TSTP Solution File: SWV178+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:47:07 EDT 2024
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 369
% Syntax : Number of formulae : 1159 ( 324 unt; 0 def)
% Number of atoms : 4110 ( 808 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 4633 (1682 ~;1842 |; 708 &)
% ( 255 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 269 ( 267 usr; 253 prp; 0-4 aty)
% Number of functors : 68 ( 68 usr; 23 con; 0-4 aty)
% Number of variables : 2102 (1945 !; 157 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3247,plain,
$false,
inference(avatar_sat_refutation,[],[f482,f487,f492,f497,f502,f507,f511,f517,f524,f529,f534,f539,f544,f549,f554,f559,f564,f569,f574,f579,f584,f589,f594,f599,f604,f609,f614,f619,f624,f629,f634,f639,f644,f649,f654,f659,f664,f669,f674,f678,f682,f687,f693,f697,f703,f712,f719,f726,f733,f741,f746,f750,f755,f760,f765,f770,f780,f786,f809,f814,f818,f859,f864,f868,f872,f893,f899,f904,f909,f914,f919,f923,f928,f932,f937,f941,f946,f950,f955,f959,f964,f969,f973,f977,f982,f986,f991,f995,f1000,f1004,f1009,f1013,f1018,f1022,f1027,f1031,f1036,f1040,f1045,f1049,f1054,f1058,f1063,f1067,f1072,f1076,f1081,f1085,f1090,f1094,f1099,f1103,f1108,f1112,f1117,f1121,f1126,f1130,f1135,f1139,f1143,f1147,f1152,f1156,f1160,f1164,f1168,f1172,f1176,f1180,f1188,f1196,f1204,f1212,f1220,f1228,f1233,f1241,f1249,f1257,f1265,f1273,f1281,f1289,f1297,f1305,f1313,f1318,f1326,f1334,f1342,f1350,f1358,f1366,f1374,f1463,f1503,f1507,f1514,f1518,f1522,f1526,f1530,f1534,f1538,f1542,f1546,f1626,f1854,f1858,f1862,f1930,f1935,f1966,f1971,f2003,f2007,f2079,f2085,f2090,f2095,f2099,f2103,f2107,f2116,f2120,f2176,f2182,f2188,f2194,f2297,f2303,f2309,f2345,f2349,f2353,f2357,f2361,f2365,f2369,f2373,f2377,f2381,f2387,f2397,f2401,f2405,f2409,f2413,f2433,f2437,f2512,f2518,f2554,f2559,f2564,f2570,f2606,f2607,f2678,f2684,f2690,f2694,f2762,f2768,f2804,f2810,f2816,f2820,f2888,f2894,f2900,f2904,f2974,f2981,f3017,f3023,f3064,f3079,f3083,f3087,f3092,f3096,f3136,f3143,f3235,f3240,f3245,f3246]) ).
fof(f3246,plain,
( ~ spl41_5
| spl41_6
| ~ spl41_4
| ~ spl41_49 ),
inference(avatar_split_clause,[],[f728,f724,f494,f504,f499]) ).
fof(f499,plain,
( spl41_5
<=> leq(sK13,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_5])]) ).
fof(f504,plain,
( spl41_6
<=> init = a_select2(sigmaold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_6])]) ).
fof(f494,plain,
( spl41_4
<=> leq(n0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_4])]) ).
fof(f724,plain,
( spl41_49
<=> ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(n0,X1)
| ~ leq(X1,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_49])]) ).
fof(f728,plain,
( init = a_select2(sigmaold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_4
| ~ spl41_49 ),
inference(resolution,[],[f725,f496]) ).
fof(f496,plain,
( leq(n0,sK13)
| ~ spl41_4 ),
inference(avatar_component_clause,[],[f494]) ).
fof(f725,plain,
( ! [X1] :
( ~ leq(n0,X1)
| init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4) )
| ~ spl41_49 ),
inference(avatar_component_clause,[],[f724]) ).
fof(f3245,plain,
( ~ spl41_2
| spl41_252
| ~ spl41_1
| ~ spl41_49 ),
inference(avatar_split_clause,[],[f727,f724,f479,f3242,f484]) ).
fof(f484,plain,
( spl41_2
<=> leq(pv40,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_2])]) ).
fof(f3242,plain,
( spl41_252
<=> init = a_select2(sigmaold_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_252])]) ).
fof(f479,plain,
( spl41_1
<=> leq(n0,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_1])]) ).
fof(f727,plain,
( init = a_select2(sigmaold_init,pv40)
| ~ leq(pv40,n4)
| ~ spl41_1
| ~ spl41_49 ),
inference(resolution,[],[f725,f481]) ).
fof(f481,plain,
( leq(n0,pv40)
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f3240,plain,
( ~ spl41_5
| spl41_251
| ~ spl41_4
| ~ spl41_48 ),
inference(avatar_split_clause,[],[f721,f717,f494,f3237,f499]) ).
fof(f3237,plain,
( spl41_251
<=> init = a_select2(rhoold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_251])]) ).
fof(f717,plain,
( spl41_48
<=> ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_48])]) ).
fof(f721,plain,
( init = a_select2(rhoold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_4
| ~ spl41_48 ),
inference(resolution,[],[f718,f496]) ).
fof(f718,plain,
( ! [X2] :
( ~ leq(n0,X2)
| init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4) )
| ~ spl41_48 ),
inference(avatar_component_clause,[],[f717]) ).
fof(f3235,plain,
( ~ spl41_2
| spl41_250
| ~ spl41_1
| ~ spl41_48 ),
inference(avatar_split_clause,[],[f720,f717,f479,f3232,f484]) ).
fof(f3232,plain,
( spl41_250
<=> init = a_select2(rhoold_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_250])]) ).
fof(f720,plain,
( init = a_select2(rhoold_init,pv40)
| ~ leq(pv40,n4)
| ~ spl41_1
| ~ spl41_48 ),
inference(resolution,[],[f718,f481]) ).
fof(f3143,plain,
( spl41_249
| ~ spl41_53
| ~ spl41_243 ),
inference(avatar_split_clause,[],[f3100,f3077,f748,f3140]) ).
fof(f3140,plain,
( spl41_249
<=> gt(plus(loopcounter,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_249])]) ).
fof(f748,plain,
( spl41_53
<=> ! [X0] : gt(plus(X0,n1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_53])]) ).
fof(f3077,plain,
( spl41_243
<=> ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_243])]) ).
fof(f3100,plain,
( gt(plus(loopcounter,n1),n1)
| ~ spl41_53
| ~ spl41_243 ),
inference(resolution,[],[f3078,f749]) ).
fof(f749,plain,
( ! [X0] : gt(plus(X0,n1),X0)
| ~ spl41_53 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f3078,plain,
( ! [X0] :
( ~ gt(X0,loopcounter)
| gt(X0,n1) )
| ~ spl41_243 ),
inference(avatar_component_clause,[],[f3077]) ).
fof(f3136,plain,
( spl41_248
| ~ spl41_241
| ~ spl41_245 ),
inference(avatar_split_clause,[],[f3088,f3085,f3057,f3134]) ).
fof(f3134,plain,
( spl41_248
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_248])]) ).
fof(f3057,plain,
( spl41_241
<=> tptp_float_0_0 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_241])]) ).
fof(f3085,plain,
( spl41_245
<=> ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_245])]) ).
fof(f3088,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) )
| ~ spl41_241
| ~ spl41_245 ),
inference(forward_demodulation,[],[f3086,f3059]) ).
fof(f3059,plain,
( tptp_float_0_0 = sK13
| ~ spl41_241 ),
inference(avatar_component_clause,[],[f3057]) ).
fof(f3086,plain,
( ! [X0] :
( ~ leq(X0,sK13)
| leq(X0,n4) )
| ~ spl41_245 ),
inference(avatar_component_clause,[],[f3085]) ).
fof(f3096,plain,
( spl41_247
| ~ spl41_4
| ~ spl41_59
| ~ spl41_163 ),
inference(avatar_split_clause,[],[f1728,f1524,f783,f494,f3094]) ).
fof(f3094,plain,
( spl41_247
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_247])]) ).
fof(f783,plain,
( spl41_59
<=> n0 = tptp_float_0_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_59])]) ).
fof(f1524,plain,
( spl41_163
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_163])]) ).
fof(f1728,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) )
| ~ spl41_4
| ~ spl41_59
| ~ spl41_163 ),
inference(forward_demodulation,[],[f1671,f785]) ).
fof(f785,plain,
( n0 = tptp_float_0_0
| ~ spl41_59 ),
inference(avatar_component_clause,[],[f783]) ).
fof(f1671,plain,
( ! [X0] :
( leq(X0,sK13)
| ~ leq(X0,n0) )
| ~ spl41_4
| ~ spl41_163 ),
inference(resolution,[],[f1525,f496]) ).
fof(f1525,plain,
( ! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1) )
| ~ spl41_163 ),
inference(avatar_component_clause,[],[f1524]) ).
fof(f3092,plain,
( spl41_246
| ~ spl41_1
| ~ spl41_59
| ~ spl41_163 ),
inference(avatar_split_clause,[],[f1727,f1524,f783,f479,f3090]) ).
fof(f3090,plain,
( spl41_246
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_246])]) ).
fof(f1727,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv40) )
| ~ spl41_1
| ~ spl41_59
| ~ spl41_163 ),
inference(forward_demodulation,[],[f1670,f785]) ).
fof(f1670,plain,
( ! [X0] :
( leq(X0,pv40)
| ~ leq(X0,n0) )
| ~ spl41_1
| ~ spl41_163 ),
inference(resolution,[],[f1525,f481]) ).
fof(f3087,plain,
( spl41_245
| ~ spl41_5
| ~ spl41_163 ),
inference(avatar_split_clause,[],[f1702,f1524,f499,f3085]) ).
fof(f1702,plain,
( ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) )
| ~ spl41_5
| ~ spl41_163 ),
inference(resolution,[],[f1525,f501]) ).
fof(f501,plain,
( leq(sK13,n4)
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f3083,plain,
( spl41_244
| ~ spl41_2
| ~ spl41_163 ),
inference(avatar_split_clause,[],[f1701,f1524,f484,f3081]) ).
fof(f3081,plain,
( spl41_244
<=> ! [X0] :
( leq(X0,n4)
| ~ leq(X0,pv40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_244])]) ).
fof(f1701,plain,
( ! [X0] :
( leq(X0,n4)
| ~ leq(X0,pv40) )
| ~ spl41_2
| ~ spl41_163 ),
inference(resolution,[],[f1525,f486]) ).
fof(f486,plain,
( leq(pv40,n4)
| ~ spl41_2 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f3079,plain,
( spl41_243
| ~ spl41_3
| ~ spl41_162 ),
inference(avatar_split_clause,[],[f1652,f1520,f489,f3077]) ).
fof(f489,plain,
( spl41_3
<=> gt(loopcounter,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_3])]) ).
fof(f1520,plain,
( spl41_162
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_162])]) ).
fof(f1652,plain,
( ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) )
| ~ spl41_3
| ~ spl41_162 ),
inference(resolution,[],[f1521,f491]) ).
fof(f491,plain,
( gt(loopcounter,n1)
| ~ spl41_3 ),
inference(avatar_component_clause,[],[f489]) ).
fof(f1521,plain,
( ! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) )
| ~ spl41_162 ),
inference(avatar_component_clause,[],[f1520]) ).
fof(f3064,plain,
( spl41_241
| spl41_242
| ~ spl41_4
| ~ spl41_59
| ~ spl41_161 ),
inference(avatar_split_clause,[],[f1617,f1516,f783,f494,f3061,f3057]) ).
fof(f3061,plain,
( spl41_242
<=> gt(sK13,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_242])]) ).
fof(f1516,plain,
( spl41_161
<=> ! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_161])]) ).
fof(f1617,plain,
( gt(sK13,tptp_float_0_0)
| tptp_float_0_0 = sK13
| ~ spl41_4
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1616,f785]) ).
fof(f1616,plain,
( tptp_float_0_0 = sK13
| gt(sK13,n0)
| ~ spl41_4
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1558,f785]) ).
fof(f1558,plain,
( n0 = sK13
| gt(sK13,n0)
| ~ spl41_4
| ~ spl41_161 ),
inference(resolution,[],[f1517,f496]) ).
fof(f1517,plain,
( ! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) )
| ~ spl41_161 ),
inference(avatar_component_clause,[],[f1516]) ).
fof(f3023,plain,
( spl41_240
| ~ spl41_59
| ~ spl41_239 ),
inference(avatar_split_clause,[],[f3019,f3015,f783,f3021]) ).
fof(f3021,plain,
( spl41_240
<=> ! [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_240])]) ).
fof(f3015,plain,
( spl41_239
<=> ! [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_239])]) ).
fof(f3019,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_59
| ~ spl41_239 ),
inference(forward_demodulation,[],[f3018,f785]) ).
fof(f3018,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_59
| ~ spl41_239 ),
inference(forward_demodulation,[],[f3016,f785]) ).
fof(f3016,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_239 ),
inference(avatar_component_clause,[],[f3015]) ).
fof(f3017,plain,
spl41_239,
inference(avatar_split_clause,[],[f428,f3015]) ).
fof(f428,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(f2981,plain,
( spl41_238
| ~ spl41_59
| ~ spl41_237 ),
inference(avatar_split_clause,[],[f2977,f2972,f783,f2979]) ).
fof(f2979,plain,
( spl41_238
<=> ! [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_238])]) ).
fof(f2972,plain,
( spl41_237
<=> ! [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_237])]) ).
fof(f2977,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_59
| ~ spl41_237 ),
inference(forward_demodulation,[],[f2976,f785]) ).
fof(f2976,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_59
| ~ spl41_237 ),
inference(forward_demodulation,[],[f2975,f785]) ).
fof(f2975,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_59
| ~ spl41_237 ),
inference(forward_demodulation,[],[f2973,f785]) ).
fof(f2973,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_237 ),
inference(avatar_component_clause,[],[f2972]) ).
fof(f2974,plain,
spl41_237,
inference(avatar_split_clause,[],[f355,f2972]) ).
fof(f355,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(f2904,plain,
( spl41_236
| ~ spl41_59
| ~ spl41_234 ),
inference(avatar_split_clause,[],[f2896,f2892,f783,f2902]) ).
fof(f2902,plain,
( spl41_236
<=> ! [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_236])]) ).
fof(f2892,plain,
( spl41_234
<=> ! [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_234])]) ).
fof(f2896,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_59
| ~ spl41_234 ),
inference(forward_demodulation,[],[f2895,f785]) ).
fof(f2895,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_59
| ~ spl41_234 ),
inference(forward_demodulation,[],[f2893,f785]) ).
fof(f2893,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_234 ),
inference(avatar_component_clause,[],[f2892]) ).
fof(f2900,plain,
( spl41_235
| ~ spl41_59
| ~ spl41_233 ),
inference(avatar_split_clause,[],[f2890,f2886,f783,f2898]) ).
fof(f2898,plain,
( spl41_235
<=> ! [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_235])]) ).
fof(f2886,plain,
( spl41_233
<=> ! [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_233])]) ).
fof(f2890,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_59
| ~ spl41_233 ),
inference(forward_demodulation,[],[f2889,f785]) ).
fof(f2889,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_59
| ~ spl41_233 ),
inference(forward_demodulation,[],[f2887,f785]) ).
fof(f2887,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_233 ),
inference(avatar_component_clause,[],[f2886]) ).
fof(f2894,plain,
spl41_234,
inference(avatar_split_clause,[],[f403,f2892]) ).
fof(f403,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(f2888,plain,
spl41_233,
inference(avatar_split_clause,[],[f392,f2886]) ).
fof(f392,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(f2820,plain,
( spl41_232
| ~ spl41_59
| ~ spl41_230 ),
inference(avatar_split_clause,[],[f2812,f2808,f783,f2818]) ).
fof(f2818,plain,
( spl41_232
<=> ! [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_232])]) ).
fof(f2808,plain,
( spl41_230
<=> ! [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_230])]) ).
fof(f2812,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_59
| ~ spl41_230 ),
inference(forward_demodulation,[],[f2811,f785]) ).
fof(f2811,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_59
| ~ spl41_230 ),
inference(forward_demodulation,[],[f2809,f785]) ).
fof(f2809,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_230 ),
inference(avatar_component_clause,[],[f2808]) ).
fof(f2816,plain,
( spl41_231
| ~ spl41_59
| ~ spl41_229 ),
inference(avatar_split_clause,[],[f2806,f2802,f783,f2814]) ).
fof(f2814,plain,
( spl41_231
<=> ! [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_231])]) ).
fof(f2802,plain,
( spl41_229
<=> ! [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_229])]) ).
fof(f2806,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_59
| ~ spl41_229 ),
inference(forward_demodulation,[],[f2805,f785]) ).
fof(f2805,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_59
| ~ spl41_229 ),
inference(forward_demodulation,[],[f2803,f785]) ).
fof(f2803,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_229 ),
inference(avatar_component_clause,[],[f2802]) ).
fof(f2810,plain,
spl41_230,
inference(avatar_split_clause,[],[f386,f2808]) ).
fof(f386,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(f2804,plain,
spl41_229,
inference(avatar_split_clause,[],[f375,f2802]) ).
fof(f375,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(f2768,plain,
( spl41_228
| ~ spl41_59
| ~ spl41_227 ),
inference(avatar_split_clause,[],[f2764,f2760,f783,f2766]) ).
fof(f2766,plain,
( spl41_228
<=> ! [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_228])]) ).
fof(f2760,plain,
( spl41_227
<=> ! [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_227])]) ).
fof(f2764,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_59
| ~ spl41_227 ),
inference(forward_demodulation,[],[f2763,f785]) ).
fof(f2763,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_59
| ~ spl41_227 ),
inference(forward_demodulation,[],[f2761,f785]) ).
fof(f2761,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_227 ),
inference(avatar_component_clause,[],[f2760]) ).
fof(f2762,plain,
spl41_227,
inference(avatar_split_clause,[],[f410,f2760]) ).
fof(f410,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(f2694,plain,
( spl41_226
| ~ spl41_59
| ~ spl41_224 ),
inference(avatar_split_clause,[],[f2686,f2682,f783,f2692]) ).
fof(f2692,plain,
( spl41_226
<=> ! [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_226])]) ).
fof(f2682,plain,
( spl41_224
<=> ! [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_224])]) ).
fof(f2686,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_59
| ~ spl41_224 ),
inference(forward_demodulation,[],[f2685,f785]) ).
fof(f2685,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_59
| ~ spl41_224 ),
inference(forward_demodulation,[],[f2683,f785]) ).
fof(f2683,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_224 ),
inference(avatar_component_clause,[],[f2682]) ).
fof(f2690,plain,
( spl41_225
| ~ spl41_59
| ~ spl41_223 ),
inference(avatar_split_clause,[],[f2680,f2676,f783,f2688]) ).
fof(f2688,plain,
( spl41_225
<=> ! [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_225])]) ).
fof(f2676,plain,
( spl41_223
<=> ! [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_223])]) ).
fof(f2680,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_59
| ~ spl41_223 ),
inference(forward_demodulation,[],[f2679,f785]) ).
fof(f2679,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_59
| ~ spl41_223 ),
inference(forward_demodulation,[],[f2677,f785]) ).
fof(f2677,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_223 ),
inference(avatar_component_clause,[],[f2676]) ).
fof(f2684,plain,
spl41_224,
inference(avatar_split_clause,[],[f349,f2682]) ).
fof(f349,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(f2678,plain,
spl41_223,
inference(avatar_split_clause,[],[f343,f2676]) ).
fof(f343,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(f2607,plain,
( spl41_138
| ~ spl41_16
| ~ spl41_208 ),
inference(avatar_split_clause,[],[f2416,f2390,f556,f1230]) ).
fof(f1230,plain,
( spl41_138
<=> init = a_select2(rho_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_138])]) ).
fof(f556,plain,
( spl41_16
<=> init = a_select2(rho_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_16])]) ).
fof(f2390,plain,
( spl41_208
<=> tptp_float_0_0 = pv40 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_208])]) ).
fof(f2416,plain,
( init = a_select2(rho_init,tptp_float_0_0)
| ~ spl41_16
| ~ spl41_208 ),
inference(superposition,[],[f558,f2392]) ).
fof(f2392,plain,
( tptp_float_0_0 = pv40
| ~ spl41_208 ),
inference(avatar_component_clause,[],[f2390]) ).
fof(f558,plain,
( init = a_select2(rho_init,pv40)
| ~ spl41_16 ),
inference(avatar_component_clause,[],[f556]) ).
fof(f2606,plain,
spl41_222,
inference(avatar_split_clause,[],[f412,f2604]) ).
fof(f2604,plain,
( spl41_222
<=> ! [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_222])]) ).
fof(f412,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(f2570,plain,
( spl41_221
| ~ spl41_59
| ~ spl41_220 ),
inference(avatar_split_clause,[],[f2566,f2562,f783,f2568]) ).
fof(f2568,plain,
( spl41_221
<=> ! [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_221])]) ).
fof(f2562,plain,
( spl41_220
<=> ! [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_220])]) ).
fof(f2566,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_59
| ~ spl41_220 ),
inference(forward_demodulation,[],[f2565,f785]) ).
fof(f2565,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_220 ),
inference(forward_demodulation,[],[f2563,f785]) ).
fof(f2563,plain,
( ! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) )
| ~ spl41_220 ),
inference(avatar_component_clause,[],[f2562]) ).
fof(f2564,plain,
spl41_220,
inference(avatar_split_clause,[],[f324,f2562]) ).
fof(f324,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(f2559,plain,
( spl41_219
| ~ spl41_59
| ~ spl41_218 ),
inference(avatar_split_clause,[],[f2555,f2552,f783,f2557]) ).
fof(f2557,plain,
( spl41_219
<=> ! [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_219])]) ).
fof(f2552,plain,
( spl41_218
<=> ! [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_218])]) ).
fof(f2555,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_59
| ~ spl41_218 ),
inference(forward_demodulation,[],[f2553,f785]) ).
fof(f2553,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_218 ),
inference(avatar_component_clause,[],[f2552]) ).
fof(f2554,plain,
spl41_218,
inference(avatar_split_clause,[],[f397,f2552]) ).
fof(f397,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(f2518,plain,
( spl41_217
| ~ spl41_59
| ~ spl41_216 ),
inference(avatar_split_clause,[],[f2514,f2510,f783,f2516]) ).
fof(f2516,plain,
( spl41_217
<=> ! [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_217])]) ).
fof(f2510,plain,
( spl41_216
<=> ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_216])]) ).
fof(f2514,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_59
| ~ spl41_216 ),
inference(forward_demodulation,[],[f2513,f785]) ).
fof(f2513,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_216 ),
inference(forward_demodulation,[],[f2511,f785]) ).
fof(f2511,plain,
( ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_216 ),
inference(avatar_component_clause,[],[f2510]) ).
fof(f2512,plain,
spl41_216,
inference(avatar_split_clause,[],[f328,f2510]) ).
fof(f328,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(f2437,plain,
( spl41_215
| ~ spl41_59
| ~ spl41_207 ),
inference(avatar_split_clause,[],[f2388,f2385,f783,f2435]) ).
fof(f2435,plain,
( spl41_215
<=> ! [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_215])]) ).
fof(f2385,plain,
( spl41_207
<=> ! [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_207])]) ).
fof(f2388,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_59
| ~ spl41_207 ),
inference(forward_demodulation,[],[f2386,f785]) ).
fof(f2386,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_207 ),
inference(avatar_component_clause,[],[f2385]) ).
fof(f2433,plain,
( spl41_214
| ~ spl41_59
| ~ spl41_206 ),
inference(avatar_split_clause,[],[f2383,f2379,f783,f2431]) ).
fof(f2431,plain,
( spl41_214
<=> ! [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_214])]) ).
fof(f2379,plain,
( spl41_206
<=> ! [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_206])]) ).
fof(f2383,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_59
| ~ spl41_206 ),
inference(forward_demodulation,[],[f2382,f785]) ).
fof(f2382,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_59
| ~ spl41_206 ),
inference(forward_demodulation,[],[f2380,f785]) ).
fof(f2380,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_206 ),
inference(avatar_component_clause,[],[f2379]) ).
fof(f2413,plain,
spl41_213,
inference(avatar_split_clause,[],[f427,f2411]) ).
fof(f2411,plain,
( spl41_213
<=> ! [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_213])]) ).
fof(f427,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(f2409,plain,
spl41_212,
inference(avatar_split_clause,[],[f422,f2407]) ).
fof(f2407,plain,
( spl41_212
<=> ! [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_212])]) ).
fof(f422,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(f2405,plain,
spl41_211,
inference(avatar_split_clause,[],[f417,f2403]) ).
fof(f2403,plain,
( spl41_211
<=> ! [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_211])]) ).
fof(f417,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(f2401,plain,
spl41_210,
inference(avatar_split_clause,[],[f402,f2399]) ).
fof(f2399,plain,
( spl41_210
<=> ! [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_210])]) ).
fof(f402,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(f2397,plain,
( spl41_208
| spl41_209
| ~ spl41_1
| ~ spl41_59
| ~ spl41_161 ),
inference(avatar_split_clause,[],[f1615,f1516,f783,f479,f2394,f2390]) ).
fof(f2394,plain,
( spl41_209
<=> gt(pv40,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_209])]) ).
fof(f1615,plain,
( gt(pv40,tptp_float_0_0)
| tptp_float_0_0 = pv40
| ~ spl41_1
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1614,f785]) ).
fof(f1614,plain,
( tptp_float_0_0 = pv40
| gt(pv40,n0)
| ~ spl41_1
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1557,f785]) ).
fof(f1557,plain,
( n0 = pv40
| gt(pv40,n0)
| ~ spl41_1
| ~ spl41_161 ),
inference(resolution,[],[f1517,f481]) ).
fof(f2387,plain,
spl41_207,
inference(avatar_split_clause,[],[f396,f2385]) ).
fof(f396,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(f2381,plain,
spl41_206,
inference(avatar_split_clause,[],[f395,f2379]) ).
fof(f395,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(f2377,plain,
spl41_205,
inference(avatar_split_clause,[],[f391,f2375]) ).
fof(f2375,plain,
( spl41_205
<=> ! [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_205])]) ).
fof(f391,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(f2373,plain,
spl41_204,
inference(avatar_split_clause,[],[f385,f2371]) ).
fof(f2371,plain,
( spl41_204
<=> ! [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_204])]) ).
fof(f385,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(f2369,plain,
spl41_203,
inference(avatar_split_clause,[],[f380,f2367]) ).
fof(f2367,plain,
( spl41_203
<=> ! [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_203])]) ).
fof(f380,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(f2365,plain,
spl41_202,
inference(avatar_split_clause,[],[f374,f2363]) ).
fof(f2363,plain,
( spl41_202
<=> ! [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_202])]) ).
fof(f374,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(f2361,plain,
spl41_201,
inference(avatar_split_clause,[],[f369,f2359]) ).
fof(f2359,plain,
( spl41_201
<=> ! [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_201])]) ).
fof(f369,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(f2357,plain,
spl41_200,
inference(avatar_split_clause,[],[f354,f2355]) ).
fof(f2355,plain,
( spl41_200
<=> ! [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_200])]) ).
fof(f354,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(f2353,plain,
spl41_199,
inference(avatar_split_clause,[],[f348,f2351]) ).
fof(f2351,plain,
( spl41_199
<=> ! [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_199])]) ).
fof(f348,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(f2349,plain,
spl41_198,
inference(avatar_split_clause,[],[f342,f2347]) ).
fof(f2347,plain,
( spl41_198
<=> ! [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_198])]) ).
fof(f342,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(f2345,plain,
spl41_197,
inference(avatar_split_clause,[],[f409,f2343]) ).
fof(f2343,plain,
( spl41_197
<=> ! [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_197])]) ).
fof(f409,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(f2309,plain,
( spl41_196
| ~ spl41_59
| ~ spl41_195 ),
inference(avatar_split_clause,[],[f2305,f2301,f783,f2307]) ).
fof(f2307,plain,
( spl41_196
<=> ! [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_196])]) ).
fof(f2301,plain,
( spl41_195
<=> ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_195])]) ).
fof(f2305,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) )
| ~ spl41_59
| ~ spl41_195 ),
inference(forward_demodulation,[],[f2304,f785]) ).
fof(f2304,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_195 ),
inference(forward_demodulation,[],[f2302,f785]) ).
fof(f2302,plain,
( ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_195 ),
inference(avatar_component_clause,[],[f2301]) ).
fof(f2303,plain,
spl41_195,
inference(avatar_split_clause,[],[f325,f2301]) ).
fof(f325,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(f2297,plain,
spl41_194,
inference(avatar_split_clause,[],[f459,f2295]) ).
fof(f2295,plain,
( spl41_194
<=> ! [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_194])]) ).
fof(f459,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,[],[f458]) ).
fof(f458,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,[],[f411]) ).
fof(f411,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(f2194,plain,
( spl41_193
| ~ spl41_59
| ~ spl41_191 ),
inference(avatar_split_clause,[],[f2184,f2180,f783,f2192]) ).
fof(f2192,plain,
( spl41_193
<=> ! [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_193])]) ).
fof(f2180,plain,
( spl41_191
<=> ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_191])]) ).
fof(f2184,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) )
| ~ spl41_59
| ~ spl41_191 ),
inference(forward_demodulation,[],[f2183,f785]) ).
fof(f2183,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_191 ),
inference(forward_demodulation,[],[f2181,f785]) ).
fof(f2181,plain,
( ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_191 ),
inference(avatar_component_clause,[],[f2180]) ).
fof(f2188,plain,
spl41_192,
inference(avatar_split_clause,[],[f394,f2186]) ).
fof(f2186,plain,
( spl41_192
<=> ! [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_192])]) ).
fof(f394,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(f2182,plain,
spl41_191,
inference(avatar_split_clause,[],[f326,f2180]) ).
fof(f326,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(f2176,plain,
spl41_190,
inference(avatar_split_clause,[],[f457,f2174]) ).
fof(f2174,plain,
( spl41_190
<=> ! [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_190])]) ).
fof(f457,plain,
! [X2,X0,X1,X4] :
( a_select2(X2,X1) = a_select2(tptp_update2(X2,X0,X4),X1)
| X0 = X1 ),
inference(equality_resolution,[],[f404]) ).
fof(f404,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(f2120,plain,
( spl41_189
| ~ spl41_59
| ~ spl41_182 ),
inference(avatar_split_clause,[],[f2091,f2088,f783,f2118]) ).
fof(f2118,plain,
( spl41_189
<=> ! [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_189])]) ).
fof(f2088,plain,
( spl41_182
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_182])]) ).
fof(f2091,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_59
| ~ spl41_182 ),
inference(forward_demodulation,[],[f2089,f785]) ).
fof(f2089,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_182 ),
inference(avatar_component_clause,[],[f2088]) ).
fof(f2116,plain,
( spl41_187
| spl41_188
| ~ spl41_5
| ~ spl41_161 ),
inference(avatar_split_clause,[],[f1589,f1516,f499,f2113,f2109]) ).
fof(f2109,plain,
( spl41_187
<=> gt(n4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_187])]) ).
fof(f2113,plain,
( spl41_188
<=> n4 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_188])]) ).
fof(f1589,plain,
( n4 = sK13
| gt(n4,sK13)
| ~ spl41_5
| ~ spl41_161 ),
inference(resolution,[],[f1517,f501]) ).
fof(f2107,plain,
( spl41_186
| ~ spl41_59
| ~ spl41_181 ),
inference(avatar_split_clause,[],[f2086,f2083,f783,f2105]) ).
fof(f2105,plain,
( spl41_186
<=> ! [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_186])]) ).
fof(f2083,plain,
( spl41_181
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_181])]) ).
fof(f2086,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_59
| ~ spl41_181 ),
inference(forward_demodulation,[],[f2084,f785]) ).
fof(f2084,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_181 ),
inference(avatar_component_clause,[],[f2083]) ).
fof(f2103,plain,
( spl41_185
| ~ spl41_59
| ~ spl41_180 ),
inference(avatar_split_clause,[],[f2081,f2077,f783,f2101]) ).
fof(f2101,plain,
( spl41_185
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_185])]) ).
fof(f2077,plain,
( spl41_180
<=> ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_180])]) ).
fof(f2081,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) )
| ~ spl41_59
| ~ spl41_180 ),
inference(forward_demodulation,[],[f2080,f785]) ).
fof(f2080,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_180 ),
inference(forward_demodulation,[],[f2078,f785]) ).
fof(f2078,plain,
( ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_180 ),
inference(avatar_component_clause,[],[f2077]) ).
fof(f2099,plain,
spl41_184,
inference(avatar_split_clause,[],[f408,f2097]) ).
fof(f2097,plain,
( spl41_184
<=> ! [X0,X3,X2,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_184])]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2095,plain,
spl41_183,
inference(avatar_split_clause,[],[f407,f2093]) ).
fof(f2093,plain,
( spl41_183
<=> ! [X0,X3,X2,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_183])]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2090,plain,
spl41_182,
inference(avatar_split_clause,[],[f406,f2088]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2085,plain,
spl41_181,
inference(avatar_split_clause,[],[f405,f2083]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2079,plain,
spl41_180,
inference(avatar_split_clause,[],[f327,f2077]) ).
fof(f327,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(f2007,plain,
spl41_179,
inference(avatar_split_clause,[],[f477,f2005]) ).
fof(f2005,plain,
( spl41_179
<=> ! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_179])]) ).
fof(f477,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f476,f441]) ).
fof(f441,plain,
! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f316,f312,f312]) ).
fof(f312,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(f316,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(f476,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f448,f441]) ).
fof(f448,plain,
! [X0] : plus(n5,X0) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f323,f312,f312,f312,f312,f312]) ).
fof(f323,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(f2003,plain,
spl41_178,
inference(avatar_split_clause,[],[f475,f2001]) ).
fof(f2001,plain,
( spl41_178
<=> ! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_178])]) ).
fof(f475,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f474,f441]) ).
fof(f474,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f447,f441]) ).
fof(f447,plain,
! [X0] : plus(X0,n5) = plus(plus(plus(plus(plus(X0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f322,f312,f312,f312,f312,f312]) ).
fof(f322,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(f1971,plain,
( spl41_177
| ~ spl41_164
| ~ spl41_166
| ~ spl41_176 ),
inference(avatar_split_clause,[],[f1967,f1964,f1536,f1528,f1969]) ).
fof(f1969,plain,
( spl41_177
<=> ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_177])]) ).
fof(f1528,plain,
( spl41_164
<=> ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_164])]) ).
fof(f1536,plain,
( spl41_166
<=> ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_166])]) ).
fof(f1964,plain,
( spl41_176
<=> ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_176])]) ).
fof(f1967,plain,
( ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1)
| ~ spl41_164
| ~ spl41_166
| ~ spl41_176 ),
inference(forward_demodulation,[],[f1965,f1748]) ).
fof(f1748,plain,
( ! [X0] : plus(X0,n3) = plus(n2,plus(X0,n1))
| ~ spl41_164
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1732,f1537]) ).
fof(f1537,plain,
( ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1)
| ~ spl41_166 ),
inference(avatar_component_clause,[],[f1536]) ).
fof(f1732,plain,
( ! [X0] : plus(n2,plus(X0,n1)) = plus(plus(n2,X0),n1)
| ~ spl41_164 ),
inference(superposition,[],[f1529,f1529]) ).
fof(f1529,plain,
( ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1)
| ~ spl41_164 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f1965,plain,
( ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_176 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f1966,plain,
spl41_176,
inference(avatar_split_clause,[],[f473,f1964]) ).
fof(f473,plain,
! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f446,f441]) ).
fof(f446,plain,
! [X0] : plus(n4,X0) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f321,f312,f312,f312,f312]) ).
fof(f321,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(f1935,plain,
( spl41_175
| ~ spl41_164
| ~ spl41_166
| ~ spl41_174 ),
inference(avatar_split_clause,[],[f1931,f1928,f1536,f1528,f1933]) ).
fof(f1933,plain,
( spl41_175
<=> ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_175])]) ).
fof(f1928,plain,
( spl41_174
<=> ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_174])]) ).
fof(f1931,plain,
( ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1)
| ~ spl41_164
| ~ spl41_166
| ~ spl41_174 ),
inference(forward_demodulation,[],[f1929,f1748]) ).
fof(f1929,plain,
( ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_174 ),
inference(avatar_component_clause,[],[f1928]) ).
fof(f1930,plain,
spl41_174,
inference(avatar_split_clause,[],[f472,f1928]) ).
fof(f472,plain,
! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f445,f441]) ).
fof(f445,plain,
! [X0] : plus(X0,n4) = plus(plus(plus(plus(X0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f320,f312,f312,f312,f312]) ).
fof(f320,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(f1862,plain,
spl41_173,
inference(avatar_split_clause,[],[f456,f1860]) ).
fof(f1860,plain,
( spl41_173
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_173])]) ).
fof(f456,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ),
inference(definition_unfolding,[],[f360,f312,f312]) ).
fof(f360,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(f1858,plain,
spl41_172,
inference(avatar_split_clause,[],[f455,f1856]) ).
fof(f1856,plain,
( spl41_172
<=> ! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_172])]) ).
fof(f455,plain,
! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f361,f312,f312]) ).
fof(f361,plain,
! [X0,X1] :
( leq(succ(X0),succ(X1))
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f209]) ).
fof(f1854,plain,
spl41_171,
inference(avatar_split_clause,[],[f393,f1852]) ).
fof(f1852,plain,
( spl41_171
<=> ! [X2,X0,X1,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_171])]) ).
fof(f393,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(f1626,plain,
( spl41_169
| spl41_170
| ~ spl41_2
| ~ spl41_161 ),
inference(avatar_split_clause,[],[f1588,f1516,f484,f1623,f1619]) ).
fof(f1619,plain,
( spl41_169
<=> gt(n4,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_169])]) ).
fof(f1623,plain,
( spl41_170
<=> n4 = pv40 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_170])]) ).
fof(f1588,plain,
( n4 = pv40
| gt(n4,pv40)
| ~ spl41_2
| ~ spl41_161 ),
inference(resolution,[],[f1517,f486]) ).
fof(f1546,plain,
( spl41_168
| ~ spl41_59
| ~ spl41_159 ),
inference(avatar_split_clause,[],[f1510,f1505,f783,f1544]) ).
fof(f1544,plain,
( spl41_168
<=> ! [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_168])]) ).
fof(f1505,plain,
( spl41_159
<=> ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_159])]) ).
fof(f1510,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 )
| ~ spl41_59
| ~ spl41_159 ),
inference(forward_demodulation,[],[f1509,f785]) ).
fof(f1509,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_159 ),
inference(forward_demodulation,[],[f1508,f785]) ).
fof(f1508,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_159 ),
inference(forward_demodulation,[],[f1506,f785]) ).
fof(f1506,plain,
( ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_159 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f1542,plain,
spl41_167,
inference(avatar_split_clause,[],[f471,f1540]) ).
fof(f1540,plain,
( spl41_167
<=> ! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_167])]) ).
fof(f471,plain,
! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f444,f441]) ).
fof(f444,plain,
! [X0] : plus(n3,X0) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f319,f312,f312,f312]) ).
fof(f319,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(f1538,plain,
spl41_166,
inference(avatar_split_clause,[],[f470,f1536]) ).
fof(f470,plain,
! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f443,f441]) ).
fof(f443,plain,
! [X0] : plus(X0,n3) = plus(plus(plus(X0,n1),n1),n1),
inference(definition_unfolding,[],[f318,f312,f312,f312]) ).
fof(f318,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(f1534,plain,
spl41_165,
inference(avatar_split_clause,[],[f442,f1532]) ).
fof(f1532,plain,
( spl41_165
<=> ! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_165])]) ).
fof(f442,plain,
! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1),
inference(definition_unfolding,[],[f317,f312,f312]) ).
fof(f317,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(f1530,plain,
spl41_164,
inference(avatar_split_clause,[],[f441,f1528]) ).
fof(f1526,plain,
spl41_163,
inference(avatar_split_clause,[],[f364,f1524]) ).
fof(f364,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(f1522,plain,
spl41_162,
inference(avatar_split_clause,[],[f363,f1520]) ).
fof(f363,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(f1518,plain,
spl41_161,
inference(avatar_split_clause,[],[f337,f1516]) ).
fof(f337,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(f1514,plain,
spl41_160,
inference(avatar_split_clause,[],[f330,f1512]) ).
fof(f1512,plain,
( spl41_160
<=> ! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_160])]) ).
fof(f330,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(f1507,plain,
spl41_159,
inference(avatar_split_clause,[],[f329,f1505]) ).
fof(f329,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(f1503,plain,
( ~ spl41_5
| spl41_158
| ~ spl41_4
| ~ spl41_45 ),
inference(avatar_split_clause,[],[f714,f701,f494,f1500,f499]) ).
fof(f1500,plain,
( spl41_158
<=> init = a_select2(muold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_158])]) ).
fof(f701,plain,
( spl41_45
<=> ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_45])]) ).
fof(f714,plain,
( init = a_select2(muold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_4
| ~ spl41_45 ),
inference(resolution,[],[f702,f496]) ).
fof(f702,plain,
( ! [X3] :
( ~ leq(n0,X3)
| init = a_select2(muold_init,X3)
| ~ leq(X3,n4) )
| ~ spl41_45 ),
inference(avatar_component_clause,[],[f701]) ).
fof(f1463,plain,
( ~ spl41_2
| spl41_157
| ~ spl41_1
| ~ spl41_45 ),
inference(avatar_split_clause,[],[f713,f701,f479,f1460,f484]) ).
fof(f1460,plain,
( spl41_157
<=> init = a_select2(muold_init,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_157])]) ).
fof(f713,plain,
( init = a_select2(muold_init,pv40)
| ~ leq(pv40,n4)
| ~ spl41_1
| ~ spl41_45 ),
inference(resolution,[],[f702,f481]) ).
fof(f1374,plain,
( spl41_156
| ~ spl41_59
| ~ spl41_119 ),
inference(avatar_split_clause,[],[f1131,f1128,f783,f1372]) ).
fof(f1372,plain,
( spl41_156
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_156])]) ).
fof(f1128,plain,
( spl41_119
<=> ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_119])]) ).
fof(f1131,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_59
| ~ spl41_119 ),
inference(forward_demodulation,[],[f1129,f785]) ).
fof(f1129,plain,
( ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_119 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f1366,plain,
( spl41_155
| ~ spl41_59
| ~ spl41_117 ),
inference(avatar_split_clause,[],[f1122,f1119,f783,f1364]) ).
fof(f1364,plain,
( spl41_155
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_155])]) ).
fof(f1119,plain,
( spl41_117
<=> ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_117])]) ).
fof(f1122,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_59
| ~ spl41_117 ),
inference(forward_demodulation,[],[f1120,f785]) ).
fof(f1120,plain,
( ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_117 ),
inference(avatar_component_clause,[],[f1119]) ).
fof(f1358,plain,
( spl41_154
| ~ spl41_59
| ~ spl41_115 ),
inference(avatar_split_clause,[],[f1113,f1110,f783,f1356]) ).
fof(f1356,plain,
( spl41_154
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_154])]) ).
fof(f1110,plain,
( spl41_115
<=> ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_115])]) ).
fof(f1113,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_59
| ~ spl41_115 ),
inference(forward_demodulation,[],[f1111,f785]) ).
fof(f1111,plain,
( ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_115 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1350,plain,
( spl41_153
| ~ spl41_59
| ~ spl41_113 ),
inference(avatar_split_clause,[],[f1104,f1101,f783,f1348]) ).
fof(f1348,plain,
( spl41_153
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_153])]) ).
fof(f1101,plain,
( spl41_113
<=> ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_113])]) ).
fof(f1104,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_59
| ~ spl41_113 ),
inference(forward_demodulation,[],[f1102,f785]) ).
fof(f1102,plain,
( ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_113 ),
inference(avatar_component_clause,[],[f1101]) ).
fof(f1342,plain,
( spl41_152
| ~ spl41_59
| ~ spl41_111 ),
inference(avatar_split_clause,[],[f1095,f1092,f783,f1340]) ).
fof(f1340,plain,
( spl41_152
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_152])]) ).
fof(f1092,plain,
( spl41_111
<=> ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_111])]) ).
fof(f1095,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_59
| ~ spl41_111 ),
inference(forward_demodulation,[],[f1093,f785]) ).
fof(f1093,plain,
( ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_111 ),
inference(avatar_component_clause,[],[f1092]) ).
fof(f1334,plain,
( spl41_151
| ~ spl41_59
| ~ spl41_109 ),
inference(avatar_split_clause,[],[f1086,f1083,f783,f1332]) ).
fof(f1332,plain,
( spl41_151
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_151])]) ).
fof(f1083,plain,
( spl41_109
<=> ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_109])]) ).
fof(f1086,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_59
| ~ spl41_109 ),
inference(forward_demodulation,[],[f1084,f785]) ).
fof(f1084,plain,
( ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_109 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f1326,plain,
( spl41_150
| ~ spl41_59
| ~ spl41_107 ),
inference(avatar_split_clause,[],[f1077,f1074,f783,f1324]) ).
fof(f1324,plain,
( spl41_150
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_150])]) ).
fof(f1074,plain,
( spl41_107
<=> ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_107])]) ).
fof(f1077,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_59
| ~ spl41_107 ),
inference(forward_demodulation,[],[f1075,f785]) ).
fof(f1075,plain,
( ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_107 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f1318,plain,
( spl41_149
| ~ spl41_42
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f798,f783,f684,f1315]) ).
fof(f1315,plain,
( spl41_149
<=> init = a_select3(center_init,pv40,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_149])]) ).
fof(f684,plain,
( spl41_42
<=> init = a_select3(center_init,pv40,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_42])]) ).
fof(f798,plain,
( init = a_select3(center_init,pv40,tptp_float_0_0)
| ~ spl41_42
| ~ spl41_59 ),
inference(superposition,[],[f686,f785]) ).
fof(f686,plain,
( init = a_select3(center_init,pv40,n0)
| ~ spl41_42 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f1313,plain,
( spl41_148
| ~ spl41_59
| ~ spl41_105 ),
inference(avatar_split_clause,[],[f1068,f1065,f783,f1311]) ).
fof(f1311,plain,
( spl41_148
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_148])]) ).
fof(f1065,plain,
( spl41_105
<=> ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_105])]) ).
fof(f1068,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_59
| ~ spl41_105 ),
inference(forward_demodulation,[],[f1066,f785]) ).
fof(f1066,plain,
( ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_105 ),
inference(avatar_component_clause,[],[f1065]) ).
fof(f1305,plain,
( spl41_147
| ~ spl41_59
| ~ spl41_103 ),
inference(avatar_split_clause,[],[f1059,f1056,f783,f1303]) ).
fof(f1303,plain,
( spl41_147
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_147])]) ).
fof(f1056,plain,
( spl41_103
<=> ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_103])]) ).
fof(f1059,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_59
| ~ spl41_103 ),
inference(forward_demodulation,[],[f1057,f785]) ).
fof(f1057,plain,
( ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_103 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1297,plain,
( spl41_146
| ~ spl41_59
| ~ spl41_101 ),
inference(avatar_split_clause,[],[f1050,f1047,f783,f1295]) ).
fof(f1295,plain,
( spl41_146
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_146])]) ).
fof(f1047,plain,
( spl41_101
<=> ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_101])]) ).
fof(f1050,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_59
| ~ spl41_101 ),
inference(forward_demodulation,[],[f1048,f785]) ).
fof(f1048,plain,
( ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_101 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1289,plain,
( spl41_145
| ~ spl41_59
| ~ spl41_99 ),
inference(avatar_split_clause,[],[f1041,f1038,f783,f1287]) ).
fof(f1287,plain,
( spl41_145
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_145])]) ).
fof(f1038,plain,
( spl41_99
<=> ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_99])]) ).
fof(f1041,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_59
| ~ spl41_99 ),
inference(forward_demodulation,[],[f1039,f785]) ).
fof(f1039,plain,
( ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_99 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1281,plain,
( spl41_144
| ~ spl41_59
| ~ spl41_97 ),
inference(avatar_split_clause,[],[f1032,f1029,f783,f1279]) ).
fof(f1279,plain,
( spl41_144
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_144])]) ).
fof(f1029,plain,
( spl41_97
<=> ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_97])]) ).
fof(f1032,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_59
| ~ spl41_97 ),
inference(forward_demodulation,[],[f1030,f785]) ).
fof(f1030,plain,
( ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_97 ),
inference(avatar_component_clause,[],[f1029]) ).
fof(f1273,plain,
( spl41_143
| ~ spl41_59
| ~ spl41_95 ),
inference(avatar_split_clause,[],[f1023,f1020,f783,f1271]) ).
fof(f1271,plain,
( spl41_143
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_143])]) ).
fof(f1020,plain,
( spl41_95
<=> ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_95])]) ).
fof(f1023,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_59
| ~ spl41_95 ),
inference(forward_demodulation,[],[f1021,f785]) ).
fof(f1021,plain,
( ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_95 ),
inference(avatar_component_clause,[],[f1020]) ).
fof(f1265,plain,
( spl41_142
| ~ spl41_59
| ~ spl41_93 ),
inference(avatar_split_clause,[],[f1014,f1011,f783,f1263]) ).
fof(f1263,plain,
( spl41_142
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_142])]) ).
fof(f1011,plain,
( spl41_93
<=> ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_93])]) ).
fof(f1014,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_59
| ~ spl41_93 ),
inference(forward_demodulation,[],[f1012,f785]) ).
fof(f1012,plain,
( ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_93 ),
inference(avatar_component_clause,[],[f1011]) ).
fof(f1257,plain,
( spl41_141
| ~ spl41_59
| ~ spl41_91 ),
inference(avatar_split_clause,[],[f1005,f1002,f783,f1255]) ).
fof(f1255,plain,
( spl41_141
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_141])]) ).
fof(f1002,plain,
( spl41_91
<=> ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_91])]) ).
fof(f1005,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_59
| ~ spl41_91 ),
inference(forward_demodulation,[],[f1003,f785]) ).
fof(f1003,plain,
( ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_91 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f1249,plain,
( spl41_140
| ~ spl41_59
| ~ spl41_89 ),
inference(avatar_split_clause,[],[f996,f993,f783,f1247]) ).
fof(f1247,plain,
( spl41_140
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_140])]) ).
fof(f993,plain,
( spl41_89
<=> ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_89])]) ).
fof(f996,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_59
| ~ spl41_89 ),
inference(forward_demodulation,[],[f994,f785]) ).
fof(f994,plain,
( ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_89 ),
inference(avatar_component_clause,[],[f993]) ).
fof(f1241,plain,
( spl41_139
| ~ spl41_59
| ~ spl41_87 ),
inference(avatar_split_clause,[],[f987,f984,f783,f1239]) ).
fof(f1239,plain,
( spl41_139
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_139])]) ).
fof(f984,plain,
( spl41_87
<=> ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_87])]) ).
fof(f987,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_59
| ~ spl41_87 ),
inference(forward_demodulation,[],[f985,f785]) ).
fof(f985,plain,
( ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_87 ),
inference(avatar_component_clause,[],[f984]) ).
fof(f1233,plain,
( ~ spl41_138
| spl41_46
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f800,f783,f705,f1230]) ).
fof(f705,plain,
( spl41_46
<=> init = a_select2(rho_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_46])]) ).
fof(f800,plain,
( init != a_select2(rho_init,tptp_float_0_0)
| spl41_46
| ~ spl41_59 ),
inference(superposition,[],[f706,f785]) ).
fof(f706,plain,
( init != a_select2(rho_init,n0)
| spl41_46 ),
inference(avatar_component_clause,[],[f705]) ).
fof(f1228,plain,
( spl41_137
| ~ spl41_59
| ~ spl41_85 ),
inference(avatar_split_clause,[],[f978,f975,f783,f1226]) ).
fof(f1226,plain,
( spl41_137
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_137])]) ).
fof(f975,plain,
( spl41_85
<=> ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_85])]) ).
fof(f978,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_59
| ~ spl41_85 ),
inference(forward_demodulation,[],[f976,f785]) ).
fof(f976,plain,
( ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_85 ),
inference(avatar_component_clause,[],[f975]) ).
fof(f1220,plain,
( spl41_136
| ~ spl41_59
| ~ spl41_81 ),
inference(avatar_split_clause,[],[f960,f957,f783,f1218]) ).
fof(f1218,plain,
( spl41_136
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_136])]) ).
fof(f957,plain,
( spl41_81
<=> ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_81])]) ).
fof(f960,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_59
| ~ spl41_81 ),
inference(forward_demodulation,[],[f958,f785]) ).
fof(f958,plain,
( ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_81 ),
inference(avatar_component_clause,[],[f957]) ).
fof(f1212,plain,
( spl41_135
| ~ spl41_59
| ~ spl41_79 ),
inference(avatar_split_clause,[],[f951,f948,f783,f1210]) ).
fof(f1210,plain,
( spl41_135
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_135])]) ).
fof(f948,plain,
( spl41_79
<=> ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_79])]) ).
fof(f951,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_59
| ~ spl41_79 ),
inference(forward_demodulation,[],[f949,f785]) ).
fof(f949,plain,
( ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_79 ),
inference(avatar_component_clause,[],[f948]) ).
fof(f1204,plain,
( spl41_134
| ~ spl41_59
| ~ spl41_77 ),
inference(avatar_split_clause,[],[f942,f939,f783,f1202]) ).
fof(f1202,plain,
( spl41_134
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_134])]) ).
fof(f939,plain,
( spl41_77
<=> ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_77])]) ).
fof(f942,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_59
| ~ spl41_77 ),
inference(forward_demodulation,[],[f940,f785]) ).
fof(f940,plain,
( ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_77 ),
inference(avatar_component_clause,[],[f939]) ).
fof(f1196,plain,
( spl41_133
| ~ spl41_59
| ~ spl41_75 ),
inference(avatar_split_clause,[],[f933,f930,f783,f1194]) ).
fof(f1194,plain,
( spl41_133
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_133])]) ).
fof(f930,plain,
( spl41_75
<=> ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_75])]) ).
fof(f933,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_59
| ~ spl41_75 ),
inference(forward_demodulation,[],[f931,f785]) ).
fof(f931,plain,
( ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_75 ),
inference(avatar_component_clause,[],[f930]) ).
fof(f1188,plain,
( spl41_132
| ~ spl41_59
| ~ spl41_73 ),
inference(avatar_split_clause,[],[f924,f921,f783,f1186]) ).
fof(f1186,plain,
( spl41_132
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_132])]) ).
fof(f921,plain,
( spl41_73
<=> ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_73])]) ).
fof(f924,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_59
| ~ spl41_73 ),
inference(forward_demodulation,[],[f922,f785]) ).
fof(f922,plain,
( ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_73 ),
inference(avatar_component_clause,[],[f921]) ).
fof(f1180,plain,
( spl41_131
| ~ spl41_59
| ~ spl41_70 ),
inference(avatar_split_clause,[],[f910,f907,f783,f1178]) ).
fof(f1178,plain,
( spl41_131
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_131])]) ).
fof(f907,plain,
( spl41_70
<=> ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_70])]) ).
fof(f910,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_59
| ~ spl41_70 ),
inference(forward_demodulation,[],[f908,f785]) ).
fof(f908,plain,
( ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_70 ),
inference(avatar_component_clause,[],[f907]) ).
fof(f1176,plain,
( spl41_130
| ~ spl41_59
| ~ spl41_69 ),
inference(avatar_split_clause,[],[f905,f902,f783,f1174]) ).
fof(f1174,plain,
( spl41_130
<=> ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_130])]) ).
fof(f902,plain,
( spl41_69
<=> ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_69])]) ).
fof(f905,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_59
| ~ spl41_69 ),
inference(forward_demodulation,[],[f903,f785]) ).
fof(f903,plain,
( ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_69 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1172,plain,
( spl41_129
| ~ spl41_59
| ~ spl41_68 ),
inference(avatar_split_clause,[],[f900,f897,f783,f1170]) ).
fof(f1170,plain,
( spl41_129
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_129])]) ).
fof(f897,plain,
( spl41_68
<=> ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_68])]) ).
fof(f900,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) )
| ~ spl41_59
| ~ spl41_68 ),
inference(forward_demodulation,[],[f898,f785]) ).
fof(f898,plain,
( ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) )
| ~ spl41_68 ),
inference(avatar_component_clause,[],[f897]) ).
fof(f1168,plain,
( spl41_128
| ~ spl41_59
| ~ spl41_67 ),
inference(avatar_split_clause,[],[f895,f891,f783,f1166]) ).
fof(f1166,plain,
( spl41_128
<=> ! [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_128])]) ).
fof(f891,plain,
( spl41_67
<=> ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_67])]) ).
fof(f895,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(tptp_float_0_0,uniform_int_rnd(X1,X0)) )
| ~ spl41_59
| ~ spl41_67 ),
inference(forward_demodulation,[],[f894,f785]) ).
fof(f894,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_67 ),
inference(forward_demodulation,[],[f892,f785]) ).
fof(f892,plain,
( ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_67 ),
inference(avatar_component_clause,[],[f891]) ).
fof(f1164,plain,
spl41_127,
inference(avatar_split_clause,[],[f454,f1162]) ).
fof(f1162,plain,
( spl41_127
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_127])]) ).
fof(f454,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f358,f314]) ).
fof(f314,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(f358,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(f1160,plain,
spl41_126,
inference(avatar_split_clause,[],[f453,f1158]) ).
fof(f1158,plain,
( spl41_126
<=> ! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_126])]) ).
fof(f453,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f359,f314]) ).
fof(f359,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f1156,plain,
spl41_125,
inference(avatar_split_clause,[],[f452,f1154]) ).
fof(f1154,plain,
( spl41_125
<=> ! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_125])]) ).
fof(f452,plain,
! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f356,f312]) ).
fof(f356,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(f1152,plain,
( ~ spl41_124
| spl41_47
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f801,f783,f709,f1149]) ).
fof(f1149,plain,
( spl41_124
<=> leq(tptp_float_0_0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_124])]) ).
fof(f709,plain,
( spl41_47
<=> leq(n0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_47])]) ).
fof(f801,plain,
( ~ leq(tptp_float_0_0,n4)
| spl41_47
| ~ spl41_59 ),
inference(superposition,[],[f711,f785]) ).
fof(f711,plain,
( ~ leq(n0,n4)
| spl41_47 ),
inference(avatar_component_clause,[],[f709]) ).
fof(f1147,plain,
spl41_123,
inference(avatar_split_clause,[],[f451,f1145]) ).
fof(f1145,plain,
( spl41_123
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_123])]) ).
fof(f451,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ),
inference(definition_unfolding,[],[f357,f312]) ).
fof(f357,plain,
! [X0,X1] :
( leq(X0,X1)
| ~ gt(succ(X1),X0) ),
inference(cnf_transformation,[],[f207]) ).
fof(f1143,plain,
spl41_122,
inference(avatar_split_clause,[],[f450,f1141]) ).
fof(f1141,plain,
( spl41_122
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_122])]) ).
fof(f450,plain,
! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ),
inference(definition_unfolding,[],[f335,f312]) ).
fof(f335,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(f1139,plain,
spl41_121,
inference(avatar_split_clause,[],[f449,f1137]) ).
fof(f1137,plain,
( spl41_121
<=> ! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_121])]) ).
fof(f449,plain,
! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ),
inference(definition_unfolding,[],[f331,f312]) ).
fof(f331,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(f1135,plain,
spl41_120,
inference(avatar_split_clause,[],[f426,f1133]) ).
fof(f1133,plain,
( spl41_120
<=> ! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_120])]) ).
fof(f426,plain,
! [X0,X1] :
( leq(sK40(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1130,plain,
spl41_119,
inference(avatar_split_clause,[],[f425,f1128]) ).
fof(f425,plain,
! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1126,plain,
spl41_118,
inference(avatar_split_clause,[],[f424,f1124]) ).
fof(f1124,plain,
( spl41_118
<=> ! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_118])]) ).
fof(f424,plain,
! [X0,X1] :
( leq(sK39(X0,X1),X1)
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1121,plain,
spl41_117,
inference(avatar_split_clause,[],[f423,f1119]) ).
fof(f423,plain,
! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1117,plain,
spl41_116,
inference(avatar_split_clause,[],[f421,f1115]) ).
fof(f1115,plain,
( spl41_116
<=> ! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_116])]) ).
fof(f421,plain,
! [X0,X1] :
( leq(sK38(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1112,plain,
spl41_115,
inference(avatar_split_clause,[],[f420,f1110]) ).
fof(f420,plain,
! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1108,plain,
spl41_114,
inference(avatar_split_clause,[],[f419,f1106]) ).
fof(f1106,plain,
( spl41_114
<=> ! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_114])]) ).
fof(f419,plain,
! [X0,X1] :
( leq(sK37(X0,X1),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1103,plain,
spl41_113,
inference(avatar_split_clause,[],[f418,f1101]) ).
fof(f418,plain,
! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1099,plain,
spl41_112,
inference(avatar_split_clause,[],[f416,f1097]) ).
fof(f1097,plain,
( spl41_112
<=> ! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_112])]) ).
fof(f416,plain,
! [X0,X1] :
( leq(sK36(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1094,plain,
spl41_111,
inference(avatar_split_clause,[],[f415,f1092]) ).
fof(f415,plain,
! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1090,plain,
spl41_110,
inference(avatar_split_clause,[],[f414,f1088]) ).
fof(f1088,plain,
( spl41_110
<=> ! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_110])]) ).
fof(f414,plain,
! [X0,X1] :
( leq(sK35(X0,X1),X1)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1085,plain,
spl41_109,
inference(avatar_split_clause,[],[f413,f1083]) ).
fof(f413,plain,
! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1081,plain,
spl41_108,
inference(avatar_split_clause,[],[f401,f1079]) ).
fof(f1079,plain,
( spl41_108
<=> ! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_108])]) ).
fof(f401,plain,
! [X0,X1] :
( leq(sK32(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1076,plain,
spl41_107,
inference(avatar_split_clause,[],[f400,f1074]) ).
fof(f400,plain,
! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1072,plain,
spl41_106,
inference(avatar_split_clause,[],[f399,f1070]) ).
fof(f1070,plain,
( spl41_106
<=> ! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_106])]) ).
fof(f399,plain,
! [X0,X1] :
( leq(sK31(X0,X1),X1)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1067,plain,
spl41_105,
inference(avatar_split_clause,[],[f398,f1065]) ).
fof(f398,plain,
! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1063,plain,
spl41_104,
inference(avatar_split_clause,[],[f390,f1061]) ).
fof(f1061,plain,
( spl41_104
<=> ! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_104])]) ).
fof(f390,plain,
! [X0,X1] :
( leq(sK29(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1058,plain,
spl41_103,
inference(avatar_split_clause,[],[f389,f1056]) ).
fof(f389,plain,
! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1054,plain,
spl41_102,
inference(avatar_split_clause,[],[f388,f1052]) ).
fof(f1052,plain,
( spl41_102
<=> ! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_102])]) ).
fof(f388,plain,
! [X0,X1] :
( leq(sK28(X0,X1),X1)
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1049,plain,
spl41_101,
inference(avatar_split_clause,[],[f387,f1047]) ).
fof(f387,plain,
! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1045,plain,
spl41_100,
inference(avatar_split_clause,[],[f384,f1043]) ).
fof(f1043,plain,
( spl41_100
<=> ! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_100])]) ).
fof(f384,plain,
! [X0,X1] :
( leq(sK27(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1040,plain,
spl41_99,
inference(avatar_split_clause,[],[f383,f1038]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1036,plain,
spl41_98,
inference(avatar_split_clause,[],[f382,f1034]) ).
fof(f1034,plain,
( spl41_98
<=> ! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_98])]) ).
fof(f382,plain,
! [X0,X1] :
( leq(sK26(X0,X1),X1)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1031,plain,
spl41_97,
inference(avatar_split_clause,[],[f381,f1029]) ).
fof(f381,plain,
! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1027,plain,
spl41_96,
inference(avatar_split_clause,[],[f379,f1025]) ).
fof(f1025,plain,
( spl41_96
<=> ! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_96])]) ).
fof(f379,plain,
! [X0,X1] :
( leq(sK25(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1022,plain,
spl41_95,
inference(avatar_split_clause,[],[f378,f1020]) ).
fof(f378,plain,
! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1018,plain,
spl41_94,
inference(avatar_split_clause,[],[f377,f1016]) ).
fof(f1016,plain,
( spl41_94
<=> ! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_94])]) ).
fof(f377,plain,
! [X0,X1] :
( leq(sK24(X0,X1),X1)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1013,plain,
spl41_93,
inference(avatar_split_clause,[],[f376,f1011]) ).
fof(f376,plain,
! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1009,plain,
spl41_92,
inference(avatar_split_clause,[],[f373,f1007]) ).
fof(f1007,plain,
( spl41_92
<=> ! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_92])]) ).
fof(f373,plain,
! [X0,X1] :
( leq(sK23(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1004,plain,
spl41_91,
inference(avatar_split_clause,[],[f372,f1002]) ).
fof(f372,plain,
! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1000,plain,
spl41_90,
inference(avatar_split_clause,[],[f371,f998]) ).
fof(f998,plain,
( spl41_90
<=> ! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_90])]) ).
fof(f371,plain,
! [X0,X1] :
( leq(sK22(X0,X1),X1)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f995,plain,
spl41_89,
inference(avatar_split_clause,[],[f370,f993]) ).
fof(f370,plain,
! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f991,plain,
spl41_88,
inference(avatar_split_clause,[],[f368,f989]) ).
fof(f989,plain,
( spl41_88
<=> ! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_88])]) ).
fof(f368,plain,
! [X0,X1] :
( leq(sK21(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f986,plain,
spl41_87,
inference(avatar_split_clause,[],[f367,f984]) ).
fof(f367,plain,
! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f982,plain,
spl41_86,
inference(avatar_split_clause,[],[f366,f980]) ).
fof(f980,plain,
( spl41_86
<=> ! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_86])]) ).
fof(f366,plain,
! [X0,X1] :
( leq(sK20(X0,X1),X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f977,plain,
spl41_85,
inference(avatar_split_clause,[],[f365,f975]) ).
fof(f365,plain,
! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f973,plain,
spl41_84,
inference(avatar_split_clause,[],[f362,f971]) ).
fof(f971,plain,
( spl41_84
<=> ! [X2,X0,X1] : a_select2(tptp_update2(X0,X1,X2),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_84])]) ).
fof(f362,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(f969,plain,
( spl41_83
| ~ spl41_3
| ~ spl41_61 ),
inference(avatar_split_clause,[],[f841,f812,f489,f966]) ).
fof(f966,plain,
( spl41_83
<=> leq(n1,loopcounter) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_83])]) ).
fof(f812,plain,
( spl41_61
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_61])]) ).
fof(f841,plain,
( leq(n1,loopcounter)
| ~ spl41_3
| ~ spl41_61 ),
inference(resolution,[],[f813,f491]) ).
fof(f813,plain,
( ! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) )
| ~ spl41_61 ),
inference(avatar_component_clause,[],[f812]) ).
fof(f964,plain,
spl41_82,
inference(avatar_split_clause,[],[f353,f962]) ).
fof(f962,plain,
( spl41_82
<=> ! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_82])]) ).
fof(f353,plain,
! [X0,X1] :
( leq(sK19(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f959,plain,
spl41_81,
inference(avatar_split_clause,[],[f352,f957]) ).
fof(f352,plain,
! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f955,plain,
spl41_80,
inference(avatar_split_clause,[],[f351,f953]) ).
fof(f953,plain,
( spl41_80
<=> ! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_80])]) ).
fof(f351,plain,
! [X0,X1] :
( leq(sK18(X0,X1),X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f950,plain,
spl41_79,
inference(avatar_split_clause,[],[f350,f948]) ).
fof(f350,plain,
! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f946,plain,
spl41_78,
inference(avatar_split_clause,[],[f347,f944]) ).
fof(f944,plain,
( spl41_78
<=> ! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_78])]) ).
fof(f347,plain,
! [X0,X1] :
( leq(sK17(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f941,plain,
spl41_77,
inference(avatar_split_clause,[],[f346,f939]) ).
fof(f346,plain,
! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f937,plain,
spl41_76,
inference(avatar_split_clause,[],[f345,f935]) ).
fof(f935,plain,
( spl41_76
<=> ! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_76])]) ).
fof(f345,plain,
! [X0,X1] :
( leq(sK16(X0,X1),X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f932,plain,
spl41_75,
inference(avatar_split_clause,[],[f344,f930]) ).
fof(f344,plain,
! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f928,plain,
spl41_74,
inference(avatar_split_clause,[],[f341,f926]) ).
fof(f926,plain,
( spl41_74
<=> ! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_74])]) ).
fof(f341,plain,
! [X0,X1] :
( leq(sK15(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f923,plain,
spl41_73,
inference(avatar_split_clause,[],[f340,f921]) ).
fof(f340,plain,
! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f919,plain,
( spl41_72
| ~ spl41_4
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f788,f783,f494,f916]) ).
fof(f916,plain,
( spl41_72
<=> leq(tptp_float_0_0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_72])]) ).
fof(f788,plain,
( leq(tptp_float_0_0,sK13)
| ~ spl41_4
| ~ spl41_59 ),
inference(superposition,[],[f496,f785]) ).
fof(f914,plain,
spl41_71,
inference(avatar_split_clause,[],[f339,f912]) ).
fof(f912,plain,
( spl41_71
<=> ! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_71])]) ).
fof(f339,plain,
! [X0,X1] :
( leq(sK14(X0,X1),X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f909,plain,
spl41_70,
inference(avatar_split_clause,[],[f338,f907]) ).
fof(f338,plain,
! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f904,plain,
spl41_69,
inference(avatar_split_clause,[],[f336,f902]) ).
fof(f336,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(f899,plain,
spl41_68,
inference(avatar_split_clause,[],[f333,f897]) ).
fof(f333,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(f893,plain,
spl41_67,
inference(avatar_split_clause,[],[f332,f891]) ).
fof(f332,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(f872,plain,
spl41_66,
inference(avatar_split_clause,[],[f440,f870]) ).
fof(f870,plain,
( spl41_66
<=> ! [X0] : plus(X0,n1) = plus(n1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_66])]) ).
fof(f440,plain,
! [X0] : plus(X0,n1) = plus(n1,X0),
inference(definition_unfolding,[],[f313,f312]) ).
fof(f313,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(f868,plain,
spl41_65,
inference(avatar_split_clause,[],[f439,f866]) ).
fof(f866,plain,
( spl41_65
<=> ! [X0] : plus(minus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_65])]) ).
fof(f439,plain,
! [X0] : plus(minus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f310,f312,f314]) ).
fof(f310,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(f864,plain,
( spl41_64
| ~ spl41_1
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f787,f783,f479,f861]) ).
fof(f861,plain,
( spl41_64
<=> leq(tptp_float_0_0,pv40) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_64])]) ).
fof(f787,plain,
( leq(tptp_float_0_0,pv40)
| ~ spl41_1
| ~ spl41_59 ),
inference(superposition,[],[f481,f785]) ).
fof(f859,plain,
spl41_63,
inference(avatar_split_clause,[],[f438,f857]) ).
fof(f857,plain,
( spl41_63
<=> ! [X0] : minus(plus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_63])]) ).
fof(f438,plain,
! [X0] : minus(plus(X0,n1),n1) = X0,
inference(definition_unfolding,[],[f309,f314,f312]) ).
fof(f309,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(f818,plain,
( spl41_62
| ~ spl41_59
| ~ spl41_60 ),
inference(avatar_split_clause,[],[f810,f807,f783,f816]) ).
fof(f816,plain,
( spl41_62
<=> ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_62])]) ).
fof(f807,plain,
( spl41_60
<=> ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_60])]) ).
fof(f810,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl41_59
| ~ spl41_60 ),
inference(forward_demodulation,[],[f808,f785]) ).
fof(f808,plain,
( ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_60 ),
inference(avatar_component_clause,[],[f807]) ).
fof(f814,plain,
spl41_61,
inference(avatar_split_clause,[],[f334,f812]) ).
fof(f334,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(f809,plain,
spl41_60,
inference(avatar_split_clause,[],[f315,f807]) ).
fof(f315,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(f786,plain,
( spl41_59
| ~ spl41_58 ),
inference(avatar_split_clause,[],[f781,f778,f783]) ).
fof(f778,plain,
( spl41_58
<=> ! [X0] : n0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_58])]) ).
fof(f781,plain,
( n0 = tptp_float_0_0
| ~ spl41_58 ),
inference(forward_demodulation,[],[f779,f315]) ).
fof(f779,plain,
( ! [X0] : n0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_58 ),
inference(avatar_component_clause,[],[f778]) ).
fof(f780,plain,
spl41_58,
inference(avatar_split_clause,[],[f311,f778]) ).
fof(f311,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(f770,plain,
spl41_57,
inference(avatar_split_clause,[],[f469,f767]) ).
fof(f767,plain,
( spl41_57
<=> n5 = plus(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_57])]) ).
fof(f469,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[],[f468,f465]) ).
fof(f465,plain,
n4 = plus(n3,n1),
inference(forward_demodulation,[],[f464,f462]) ).
fof(f462,plain,
n3 = plus(n2,n1),
inference(forward_demodulation,[],[f461,f460]) ).
fof(f460,plain,
n2 = plus(n1,n1),
inference(forward_demodulation,[],[f433,f431]) ).
fof(f431,plain,
n1 = plus(n0,n1),
inference(definition_unfolding,[],[f300,f312]) ).
fof(f300,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f91,axiom,
n1 = succ(n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_1) ).
fof(f433,plain,
n2 = plus(plus(n0,n1),n1),
inference(definition_unfolding,[],[f302,f312,f312]) ).
fof(f302,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(f461,plain,
n3 = plus(plus(n1,n1),n1),
inference(forward_demodulation,[],[f434,f431]) ).
fof(f434,plain,
n3 = plus(plus(plus(n0,n1),n1),n1),
inference(definition_unfolding,[],[f303,f312,f312,f312]) ).
fof(f303,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(f464,plain,
n4 = plus(plus(n2,n1),n1),
inference(forward_demodulation,[],[f463,f460]) ).
fof(f463,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f435,f431]) ).
fof(f435,plain,
n4 = plus(plus(plus(plus(n0,n1),n1),n1),n1),
inference(definition_unfolding,[],[f304,f312,f312,f312,f312]) ).
fof(f304,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(f468,plain,
n5 = plus(plus(n3,n1),n1),
inference(forward_demodulation,[],[f467,f462]) ).
fof(f467,plain,
n5 = plus(plus(plus(n2,n1),n1),n1),
inference(forward_demodulation,[],[f466,f460]) ).
fof(f466,plain,
n5 = plus(plus(plus(plus(n1,n1),n1),n1),n1),
inference(forward_demodulation,[],[f436,f431]) ).
fof(f436,plain,
n5 = plus(plus(plus(plus(plus(n0,n1),n1),n1),n1),n1),
inference(definition_unfolding,[],[f305,f312,f312,f312,f312,f312]) ).
fof(f305,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(f765,plain,
spl41_56,
inference(avatar_split_clause,[],[f465,f762]) ).
fof(f762,plain,
( spl41_56
<=> n4 = plus(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_56])]) ).
fof(f760,plain,
spl41_55,
inference(avatar_split_clause,[],[f462,f757]) ).
fof(f757,plain,
( spl41_55
<=> n3 = plus(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_55])]) ).
fof(f755,plain,
spl41_54,
inference(avatar_split_clause,[],[f460,f752]) ).
fof(f752,plain,
( spl41_54
<=> n2 = plus(n1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_54])]) ).
fof(f750,plain,
spl41_53,
inference(avatar_split_clause,[],[f437,f748]) ).
fof(f437,plain,
! [X0] : gt(plus(X0,n1),X0),
inference(definition_unfolding,[],[f308,f312]) ).
fof(f308,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(f746,plain,
spl41_52,
inference(avatar_split_clause,[],[f432,f743]) ).
fof(f743,plain,
( spl41_52
<=> n0 = plus(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_52])]) ).
fof(f432,plain,
n0 = plus(tptp_minus_1,n1),
inference(definition_unfolding,[],[f301,f312]) ).
fof(f301,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(f741,plain,
spl41_51,
inference(avatar_split_clause,[],[f431,f738]) ).
fof(f738,plain,
( spl41_51
<=> n1 = plus(n0,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_51])]) ).
fof(f733,plain,
spl41_50,
inference(avatar_split_clause,[],[f260,f731]) ).
fof(f731,plain,
( spl41_50
<=> ! [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_50])]) ).
fof(f260,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(sigmaold_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(pv40,n4)
& leq(n0,pv40) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f192,f193]) ).
fof(f193,plain,
( ? [X0] :
( init != a_select2(sigmaold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
=> ( init != a_select2(sigmaold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
( ? [X0] :
( init != a_select2(sigmaold_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(pv40,n4)
& leq(n0,pv40) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
( ? [X9] :
( init != a_select2(sigmaold_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(pv40,n4)
& leq(n0,pv40) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
( ? [X9] :
( init != a_select2(sigmaold_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(pv40,n4)
& 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(pv40,n4)
& leq(n0,pv40) )
=> ! [X9] :
( ( leq(X9,n4)
& leq(n0,X9) )
=> init = a_select2(sigmaold_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(pv40,n4)
& leq(n0,pv40) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(sigmaold_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(pv40,n4)
& leq(n0,pv40) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(sigmaold_init,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0066) ).
fof(f726,plain,
( ~ spl41_3
| spl41_49 ),
inference(avatar_split_clause,[],[f267,f724,f489]) ).
fof(f267,plain,
! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f719,plain,
( ~ spl41_3
| spl41_48 ),
inference(avatar_split_clause,[],[f266,f717,f489]) ).
fof(f266,plain,
! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f712,plain,
( spl41_46
| ~ spl41_47
| ~ spl41_7
| ~ spl41_41 ),
inference(avatar_split_clause,[],[f689,f680,f509,f709,f705]) ).
fof(f509,plain,
( spl41_7
<=> ! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_7])]) ).
fof(f680,plain,
( spl41_41
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_41])]) ).
fof(f689,plain,
( ~ leq(n0,n4)
| init = a_select2(rho_init,n0)
| ~ spl41_7
| ~ spl41_41 ),
inference(resolution,[],[f681,f510]) ).
fof(f510,plain,
( ! [X7] :
( ~ leq(n0,X7)
| ~ leq(X7,n4)
| init = a_select2(rho_init,X7) )
| ~ spl41_7 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f681,plain,
( ! [X0] : leq(X0,X0)
| ~ spl41_41 ),
inference(avatar_component_clause,[],[f680]) ).
fof(f703,plain,
( ~ spl41_3
| spl41_45 ),
inference(avatar_split_clause,[],[f265,f701,f489]) ).
fof(f265,plain,
! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f697,plain,
spl41_44,
inference(avatar_split_clause,[],[f430,f695]) ).
fof(f695,plain,
( spl41_44
<=> ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,minus(pv40,n1))
| ~ leq(n0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_44])]) ).
fof(f430,plain,
! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,minus(pv40,n1))
| ~ leq(n0,X6) ),
inference(definition_unfolding,[],[f262,f314]) ).
fof(f262,plain,
! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,pred(pv40))
| ~ leq(n0,X6) ),
inference(cnf_transformation,[],[f194]) ).
fof(f693,plain,
spl41_43,
inference(avatar_split_clause,[],[f429,f691]) ).
fof(f691,plain,
( spl41_43
<=> ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,minus(pv40,n1))
| ~ leq(n0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_43])]) ).
fof(f429,plain,
! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,minus(pv40,n1))
| ~ leq(n0,X5) ),
inference(definition_unfolding,[],[f263,f314]) ).
fof(f263,plain,
! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,pred(pv40))
| ~ leq(n0,X5) ),
inference(cnf_transformation,[],[f194]) ).
fof(f687,plain,
( spl41_42
| ~ spl41_2
| ~ spl41_1
| ~ spl41_8 ),
inference(avatar_split_clause,[],[f518,f515,f479,f484,f684]) ).
fof(f515,plain,
( spl41_8
<=> ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_8])]) ).
fof(f518,plain,
( ~ leq(pv40,n4)
| init = a_select3(center_init,pv40,n0)
| ~ spl41_1
| ~ spl41_8 ),
inference(resolution,[],[f516,f481]) ).
fof(f516,plain,
( ! [X4] :
( ~ leq(n0,X4)
| ~ leq(X4,n4)
| init = a_select3(center_init,X4,n0) )
| ~ spl41_8 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f682,plain,
spl41_41,
inference(avatar_split_clause,[],[f307,f680]) ).
fof(f307,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(f678,plain,
spl41_40,
inference(avatar_split_clause,[],[f306,f676]) ).
fof(f676,plain,
( spl41_40
<=> ! [X0] : ~ gt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_40])]) ).
fof(f306,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(f674,plain,
spl41_39,
inference(avatar_split_clause,[],[f299,f671]) ).
fof(f671,plain,
( spl41_39
<=> gt(n0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_39])]) ).
fof(f299,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(f669,plain,
spl41_38,
inference(avatar_split_clause,[],[f298,f666]) ).
fof(f666,plain,
( spl41_38
<=> gt(n1,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_38])]) ).
fof(f298,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(f664,plain,
( spl41_37
| ~ spl41_5
| ~ spl41_4
| ~ spl41_7 ),
inference(avatar_split_clause,[],[f513,f509,f494,f499,f661]) ).
fof(f661,plain,
( spl41_37
<=> init = a_select2(rho_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_37])]) ).
fof(f513,plain,
( ~ leq(sK13,n4)
| init = a_select2(rho_init,sK13)
| ~ spl41_4
| ~ spl41_7 ),
inference(resolution,[],[f510,f496]) ).
fof(f659,plain,
spl41_36,
inference(avatar_split_clause,[],[f297,f656]) ).
fof(f656,plain,
( spl41_36
<=> gt(n4,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_36])]) ).
fof(f297,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(f654,plain,
spl41_35,
inference(avatar_split_clause,[],[f296,f651]) ).
fof(f651,plain,
( spl41_35
<=> gt(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_35])]) ).
fof(f296,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(f649,plain,
spl41_34,
inference(avatar_split_clause,[],[f295,f646]) ).
fof(f646,plain,
( spl41_34
<=> gt(n4,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_34])]) ).
fof(f295,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(f644,plain,
spl41_33,
inference(avatar_split_clause,[],[f294,f641]) ).
fof(f641,plain,
( spl41_33
<=> gt(n4,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_33])]) ).
fof(f294,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(f639,plain,
spl41_32,
inference(avatar_split_clause,[],[f293,f636]) ).
fof(f636,plain,
( spl41_32
<=> gt(n1,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_32])]) ).
fof(f293,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(f634,plain,
spl41_31,
inference(avatar_split_clause,[],[f292,f631]) ).
fof(f631,plain,
( spl41_31
<=> gt(n4,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_31])]) ).
fof(f292,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(f629,plain,
spl41_30,
inference(avatar_split_clause,[],[f291,f626]) ).
fof(f626,plain,
( spl41_30
<=> gt(n2,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_30])]) ).
fof(f291,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(f624,plain,
spl41_29,
inference(avatar_split_clause,[],[f290,f621]) ).
fof(f621,plain,
( spl41_29
<=> gt(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_29])]) ).
fof(f290,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(f619,plain,
spl41_28,
inference(avatar_split_clause,[],[f289,f616]) ).
fof(f616,plain,
( spl41_28
<=> gt(n2,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_28])]) ).
fof(f289,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(f614,plain,
spl41_27,
inference(avatar_split_clause,[],[f288,f611]) ).
fof(f611,plain,
( spl41_27
<=> gt(n3,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_27])]) ).
fof(f288,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(f609,plain,
spl41_26,
inference(avatar_split_clause,[],[f287,f606]) ).
fof(f606,plain,
( spl41_26
<=> gt(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_26])]) ).
fof(f287,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(f604,plain,
spl41_25,
inference(avatar_split_clause,[],[f286,f601]) ).
fof(f601,plain,
( spl41_25
<=> gt(n3,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_25])]) ).
fof(f286,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(f599,plain,
spl41_24,
inference(avatar_split_clause,[],[f285,f596]) ).
fof(f596,plain,
( spl41_24
<=> gt(n3,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_24])]) ).
fof(f285,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(f594,plain,
spl41_23,
inference(avatar_split_clause,[],[f284,f591]) ).
fof(f591,plain,
( spl41_23
<=> gt(n5,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_23])]) ).
fof(f284,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(f589,plain,
spl41_22,
inference(avatar_split_clause,[],[f283,f586]) ).
fof(f586,plain,
( spl41_22
<=> gt(n5,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_22])]) ).
fof(f283,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(f584,plain,
spl41_21,
inference(avatar_split_clause,[],[f282,f581]) ).
fof(f581,plain,
( spl41_21
<=> gt(n5,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_21])]) ).
fof(f282,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(f579,plain,
spl41_20,
inference(avatar_split_clause,[],[f281,f576]) ).
fof(f576,plain,
( spl41_20
<=> gt(n5,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_20])]) ).
fof(f281,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(f574,plain,
spl41_19,
inference(avatar_split_clause,[],[f280,f571]) ).
fof(f571,plain,
( spl41_19
<=> gt(n5,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_19])]) ).
fof(f280,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(f569,plain,
spl41_18,
inference(avatar_split_clause,[],[f279,f566]) ).
fof(f566,plain,
( spl41_18
<=> gt(n5,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_18])]) ).
fof(f279,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(f564,plain,
spl41_17,
inference(avatar_split_clause,[],[f278,f561]) ).
fof(f561,plain,
( spl41_17
<=> gt(n135299,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_17])]) ).
fof(f278,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(f559,plain,
( spl41_16
| ~ spl41_2
| ~ spl41_1
| ~ spl41_7 ),
inference(avatar_split_clause,[],[f512,f509,f479,f484,f556]) ).
fof(f512,plain,
( ~ leq(pv40,n4)
| init = a_select2(rho_init,pv40)
| ~ spl41_1
| ~ spl41_7 ),
inference(resolution,[],[f510,f481]) ).
fof(f554,plain,
spl41_15,
inference(avatar_split_clause,[],[f277,f551]) ).
fof(f551,plain,
( spl41_15
<=> gt(n135299,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_15])]) ).
fof(f277,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(f549,plain,
spl41_14,
inference(avatar_split_clause,[],[f276,f546]) ).
fof(f546,plain,
( spl41_14
<=> gt(n135299,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_14])]) ).
fof(f276,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(f544,plain,
spl41_13,
inference(avatar_split_clause,[],[f275,f541]) ).
fof(f541,plain,
( spl41_13
<=> gt(n135299,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_13])]) ).
fof(f275,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(f539,plain,
spl41_12,
inference(avatar_split_clause,[],[f274,f536]) ).
fof(f536,plain,
( spl41_12
<=> gt(n135299,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_12])]) ).
fof(f274,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(f534,plain,
spl41_11,
inference(avatar_split_clause,[],[f273,f531]) ).
fof(f531,plain,
( spl41_11
<=> gt(n135299,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_11])]) ).
fof(f273,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(f529,plain,
spl41_10,
inference(avatar_split_clause,[],[f272,f526]) ).
fof(f526,plain,
( spl41_10
<=> gt(n135299,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_10])]) ).
fof(f272,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(f524,plain,
~ spl41_9,
inference(avatar_split_clause,[],[f271,f521]) ).
fof(f521,plain,
( spl41_9
<=> def = use ),
introduced(avatar_definition,[new_symbols(naming,[spl41_9])]) ).
fof(f271,plain,
def != use,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
def != use,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defuse) ).
fof(f517,plain,
spl41_8,
inference(avatar_split_clause,[],[f264,f515]) ).
fof(f264,plain,
! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ),
inference(cnf_transformation,[],[f194]) ).
fof(f511,plain,
spl41_7,
inference(avatar_split_clause,[],[f261,f509]) ).
fof(f261,plain,
! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) ),
inference(cnf_transformation,[],[f194]) ).
fof(f507,plain,
~ spl41_6,
inference(avatar_split_clause,[],[f270,f504]) ).
fof(f270,plain,
init != a_select2(sigmaold_init,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f502,plain,
spl41_5,
inference(avatar_split_clause,[],[f269,f499]) ).
fof(f269,plain,
leq(sK13,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f497,plain,
spl41_4,
inference(avatar_split_clause,[],[f268,f494]) ).
fof(f268,plain,
leq(n0,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f492,plain,
spl41_3,
inference(avatar_split_clause,[],[f259,f489]) ).
fof(f259,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f194]) ).
fof(f487,plain,
spl41_2,
inference(avatar_split_clause,[],[f258,f484]) ).
fof(f258,plain,
leq(pv40,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f482,plain,
spl41_1,
inference(avatar_split_clause,[],[f257,f479]) ).
fof(f257,plain,
leq(n0,pv40),
inference(cnf_transformation,[],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWV178+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.10/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.32 % Computer : n010.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Fri May 3 21:09:07 EDT 2024
% 0.18/0.32 % CPUTime :
% 0.18/0.33 % (17126)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.34 % (17130)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.18/0.35 % (17129)WARNING: value z3 for option sas not known
% 0.18/0.35 % (17127)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.18/0.35 % (17128)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.18/0.35 % (17129)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)
% 0.18/0.35 % (17131)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)
% 0.18/0.35 % (17132)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)
% 0.18/0.35 % (17133)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)
% 0.18/0.40 TRYING [1]
% 0.18/0.41 TRYING [2]
% 0.18/0.45 % (17131)First to succeed.
% 0.18/0.46 % (17131)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17126"
% 0.18/0.47 % (17131)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (17131)------------------------------
% 0.18/0.47 % (17131)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.18/0.47 % (17131)Termination reason: Refutation
% 0.18/0.47
% 0.18/0.47 % (17131)Memory used [KB]: 3062
% 0.18/0.47 % (17131)Time elapsed: 0.118 s
% 0.18/0.47 % (17131)Instructions burned: 240 (million)
% 0.18/0.47 % (17126)Success in time 0.142 s
%------------------------------------------------------------------------------