(avatar_component_clause,[],[f2418]) ).
fof(f2452,plain,
( spl41_215
| spl41_216
| ~ spl41_7
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1614,f1538,f511,f2449,f2445]) ).
fof(f2445,plain,
( spl41_215
<=> gt(n4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_215])]) ).
fof(f2449,plain,
( spl41_216
<=> n4 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_216])]) ).
fof(f1614,plain,
( n4 = sK13
| gt(n4,sK13)
| ~ spl41_7
| ~ spl41_164 ),
inference(resolution,[],[f1539,f513]) ).
fof(f2443,plain,
spl41_214,
inference(avatar_split_clause,[],[f429,f2441]) ).
fof(f2441,plain,
( spl41_214
<=> ! [X0,X1] :
( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_214])]) ).
fof(f429,plain,
! [X0,X1] :
( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1] :
( ( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
& leq(sK40(X0,X1),X1)
& leq(n0,sK40(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1)) )
| ~ sP10(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
& leq(sK40(X0,X1),X1)
& leq(n0,sK40(X0,X1))
& leq(sK39(X0,X1),X1)
& leq(n0,sK39(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f253,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP10(X0,X1) ),
inference(rectify,[],[f252]) ).
fof(f252,plain,
! [X3,X7] :
( ? [X12,X13] :
( a_select3(X3,X12,X13) != a_select3(X3,X13,X12)
& leq(X13,X7)
& leq(n0,X13)
& leq(X12,X7)
& leq(n0,X12) )
| ~ sP10(X3,X7) ),
inference(nnf_transformation,[],[f188]) ).
fof(f2439,plain,
spl41_213,
inference(avatar_split_clause,[],[f424,f2437]) ).
fof(f2437,plain,
( spl41_213
<=> ! [X0,X1] :
( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_213])]) ).
fof(f424,plain,
! [X0,X1] :
( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0,X1] :
( ( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1)) )
| ~ sP11(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f249,f250]) ).
fof(f250,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
& leq(sK38(X0,X1),X1)
& leq(n0,sK38(X0,X1))
& leq(sK37(X0,X1),X1)
& leq(n0,sK37(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f249,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP11(X0,X1) ),
inference(rectify,[],[f248]) ).
fof(f248,plain,
! [X0,X6] :
( ? [X10,X11] :
( a_select3(X0,X10,X11) != a_select3(X0,X11,X10)
& leq(X11,X6)
& leq(n0,X11)
& leq(X10,X6)
& leq(n0,X10) )
| ~ sP11(X0,X6) ),
inference(nnf_transformation,[],[f189]) ).
fof(f2435,plain,
spl41_212,
inference(avatar_split_clause,[],[f419,f2433]) ).
fof(f2433,plain,
( spl41_212
<=> ! [X0,X1] :
( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_212])]) ).
fof(f419,plain,
! [X0,X1] :
( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f247,plain,
! [X0,X1] :
( ( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1)) )
| ~ sP12(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f245,f246]) ).
fof(f246,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
& leq(sK36(X0,X1),X1)
& leq(n0,sK36(X0,X1))
& leq(sK35(X0,X1),X1)
& leq(n0,sK35(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f245,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP12(X0,X1) ),
inference(rectify,[],[f244]) ).
fof(f244,plain,
! [X5,X6] :
( ? [X8,X9] :
( a_select3(X5,X8,X9) != a_select3(X5,X9,X8)
& leq(X9,X6)
& leq(n0,X9)
& leq(X8,X6)
& leq(n0,X8) )
| ~ sP12(X5,X6) ),
inference(nnf_transformation,[],[f190]) ).
fof(f2431,plain,
spl41_211,
inference(avatar_split_clause,[],[f404,f2429]) ).
fof(f2429,plain,
( spl41_211
<=> ! [X0,X1] :
( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_211])]) ).
fof(f404,plain,
! [X0,X1] :
( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f238,plain,
! [X0,X1] :
( ( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
& leq(sK32(X0,X1),X1)
& leq(n0,sK32(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1)) )
| ~ sP8(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f236,f237]) ).
fof(f237,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
& leq(sK32(X0,X1),X1)
& leq(n0,sK32(X0,X1))
& leq(sK31(X0,X1),X1)
& leq(n0,sK31(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f236,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP8(X0,X1) ),
inference(rectify,[],[f235]) ).
fof(f235,plain,
! [X1,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != a_select3(X1,X5,X4)
& leq(X5,X3)
& leq(n0,X5)
& leq(X4,X3)
& leq(n0,X4) )
| ~ sP8(X1,X3) ),
inference(nnf_transformation,[],[f184]) ).
fof(f2426,plain,
spl41_210,
inference(avatar_split_clause,[],[f398,f2424]) ).
fof(f398,plain,
! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(sK30(X1,X2,X3),X1) ),
inference(cnf_transformation,[],[f234]) ).
fof(f2420,plain,
spl41_209,
inference(avatar_split_clause,[],[f397,f2418]) ).
fof(f397,plain,
! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(n0,sK30(X1,X2,X3)) ),
inference(cnf_transformation,[],[f234]) ).
fof(f2416,plain,
spl41_208,
inference(avatar_split_clause,[],[f393,f2414]) ).
fof(f2414,plain,
( spl41_208
<=> ! [X0,X1] :
( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_208])]) ).
fof(f393,plain,
! [X0,X1] :
( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0,X1] :
( ( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
& leq(sK29(X0,X1),X1)
& leq(n0,sK29(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1)) )
| ~ sP7(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f229,f230]) ).
fof(f230,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
& leq(sK29(X0,X1),X1)
& leq(n0,sK29(X0,X1))
& leq(sK28(X0,X1),X1)
& leq(n0,sK28(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f229,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP7(X0,X1) ),
inference(rectify,[],[f228]) ).
fof(f228,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP7(X1,X2) ),
inference(nnf_transformation,[],[f182]) ).
fof(f2412,plain,
spl41_207,
inference(avatar_split_clause,[],[f387,f2410]) ).
fof(f2410,plain,
( spl41_207
<=> ! [X0,X1] :
( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_207])]) ).
fof(f387,plain,
! [X0,X1] :
( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f226,plain,
! [X0,X1] :
( ( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1)) )
| ~ sP5(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f224,f225]) ).
fof(f225,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
& leq(sK27(X0,X1),X1)
& leq(n0,sK27(X0,X1))
& leq(sK26(X0,X1),X1)
& leq(n0,sK26(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP5(X0,X1) ),
inference(rectify,[],[f223]) ).
fof(f223,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP5(X0,X2) ),
inference(nnf_transformation,[],[f179]) ).
fof(f2408,plain,
spl41_206,
inference(avatar_split_clause,[],[f382,f2406]) ).
fof(f2406,plain,
( spl41_206
<=> ! [X0,X1] :
( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_206])]) ).
fof(f382,plain,
! [X0,X1] :
( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0,X1] :
( ( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1)) )
| ~ sP6(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK24,sK25])],[f220,f221]) ).
fof(f221,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
& leq(sK25(X0,X1),X1)
& leq(n0,sK25(X0,X1))
& leq(sK24(X0,X1),X1)
& leq(n0,sK24(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f220,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP6(X0,X1) ),
inference(rectify,[],[f219]) ).
fof(f219,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP6(X1,X2) ),
inference(nnf_transformation,[],[f180]) ).
fof(f2404,plain,
spl41_205,
inference(avatar_split_clause,[],[f376,f2402]) ).
fof(f2402,plain,
( spl41_205
<=> ! [X0,X1] :
( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_205])]) ).
fof(f376,plain,
! [X0,X1] :
( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0,X1] :
( ( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1)) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23])],[f215,f216]) ).
fof(f216,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
& leq(sK23(X0,X1),X1)
& leq(n0,sK23(X0,X1))
& leq(sK22(X0,X1),X1)
& leq(n0,sK22(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f215,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f214]) ).
fof(f214,plain,
! [X0,X2] :
( ? [X5,X6] :
( a_select3(X0,X5,X6) != a_select3(X0,X6,X5)
& leq(X6,X2)
& leq(n0,X6)
& leq(X5,X2)
& leq(n0,X5) )
| ~ sP3(X0,X2) ),
inference(nnf_transformation,[],[f176]) ).
fof(f2400,plain,
spl41_204,
inference(avatar_split_clause,[],[f371,f2398]) ).
fof(f2398,plain,
( spl41_204
<=> ! [X0,X1] :
( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_204])]) ).
fof(f371,plain,
! [X0,X1] :
( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0,X1] :
( ( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1)) )
| ~ sP4(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f211,f212]) ).
fof(f212,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
& leq(sK21(X0,X1),X1)
& leq(n0,sK21(X0,X1))
& leq(sK20(X0,X1),X1)
& leq(n0,sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f211,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f210]) ).
fof(f210,plain,
! [X1,X2] :
( ? [X3,X4] :
( a_select3(X1,X3,X4) != a_select3(X1,X4,X3)
& leq(X4,X2)
& leq(n0,X4)
& leq(X3,X2)
& leq(n0,X3) )
| ~ sP4(X1,X2) ),
inference(nnf_transformation,[],[f177]) ).
fof(f2396,plain,
spl41_203,
inference(avatar_split_clause,[],[f356,f2394]) ).
fof(f2394,plain,
( spl41_203
<=> ! [X0,X1] :
( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_203])]) ).
fof(f356,plain,
! [X0,X1] :
( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f205,plain,
! [X0,X1] :
( ( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1)) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK18,sK19])],[f203,f204]) ).
fof(f204,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
& leq(sK19(X0,X1),X1)
& leq(n0,sK19(X0,X1))
& leq(sK18(X0,X1),X1)
& leq(n0,sK18(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f203,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f174]) ).
fof(f2392,plain,
spl41_202,
inference(avatar_split_clause,[],[f350,f2390]) ).
fof(f2390,plain,
( spl41_202
<=> ! [X0,X1] :
( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_202])]) ).
fof(f350,plain,
! [X0,X1] :
( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0,X1] :
( ( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17])],[f199,f200]) ).
fof(f200,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
& leq(sK17(X0,X1),X1)
& leq(n0,sK17(X0,X1))
& leq(sK16(X0,X1),X1)
& leq(n0,sK16(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f199,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f172]) ).
fof(f2388,plain,
spl41_201,
inference(avatar_split_clause,[],[f344,f2386]) ).
fof(f2386,plain,
( spl41_201
<=> ! [X0,X1] :
( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_201])]) ).
fof(f344,plain,
! [X0,X1] :
( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f197,plain,
! [X0,X1] :
( ( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1)) )
| ~ sP0(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f195,f196]) ).
fof(f196,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
=> ( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
& leq(sK15(X0,X1),X1)
& leq(n0,sK15(X0,X1))
& leq(sK14(X0,X1),X1)
& leq(n0,sK14(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f195,plain,
! [X0,X1] :
( ? [X2,X3] :
( a_select3(X0,X2,X3) != a_select3(X0,X3,X2)
& leq(X3,X1)
& leq(n0,X3)
& leq(X2,X1)
& leq(n0,X2) )
| ~ sP0(X0,X1) ),
inference(nnf_transformation,[],[f170]) ).
fof(f2384,plain,
spl41_200,
inference(avatar_split_clause,[],[f411,f2382]) ).
fof(f2382,plain,
( spl41_200
<=> ! [X0,X3,X2,X1] :
( a_select3(X1,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)) != X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_200])]) ).
fof(f411,plain,
! [X2,X3,X0,X1] :
( a_select3(X1,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)) != X0
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0,X1,X2,X3] :
( ( a_select3(X1,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)) != X0
& leq(sK34(X0,X1,X2,X3),X2)
& leq(sK33(X0,X1,X2,X3),X3)
& leq(n0,sK34(X0,X1,X2,X3))
& leq(n0,sK33(X0,X1,X2,X3)) )
| ~ sP9(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f241,f242]) ).
fof(f242,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != X0
& leq(X5,X2)
& leq(X4,X3)
& leq(n0,X5)
& leq(n0,X4) )
=> ( a_select3(X1,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)) != X0
& leq(sK34(X0,X1,X2,X3),X2)
& leq(sK33(X0,X1,X2,X3),X3)
& leq(n0,sK34(X0,X1,X2,X3))
& leq(n0,sK33(X0,X1,X2,X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f241,plain,
! [X0,X1,X2,X3] :
( ? [X4,X5] :
( a_select3(X1,X4,X5) != X0
& leq(X5,X2)
& leq(X4,X3)
& leq(n0,X5)
& leq(n0,X4) )
| ~ sP9(X0,X1,X2,X3) ),
inference(rectify,[],[f240]) ).
fof(f240,plain,
! [X5,X4,X3,X2] :
( ? [X6,X7] :
( a_select3(X4,X6,X7) != X5
& leq(X7,X3)
& leq(X6,X2)
& leq(n0,X7)
& leq(n0,X6) )
| ~ sP9(X5,X4,X3,X2) ),
inference(nnf_transformation,[],[f186]) ).
fof(f2347,plain,
( spl41_199
| ~ spl41_62
| ~ spl41_198 ),
inference(avatar_split_clause,[],[f2341,f2337,f805,f2345]) ).
fof(f2345,plain,
( spl41_199
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_199])]) ).
fof(f2337,plain,
( spl41_198
<=> ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_198])]) ).
fof(f2341,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) )
| ~ spl41_62
| ~ spl41_198 ),
inference(forward_demodulation,[],[f2340,f807]) ).
fof(f2340,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_198 ),
inference(forward_demodulation,[],[f2338,f807]) ).
fof(f2338,plain,
( ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_198 ),
inference(avatar_component_clause,[],[f2337]) ).
fof(f2339,plain,
spl41_198,
inference(avatar_split_clause,[],[f327,f2337]) ).
fof(f327,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ( leq(X0,n3)
& leq(n0,X0) )
=> ( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_3) ).
fof(f2333,plain,
spl41_197,
inference(avatar_split_clause,[],[f461,f2331]) ).
fof(f2331,plain,
( spl41_197
<=> ! [X3,X4,X0,X6,X2] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_197])]) ).
fof(f461,plain,
! [X2,X3,X0,X6,X4] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3)
| X0 = X2 ),
inference(equality_resolution,[],[f460]) ).
fof(f460,plain,
! [X2,X3,X0,X1,X6,X4] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X1,X6),X2,X3)
| X1 != X3
| X0 = X2 ),
inference(equality_resolution,[],[f413]) ).
fof(f413,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(cnf_transformation,[],[f165]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5
| a_select3(X4,X2,X3) != X5
| X1 != X3
| X0 = X2 ),
inference(ennf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ( a_select3(X4,X2,X3) = X5
& X1 = X3
& X0 != X2 )
=> a_select3(tptp_update3(X4,X0,X1,X6),X2,X3) = X5 ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X4,X10,X6,X23,X0,X16,X24] :
( ( a_select3(X0,X6,X23) = X16
& X10 = X23
& X4 != X6 )
=> a_select3(tptp_update3(X0,X4,X10,X24),X6,X23) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_2) ).
fof(f2225,plain,
( spl41_196
| ~ spl41_62
| ~ spl41_194 ),
inference(avatar_split_clause,[],[f2217,f2213,f805,f2223]) ).
fof(f2223,plain,
( spl41_196
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_196])]) ).
fof(f2213,plain,
( spl41_194
<=> ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_194])]) ).
fof(f2217,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) )
| ~ spl41_62
| ~ spl41_194 ),
inference(forward_demodulation,[],[f2216,f807]) ).
fof(f2216,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_194 ),
inference(forward_demodulation,[],[f2214,f807]) ).
fof(f2214,plain,
( ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_194 ),
inference(avatar_component_clause,[],[f2213]) ).
fof(f2221,plain,
spl41_195,
inference(avatar_split_clause,[],[f396,f2219]) ).
fof(f2219,plain,
( spl41_195
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_195])]) ).
fof(f396,plain,
! [X2,X3,X0,X1] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(flattening,[],[f154]) ).
fof(f154,plain,
! [X0,X1,X2,X3] :
( a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3
| ~ leq(X0,X2)
| ~ leq(X1,X0) ),
inference(ennf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( ( leq(X0,X2)
& leq(X1,X0) )
=> a_select2(tptp_const_array1(dim(X1,X2),X3),X0) = X3 ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X4,X5,X6,X7] :
( ( leq(X4,X6)
& leq(X5,X4) )
=> a_select2(tptp_const_array1(dim(X5,X6),X7),X4) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',const_array1_select) ).
fof(f2215,plain,
spl41_194,
inference(avatar_split_clause,[],[f328,f2213]) ).
fof(f328,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(flattening,[],[f122]) ).
fof(f122,plain,
! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ( leq(X0,n2)
& leq(n0,X0) )
=> ( n2 = X0
| n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_2) ).
fof(f2209,plain,
spl41_193,
inference(avatar_split_clause,[],[f459,f2207]) ).
fof(f2207,plain,
( spl41_193
<=> ! [X2,X4,X0,X1] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_193])]) ).
fof(f459,plain,
! [X2,X0,X1,X4] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ),
inference(equality_resolution,[],[f406]) ).
fof(f406,plain,
! [X2,X3,X0,X1,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(cnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(flattening,[],[f160]) ).
fof(f160,plain,
! [X0,X1,X2,X3,X4] :
( a_select2(tptp_update2(X2,X0,X4),X1) = X3
| a_select2(X2,X1) != X3
| X0 = X1 ),
inference(ennf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0,X1,X2,X3,X4] :
( ( a_select2(X2,X1) = X3
& X0 != X1 )
=> a_select2(tptp_update2(X2,X0,X4),X1) = X3 ),
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X4,X6,X0,X16,X24] :
( ( a_select2(X0,X6) = X16
& X4 != X6 )
=> a_select2(tptp_update2(X0,X4,X24),X6) = X16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_2) ).
fof(f2205,plain,
( spl41_191
| spl41_192
| ~ spl41_4
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1613,f1538,f496,f2202,f2198]) ).
fof(f2198,plain,
( spl41_191
<=> gt(n135299,pv45) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_191])]) ).
fof(f2202,plain,
( spl41_192
<=> pv45 = n135299 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_192])]) ).
fof(f1613,plain,
( pv45 = n135299
| gt(n135299,pv45)
| ~ spl41_4
| ~ spl41_164 ),
inference(resolution,[],[f1539,f498]) ).
fof(f2143,plain,
( spl41_190
| ~ spl41_62
| ~ spl41_185 ),
inference(avatar_split_clause,[],[f2123,f2120,f805,f2141]) ).
fof(f2141,plain,
( spl41_190
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_190])]) ).
fof(f2120,plain,
( spl41_185
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_185])]) ).
fof(f2123,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_62
| ~ spl41_185 ),
inference(forward_demodulation,[],[f2121,f807]) ).
fof(f2121,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_185 ),
inference(avatar_component_clause,[],[f2120]) ).
fof(f2139,plain,
( spl41_189
| ~ spl41_62
| ~ spl41_184 ),
inference(avatar_split_clause,[],[f2118,f2115,f805,f2137]) ).
fof(f2137,plain,
( spl41_189
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_189])]) ).
fof(f2115,plain,
( spl41_184
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_184])]) ).
fof(f2118,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_62
| ~ spl41_184 ),
inference(forward_demodulation,[],[f2116,f807]) ).
fof(f2116,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_184 ),
inference(avatar_component_clause,[],[f2115]) ).
fof(f2135,plain,
( spl41_188
| ~ spl41_62
| ~ spl41_183 ),
inference(avatar_split_clause,[],[f2113,f2109,f805,f2133]) ).
fof(f2133,plain,
( spl41_188
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_188])]) ).
fof(f2109,plain,
( spl41_183
<=> ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_183])]) ).
fof(f2113,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) )
| ~ spl41_62
| ~ spl41_183 ),
inference(forward_demodulation,[],[f2112,f807]) ).
fof(f2112,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_183 ),
inference(forward_demodulation,[],[f2110,f807]) ).
fof(f2110,plain,
( ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_183 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f2131,plain,
spl41_187,
inference(avatar_split_clause,[],[f410,f2129]) ).
fof(f2129,plain,
( spl41_187
<=> ! [X0,X3,X2,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_187])]) ).
fof(f410,plain,
! [X2,X3,X0,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2127,plain,
spl41_186,
inference(avatar_split_clause,[],[f409,f2125]) ).
fof(f2125,plain,
( spl41_186
<=> ! [X0,X3,X2,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_186])]) ).
fof(f409,plain,
! [X2,X3,X0,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2122,plain,
spl41_185,
inference(avatar_split_clause,[],[f408,f2120]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2117,plain,
spl41_184,
inference(avatar_split_clause,[],[f407,f2115]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2111,plain,
spl41_183,
inference(avatar_split_clause,[],[f329,f2109]) ).
fof(f329,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(flattening,[],[f124]) ).
fof(f124,plain,
! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ( leq(X0,n1)
& leq(n0,X0) )
=> ( n1 = X0
| n0 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_1) ).
fof(f2039,plain,
spl41_182,
inference(avatar_split_clause,[],[f479,f2037]) ).
fof(f2037,plain,
( spl41_182
<=> ! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_182])]) ).
fof(f479,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f478,f443]) ).
fof(f443,plain,
! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f318,f314,f314]) ).
fof(f314,plain,
! [X0] : succ(X0) = plus(X0,n1),
inference(cnf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] : succ(X0) = plus(X0,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_r) ).
fof(f318,plain,
! [X0] : succ(succ(X0)) = plus(n2,X0),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : succ(succ(X0)) = plus(n2,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_l) ).
fof(f478,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f450,f443]) ).
fof(f450,plain,
! [X0] : plus(n5,X0) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f325,f314,f314,f314,f314,f314]) ).
fof(f325,plain,
! [X0] : succ(succ(succ(succ(succ(X0))))) = plus(n5,X0),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] : succ(succ(succ(succ(succ(X0))))) = plus(n5,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_l) ).
fof(f2035,plain,
spl41_181,
inference(avatar_split_clause,[],[f477,f2033]) ).
fof(f2033,plain,
( spl41_181
<=> ! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_181])]) ).
fof(f477,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f476,f443]) ).
fof(f476,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f449,f443]) ).
fof(f449,plain,
! [X0] : plus(X0,n5) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f324,f314,f314,f314,f314,f314]) ).
fof(f324,plain,
! [X0] : plus(X0,n5) = succ(succ(succ(succ(succ(X0))))),
inference(cnf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] : plus(X0,n5) = succ(succ(succ(succ(succ(X0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_5_r) ).
fof(f2003,plain,
( spl41_180
| ~ spl41_167
| ~ spl41_169
| ~ spl41_179 ),
inference(avatar_split_clause,[],[f1999,f1996,f1558,f1550,f2001]) ).
fof(f2001,plain,
( spl41_180
<=> ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_180])]) ).
fof(f1550,plain,
( spl41_167
<=> ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_167])]) ).
fof(f1558,plain,
( spl41_169
<=> ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_169])]) ).
fof(f1996,plain,
( spl41_179
<=> ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_179])]) ).
fof(f1999,plain,
( ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1)
| ~ spl41_167
| ~ spl41_169
| ~ spl41_179 ),
inference(forward_demodulation,[],[f1997,f1770]) ).
fof(f1770,plain,
( ! [X0] : plus(X0,n3) = plus(n2,plus(X0,n1))
| ~ spl41_167
| ~ spl41_169 ),
inference(forward_demodulation,[],[f1754,f1559]) ).
fof(f1559,plain,
( ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1)
| ~ spl41_169 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f1754,plain,
( ! [X0] : plus(n2,plus(X0,n1)) = plus(plus(n2,X0),n1)
| ~ spl41_167 ),
inference(superposition,[],[f1551,f1551]) ).
fof(f1551,plain,
( ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1)
| ~ spl41_167 ),
inference(avatar_component_clause,[],[f1550]) ).
fof(f1997,plain,
( ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_179 ),
inference(avatar_component_clause,[],[f1996]) ).
fof(f1998,plain,
spl41_179,
inference(avatar_split_clause,[],[f475,f1996]) ).
fof(f475,plain,
! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f448,f443]) ).
fof(f448,plain,
! [X0] : plus(n4,X0) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f323,f314,f314,f314,f314]) ).
fof(f323,plain,
! [X0] : succ(succ(succ(succ(X0)))) = plus(n4,X0),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] : succ(succ(succ(succ(X0)))) = plus(n4,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_l) ).
fof(f1965,plain,
( spl41_178
| ~ spl41_167
| ~ spl41_169
| ~ spl41_177 ),
inference(avatar_split_clause,[],[f1961,f1958,f1558,f1550,f1963]) ).
fof(f1963,plain,
( spl41_178
<=> ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_178])]) ).
fof(f1958,plain,
( spl41_177
<=> ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_177])]) ).
fof(f1961,plain,
( ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1)
| ~ spl41_167
| ~ spl41_169
| ~ spl41_177 ),
inference(forward_demodulation,[],[f1959,f1770]) ).
fof(f1959,plain,
( ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_177 ),
inference(avatar_component_clause,[],[f1958]) ).
fof(f1960,plain,
spl41_177,
inference(avatar_split_clause,[],[f474,f1958]) ).
fof(f474,plain,
! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f447,f443]) ).
fof(f447,plain,
! [X0] : plus(X0,n4) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f322,f314,f314,f314,f314]) ).
fof(f322,plain,
! [X0] : plus(X0,n4) = succ(succ(succ(succ(X0)))),
inference(cnf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] : plus(X0,n4) = succ(succ(succ(succ(X0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_4_r) ).
fof(f1894,plain,
spl41_176,
inference(avatar_split_clause,[],[f458,f1892]) ).
fof(f1892,plain,
( spl41_176
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_176])]) ).
fof(f458,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ),
inference(definition_unfolding,[],[f362,f314,f314]) ).
fof(f362,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0,X1] :
( ( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) )
& ( leq(X0,X1)
| ~ leq(succ(X0),succ(X1)) ) ),
inference(nnf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
( leq(succ(X0),succ(X1))
<=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_succ) ).
fof(f1890,plain,
spl41_175,
inference(avatar_split_clause,[],[f457,f1888]) ).
fof(f1888,plain,
( spl41_175
<=> ! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_175])]) ).
fof(f457,plain,
! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f363,f314,f314]) ).
fof(f363,plain,
! [X0,X1] :
( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
fof(f1886,plain,
spl41_174,
inference(avatar_split_clause,[],[f395,f1884]) ).
fof(f1884,plain,
( spl41_174
<=> ! [X2,X0,X1,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_174])]) ).
fof(f395,plain,
! [X2,X3,X0,X1] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0,X1,X2,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3,
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X0,X6,X23,X16] : a_select3(tptp_update3(X0,X6,X23,X16),X6,X23) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel3_update_1) ).
fof(f1851,plain,
( spl41_172
| spl41_173
| ~ spl41_3
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1612,f1538,f491,f1848,f1844]) ).
fof(f1844,plain,
( spl41_172
<=> gt(n4,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_172])]) ).
fof(f1848,plain,
( spl41_173
<=> n4 = pv40 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_173])]) ).
fof(f1612,plain,
( n4 = pv40
| gt(n4,pv40)
| ~ spl41_3
| ~ spl41_164 ),
inference(resolution,[],[f1539,f493]) ).
fof(f1568,plain,
( spl41_171
| ~ spl41_62
| ~ spl41_162 ),
inference(avatar_split_clause,[],[f1532,f1527,f805,f1566]) ).
fof(f1566,plain,
( spl41_171
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_171])]) ).
fof(f1527,plain,
( spl41_162
<=> ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_162])]) ).
fof(f1532,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 )
| ~ spl41_62
| ~ spl41_162 ),
inference(forward_demodulation,[],[f1531,f807]) ).
fof(f1531,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_162 ),
inference(forward_demodulation,[],[f1530,f807]) ).
fof(f1530,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_162 ),
inference(forward_demodulation,[],[f1528,f807]) ).
fof(f1528,plain,
( ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_162 ),
inference(avatar_component_clause,[],[f1527]) ).
fof(f1564,plain,
spl41_170,
inference(avatar_split_clause,[],[f473,f1562]) ).
fof(f1562,plain,
( spl41_170
<=> ! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_170])]) ).
fof(f473,plain,
! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f446,f443]) ).
fof(f446,plain,
! [X0] : plus(n3,X0) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f321,f314,f314,f314]) ).
fof(f321,plain,
! [X0] : succ(succ(succ(X0))) = plus(n3,X0),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] : succ(succ(succ(X0))) = plus(n3,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_l) ).
fof(f1560,plain,
spl41_169,
inference(avatar_split_clause,[],[f472,f1558]) ).
fof(f472,plain,
! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f445,f443]) ).
fof(f445,plain,
! [X0] : plus(X0,n3) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f320,f314,f314,f314]) ).
fof(f320,plain,
! [X0] : plus(X0,n3) = succ(succ(succ(X0))),
inference(cnf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] : plus(X0,n3) = succ(succ(succ(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_3_r) ).
fof(f1556,plain,
spl41_168,
inference(avatar_split_clause,[],[f444,f1554]) ).
fof(f1554,plain,
( spl41_168
<=> ! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_168])]) ).
fof(f444,plain,
! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f319,f314,f314]) ).
fof(f319,plain,
! [X0] : plus(X0,n2) = succ(succ(X0)),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : plus(X0,n2) = succ(succ(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_2_r) ).
fof(f1552,plain,
spl41_167,
inference(avatar_split_clause,[],[f443,f1550]) ).
fof(f1548,plain,
spl41_166,
inference(avatar_split_clause,[],[f366,f1546]) ).
fof(f366,plain,
! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(flattening,[],[f146]) ).
fof(f146,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_leq) ).
fof(f1544,plain,
spl41_165,
inference(avatar_split_clause,[],[f365,f1542]) ).
fof(f365,plain,
! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(flattening,[],[f144]) ).
fof(f144,plain,
! [X0,X1,X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_gt) ).
fof(f1540,plain,
spl41_164,
inference(avatar_split_clause,[],[f339,f1538]) ).
fof(f339,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(flattening,[],[f136]) ).
fof(f136,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt2) ).
fof(f1536,plain,
spl41_163,
inference(avatar_split_clause,[],[f332,f1534]) ).
fof(f1534,plain,
( spl41_163
<=> ! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_163])]) ).
fof(f332,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f1529,plain,
spl41_162,
inference(avatar_split_clause,[],[f331,f1527]) ).
fof(f331,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ( leq(X0,n0)
& leq(n0,X0) )
=> n0 = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f1525,plain,
( ~ spl41_7
| spl41_161
| ~ spl41_6
| ~ spl41_48 ),
inference(avatar_split_clause,[],[f724,f719,f506,f1522,f511]) ).
fof(f1522,plain,
( spl41_161
<=> init = a_select2(muold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_161])]) ).
fof(f719,plain,
( spl41_48
<=> ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_48])]) ).
fof(f724,plain,
( init = a_select2(muold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_6
| ~ spl41_48 ),
inference(resolution,[],[f720,f508]) ).
fof(f720,plain,
( ! [X3] :
( ~ leq(n0,X3)
| init = a_select2(muold_init,X3)
| ~ leq(X3,n4) )
| ~ spl41_48 ),
inference(avatar_component_clause,[],[f719]) ).
fof(f1520,plain,
( ~ spl41_3
| spl41_160
| ~ spl41_1
| ~ spl41_48 ),
inference(avatar_split_clause,[],[f722,f719,f481,f1517,f491]) ).
fof(f1517,plain,
( spl41_160
<=> init = a_select2(muold_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_160])]) ).
fof(f722,plain,
( init = a_select2(muold_init,pv40)
| ~ leq(pv40,n4)
| ~ spl41_1
| ~ spl41_48 ),
inference(resolution,[],[f720,f483]) ).
fof(f1396,plain,
( spl41_159
| ~ spl41_62
| ~ spl41_123 ),
inference(avatar_split_clause,[],[f1157,f1154,f805,f1394]) ).
fof(f1394,plain,
( spl41_159
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_159])]) ).
fof(f1154,plain,
( spl41_123
<=> ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_123])]) ).
fof(f1157,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_62
| ~ spl41_123 ),
inference(forward_demodulation,[],[f1155,f807]) ).
fof(f1155,plain,
( ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_123 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1388,plain,
( spl41_158
| ~ spl41_62
| ~ spl41_121 ),
inference(avatar_split_clause,[],[f1148,f1145,f805,f1386]) ).
fof(f1386,plain,
( spl41_158
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_158])]) ).
fof(f1145,plain,
( spl41_121
<=> ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_121])]) ).
fof(f1148,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_62
| ~ spl41_121 ),
inference(forward_demodulation,[],[f1146,f807]) ).
fof(f1146,plain,
( ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_121 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f1380,plain,
( spl41_157
| ~ spl41_62
| ~ spl41_119 ),
inference(avatar_split_clause,[],[f1139,f1136,f805,f1378]) ).
fof(f1378,plain,
( spl41_157
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_157])]) ).
fof(f1136,plain,
( spl41_119
<=> ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_119])]) ).
fof(f1139,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_62
| ~ spl41_119 ),
inference(forward_demodulation,[],[f1137,f807]) ).
fof(f1137,plain,
( ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_119 ),
inference(avatar_component_clause,[],[f1136]) ).
fof(f1372,plain,
( spl41_156
| ~ spl41_62
| ~ spl41_117 ),
inference(avatar_split_clause,[],[f1130,f1127,f805,f1370]) ).
fof(f1370,plain,
( spl41_156
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_156])]) ).
fof(f1127,plain,
( spl41_117
<=> ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_117])]) ).
fof(f1130,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_62
| ~ spl41_117 ),
inference(forward_demodulation,[],[f1128,f807]) ).
fof(f1128,plain,
( ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_117 ),
inference(avatar_component_clause,[],[f1127]) ).
fof(f1364,plain,
( ~ spl41_155
| spl41_52
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f1319,f805,f747,f1361]) ).
fof(f747,plain,
( spl41_52
<=> init = a_select2(rho_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_52])]) ).
fof(f1319,plain,
( init != a_select2(rho_init,tptp_float_0_0)
| spl41_52
| ~ spl41_62 ),
inference(superposition,[],[f748,f807]) ).
fof(f748,plain,
( init != a_select2(rho_init,n0)
| spl41_52 ),
inference(avatar_component_clause,[],[f747]) ).
fof(f1359,plain,
( spl41_154
| ~ spl41_62
| ~ spl41_115 ),
inference(avatar_split_clause,[],[f1121,f1118,f805,f1357]) ).
fof(f1357,plain,
( spl41_154
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_154])]) ).
fof(f1118,plain,
( spl41_115
<=> ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_115])]) ).
fof(f1121,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_62
| ~ spl41_115 ),
inference(forward_demodulation,[],[f1119,f807]) ).
fof(f1119,plain,
( ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_115 ),
inference(avatar_component_clause,[],[f1118]) ).
fof(f1351,plain,
( spl41_153
| ~ spl41_62
| ~ spl41_113 ),
inference(avatar_split_clause,[],[f1112,f1109,f805,f1349]) ).
fof(f1349,plain,
( spl41_153
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_153])]) ).
fof(f1109,plain,
( spl41_113
<=> ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_113])]) ).
fof(f1112,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_62
| ~ spl41_113 ),
inference(forward_demodulation,[],[f1110,f807]) ).
fof(f1110,plain,
( ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_113 ),
inference(avatar_component_clause,[],[f1109]) ).
fof(f1343,plain,
( spl41_152
| ~ spl41_62
| ~ spl41_111 ),
inference(avatar_split_clause,[],[f1103,f1100,f805,f1341]) ).
fof(f1341,plain,
( spl41_152
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_152])]) ).
fof(f1100,plain,
( spl41_111
<=> ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_111])]) ).
fof(f1103,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_62
| ~ spl41_111 ),
inference(forward_demodulation,[],[f1101,f807]) ).
fof(f1101,plain,
( ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_111 ),
inference(avatar_component_clause,[],[f1100]) ).
fof(f1335,plain,
( spl41_151
| ~ spl41_62
| ~ spl41_109 ),
inference(avatar_split_clause,[],[f1094,f1091,f805,f1333]) ).
fof(f1333,plain,
( spl41_151
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_151])]) ).
fof(f1091,plain,
( spl41_109
<=> ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_109])]) ).
fof(f1094,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_62
| ~ spl41_109 ),
inference(forward_demodulation,[],[f1092,f807]) ).
fof(f1092,plain,
( ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_109 ),
inference(avatar_component_clause,[],[f1091]) ).
fof(f1327,plain,
( spl41_150
| ~ spl41_62
| ~ spl41_107 ),
inference(avatar_split_clause,[],[f1085,f1082,f805,f1325]) ).
fof(f1325,plain,
( spl41_150
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_150])]) ).
fof(f1082,plain,
( spl41_107
<=> ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_107])]) ).
fof(f1085,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_62
| ~ spl41_107 ),
inference(forward_demodulation,[],[f1083,f807]) ).
fof(f1083,plain,
( ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_107 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f1318,plain,
( spl41_149
| ~ spl41_62
| ~ spl41_105 ),
inference(avatar_split_clause,[],[f1076,f1073,f805,f1316]) ).
fof(f1316,plain,
( spl41_149
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_149])]) ).
fof(f1073,plain,
( spl41_105
<=> ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_105])]) ).
fof(f1076,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_62
| ~ spl41_105 ),
inference(forward_demodulation,[],[f1074,f807]) ).
fof(f1074,plain,
( ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_105 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f1310,plain,
( spl41_148
| ~ spl41_62
| ~ spl41_102 ),
inference(avatar_split_clause,[],[f1062,f1059,f805,f1308]) ).
fof(f1308,plain,
( spl41_148
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_148])]) ).
fof(f1059,plain,
( spl41_102
<=> ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_102])]) ).
fof(f1062,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_62
| ~ spl41_102 ),
inference(forward_demodulation,[],[f1060,f807]) ).
fof(f1060,plain,
( ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_102 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1302,plain,
( spl41_147
| ~ spl41_62
| ~ spl41_100 ),
inference(avatar_split_clause,[],[f1053,f1050,f805,f1300]) ).
fof(f1300,plain,
( spl41_147
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_147])]) ).
fof(f1050,plain,
( spl41_100
<=> ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_100])]) ).
fof(f1053,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_62
| ~ spl41_100 ),
inference(forward_demodulation,[],[f1051,f807]) ).
fof(f1051,plain,
( ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_100 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f1294,plain,
( spl41_146
| ~ spl41_62
| ~ spl41_98 ),
inference(avatar_split_clause,[],[f1044,f1041,f805,f1292]) ).
fof(f1292,plain,
( spl41_146
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_146])]) ).
fof(f1041,plain,
( spl41_98
<=> ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_98])]) ).
fof(f1044,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_62
| ~ spl41_98 ),
inference(forward_demodulation,[],[f1042,f807]) ).
fof(f1042,plain,
( ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_98 ),
inference(avatar_component_clause,[],[f1041]) ).
fof(f1286,plain,
( spl41_145
| ~ spl41_62
| ~ spl41_96 ),
inference(avatar_split_clause,[],[f1035,f1032,f805,f1284]) ).
fof(f1284,plain,
( spl41_145
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_145])]) ).
fof(f1032,plain,
( spl41_96
<=> ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_96])]) ).
fof(f1035,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_62
| ~ spl41_96 ),
inference(forward_demodulation,[],[f1033,f807]) ).
fof(f1033,plain,
( ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_96 ),
inference(avatar_component_clause,[],[f1032]) ).
fof(f1278,plain,
( spl41_144
| ~ spl41_62
| ~ spl41_94 ),
inference(avatar_split_clause,[],[f1026,f1023,f805,f1276]) ).
fof(f1276,plain,
( spl41_144
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_144])]) ).
fof(f1023,plain,
( spl41_94
<=> ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_94])]) ).
fof(f1026,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_62
| ~ spl41_94 ),
inference(forward_demodulation,[],[f1024,f807]) ).
fof(f1024,plain,
( ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_94 ),
inference(avatar_component_clause,[],[f1023]) ).
fof(f1270,plain,
( spl41_143
| ~ spl41_62
| ~ spl41_92 ),
inference(avatar_split_clause,[],[f1017,f1014,f805,f1268]) ).
fof(f1268,plain,
( spl41_143
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_143])]) ).
fof(f1014,plain,
( spl41_92
<=> ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_92])]) ).
fof(f1017,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_62
| ~ spl41_92 ),
inference(forward_demodulation,[],[f1015,f807]) ).
fof(f1015,plain,
( ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_92 ),
inference(avatar_component_clause,[],[f1014]) ).
fof(f1262,plain,
( spl41_142
| ~ spl41_62
| ~ spl41_90 ),
inference(avatar_split_clause,[],[f1008,f1005,f805,f1260]) ).
fof(f1260,plain,
( spl41_142
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_142])]) ).
fof(f1005,plain,
( spl41_90
<=> ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_90])]) ).
fof(f1008,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_62
| ~ spl41_90 ),
inference(forward_demodulation,[],[f1006,f807]) ).
fof(f1006,plain,
( ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_90 ),
inference(avatar_component_clause,[],[f1005]) ).
fof(f1254,plain,
( spl41_141
| ~ spl41_62
| ~ spl41_88 ),
inference(avatar_split_clause,[],[f999,f996,f805,f1252]) ).
fof(f1252,plain,
( spl41_141
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_141])]) ).
fof(f996,plain,
( spl41_88
<=> ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_88])]) ).
fof(f999,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_62
| ~ spl41_88 ),
inference(forward_demodulation,[],[f997,f807]) ).
fof(f997,plain,
( ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_88 ),
inference(avatar_component_clause,[],[f996]) ).
fof(f1246,plain,
( spl41_140
| ~ spl41_62
| ~ spl41_85 ),
inference(avatar_split_clause,[],[f986,f983,f805,f1244]) ).
fof(f1244,plain,
( spl41_140
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_140])]) ).
fof(f983,plain,
( spl41_85
<=> ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_85])]) ).
fof(f986,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_62
| ~ spl41_85 ),
inference(forward_demodulation,[],[f984,f807]) ).
fof(f984,plain,
( ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_85 ),
inference(avatar_component_clause,[],[f983]) ).
fof(f1242,plain,
( ~ spl41_139
| spl41_53
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f825,f805,f751,f1239]) ).
fof(f1239,plain,
( spl41_139
<=> leq(tptp_float_0_0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_139])]) ).
fof(f751,plain,
( spl41_53
<=> leq(n0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_53])]) ).
fof(f825,plain,
( ~ leq(tptp_float_0_0,n4)
| spl41_53
| ~ spl41_62 ),
inference(superposition,[],[f753,f807]) ).
fof(f753,plain,
( ~ leq(n0,n4)
| spl41_53 ),
inference(avatar_component_clause,[],[f751]) ).
fof(f1233,plain,
( spl41_138
| ~ spl41_62
| ~ spl41_83 ),
inference(avatar_split_clause,[],[f977,f974,f805,f1231]) ).
fof(f1231,plain,
( spl41_138
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_138])]) ).
fof(f974,plain,
( spl41_83
<=> ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_83])]) ).
fof(f977,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_62
| ~ spl41_83 ),
inference(forward_demodulation,[],[f975,f807]) ).
fof(f975,plain,
( ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_83 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f1225,plain,
( spl41_137
| ~ spl41_62
| ~ spl41_80 ),
inference(avatar_split_clause,[],[f963,f960,f805,f1223]) ).
fof(f1223,plain,
( spl41_137
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_137])]) ).
fof(f960,plain,
( spl41_80
<=> ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_80])]) ).
fof(f963,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_62
| ~ spl41_80 ),
inference(forward_demodulation,[],[f961,f807]) ).
fof(f961,plain,
( ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_80 ),
inference(avatar_component_clause,[],[f960]) ).
fof(f1217,plain,
( spl41_136
| ~ spl41_62
| ~ spl41_78 ),
inference(avatar_split_clause,[],[f954,f951,f805,f1215]) ).
fof(f1215,plain,
( spl41_136
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_136])]) ).
fof(f951,plain,
( spl41_78
<=> ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_78])]) ).
fof(f954,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_62
| ~ spl41_78 ),
inference(forward_demodulation,[],[f952,f807]) ).
fof(f952,plain,
( ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_78 ),
inference(avatar_component_clause,[],[f951]) ).
fof(f1209,plain,
( spl41_135
| ~ spl41_62
| ~ spl41_76 ),
inference(avatar_split_clause,[],[f945,f942,f805,f1207]) ).
fof(f1207,plain,
( spl41_135
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_135])]) ).
fof(f942,plain,
( spl41_76
<=> ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_76])]) ).
fof(f945,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_62
| ~ spl41_76 ),
inference(forward_demodulation,[],[f943,f807]) ).
fof(f943,plain,
( ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_76 ),
inference(avatar_component_clause,[],[f942]) ).
fof(f1201,plain,
( spl41_134
| ~ spl41_62
| ~ spl41_74 ),
inference(avatar_split_clause,[],[f936,f933,f805,f1199]) ).
fof(f1199,plain,
( spl41_134
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_134])]) ).
fof(f933,plain,
( spl41_74
<=> ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_74])]) ).
fof(f936,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_62
| ~ spl41_74 ),
inference(forward_demodulation,[],[f934,f807]) ).
fof(f934,plain,
( ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_74 ),
inference(avatar_component_clause,[],[f933]) ).
fof(f1197,plain,
( spl41_133
| ~ spl41_62
| ~ spl41_73 ),
inference(avatar_split_clause,[],[f931,f928,f805,f1195]) ).
fof(f1195,plain,
( spl41_133
<=> ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_133])]) ).
fof(f928,plain,
( spl41_73
<=> ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_73])]) ).
fof(f931,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_62
| ~ spl41_73 ),
inference(forward_demodulation,[],[f929,f807]) ).
fof(f929,plain,
( ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_73 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f1193,plain,
( spl41_132
| ~ spl41_62
| ~ spl41_72 ),
inference(avatar_split_clause,[],[f926,f923,f805,f1191]) ).
fof(f1191,plain,
( spl41_132
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_132])]) ).
fof(f923,plain,
( spl41_72
<=> ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_72])]) ).
fof(f926,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) )
| ~ spl41_62
| ~ spl41_72 ),
inference(forward_demodulation,[],[f924,f807]) ).
fof(f924,plain,
( ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) )
| ~ spl41_72 ),
inference(avatar_component_clause,[],[f923]) ).
fof(f1189,plain,
( spl41_131
| ~ spl41_62
| ~ spl41_70 ),
inference(avatar_split_clause,[],[f916,f912,f805,f1187]) ).
fof(f1187,plain,
( spl41_131
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_131])]) ).
fof(f912,plain,
( spl41_70
<=> ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_70])]) ).
fof(f916,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) )
| ~ spl41_62
| ~ spl41_70 ),
inference(forward_demodulation,[],[f915,f807]) ).
fof(f915,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_62
| ~ spl41_70 ),
inference(forward_demodulation,[],[f913,f807]) ).
fof(f913,plain,
( ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_70 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f1185,plain,
spl41_130,
inference(avatar_split_clause,[],[f456,f1183]) ).
fof(f1183,plain,
( spl41_130
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_130])]) ).
fof(f456,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f360,f316]) ).
fof(f316,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f360,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f1181,plain,
spl41_129,
inference(avatar_split_clause,[],[f455,f1179]) ).
fof(f1179,plain,
( spl41_129
<=> ! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_129])]) ).
fof(f455,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f361,f316]) ).
fof(f361,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1177,plain,
spl41_128,
inference(avatar_split_clause,[],[f454,f1175]) ).
fof(f1175,plain,
( spl41_128
<=> ! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_128])]) ).
fof(f454,plain,
! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f358,f314]) ).
fof(f358,plain,
! [X0,X1] :
( gt(succ(X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
fof(f207,plain,
! [X0,X1] :
( ( leq(X0,X1)
| ~ gt(succ(X1),X0) )
& ( gt(succ(X1),X0)
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt_equiv) ).
fof(f1173,plain,
spl41_127,
inference(avatar_split_clause,[],[f453,f1171]) ).
fof(f1171,plain,
( spl41_127
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_127])]) ).
fof(f453,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ),
inference(definition_unfolding,[],[f359,f314]) ).
fof(f359,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(succ(X1),X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f1169,plain,
spl41_126,
inference(avatar_split_clause,[],[f452,f1167]) ).
fof(f1167,plain,
( spl41_126
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_126])]) ).
fof(f452,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ),
inference(definition_unfolding,[],[f337,f314]) ).
fof(f337,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(succ(X0),X1) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
( leq(succ(X0),X1)
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ_gt) ).
fof(f1165,plain,
spl41_125,
inference(avatar_split_clause,[],[f451,f1163]) ).
fof(f1163,plain,
( spl41_125
<=> ! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_125])]) ).
fof(f451,plain,
! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f333,f314]) ).
fof(f333,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0,X1] :
( leq(X0,succ(X1))
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
=> leq(X0,succ(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_succ) ).
fof(f1161,plain,
spl41_124,
inference(avatar_split_clause,[],[f428,f1159]) ).
fof(f1159,plain,
( spl41_124
<=> ! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_124])]) ).
fof(f428,plain,
! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1156,plain,
spl41_123,
inference(avatar_split_clause,[],[f427,f1154]) ).
fof(f427,plain,
! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1152,plain,
spl41_122,
inference(avatar_split_clause,[],[f426,f1150]) ).
fof(f1150,plain,
( spl41_122
<=> ! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_122])]) ).
fof(f426,plain,
! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1147,plain,
spl41_121,
inference(avatar_split_clause,[],[f425,f1145]) ).
fof(f425,plain,
! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1143,plain,
spl41_120,
inference(avatar_split_clause,[],[f423,f1141]) ).
fof(f1141,plain,
( spl41_120
<=> ! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_120])]) ).
fof(f423,plain,
! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1138,plain,
spl41_119,
inference(avatar_split_clause,[],[f422,f1136]) ).
fof(f422,plain,
! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1134,plain,
spl41_118,
inference(avatar_split_clause,[],[f421,f1132]) ).
fof(f1132,plain,
( spl41_118
<=> ! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_118])]) ).
fof(f421,plain,
! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1129,plain,
spl41_117,
inference(avatar_split_clause,[],[f420,f1127]) ).
fof(f420,plain,
! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1125,plain,
spl41_116,
inference(avatar_split_clause,[],[f418,f1123]) ).
fof(f1123,plain,
( spl41_116
<=> ! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_116])]) ).
fof(f418,plain,
! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1120,plain,
spl41_115,
inference(avatar_split_clause,[],[f417,f1118]) ).
fof(f417,plain,
! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1116,plain,
spl41_114,
inference(avatar_split_clause,[],[f416,f1114]) ).
fof(f1114,plain,
( spl41_114
<=> ! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_114])]) ).
fof(f416,plain,
! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1111,plain,
spl41_113,
inference(avatar_split_clause,[],[f415,f1109]) ).
fof(f415,plain,
! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1107,plain,
spl41_112,
inference(avatar_split_clause,[],[f403,f1105]) ).
fof(f1105,plain,
( spl41_112
<=> ! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_112])]) ).
fof(f403,plain,
! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1102,plain,
spl41_111,
inference(avatar_split_clause,[],[f402,f1100]) ).
fof(f402,plain,
! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1098,plain,
spl41_110,
inference(avatar_split_clause,[],[f401,f1096]) ).
fof(f1096,plain,
( spl41_110
<=> ! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_110])]) ).
fof(f401,plain,
! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1093,plain,
spl41_109,
inference(avatar_split_clause,[],[f400,f1091]) ).
fof(f400,plain,
! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1089,plain,
spl41_108,
inference(avatar_split_clause,[],[f392,f1087]) ).
fof(f1087,plain,
( spl41_108
<=> ! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_108])]) ).
fof(f392,plain,
! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1084,plain,
spl41_107,
inference(avatar_split_clause,[],[f391,f1082]) ).
fof(f391,plain,
! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1080,plain,
spl41_106,
inference(avatar_split_clause,[],[f390,f1078]) ).
fof(f1078,plain,
( spl41_106
<=> ! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_106])]) ).
fof(f390,plain,
! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1075,plain,
spl41_105,
inference(avatar_split_clause,[],[f389,f1073]) ).
fof(f389,plain,
! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1071,plain,
spl41_104,
inference(avatar_split_clause,[],[f386,f1069]) ).
fof(f1069,plain,
( spl41_104
<=> ! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_104])]) ).
fof(f386,plain,
! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1067,plain,
( spl41_103
| ~ spl41_5
| ~ spl41_64 ),
inference(avatar_split_clause,[],[f874,f833,f501,f1064]) ).
fof(f1064,plain,
( spl41_103
<=> leq(n1,loopcounter) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_103])]) ).
fof(f833,plain,
( spl41_64
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_64])]) ).
fof(f874,plain,
( leq(n1,loopcounter)
| ~ spl41_5
| ~ spl41_64 ),
inference(resolution,[],[f834,f503]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) )
| ~ spl41_64 ),
inference(avatar_component_clause,[],[f833]) ).
fof(f1061,plain,
spl41_102,
inference(avatar_split_clause,[],[f385,f1059]) ).
fof(f385,plain,
! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1057,plain,
spl41_101,
inference(avatar_split_clause,[],[f384,f1055]) ).
fof(f1055,plain,
( spl41_101
<=> ! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_101])]) ).
fof(f384,plain,
! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1052,plain,
spl41_100,
inference(avatar_split_clause,[],[f383,f1050]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1048,plain,
spl41_99,
inference(avatar_split_clause,[],[f381,f1046]) ).
fof(f1046,plain,
( spl41_99
<=> ! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_99])]) ).
fof(f381,plain,
! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1043,plain,
spl41_98,
inference(avatar_split_clause,[],[f380,f1041]) ).
fof(f380,plain,
! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1039,plain,
spl41_97,
inference(avatar_split_clause,[],[f379,f1037]) ).
fof(f1037,plain,
( spl41_97
<=> ! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_97])]) ).
fof(f379,plain,
! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1034,plain,
spl41_96,
inference(avatar_split_clause,[],[f378,f1032]) ).
fof(f378,plain,
! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1030,plain,
spl41_95,
inference(avatar_split_clause,[],[f375,f1028]) ).
fof(f1028,plain,
( spl41_95
<=> ! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_95])]) ).
fof(f375,plain,
! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1025,plain,
spl41_94,
inference(avatar_split_clause,[],[f374,f1023]) ).
fof(f374,plain,
! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1021,plain,
spl41_93,
inference(avatar_split_clause,[],[f373,f1019]) ).
fof(f1019,plain,
( spl41_93
<=> ! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_93])]) ).
fof(f373,plain,
! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1016,plain,
spl41_92,
inference(avatar_split_clause,[],[f372,f1014]) ).
fof(f372,plain,
! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1012,plain,
spl41_91,
inference(avatar_split_clause,[],[f370,f1010]) ).
fof(f1010,plain,
( spl41_91
<=> ! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_91])]) ).
fof(f370,plain,
! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1007,plain,
spl41_90,
inference(avatar_split_clause,[],[f369,f1005]) ).
fof(f369,plain,
! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f1003,plain,
spl41_89,
inference(avatar_split_clause,[],[f368,f1001]) ).
fof(f1001,plain,
( spl41_89
<=> ! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_89])]) ).
fof(f368,plain,
! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f998,plain,
spl41_88,
inference(avatar_split_clause,[],[f367,f996]) ).
fof(f367,plain,
! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f994,plain,
spl41_87,
inference(avatar_split_clause,[],[f364,f992]) ).
fof(f992,plain,
( spl41_87
<=> ! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_87])]) ).
fof(f364,plain,
! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0,X1,X2] : a_select2(tptp_update2(X0,X1,X2),X1) = X2,
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X0,X6,X16] : a_select2(tptp_update2(X0,X6,X16),X6) = X16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sel2_update_1) ).
fof(f990,plain,
spl41_86,
inference(avatar_split_clause,[],[f355,f988]) ).
fof(f988,plain,
( spl41_86
<=> ! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_86])]) ).
fof(f355,plain,
! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f985,plain,
spl41_85,
inference(avatar_split_clause,[],[f354,f983]) ).
fof(f354,plain,
! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f981,plain,
spl41_84,
inference(avatar_split_clause,[],[f353,f979]) ).
fof(f979,plain,
( spl41_84
<=> ! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_84])]) ).
fof(f353,plain,
! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f976,plain,
spl41_83,
inference(avatar_split_clause,[],[f352,f974]) ).
fof(f352,plain,
! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f972,plain,
( spl41_82
| ~ spl41_6
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f811,f805,f506,f969]) ).
fof(f969,plain,
( spl41_82
<=> leq(tptp_float_0_0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_82])]) ).
fof(f811,plain,
( leq(tptp_float_0_0,sK13)
| ~ spl41_6
| ~ spl41_62 ),
inference(superposition,[],[f508,f807]) ).
fof(f967,plain,
spl41_81,
inference(avatar_split_clause,[],[f349,f965]) ).
fof(f965,plain,
( spl41_81
<=> ! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_81])]) ).
fof(f349,plain,
! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f962,plain,
spl41_80,
inference(avatar_split_clause,[],[f348,f960]) ).
fof(f348,plain,
! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f958,plain,
spl41_79,
inference(avatar_split_clause,[],[f347,f956]) ).
fof(f956,plain,
( spl41_79
<=> ! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_79])]) ).
fof(f347,plain,
! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f953,plain,
spl41_78,
inference(avatar_split_clause,[],[f346,f951]) ).
fof(f346,plain,
! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f949,plain,
spl41_77,
inference(avatar_split_clause,[],[f343,f947]) ).
fof(f947,plain,
( spl41_77
<=> ! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_77])]) ).
fof(f343,plain,
! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f944,plain,
spl41_76,
inference(avatar_split_clause,[],[f342,f942]) ).
fof(f342,plain,
! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f940,plain,
spl41_75,
inference(avatar_split_clause,[],[f341,f938]) ).
fof(f938,plain,
( spl41_75
<=> ! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_75])]) ).
fof(f341,plain,
! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f935,plain,
spl41_74,
inference(avatar_split_clause,[],[f340,f933]) ).
fof(f340,plain,
! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f930,plain,
spl41_73,
inference(avatar_split_clause,[],[f338,f928]) ).
fof(f338,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0,X1] :
( leq(minus(X0,X1),X0)
=> leq(n0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_minus) ).
fof(f925,plain,
spl41_72,
inference(avatar_split_clause,[],[f335,f923]) ).
fof(f335,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X1,X0),X0) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(uniform_int_rnd(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_hi) ).
fof(f921,plain,
( spl41_71
| ~ spl41_2
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f810,f805,f486,f918]) ).
fof(f918,plain,
( spl41_71
<=> leq(tptp_float_0_0,pv45) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_71])]) ).
fof(f810,plain,
( leq(tptp_float_0_0,pv45)
| ~ spl41_2
| ~ spl41_62 ),
inference(superposition,[],[f488,f807]) ).
fof(f914,plain,
spl41_70,
inference(avatar_split_clause,[],[f334,f912]) ).
fof(f334,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X1,X0)) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X0,X3] :
( leq(n0,X0)
=> leq(n0,uniform_int_rnd(X3,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniform_int_rand_ranges_lo) ).
fof(f893,plain,
spl41_69,
inference(avatar_split_clause,[],[f442,f891]) ).
fof(f891,plain,
( spl41_69
<=> ! [X0] : plus(X0,n1) = plus(n1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_69])]) ).
fof(f442,plain,
! [X0] : plus(X0,n1) = plus(n1,X0),
inference(definition_unfolding,[],[f315,f314]) ).
fof(f315,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] : succ(X0) = plus(n1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_plus_1_l) ).
fof(f889,plain,
spl41_68,
inference(avatar_split_clause,[],[f441,f887]) ).
fof(f887,plain,
( spl41_68
<=> ! [X0] : plus(minus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_68])]) ).
fof(f441,plain,
! [X0] : plus(minus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f312,f314,f316]) ).
fof(f312,plain,
! [X0] : succ(pred(X0)) = X0,
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : succ(pred(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_pred) ).
fof(f885,plain,
spl41_67,
inference(avatar_split_clause,[],[f440,f883]) ).
fof(f883,plain,
( spl41_67
<=> ! [X0] : minus(plus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_67])]) ).
fof(f440,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f311,f316,f314]) ).
fof(f311,plain,
! [X0] : pred(succ(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : pred(succ(X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pred_succ) ).
fof(f844,plain,
( spl41_66
| ~ spl41_62
| ~ spl41_63 ),
inference(avatar_split_clause,[],[f831,f828,f805,f842]) ).
fof(f842,plain,
( spl41_66
<=> ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_66])]) ).
fof(f828,plain,
( spl41_63
<=> ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_63])]) ).
fof(f831,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl41_62
| ~ spl41_63 ),
inference(forward_demodulation,[],[f829,f807]) ).
fof(f829,plain,
( ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_63 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f840,plain,
( spl41_65
| ~ spl41_1
| ~ spl41_62 ),
inference(avatar_split_clause,[],[f809,f805,f481,f837]) ).
fof(f837,plain,
( spl41_65
<=> leq(tptp_float_0_0,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_65])]) ).
fof(f809,plain,
( leq(tptp_float_0_0,pv40)
| ~ spl41_1
| ~ spl41_62 ),
inference(superposition,[],[f483,f807]) ).
fof(f835,plain,
spl41_64,
inference(avatar_split_clause,[],[f336,f833]) ).
fof(f336,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',leq_gt1) ).
fof(f830,plain,
spl41_63,
inference(avatar_split_clause,[],[f317,f828]) ).
fof(f317,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X22] : sum(n0,tptp_minus_1,X22) = tptp_float_0_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base_float) ).
fof(f808,plain,
( spl41_62
| ~ spl41_61 ),
inference(avatar_split_clause,[],[f803,f800,f805]) ).
fof(f800,plain,
( spl41_61
<=> ! [X0] : n0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_61])]) ).
fof(f803,plain,
( n0 = tptp_float_0_0
| ~ spl41_61 ),
inference(forward_demodulation,[],[f801,f317]) ).
fof(f801,plain,
( ! [X0] : n0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_61 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f802,plain,
spl41_61,
inference(avatar_split_clause,[],[f313,f800]) ).
fof(f313,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0] : n0 = sum(n0,tptp_minus_1,X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X22] : n0 = sum(n0,tptp_minus_1,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_plus_base) ).
fof(f792,plain,
spl41_60,
inference(avatar_split_clause,[],[f471,f789]) ).
fof(f789,plain,
( spl41_60
<=> n5 = plus(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_60])]) ).
fof(f471,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[],[f470,f467]) ).
fof(f467,plain,
n4 = plus(n3,n1),
inference(forward_demodulation,[],[f466,f464]) ).
fof(f464,plain,
n3 = plus(n2,n1),
inference(forward_demodulation,[],[f463,f462]) ).
fof(f462,plain,
n2 = plus(n1,n1),
inference(forward_demodulation,[],[f435,f433]) ).
fof(f433,plain,
n1 = plus(n0,n1),
inference(definition_unfolding,[],[f302,f314]) ).
fof(f302,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f91,axiom,
n1 = succ(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(f435,plain,
n2 = plus(plus(n0,n1),n1),
inference(definition_unfolding,[],[f304,f314,f314]) ).
fof(f304,plain,
n2 = succ(succ(n0)),
inference(cnf_transformation,[],[f92]) ).
fof(f92,axiom,
n2 = succ(succ(n0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_2) ).
fof(f463,plain,
n3 = plus(plus(n1,n1),n1),
inference(forward_demodulation,[],[f436,f433]) ).
fof(f436,plain,
n3 = plus(plus(plus(n0,n1),n1),n1),
inference(definition_unfolding,[],[f305,f314,f314,f314]) ).
fof(f305,plain,
n3 = succ(succ(succ(n0))),
inference(cnf_transformation,[],[f93]) ).
fof(f93,axiom,
n3 = succ(succ(succ(n0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_3) ).
fof(f466,plain,
n4 = plus(plus(n2,n1),n1),
inference(forward_demodulation,[],[f465,f462]) ).
fof(f465,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f437,f433]) ).
fof(f437,plain,
n4 = plus(plus(plus(plus(n0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f306,f314,f314,f314,f314]) ).
fof(f306,plain,
n4 = succ(succ(succ(succ(n0)))),
inference(cnf_transformation,[],[f89]) ).
fof(f89,axiom,
n4 = succ(succ(succ(succ(n0)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_4) ).
fof(f470,plain,
n5 = plus(plus(n3,n1),n1),
inference(forward_demodulation,[],[f469,f464]) ).
fof(f469,plain,
n5 = plus(plus(plus(n2,n1),n1),n1),
inference(forward_demodulation,[],[f468,f462]) ).
fof(f468,plain,
n5 = plus(plus(plus(plus(n1,n1),n1),n1),n1),
inference(forward_demodulation,[],[f438,f433]) ).
fof(f438,plain,
n5 = plus(plus(plus(plus(plus(n0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f307,f314,f314,f314,f314,f314]) ).
fof(f307,plain,
n5 = succ(succ(succ(succ(succ(n0))))),
inference(cnf_transformation,[],[f90]) ).
fof(f90,axiom,
n5 = succ(succ(succ(succ(succ(n0))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_5) ).
fof(f787,plain,
spl41_59,
inference(avatar_split_clause,[],[f467,f784]) ).
fof(f784,plain,
( spl41_59
<=> n4 = plus(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_59])]) ).
fof(f782,plain,
spl41_58,
inference(avatar_split_clause,[],[f464,f779]) ).
fof(f779,plain,
( spl41_58
<=> n3 = plus(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_58])]) ).
fof(f777,plain,
spl41_57,
inference(avatar_split_clause,[],[f462,f774]) ).
fof(f774,plain,
( spl41_57
<=> n2 = plus(n1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_57])]) ).
fof(f772,plain,
spl41_56,
inference(avatar_split_clause,[],[f439,f770]) ).
fof(f439,plain,
! [X0] : gt(plus(X0,n1),X0),
inference(definition_unfolding,[],[f310,f314]) ).
fof(f310,plain,
! [X0] : gt(succ(X0),X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : gt(succ(X0),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_succ) ).
fof(f768,plain,
spl41_55,
inference(avatar_split_clause,[],[f434,f765]) ).
fof(f765,plain,
( spl41_55
<=> n0 = plus(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_55])]) ).
fof(f434,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f303,f314]) ).
fof(f303,plain,
n0 = succ(tptp_minus_1),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
n0 = succ(tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',succ_tptp_minus_1) ).
fof(f763,plain,
spl41_54,
inference(avatar_split_clause,[],[f433,f760]) ).
fof(f760,plain,
( spl41_54
<=> n1 = plus(n0,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_54])]) ).
fof(f754,plain,
( spl41_52
| ~ spl41_53
| ~ spl41_9
| ~ spl41_44 ),
inference(avatar_split_clause,[],[f707,f698,f521,f751,f747]) ).
fof(f521,plain,
( spl41_9
<=> ! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_9])]) ).
fof(f698,plain,
( spl41_44
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_44])]) ).
fof(f707,plain,
( ~ leq(n0,n4)
| init = a_select2(rho_init,n0)
| ~ spl41_9
| ~ spl41_44 ),
inference(resolution,[],[f699,f522]) ).
fof(f522,plain,
( ! [X7] :
( ~ leq(n0,X7)
| ~ leq(X7,n4)
| init = a_select2(rho_init,X7) )
| ~ spl41_9 ),
inference(avatar_component_clause,[],[f521]) ).
fof(f699,plain,
( ! [X0] : leq(X0,X0)
| ~ spl41_44 ),
inference(avatar_component_clause,[],[f698]) ).
fof(f745,plain,
spl41_51,
inference(avatar_split_clause,[],[f262,f743]) ).
fof(f743,plain,
( spl41_51
<=> ! [X9,X8] :
( init = a_select3(q_init,X8,X9)
| ~ leq(X9,n4)
| ~ leq(n0,X9)
| ~ leq(X8,n135299)
| ~ leq(n0,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_51])]) ).
fof(f262,plain,
! [X8,X9] :
( init = a_select3(q_init,X8,X9)
| ~ leq(X9,n4)
| ~ leq(n0,X9)
| ~ leq(X8,n135299)
| ~ leq(n0,X8) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
( init != a_select2(rhoold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13)
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,pred(pv40))
| ~ leq(n0,X6) )
& ! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) )
& ! [X8] :
( ! [X9] :
( init = a_select3(q_init,X8,X9)
| ~ leq(X9,n4)
| ~ leq(n0,X9) )
| ~ leq(X8,n135299)
| ~ leq(n0,X8) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f192,f193]) ).
fof(f193,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
=> ( init != a_select2(rhoold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,pred(pv40))
| ~ leq(n0,X6) )
& ! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) )
& ! [X8] :
( ! [X9] :
( init = a_select3(q_init,X8,X9)
| ~ leq(X9,n4)
| ~ leq(n0,X9) )
| ~ leq(X8,n135299)
| ~ leq(n0,X8) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(X9,n4)
& leq(n0,X9) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(sigma_init,X4)
| ~ leq(X4,pred(pv40))
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(mu_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(rho_init,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) )
& ! [X7] :
( ! [X8] :
( init = a_select3(q_init,X7,X8)
| ~ leq(X8,n4)
| ~ leq(n0,X8) )
| ~ leq(X7,n135299)
| ~ leq(n0,X7) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(X9,n4)
& leq(n0,X9) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(sigma_init,X4)
| ~ leq(X4,pred(pv40))
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(mu_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(rho_init,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) )
& ! [X7] :
( ! [X8] :
( init = a_select3(q_init,X7,X8)
| ~ leq(X8,n4)
| ~ leq(n0,X8) )
| ~ leq(X7,n135299)
| ~ leq(n0,X7) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,plain,
~ ( ( ( gt(loopcounter,n1)
=> ! [X0] :
( ( leq(X0,n4)
& leq(n0,X0) )
=> init = a_select2(sigmaold_init,X0) ) )
& ( gt(loopcounter,n1)
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> init = a_select2(rhoold_init,X1) ) )
& ( gt(loopcounter,n1)
=> ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> init = a_select2(muold_init,X2) ) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select3(center_init,X3,n0) )
& ! [X4] :
( ( leq(X4,pred(pv40))
& leq(n0,X4) )
=> init = a_select2(sigma_init,X4) )
& ! [X5] :
( ( leq(X5,pred(pv40))
& leq(n0,X5) )
=> init = a_select2(mu_init,X5) )
& ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> init = a_select2(rho_init,X6) )
& ! [X7] :
( ( leq(X7,n135299)
& leq(n0,X7) )
=> ! [X8] :
( ( leq(X8,n4)
& leq(n0,X8) )
=> init = a_select3(q_init,X7,X8) ) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) )
=> ! [X9] :
( ( leq(X9,n4)
& leq(n0,X9) )
=> init = a_select2(rhoold_init,X9) ) ),
inference(rectify,[],[f54]) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> init = a_select2(sigmaold_init,X4) ) )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(rhoold_init,X28) ) )
& ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(muold_init,X27) ) )
& ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select3(center_init,X21,n0) )
& ! [X20] :
( ( leq(X20,pred(pv40))
& leq(n0,X20) )
=> init = a_select2(sigma_init,X20) )
& ! [X19] :
( ( leq(X19,pred(pv40))
& leq(n0,X19) )
=> init = a_select2(mu_init,X19) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select2(rho_init,X3) )
& ! [X13] :
( ( leq(X13,n135299)
& leq(n0,X13) )
=> ! [X17] :
( ( leq(X17,n4)
& leq(n0,X17) )
=> a_select3(q_init,X13,X17) = init ) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(rhoold_init,X10) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> init = a_select2(sigmaold_init,X4) ) )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(rhoold_init,X28) ) )
& ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(muold_init,X27) ) )
& ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select3(center_init,X21,n0) )
& ! [X20] :
( ( leq(X20,pred(pv40))
& leq(n0,X20) )
=> init = a_select2(sigma_init,X20) )
& ! [X19] :
( ( leq(X19,pred(pv40))
& leq(n0,X19) )
=> init = a_select2(mu_init,X19) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> init = a_select2(rho_init,X3) )
& ! [X13] :
( ( leq(X13,n135299)
& leq(n0,X13) )
=> ! [X17] :
( ( leq(X17,n4)
& leq(n0,X17) )
=> a_select3(q_init,X13,X17) = init ) )
& gt(loopcounter,n1)
& leq(pv45,n135299)
& leq(pv40,n4)
& leq(n0,pv45)
& leq(n0,pv40) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(rhoold_init,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0061) ).
fof(f737,plain,
( ~ spl41_5
| spl41_50 ),
inference(avatar_split_clause,[],[f269,f735,f501]) ).
fof(f735,plain,
( spl41_50
<=> ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(n0,X1)
| ~ leq(X1,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_50])]) ).
fof(f269,plain,
! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f729,plain,
( ~ spl41_5
| spl41_49 ),
inference(avatar_split_clause,[],[f268,f727,f501]) ).
fof(f268,plain,
! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f721,plain,
( ~ spl41_5
| spl41_48 ),
inference(avatar_split_clause,[],[f267,f719,f501]) ).
fof(f267,plain,
! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f715,plain,
spl41_47,
inference(avatar_split_clause,[],[f432,f713]) ).
fof(f713,plain,
( spl41_47
<=> ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,minus(pv40,n1))
| ~ leq(n0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_47])]) ).
fof(f432,plain,
! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,minus(pv40,n1))
| ~ leq(n0,X6) ),
inference(definition_unfolding,[],[f264,f316]) ).
fof(f264,plain,
! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,pred(pv40))
| ~ leq(n0,X6) ),
inference(cnf_transformation,[],[f194]) ).
fof(f711,plain,
spl41_46,
inference(avatar_split_clause,[],[f431,f709]) ).
fof(f709,plain,
( spl41_46
<=> ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,minus(pv40,n1))
| ~ leq(n0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_46])]) ).
fof(f431,plain,
! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,minus(pv40,n1))
| ~ leq(n0,X5) ),
inference(definition_unfolding,[],[f265,f316]) ).
fof(f265,plain,
! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) ),
inference(cnf_transformation,[],[f194]) ).
fof(f705,plain,
( spl41_45
| ~ spl41_7
| ~ spl41_6
| ~ spl41_9 ),
inference(avatar_split_clause,[],[f526,f521,f506,f511,f702]) ).
fof(f702,plain,
( spl41_45
<=> init = a_select2(rho_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_45])]) ).
fof(f526,plain,
( ~ leq(sK13,n4)
| init = a_select2(rho_init,sK13)
| ~ spl41_6
| ~ spl41_9 ),
inference(resolution,[],[f522,f508]) ).
fof(f700,plain,
spl41_44,
inference(avatar_split_clause,[],[f309,f698]) ).
fof(f309,plain,
! [X0] : leq(X0,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : leq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_leq) ).
fof(f696,plain,
spl41_43,
inference(avatar_split_clause,[],[f308,f694]) ).
fof(f694,plain,
( spl41_43
<=> ! [X0] : ~ gt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_43])]) ).
fof(f308,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f692,plain,
spl41_42,
inference(avatar_split_clause,[],[f301,f689]) ).
fof(f689,plain,
( spl41_42
<=> gt(n0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_42])]) ).
fof(f301,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f687,plain,
spl41_41,
inference(avatar_split_clause,[],[f300,f684]) ).
fof(f684,plain,
( spl41_41
<=> gt(n1,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_41])]) ).
fof(f300,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f68]) ).
fof(f68,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
fof(f682,plain,
spl41_40,
inference(avatar_split_clause,[],[f299,f679]) ).
fof(f679,plain,
( spl41_40
<=> gt(n4,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_40])]) ).
fof(f299,plain,
gt(n4,n0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,axiom,
gt(n4,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_0) ).
fof(f677,plain,
spl41_39,
inference(avatar_split_clause,[],[f298,f674]) ).
fof(f674,plain,
( spl41_39
<=> gt(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_39])]) ).
fof(f298,plain,
gt(n4,n1),
inference(cnf_transformation,[],[f71]) ).
fof(f71,axiom,
gt(n4,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_1) ).
fof(f672,plain,
spl41_38,
inference(avatar_split_clause,[],[f297,f669]) ).
fof(f669,plain,
( spl41_38
<=> gt(n4,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_38])]) ).
fof(f297,plain,
gt(n4,n2),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
gt(n4,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_2) ).
fof(f667,plain,
spl41_37,
inference(avatar_split_clause,[],[f296,f664]) ).
fof(f664,plain,
( spl41_37
<=> gt(n4,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_37])]) ).
fof(f296,plain,
gt(n4,n3),
inference(cnf_transformation,[],[f80]) ).
fof(f80,axiom,
gt(n4,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_3) ).
fof(f662,plain,
( spl41_35
| ~ spl41_36
| ~ spl41_2
| ~ spl41_9 ),
inference(avatar_split_clause,[],[f525,f521,f486,f659,f655]) ).
fof(f655,plain,
( spl41_35
<=> init = a_select2(rho_init,pv45) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_35])]) ).
fof(f659,plain,
( spl41_36
<=> leq(pv45,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_36])]) ).
fof(f525,plain,
( ~ leq(pv45,n4)
| init = a_select2(rho_init,pv45)
| ~ spl41_2
| ~ spl41_9 ),
inference(resolution,[],[f522,f488]) ).
fof(f653,plain,
spl41_34,
inference(avatar_split_clause,[],[f295,f650]) ).
fof(f650,plain,
( spl41_34
<=> gt(n1,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_34])]) ).
fof(f295,plain,
gt(n1,tptp_minus_1),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
gt(n1,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_tptp_minus_1) ).
fof(f648,plain,
spl41_33,
inference(avatar_split_clause,[],[f294,f645]) ).
fof(f645,plain,
( spl41_33
<=> gt(n4,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_33])]) ).
fof(f294,plain,
gt(n4,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
gt(n4,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
fof(f643,plain,
spl41_32,
inference(avatar_split_clause,[],[f293,f640]) ).
fof(f640,plain,
( spl41_32
<=> gt(n2,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_32])]) ).
fof(f293,plain,
gt(n2,n0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
gt(n2,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_0) ).
fof(f638,plain,
spl41_31,
inference(avatar_split_clause,[],[f292,f635]) ).
fof(f635,plain,
( spl41_31
<=> gt(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_31])]) ).
fof(f292,plain,
gt(n2,n1),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
gt(n2,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_1) ).
fof(f633,plain,
spl41_30,
inference(avatar_split_clause,[],[f291,f630]) ).
fof(f630,plain,
( spl41_30
<=> gt(n2,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_30])]) ).
fof(f291,plain,
gt(n2,tptp_minus_1),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
gt(n2,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_2_tptp_minus_1) ).
fof(f628,plain,
spl41_29,
inference(avatar_split_clause,[],[f290,f625]) ).
fof(f625,plain,
( spl41_29
<=> gt(n3,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_29])]) ).
fof(f290,plain,
gt(n3,n0),
inference(cnf_transformation,[],[f70]) ).
fof(f70,axiom,
gt(n3,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_0) ).
fof(f623,plain,
spl41_28,
inference(avatar_split_clause,[],[f289,f620]) ).
fof(f620,plain,
( spl41_28
<=> gt(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_28])]) ).
fof(f289,plain,
gt(n3,n1),
inference(cnf_transformation,[],[f75]) ).
fof(f75,axiom,
gt(n3,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_1) ).
fof(f618,plain,
spl41_27,
inference(avatar_split_clause,[],[f288,f615]) ).
fof(f615,plain,
( spl41_27
<=> gt(n3,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_27])]) ).
fof(f288,plain,
gt(n3,n2),
inference(cnf_transformation,[],[f79]) ).
fof(f79,axiom,
gt(n3,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_2) ).
fof(f613,plain,
spl41_26,
inference(avatar_split_clause,[],[f287,f610]) ).
fof(f610,plain,
( spl41_26
<=> gt(n3,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_26])]) ).
fof(f287,plain,
gt(n3,tptp_minus_1),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
gt(n3,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_3_tptp_minus_1) ).
fof(f608,plain,
spl41_25,
inference(avatar_split_clause,[],[f286,f605]) ).
fof(f605,plain,
( spl41_25
<=> gt(n5,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_25])]) ).
fof(f286,plain,
gt(n5,n0),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
gt(n5,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_0) ).
fof(f603,plain,
spl41_24,
inference(avatar_split_clause,[],[f285,f600]) ).
fof(f600,plain,
( spl41_24
<=> gt(n5,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_24])]) ).
fof(f285,plain,
gt(n5,n1),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
gt(n5,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_1) ).
fof(f598,plain,
spl41_23,
inference(avatar_split_clause,[],[f284,f595]) ).
fof(f595,plain,
( spl41_23
<=> gt(n5,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_23])]) ).
fof(f284,plain,
gt(n5,n4),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
gt(n5,n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_4) ).
fof(f593,plain,
spl41_22,
inference(avatar_split_clause,[],[f283,f590]) ).
fof(f590,plain,
( spl41_22
<=> gt(n5,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_22])]) ).
fof(f283,plain,
gt(n5,n2),
inference(cnf_transformation,[],[f77]) ).
fof(f77,axiom,
gt(n5,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_2) ).
fof(f588,plain,
spl41_21,
inference(avatar_split_clause,[],[f282,f585]) ).
fof(f585,plain,
( spl41_21
<=> gt(n5,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_21])]) ).
fof(f282,plain,
gt(n5,n3),
inference(cnf_transformation,[],[f81]) ).
fof(f81,axiom,
gt(n5,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_3) ).
fof(f583,plain,
spl41_20,
inference(avatar_split_clause,[],[f281,f580]) ).
fof(f580,plain,
( spl41_20
<=> gt(n5,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_20])]) ).
fof(f281,plain,
gt(n5,tptp_minus_1),
inference(cnf_transformation,[],[f59]) ).
fof(f59,axiom,
gt(n5,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_5_tptp_minus_1) ).
fof(f578,plain,
spl41_19,
inference(avatar_split_clause,[],[f280,f575]) ).
fof(f575,plain,
( spl41_19
<=> gt(n135299,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_19])]) ).
fof(f280,plain,
gt(n135299,n0),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
gt(n135299,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_0) ).
fof(f573,plain,
spl41_18,
inference(avatar_split_clause,[],[f279,f570]) ).
fof(f570,plain,
( spl41_18
<=> gt(n135299,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_18])]) ).
fof(f279,plain,
gt(n135299,n4),
inference(cnf_transformation,[],[f56]) ).
fof(f56,axiom,
gt(n135299,n4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_4) ).
fof(f568,plain,
spl41_17,
inference(avatar_split_clause,[],[f278,f565]) ).
fof(f565,plain,
( spl41_17
<=> gt(n135299,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_17])]) ).
fof(f278,plain,
gt(n135299,n1),
inference(cnf_transformation,[],[f73]) ).
fof(f73,axiom,
gt(n135299,n1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_1) ).
fof(f563,plain,
spl41_16,
inference(avatar_split_clause,[],[f277,f560]) ).
fof(f560,plain,
( spl41_16
<=> gt(n135299,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_16])]) ).
fof(f277,plain,
gt(n135299,n2),
inference(cnf_transformation,[],[f78]) ).
fof(f78,axiom,
gt(n135299,n2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_2) ).
fof(f558,plain,
spl41_15,
inference(avatar_split_clause,[],[f276,f555]) ).
fof(f555,plain,
( spl41_15
<=> gt(n135299,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_15])]) ).
fof(f276,plain,
gt(n135299,n3),
inference(cnf_transformation,[],[f82]) ).
fof(f82,axiom,
gt(n135299,n3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_3) ).
fof(f553,plain,
( spl41_14
| ~ spl41_3
| ~ spl41_1
| ~ spl41_9 ),
inference(avatar_split_clause,[],[f524,f521,f481,f491,f550]) ).
fof(f524,plain,
( ~ leq(pv40,n4)
| init = a_select2(rho_init,pv40)
| ~ spl41_1
| ~ spl41_9 ),
inference(resolution,[],[f522,f483]) ).
fof(f548,plain,
spl41_13,
inference(avatar_split_clause,[],[f275,f545]) ).
fof(f545,plain,
( spl41_13
<=> gt(n135299,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_13])]) ).
fof(f275,plain,
gt(n135299,n5),
inference(cnf_transformation,[],[f57]) ).
fof(f57,axiom,
gt(n135299,n5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_5) ).
fof(f543,plain,
spl41_12,
inference(avatar_split_clause,[],[f274,f540]) ).
fof(f540,plain,
( spl41_12
<=> gt(n135299,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_12])]) ).
fof(f274,plain,
gt(n135299,tptp_minus_1),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
gt(n135299,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_135299_tptp_minus_1) ).
fof(f538,plain,
~ spl41_11,
inference(avatar_split_clause,[],[f273,f535]) ).
fof(f535,plain,
( spl41_11
<=> def = use ),
introduced(avatar_definition,[new_symbols(naming,[spl41_11])]) ).
fof(f273,plain,
def != use,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
def != use,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defuse) ).
fof(f530,plain,
spl41_10,
inference(avatar_split_clause,[],[f266,f528]) ).
fof(f528,plain,
( spl41_10
<=> ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_10])]) ).
fof(f266,plain,
! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ),
inference(cnf_transformation,[],[f194]) ).
fof(f523,plain,
spl41_9,
inference(avatar_split_clause,[],[f263,f521]) ).
fof(f263,plain,
! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) ),
inference(cnf_transformation,[],[f194]) ).
fof(f519,plain,
~ spl41_8,
inference(avatar_split_clause,[],[f272,f516]) ).
fof(f272,plain,
init != a_select2(rhoold_init,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f514,plain,
spl41_7,
inference(avatar_split_clause,[],[f271,f511]) ).
fof(f271,plain,
leq(sK13,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f509,plain,
spl41_6,
inference(avatar_split_clause,[],[f270,f506]) ).
fof(f270,plain,
leq(n0,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f504,plain,
spl41_5,
inference(avatar_split_clause,[],[f261,f501]) ).
fof(f261,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f194]) ).
fof(f499,plain,
spl41_4,
inference(avatar_split_clause,[],[f260,f496]) ).
fof(f260,plain,
leq(pv45,n135299),
inference(cnf_transformation,[],[f194]) ).
fof(f494,plain,
spl41_3,
inference(avatar_split_clause,[],[f259,f491]) ).
fof(f259,plain,
leq(pv40,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f489,plain,
spl41_2,
inference(avatar_split_clause,[],[f258,f486]) ).
fof(f258,plain,
leq(n0,pv45),
inference(cnf_transformation,[],[f194]) ).
fof(f484,plain,
spl41_1,
inference(avatar_split_clause,[],[f257,f481]) ).
fof(f257,plain,
leq(n0,pv40),
inference(cnf_transformation,[],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV177+1 : TPTP v8.2.0. Bugfixed v3.3.0.
% 0.03/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n005.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 : Sun May 19 08:17:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (26164)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (26167)WARNING: value z3 for option sas not known
% 0.21/0.38 % (26166)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (26168)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (26169)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (26167)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (26170)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (26171)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.38 % (26165)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.48 % (26169)First to succeed.
% 0.21/0.49 TRYING [1]
% 0.21/0.49 % (26169)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26164"
% 0.21/0.49 % (26169)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.50 % (26169)------------------------------
% 0.21/0.50 % (26169)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.50 % (26169)Termination reason: Refutation
% 0.21/0.50
% 0.21/0.50 % (26169)Memory used [KB]: 3116
% 0.21/0.50 % (26169)Time elapsed: 0.108 s
% 0.21/0.50 % (26169)Instructions burned: 250 (million)
% 0.21/0.50 % (26164)Success in time 0.119 s
%------------------------------------------------------------------------------