TSTP Solution File: SWV173+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV173+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 : n007.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 10:47:02 EDT 2024
% Result : Theorem 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 373
% Syntax : Number of formulae : 1166 ( 324 unt; 0 def)
% Number of atoms : 4128 ( 813 equ)
% Maximal formula atoms : 35 ( 3 avg)
% Number of connectives : 4651 (1689 ~;1849 |; 708 &)
% ( 259 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 273 ( 271 usr; 257 prp; 0-4 aty)
% Number of functors : 68 ( 68 usr; 23 con; 0-4 aty)
% Number of variables : 2101 (1944 !; 157 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3196,plain,
$false,
inference(avatar_sat_refutation,[],[f480,f485,f490,f495,f500,f505,f509,f513,f517,f527,f534,f539,f544,f553,f558,f563,f568,f573,f578,f583,f588,f593,f598,f603,f608,f613,f618,f623,f628,f633,f638,f643,f648,f653,f658,f663,f668,f673,f678,f683,f687,f691,f696,f701,f709,f716,f723,f730,f738,f743,f747,f752,f757,f762,f767,f772,f782,f788,f810,f815,f819,f860,f865,f869,f873,f894,f900,f905,f910,f915,f920,f924,f929,f933,f938,f942,f947,f951,f956,f960,f965,f970,f974,f978,f983,f987,f992,f996,f1001,f1005,f1010,f1014,f1019,f1023,f1028,f1032,f1037,f1041,f1046,f1050,f1055,f1059,f1064,f1068,f1073,f1077,f1082,f1086,f1091,f1095,f1100,f1104,f1109,f1113,f1118,f1122,f1127,f1131,f1136,f1140,f1144,f1148,f1157,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1196,f1200,f1204,f1208,f1212,f1216,f1220,f1224,f1228,f1232,f1236,f1241,f1245,f1249,f1253,f1257,f1261,f1265,f1269,f1273,f1277,f1281,f1286,f1291,f1295,f1384,f1420,f1425,f1432,f1437,f1441,f1445,f1449,f1453,f1457,f1461,f1465,f1469,f1768,f1772,f1776,f1785,f1851,f1856,f1887,f1892,f1924,f1930,f2002,f2008,f2013,f2018,f2022,f2026,f2030,f2034,f2082,f2088,f2094,f2103,f2107,f2210,f2216,f2222,f2258,f2264,f2268,f2272,f2276,f2280,f2284,f2288,f2292,f2296,f2302,f2307,f2311,f2315,f2319,f2328,f2332,f2336,f2415,f2421,f2457,f2462,f2467,f2473,f2509,f2588,f2594,f2600,f2604,f2676,f2682,f2725,f2729,f2735,f2741,f2745,f2821,f2827,f2833,f2837,f2922,f2929,f2969,f2975,f3018,f3023,f3027,f3032,f3037,f3042,f3051,f3089,f3183,f3188,f3194,f3195]) ).
fof(f3195,plain,
( ~ spl41_5
| spl41_6
| ~ spl41_4
| ~ spl41_47 ),
inference(avatar_split_clause,[],[f718,f714,f492,f502,f497]) ).
fof(f497,plain,
( spl41_5
<=> leq(sK13,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_5])]) ).
fof(f502,plain,
( spl41_6
<=> init = a_select2(rhoold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_6])]) ).
fof(f492,plain,
( spl41_4
<=> leq(n0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_4])]) ).
fof(f714,plain,
( spl41_47
<=> ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(n0,X2)
| ~ leq(X2,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_47])]) ).
fof(f718,plain,
( init = a_select2(rhoold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_4
| ~ spl41_47 ),
inference(resolution,[],[f715,f494]) ).
fof(f494,plain,
( leq(n0,sK13)
| ~ spl41_4 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f715,plain,
( ! [X2] :
( ~ leq(n0,X2)
| init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4) )
| ~ spl41_47 ),
inference(avatar_component_clause,[],[f714]) ).
fof(f3194,plain,
( ~ spl41_256
| ~ spl41_59
| spl41_255 ),
inference(avatar_split_clause,[],[f3189,f3185,f785,f3191]) ).
fof(f3191,plain,
( spl41_256
<=> init = a_select2(muold_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_256])]) ).
fof(f785,plain,
( spl41_59
<=> n0 = tptp_float_0_0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_59])]) ).
fof(f3185,plain,
( spl41_255
<=> init = a_select2(muold_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_255])]) ).
fof(f3189,plain,
( init != a_select2(muold_init,tptp_float_0_0)
| ~ spl41_59
| spl41_255 ),
inference(forward_demodulation,[],[f3186,f787]) ).
fof(f787,plain,
( n0 = tptp_float_0_0
| ~ spl41_59 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f3186,plain,
( init != a_select2(muold_init,n0)
| spl41_255 ),
inference(avatar_component_clause,[],[f3185]) ).
fof(f3188,plain,
( ~ spl41_125
| spl41_255
| ~ spl41_43
| ~ spl41_46 ),
inference(avatar_split_clause,[],[f712,f707,f689,f3185,f1154]) ).
fof(f1154,plain,
( spl41_125
<=> leq(n0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_125])]) ).
fof(f689,plain,
( spl41_43
<=> ! [X0] : leq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_43])]) ).
fof(f707,plain,
( spl41_46
<=> ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(n0,X3)
| ~ leq(X3,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_46])]) ).
fof(f712,plain,
( init = a_select2(muold_init,n0)
| ~ leq(n0,n4)
| ~ spl41_43
| ~ spl41_46 ),
inference(resolution,[],[f708,f690]) ).
fof(f690,plain,
( ! [X0] : leq(X0,X0)
| ~ spl41_43 ),
inference(avatar_component_clause,[],[f689]) ).
fof(f708,plain,
( ! [X3] :
( ~ leq(n0,X3)
| init = a_select2(muold_init,X3)
| ~ leq(X3,n4) )
| ~ spl41_46 ),
inference(avatar_component_clause,[],[f707]) ).
fof(f3183,plain,
( ~ spl41_5
| spl41_254
| ~ spl41_4
| ~ spl41_46 ),
inference(avatar_split_clause,[],[f711,f707,f492,f3180,f497]) ).
fof(f3180,plain,
( spl41_254
<=> init = a_select2(muold_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_254])]) ).
fof(f711,plain,
( init = a_select2(muold_init,sK13)
| ~ leq(sK13,n4)
| ~ spl41_4
| ~ spl41_46 ),
inference(resolution,[],[f708,f494]) ).
fof(f3089,plain,
( spl41_253
| ~ spl41_232
| ~ spl41_249 ),
inference(avatar_split_clause,[],[f3033,f3030,f2718,f3087]) ).
fof(f3087,plain,
( spl41_253
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_253])]) ).
fof(f2718,plain,
( spl41_232
<=> tptp_float_0_0 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_232])]) ).
fof(f3030,plain,
( spl41_249
<=> ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_249])]) ).
fof(f3033,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n4) )
| ~ spl41_232
| ~ spl41_249 ),
inference(forward_demodulation,[],[f3031,f2720]) ).
fof(f2720,plain,
( tptp_float_0_0 = sK13
| ~ spl41_232 ),
inference(avatar_component_clause,[],[f2718]) ).
fof(f3031,plain,
( ! [X0] :
( ~ leq(X0,sK13)
| leq(X0,n4) )
| ~ spl41_249 ),
inference(avatar_component_clause,[],[f3030]) ).
fof(f3051,plain,
( spl41_252
| ~ spl41_215
| ~ spl41_248 ),
inference(avatar_split_clause,[],[f3028,f3025,f2321,f3049]) ).
fof(f3049,plain,
( spl41_252
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n135299) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_252])]) ).
fof(f2321,plain,
( spl41_215
<=> tptp_float_0_0 = pv10 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_215])]) ).
fof(f3025,plain,
( spl41_248
<=> ! [X0] :
( leq(X0,n135299)
| ~ leq(X0,pv10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_248])]) ).
fof(f3028,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,n135299) )
| ~ spl41_215
| ~ spl41_248 ),
inference(forward_demodulation,[],[f3026,f2323]) ).
fof(f2323,plain,
( tptp_float_0_0 = pv10
| ~ spl41_215 ),
inference(avatar_component_clause,[],[f2321]) ).
fof(f3026,plain,
( ! [X0] :
( ~ leq(X0,pv10)
| leq(X0,n135299) )
| ~ spl41_248 ),
inference(avatar_component_clause,[],[f3025]) ).
fof(f3042,plain,
( spl41_251
| ~ spl41_4
| ~ spl41_59
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1642,f1447,f785,f492,f3040]) ).
fof(f3040,plain,
( spl41_251
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_251])]) ).
fof(f1447,plain,
( spl41_166
<=> ! [X2,X0,X1] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_166])]) ).
fof(f1642,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,sK13) )
| ~ spl41_4
| ~ spl41_59
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1585,f787]) ).
fof(f1585,plain,
( ! [X0] :
( leq(X0,sK13)
| ~ leq(X0,n0) )
| ~ spl41_4
| ~ spl41_166 ),
inference(resolution,[],[f1448,f494]) ).
fof(f1448,plain,
( ! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1) )
| ~ spl41_166 ),
inference(avatar_component_clause,[],[f1447]) ).
fof(f3037,plain,
( spl41_250
| ~ spl41_1
| ~ spl41_59
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1641,f1447,f785,f477,f3035]) ).
fof(f3035,plain,
( spl41_250
<=> ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_250])]) ).
fof(f477,plain,
( spl41_1
<=> leq(n0,pv10) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_1])]) ).
fof(f1641,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| leq(X0,pv10) )
| ~ spl41_1
| ~ spl41_59
| ~ spl41_166 ),
inference(forward_demodulation,[],[f1584,f787]) ).
fof(f1584,plain,
( ! [X0] :
( leq(X0,pv10)
| ~ leq(X0,n0) )
| ~ spl41_1
| ~ spl41_166 ),
inference(resolution,[],[f1448,f479]) ).
fof(f479,plain,
( leq(n0,pv10)
| ~ spl41_1 ),
inference(avatar_component_clause,[],[f477]) ).
fof(f3032,plain,
( spl41_249
| ~ spl41_5
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1616,f1447,f497,f3030]) ).
fof(f1616,plain,
( ! [X0] :
( leq(X0,n4)
| ~ leq(X0,sK13) )
| ~ spl41_5
| ~ spl41_166 ),
inference(resolution,[],[f1448,f499]) ).
fof(f499,plain,
( leq(sK13,n4)
| ~ spl41_5 ),
inference(avatar_component_clause,[],[f497]) ).
fof(f3027,plain,
( spl41_248
| ~ spl41_2
| ~ spl41_166 ),
inference(avatar_split_clause,[],[f1615,f1447,f482,f3025]) ).
fof(f482,plain,
( spl41_2
<=> leq(pv10,n135299) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_2])]) ).
fof(f1615,plain,
( ! [X0] :
( leq(X0,n135299)
| ~ leq(X0,pv10) )
| ~ spl41_2
| ~ spl41_166 ),
inference(resolution,[],[f1448,f484]) ).
fof(f484,plain,
( leq(pv10,n135299)
| ~ spl41_2 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f3023,plain,
( ~ spl41_247
| spl41_6
| ~ spl41_232 ),
inference(avatar_split_clause,[],[f2840,f2718,f502,f3020]) ).
fof(f3020,plain,
( spl41_247
<=> init = a_select2(rhoold_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_247])]) ).
fof(f2840,plain,
( init != a_select2(rhoold_init,tptp_float_0_0)
| spl41_6
| ~ spl41_232 ),
inference(superposition,[],[f504,f2720]) ).
fof(f504,plain,
( init != a_select2(rhoold_init,sK13)
| spl41_6 ),
inference(avatar_component_clause,[],[f502]) ).
fof(f3018,plain,
( spl41_246
| ~ spl41_3
| ~ spl41_165 ),
inference(avatar_split_clause,[],[f1573,f1443,f487,f3016]) ).
fof(f3016,plain,
( spl41_246
<=> ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_246])]) ).
fof(f487,plain,
( spl41_3
<=> gt(loopcounter,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_3])]) ).
fof(f1443,plain,
( spl41_165
<=> ! [X2,X0,X1] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_165])]) ).
fof(f1573,plain,
( ! [X0] :
( gt(X0,n1)
| ~ gt(X0,loopcounter) )
| ~ spl41_3
| ~ spl41_165 ),
inference(resolution,[],[f1444,f489]) ).
fof(f489,plain,
( gt(loopcounter,n1)
| ~ spl41_3 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f1444,plain,
( ! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1) )
| ~ spl41_165 ),
inference(avatar_component_clause,[],[f1443]) ).
fof(f2975,plain,
( spl41_245
| ~ spl41_59
| ~ spl41_244 ),
inference(avatar_split_clause,[],[f2971,f2967,f785,f2973]) ).
fof(f2973,plain,
( spl41_245
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( ~ leq(tptp_float_0_0,X8)
| ~ leq(tptp_float_0_0,X9)
| a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(X8,X6)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_245])]) ).
fof(f2967,plain,
( spl41_244
<=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_244])]) ).
fof(f2971,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_244 ),
inference(forward_demodulation,[],[f2970,f787]) ).
fof(f2970,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_244 ),
inference(forward_demodulation,[],[f2968,f787]) ).
fof(f2968,plain,
( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
( a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X8,X9) = a_select3(tptp_madd(X0,tptp_mmul(X1,tptp_mmul(tptp_madd(tptp_mmul(X2,tptp_mmul(X3,trans(X2))),tptp_mmul(X4,tptp_mmul(X5,trans(X4)))),trans(X1)))),X9,X8)
| ~ leq(X9,X6)
| ~ leq(n0,X9)
| ~ leq(X8,X6)
| ~ leq(n0,X8)
| sP12(X5,X6)
| sP11(X0,X6)
| sP10(X3,X7) )
| ~ spl41_244 ),
inference(avatar_component_clause,[],[f2967]) ).
fof(f2969,plain,
spl41_244,
inference(avatar_split_clause,[],[f428,f2967]) ).
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(f2929,plain,
( spl41_243
| ~ spl41_59
| ~ spl41_242 ),
inference(avatar_split_clause,[],[f2925,f2920,f785,f2927]) ).
fof(f2927,plain,
( spl41_243
<=> ! [X3,X4,X0,X5,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_243])]) ).
fof(f2920,plain,
( spl41_242
<=> ! [X3,X4,X0,X5,X2,X1] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_242])]) ).
fof(f2925,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_242 ),
inference(forward_demodulation,[],[f2924,f787]) ).
fof(f2924,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_242 ),
inference(forward_demodulation,[],[f2923,f787]) ).
fof(f2923,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_242 ),
inference(forward_demodulation,[],[f2921,f787]) ).
fof(f2921,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_update3(X0,X4,X4,X5),X2,X3) = a_select3(tptp_update3(X0,X4,X4,X5),X3,X2)
| ~ leq(X4,X1)
| ~ leq(n0,X4)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP2(X0,X1) )
| ~ spl41_242 ),
inference(avatar_component_clause,[],[f2920]) ).
fof(f2922,plain,
spl41_242,
inference(avatar_split_clause,[],[f355,f2920]) ).
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(f2837,plain,
( spl41_241
| ~ spl41_59
| ~ spl41_239 ),
inference(avatar_split_clause,[],[f2829,f2825,f785,f2835]) ).
fof(f2835,plain,
( spl41_241
<=> ! [X2,X3,X4,X0,X5,X1] :
( ~ leq(tptp_float_0_0,X4)
| ~ leq(tptp_float_0_0,X5)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(X4,X2)
| sP8(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_241])]) ).
fof(f2825,plain,
( spl41_239
<=> ! [X2,X3,X4,X0,X5,X1] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_239])]) ).
fof(f2829,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_239 ),
inference(forward_demodulation,[],[f2828,f787]) ).
fof(f2828,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_239 ),
inference(forward_demodulation,[],[f2826,f787]) ).
fof(f2826,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X5) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X5,X4)
| ~ leq(X5,X2)
| ~ leq(n0,X5)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| sP8(X1,X3) )
| ~ spl41_239 ),
inference(avatar_component_clause,[],[f2825]) ).
fof(f2833,plain,
( spl41_240
| ~ spl41_59
| ~ spl41_238 ),
inference(avatar_split_clause,[],[f2823,f2819,f785,f2831]) ).
fof(f2831,plain,
( spl41_240
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP7(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_240])]) ).
fof(f2819,plain,
( spl41_238
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_238])]) ).
fof(f2823,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_238 ),
inference(forward_demodulation,[],[f2822,f787]) ).
fof(f2822,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_238 ),
inference(forward_demodulation,[],[f2820,f787]) ).
fof(f2820,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X3,X4) = a_select3(tptp_mmul(X0,tptp_mmul(X1,trans(X0))),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP7(X1,X2) )
| ~ spl41_238 ),
inference(avatar_component_clause,[],[f2819]) ).
fof(f2827,plain,
spl41_239,
inference(avatar_split_clause,[],[f403,f2825]) ).
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(f2821,plain,
spl41_238,
inference(avatar_split_clause,[],[f392,f2819]) ).
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(f2745,plain,
( spl41_237
| ~ spl41_59
| ~ spl41_235 ),
inference(avatar_split_clause,[],[f2737,f2733,f785,f2743]) ).
fof(f2743,plain,
( spl41_237
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP6(X1,X2)
| sP5(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_237])]) ).
fof(f2733,plain,
( spl41_235
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_235])]) ).
fof(f2737,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_235 ),
inference(forward_demodulation,[],[f2736,f787]) ).
fof(f2736,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_235 ),
inference(forward_demodulation,[],[f2734,f787]) ).
fof(f2734,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_madd(X0,X1),X3,X4) = a_select3(tptp_madd(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP6(X1,X2)
| sP5(X0,X2) )
| ~ spl41_235 ),
inference(avatar_component_clause,[],[f2733]) ).
fof(f2741,plain,
( spl41_236
| ~ spl41_59
| ~ spl41_234 ),
inference(avatar_split_clause,[],[f2731,f2727,f785,f2739]) ).
fof(f2739,plain,
( spl41_236
<=> ! [X2,X4,X0,X3,X1] :
( ~ leq(tptp_float_0_0,X3)
| ~ leq(tptp_float_0_0,X4)
| a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(X3,X2)
| sP4(X1,X2)
| sP3(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_236])]) ).
fof(f2727,plain,
( spl41_234
<=> ! [X2,X4,X0,X3,X1] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_234])]) ).
fof(f2731,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_234 ),
inference(forward_demodulation,[],[f2730,f787]) ).
fof(f2730,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_234 ),
inference(forward_demodulation,[],[f2728,f787]) ).
fof(f2728,plain,
( ! [X2,X3,X0,X1,X4] :
( a_select3(tptp_msub(X0,X1),X3,X4) = a_select3(tptp_msub(X0,X1),X4,X3)
| ~ leq(X4,X2)
| ~ leq(n0,X4)
| ~ leq(X3,X2)
| ~ leq(n0,X3)
| sP4(X1,X2)
| sP3(X0,X2) )
| ~ spl41_234 ),
inference(avatar_component_clause,[],[f2727]) ).
fof(f2735,plain,
spl41_235,
inference(avatar_split_clause,[],[f386,f2733]) ).
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(f2729,plain,
spl41_234,
inference(avatar_split_clause,[],[f375,f2727]) ).
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(f2725,plain,
( spl41_232
| spl41_233
| ~ spl41_4
| ~ spl41_59
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1540,f1439,f785,f492,f2722,f2718]) ).
fof(f2722,plain,
( spl41_233
<=> gt(sK13,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_233])]) ).
fof(f1439,plain,
( spl41_164
<=> ! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_164])]) ).
fof(f1540,plain,
( gt(sK13,tptp_float_0_0)
| tptp_float_0_0 = sK13
| ~ spl41_4
| ~ spl41_59
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1539,f787]) ).
fof(f1539,plain,
( tptp_float_0_0 = sK13
| gt(sK13,n0)
| ~ spl41_4
| ~ spl41_59
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1481,f787]) ).
fof(f1481,plain,
( n0 = sK13
| gt(sK13,n0)
| ~ spl41_4
| ~ spl41_164 ),
inference(resolution,[],[f1440,f494]) ).
fof(f1440,plain,
( ! [X0,X1] :
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) )
| ~ spl41_164 ),
inference(avatar_component_clause,[],[f1439]) ).
fof(f2682,plain,
( spl41_231
| ~ spl41_59
| ~ spl41_230 ),
inference(avatar_split_clause,[],[f2678,f2674,f785,f2680]) ).
fof(f2680,plain,
( spl41_231
<=> ! [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_231])]) ).
fof(f2674,plain,
( spl41_230
<=> ! [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_230])]) ).
fof(f2678,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_230 ),
inference(forward_demodulation,[],[f2677,f787]) ).
fof(f2677,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_230 ),
inference(forward_demodulation,[],[f2675,f787]) ).
fof(f2675,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_230 ),
inference(avatar_component_clause,[],[f2674]) ).
fof(f2676,plain,
spl41_230,
inference(avatar_split_clause,[],[f410,f2674]) ).
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(f2604,plain,
( spl41_229
| ~ spl41_59
| ~ spl41_227 ),
inference(avatar_split_clause,[],[f2596,f2592,f785,f2602]) ).
fof(f2602,plain,
( spl41_229
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_229])]) ).
fof(f2592,plain,
( spl41_227
<=> ! [X0,X3,X2,X1] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_227])]) ).
fof(f2596,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_227 ),
inference(forward_demodulation,[],[f2595,f787]) ).
fof(f2595,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_227 ),
inference(forward_demodulation,[],[f2593,f787]) ).
fof(f2593,plain,
( ! [X2,X3,X0,X1] :
( a_select3(trans(X0),X2,X3) = a_select3(trans(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP1(X0,X1) )
| ~ spl41_227 ),
inference(avatar_component_clause,[],[f2592]) ).
fof(f2600,plain,
( spl41_228
| ~ spl41_59
| ~ spl41_226 ),
inference(avatar_split_clause,[],[f2590,f2586,f785,f2598]) ).
fof(f2598,plain,
( spl41_228
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X2)
| ~ leq(tptp_float_0_0,X3)
| a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(X2,X1)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_228])]) ).
fof(f2586,plain,
( spl41_226
<=> ! [X0,X3,X2,X1] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_226])]) ).
fof(f2590,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_226 ),
inference(forward_demodulation,[],[f2589,f787]) ).
fof(f2589,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_226 ),
inference(forward_demodulation,[],[f2587,f787]) ).
fof(f2587,plain,
( ! [X2,X3,X0,X1] :
( a_select3(inv(X0),X2,X3) = a_select3(inv(X0),X3,X2)
| ~ leq(X3,X1)
| ~ leq(n0,X3)
| ~ leq(X2,X1)
| ~ leq(n0,X2)
| sP0(X0,X1) )
| ~ spl41_226 ),
inference(avatar_component_clause,[],[f2586]) ).
fof(f2594,plain,
spl41_227,
inference(avatar_split_clause,[],[f349,f2592]) ).
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(f2588,plain,
spl41_226,
inference(avatar_split_clause,[],[f343,f2586]) ).
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(f2509,plain,
spl41_225,
inference(avatar_split_clause,[],[f412,f2507]) ).
fof(f2507,plain,
( spl41_225
<=> ! [X5,X4,X2,X0,X6,X3,X1] :
( a_select3(tptp_const_array2(dim(X1,X2),dim(X4,X5),X6),X0,X3) = X6
| ~ leq(X3,X5)
| ~ leq(X4,X3)
| ~ leq(X0,X2)
| ~ leq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_225])]) ).
fof(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(f2473,plain,
( spl41_224
| ~ spl41_59
| ~ spl41_223 ),
inference(avatar_split_clause,[],[f2469,f2465,f785,f2471]) ).
fof(f2471,plain,
( spl41_224
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_224])]) ).
fof(f2465,plain,
( spl41_223
<=> ! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_223])]) ).
fof(f2469,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_223 ),
inference(forward_demodulation,[],[f2468,f787]) ).
fof(f2468,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_223 ),
inference(forward_demodulation,[],[f2466,f787]) ).
fof(f2466,plain,
( ! [X0] :
( n5 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n5)
| ~ leq(n0,X0) )
| ~ spl41_223 ),
inference(avatar_component_clause,[],[f2465]) ).
fof(f2467,plain,
spl41_223,
inference(avatar_split_clause,[],[f324,f2465]) ).
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(f2462,plain,
( spl41_222
| ~ spl41_59
| ~ spl41_221 ),
inference(avatar_split_clause,[],[f2458,f2455,f785,f2460]) ).
fof(f2460,plain,
( spl41_222
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| a_select2(X2,sK30(X1,X2,X3)) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_222])]) ).
fof(f2455,plain,
( spl41_221
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| a_select2(X2,sK30(X1,X2,X3)) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_221])]) ).
fof(f2458,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_221 ),
inference(forward_demodulation,[],[f2456,f787]) ).
fof(f2456,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| a_select2(X2,sK30(X1,X2,X3)) != X3 )
| ~ spl41_221 ),
inference(avatar_component_clause,[],[f2455]) ).
fof(f2457,plain,
spl41_221,
inference(avatar_split_clause,[],[f397,f2455]) ).
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(f2421,plain,
( spl41_220
| ~ spl41_59
| ~ spl41_219 ),
inference(avatar_split_clause,[],[f2417,f2413,f785,f2419]) ).
fof(f2419,plain,
( spl41_220
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_220])]) ).
fof(f2413,plain,
( spl41_219
<=> ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_219])]) ).
fof(f2417,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_219 ),
inference(forward_demodulation,[],[f2416,f787]) ).
fof(f2416,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_219 ),
inference(forward_demodulation,[],[f2414,f787]) ).
fof(f2414,plain,
( ! [X0] :
( n4 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ spl41_219 ),
inference(avatar_component_clause,[],[f2413]) ).
fof(f2415,plain,
spl41_219,
inference(avatar_split_clause,[],[f328,f2413]) ).
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(f2336,plain,
( spl41_218
| ~ spl41_59
| ~ spl41_210 ),
inference(avatar_split_clause,[],[f2303,f2300,f785,f2334]) ).
fof(f2334,plain,
( spl41_218
<=> ! [X0,X3,X2,X1] :
( ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| leq(sK30(X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_218])]) ).
fof(f2300,plain,
( spl41_210
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(sK30(X1,X2,X3),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_210])]) ).
fof(f2303,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_210 ),
inference(forward_demodulation,[],[f2301,f787]) ).
fof(f2301,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(sK30(X1,X2,X3),X1) )
| ~ spl41_210 ),
inference(avatar_component_clause,[],[f2300]) ).
fof(f2332,plain,
( spl41_217
| ~ spl41_59
| ~ spl41_209 ),
inference(avatar_split_clause,[],[f2298,f2294,f785,f2330]) ).
fof(f2330,plain,
( spl41_217
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK30(X1,X2,X3))
| ~ leq(tptp_float_0_0,X0)
| a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_217])]) ).
fof(f2294,plain,
( spl41_209
<=> ! [X0,X3,X2,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(n0,sK30(X1,X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_209])]) ).
fof(f2298,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_209 ),
inference(forward_demodulation,[],[f2297,f787]) ).
fof(f2297,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_209 ),
inference(forward_demodulation,[],[f2295,f787]) ).
fof(f2295,plain,
( ! [X2,X3,X0,X1] :
( a_select2(tptp_update2(X2,X1,X3),X0) = X3
| ~ leq(X0,X1)
| ~ leq(n0,X0)
| leq(n0,sK30(X1,X2,X3)) )
| ~ spl41_209 ),
inference(avatar_component_clause,[],[f2294]) ).
fof(f2328,plain,
( spl41_215
| spl41_216
| ~ spl41_1
| ~ spl41_59
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1538,f1439,f785,f477,f2325,f2321]) ).
fof(f2325,plain,
( spl41_216
<=> gt(pv10,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_216])]) ).
fof(f1538,plain,
( gt(pv10,tptp_float_0_0)
| tptp_float_0_0 = pv10
| ~ spl41_1
| ~ spl41_59
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1537,f787]) ).
fof(f1537,plain,
( tptp_float_0_0 = pv10
| gt(pv10,n0)
| ~ spl41_1
| ~ spl41_59
| ~ spl41_164 ),
inference(forward_demodulation,[],[f1480,f787]) ).
fof(f1480,plain,
( n0 = pv10
| gt(pv10,n0)
| ~ spl41_1
| ~ spl41_164 ),
inference(resolution,[],[f1440,f479]) ).
fof(f2319,plain,
spl41_214,
inference(avatar_split_clause,[],[f427,f2317]) ).
fof(f2317,plain,
( spl41_214
<=> ! [X0,X1] :
( a_select3(X0,sK39(X0,X1),sK40(X0,X1)) != a_select3(X0,sK40(X0,X1),sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_214])]) ).
fof(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(f2315,plain,
spl41_213,
inference(avatar_split_clause,[],[f422,f2313]) ).
fof(f2313,plain,
( spl41_213
<=> ! [X0,X1] :
( a_select3(X0,sK37(X0,X1),sK38(X0,X1)) != a_select3(X0,sK38(X0,X1),sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_213])]) ).
fof(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(f2311,plain,
spl41_212,
inference(avatar_split_clause,[],[f417,f2309]) ).
fof(f2309,plain,
( spl41_212
<=> ! [X0,X1] :
( a_select3(X0,sK35(X0,X1),sK36(X0,X1)) != a_select3(X0,sK36(X0,X1),sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_212])]) ).
fof(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(f2307,plain,
spl41_211,
inference(avatar_split_clause,[],[f402,f2305]) ).
fof(f2305,plain,
( spl41_211
<=> ! [X0,X1] :
( a_select3(X0,sK31(X0,X1),sK32(X0,X1)) != a_select3(X0,sK32(X0,X1),sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_211])]) ).
fof(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(f2302,plain,
spl41_210,
inference(avatar_split_clause,[],[f396,f2300]) ).
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(f2296,plain,
spl41_209,
inference(avatar_split_clause,[],[f395,f2294]) ).
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(f2292,plain,
spl41_208,
inference(avatar_split_clause,[],[f391,f2290]) ).
fof(f2290,plain,
( spl41_208
<=> ! [X0,X1] :
( a_select3(X0,sK28(X0,X1),sK29(X0,X1)) != a_select3(X0,sK29(X0,X1),sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_208])]) ).
fof(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(f2288,plain,
spl41_207,
inference(avatar_split_clause,[],[f385,f2286]) ).
fof(f2286,plain,
( spl41_207
<=> ! [X0,X1] :
( a_select3(X0,sK26(X0,X1),sK27(X0,X1)) != a_select3(X0,sK27(X0,X1),sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_207])]) ).
fof(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(f2284,plain,
spl41_206,
inference(avatar_split_clause,[],[f380,f2282]) ).
fof(f2282,plain,
( spl41_206
<=> ! [X0,X1] :
( a_select3(X0,sK24(X0,X1),sK25(X0,X1)) != a_select3(X0,sK25(X0,X1),sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_206])]) ).
fof(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(f2280,plain,
spl41_205,
inference(avatar_split_clause,[],[f374,f2278]) ).
fof(f2278,plain,
( spl41_205
<=> ! [X0,X1] :
( a_select3(X0,sK22(X0,X1),sK23(X0,X1)) != a_select3(X0,sK23(X0,X1),sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_205])]) ).
fof(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(f2276,plain,
spl41_204,
inference(avatar_split_clause,[],[f369,f2274]) ).
fof(f2274,plain,
( spl41_204
<=> ! [X0,X1] :
( a_select3(X0,sK20(X0,X1),sK21(X0,X1)) != a_select3(X0,sK21(X0,X1),sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_204])]) ).
fof(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(f2272,plain,
spl41_203,
inference(avatar_split_clause,[],[f354,f2270]) ).
fof(f2270,plain,
( spl41_203
<=> ! [X0,X1] :
( a_select3(X0,sK18(X0,X1),sK19(X0,X1)) != a_select3(X0,sK19(X0,X1),sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_203])]) ).
fof(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(f2268,plain,
spl41_202,
inference(avatar_split_clause,[],[f348,f2266]) ).
fof(f2266,plain,
( spl41_202
<=> ! [X0,X1] :
( a_select3(X0,sK16(X0,X1),sK17(X0,X1)) != a_select3(X0,sK17(X0,X1),sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_202])]) ).
fof(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(f2264,plain,
spl41_201,
inference(avatar_split_clause,[],[f342,f2262]) ).
fof(f2262,plain,
( spl41_201
<=> ! [X0,X1] :
( a_select3(X0,sK14(X0,X1),sK15(X0,X1)) != a_select3(X0,sK15(X0,X1),sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_201])]) ).
fof(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(f2258,plain,
spl41_200,
inference(avatar_split_clause,[],[f409,f2256]) ).
fof(f2256,plain,
( spl41_200
<=> ! [X0,X3,X2,X1] :
( a_select3(X1,sK33(X0,X1,X2,X3),sK34(X0,X1,X2,X3)) != X0
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_200])]) ).
fof(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(f2222,plain,
( spl41_199
| ~ spl41_59
| ~ spl41_198 ),
inference(avatar_split_clause,[],[f2218,f2214,f785,f2220]) ).
fof(f2220,plain,
( spl41_199
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_199])]) ).
fof(f2214,plain,
( spl41_198
<=> ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_198])]) ).
fof(f2218,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_198 ),
inference(forward_demodulation,[],[f2217,f787]) ).
fof(f2217,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n3 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_198 ),
inference(forward_demodulation,[],[f2215,f787]) ).
fof(f2215,plain,
( ! [X0] :
( n3 = X0
| n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n3)
| ~ leq(n0,X0) )
| ~ spl41_198 ),
inference(avatar_component_clause,[],[f2214]) ).
fof(f2216,plain,
spl41_198,
inference(avatar_split_clause,[],[f325,f2214]) ).
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(f2210,plain,
spl41_197,
inference(avatar_split_clause,[],[f457,f2208]) ).
fof(f2208,plain,
( spl41_197
<=> ! [X3,X4,X0,X6,X2] :
( a_select3(X4,X2,X3) = a_select3(tptp_update3(X4,X0,X3,X6),X2,X3)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_197])]) ).
fof(f457,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,[],[f456]) ).
fof(f456,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(f2107,plain,
( spl41_196
| ~ spl41_59
| ~ spl41_192 ),
inference(avatar_split_clause,[],[f2090,f2086,f785,f2105]) ).
fof(f2105,plain,
( spl41_196
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_196])]) ).
fof(f2086,plain,
( spl41_192
<=> ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_192])]) ).
fof(f2090,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2) )
| ~ spl41_59
| ~ spl41_192 ),
inference(forward_demodulation,[],[f2089,f787]) ).
fof(f2089,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n2 = X0
| n1 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_192 ),
inference(forward_demodulation,[],[f2087,f787]) ).
fof(f2087,plain,
( ! [X0] :
( n2 = X0
| n1 = X0
| n0 = X0
| ~ leq(X0,n2)
| ~ leq(n0,X0) )
| ~ spl41_192 ),
inference(avatar_component_clause,[],[f2086]) ).
fof(f2103,plain,
( spl41_194
| spl41_195
| ~ spl41_5
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1512,f1439,f497,f2100,f2096]) ).
fof(f2096,plain,
( spl41_194
<=> gt(n4,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_194])]) ).
fof(f2100,plain,
( spl41_195
<=> n4 = sK13 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_195])]) ).
fof(f1512,plain,
( n4 = sK13
| gt(n4,sK13)
| ~ spl41_5
| ~ spl41_164 ),
inference(resolution,[],[f1440,f499]) ).
fof(f2094,plain,
spl41_193,
inference(avatar_split_clause,[],[f394,f2092]) ).
fof(f2092,plain,
( spl41_193
<=> ! [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_193])]) ).
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(f2088,plain,
spl41_192,
inference(avatar_split_clause,[],[f326,f2086]) ).
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(f2082,plain,
spl41_191,
inference(avatar_split_clause,[],[f455,f2080]) ).
fof(f2080,plain,
( spl41_191
<=> ! [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_191])]) ).
fof(f455,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(f2034,plain,
( spl41_190
| ~ spl41_59
| ~ spl41_185 ),
inference(avatar_split_clause,[],[f2014,f2011,f785,f2032]) ).
fof(f2032,plain,
( spl41_190
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_190])]) ).
fof(f2011,plain,
( spl41_185
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_185])]) ).
fof(f2014,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_59
| ~ spl41_185 ),
inference(forward_demodulation,[],[f2012,f787]) ).
fof(f2012,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_185 ),
inference(avatar_component_clause,[],[f2011]) ).
fof(f2030,plain,
( spl41_189
| ~ spl41_59
| ~ spl41_184 ),
inference(avatar_split_clause,[],[f2009,f2006,f785,f2028]) ).
fof(f2028,plain,
( spl41_189
<=> ! [X0,X3,X2,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_189])]) ).
fof(f2006,plain,
( spl41_184
<=> ! [X0,X3,X2,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_184])]) ).
fof(f2009,plain,
( ! [X2,X3,X0,X1] :
( leq(tptp_float_0_0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_59
| ~ spl41_184 ),
inference(forward_demodulation,[],[f2007,f787]) ).
fof(f2007,plain,
( ! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) )
| ~ spl41_184 ),
inference(avatar_component_clause,[],[f2006]) ).
fof(f2026,plain,
( spl41_188
| ~ spl41_59
| ~ spl41_183 ),
inference(avatar_split_clause,[],[f2004,f2000,f785,f2024]) ).
fof(f2024,plain,
( spl41_188
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_188])]) ).
fof(f2000,plain,
( spl41_183
<=> ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_183])]) ).
fof(f2004,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1) )
| ~ spl41_59
| ~ spl41_183 ),
inference(forward_demodulation,[],[f2003,f787]) ).
fof(f2003,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| n1 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_183 ),
inference(forward_demodulation,[],[f2001,f787]) ).
fof(f2001,plain,
( ! [X0] :
( n1 = X0
| n0 = X0
| ~ leq(X0,n1)
| ~ leq(n0,X0) )
| ~ spl41_183 ),
inference(avatar_component_clause,[],[f2000]) ).
fof(f2022,plain,
spl41_187,
inference(avatar_split_clause,[],[f408,f2020]) ).
fof(f2020,plain,
( spl41_187
<=> ! [X0,X3,X2,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_187])]) ).
fof(f408,plain,
! [X2,X3,X0,X1] :
( leq(sK34(X0,X1,X2,X3),X2)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2018,plain,
spl41_186,
inference(avatar_split_clause,[],[f407,f2016]) ).
fof(f2016,plain,
( spl41_186
<=> ! [X0,X3,X2,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_186])]) ).
fof(f407,plain,
! [X2,X3,X0,X1] :
( leq(sK33(X0,X1,X2,X3),X3)
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2013,plain,
spl41_185,
inference(avatar_split_clause,[],[f406,f2011]) ).
fof(f406,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK34(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2008,plain,
spl41_184,
inference(avatar_split_clause,[],[f405,f2006]) ).
fof(f405,plain,
! [X2,X3,X0,X1] :
( leq(n0,sK33(X0,X1,X2,X3))
| ~ sP9(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f243]) ).
fof(f2002,plain,
spl41_183,
inference(avatar_split_clause,[],[f327,f2000]) ).
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(f1930,plain,
spl41_182,
inference(avatar_split_clause,[],[f475,f1928]) ).
fof(f1928,plain,
( spl41_182
<=> ! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_182])]) ).
fof(f475,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f474,f439]) ).
fof(f439,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(f474,plain,
! [X0] : plus(n5,X0) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f446,f439]) ).
fof(f446,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(f1924,plain,
spl41_181,
inference(avatar_split_clause,[],[f473,f1922]) ).
fof(f1922,plain,
( spl41_181
<=> ! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_181])]) ).
fof(f473,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(n2,X0)),n1),
inference(forward_demodulation,[],[f472,f439]) ).
fof(f472,plain,
! [X0] : plus(X0,n5) = plus(plus(n2,plus(plus(X0,n1),n1)),n1),
inference(forward_demodulation,[],[f445,f439]) ).
fof(f445,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(f1892,plain,
( spl41_180
| ~ spl41_167
| ~ spl41_169
| ~ spl41_179 ),
inference(avatar_split_clause,[],[f1888,f1885,f1459,f1451,f1890]) ).
fof(f1890,plain,
( spl41_180
<=> ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_180])]) ).
fof(f1451,plain,
( spl41_167
<=> ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_167])]) ).
fof(f1459,plain,
( spl41_169
<=> ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_169])]) ).
fof(f1885,plain,
( spl41_179
<=> ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_179])]) ).
fof(f1888,plain,
( ! [X0] : plus(n4,X0) = plus(plus(X0,n3),n1)
| ~ spl41_167
| ~ spl41_169
| ~ spl41_179 ),
inference(forward_demodulation,[],[f1886,f1662]) ).
fof(f1662,plain,
( ! [X0] : plus(X0,n3) = plus(n2,plus(X0,n1))
| ~ spl41_167
| ~ spl41_169 ),
inference(forward_demodulation,[],[f1646,f1460]) ).
fof(f1460,plain,
( ! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1)
| ~ spl41_169 ),
inference(avatar_component_clause,[],[f1459]) ).
fof(f1646,plain,
( ! [X0] : plus(n2,plus(X0,n1)) = plus(plus(n2,X0),n1)
| ~ spl41_167 ),
inference(superposition,[],[f1452,f1452]) ).
fof(f1452,plain,
( ! [X0] : plus(n2,X0) = plus(plus(X0,n1),n1)
| ~ spl41_167 ),
inference(avatar_component_clause,[],[f1451]) ).
fof(f1886,plain,
( ! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_179 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f1887,plain,
spl41_179,
inference(avatar_split_clause,[],[f471,f1885]) ).
fof(f471,plain,
! [X0] : plus(n4,X0) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f444,f439]) ).
fof(f444,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(f1856,plain,
( spl41_178
| ~ spl41_167
| ~ spl41_169
| ~ spl41_177 ),
inference(avatar_split_clause,[],[f1852,f1849,f1459,f1451,f1854]) ).
fof(f1854,plain,
( spl41_178
<=> ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_178])]) ).
fof(f1849,plain,
( spl41_177
<=> ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_177])]) ).
fof(f1852,plain,
( ! [X0] : plus(X0,n4) = plus(plus(X0,n3),n1)
| ~ spl41_167
| ~ spl41_169
| ~ spl41_177 ),
inference(forward_demodulation,[],[f1850,f1662]) ).
fof(f1850,plain,
( ! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1)
| ~ spl41_177 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f1851,plain,
spl41_177,
inference(avatar_split_clause,[],[f470,f1849]) ).
fof(f470,plain,
! [X0] : plus(X0,n4) = plus(plus(n2,plus(X0,n1)),n1),
inference(forward_demodulation,[],[f443,f439]) ).
fof(f443,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(f1785,plain,
( spl41_175
| spl41_176
| ~ spl41_2
| ~ spl41_164 ),
inference(avatar_split_clause,[],[f1511,f1439,f482,f1782,f1778]) ).
fof(f1778,plain,
( spl41_175
<=> gt(n135299,pv10) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_175])]) ).
fof(f1782,plain,
( spl41_176
<=> pv10 = n135299 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_176])]) ).
fof(f1511,plain,
( pv10 = n135299
| gt(n135299,pv10)
| ~ spl41_2
| ~ spl41_164 ),
inference(resolution,[],[f1440,f484]) ).
fof(f1776,plain,
spl41_174,
inference(avatar_split_clause,[],[f454,f1774]) ).
fof(f1774,plain,
( spl41_174
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ leq(plus(X0,n1),plus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_174])]) ).
fof(f454,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(f1772,plain,
spl41_173,
inference(avatar_split_clause,[],[f453,f1770]) ).
fof(f1770,plain,
( spl41_173
<=> ! [X0,X1] :
( leq(plus(X0,n1),plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_173])]) ).
fof(f453,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(f1768,plain,
spl41_172,
inference(avatar_split_clause,[],[f393,f1766]) ).
fof(f1766,plain,
( spl41_172
<=> ! [X2,X0,X1,X3] : a_select3(tptp_update3(X0,X1,X2,X3),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_172])]) ).
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(f1469,plain,
( spl41_171
| ~ spl41_59
| ~ spl41_161 ),
inference(avatar_split_clause,[],[f1428,f1423,f785,f1467]) ).
fof(f1467,plain,
( spl41_171
<=> ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_171])]) ).
fof(f1423,plain,
( spl41_161
<=> ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_161])]) ).
fof(f1428,plain,
( ! [X0] :
( ~ leq(tptp_float_0_0,X0)
| ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0 )
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1427,f787]) ).
fof(f1427,plain,
( ! [X0] :
( ~ leq(X0,tptp_float_0_0)
| tptp_float_0_0 = X0
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1426,f787]) ).
fof(f1426,plain,
( ! [X0] :
( tptp_float_0_0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_161 ),
inference(forward_demodulation,[],[f1424,f787]) ).
fof(f1424,plain,
( ! [X0] :
( n0 = X0
| ~ leq(X0,n0)
| ~ leq(n0,X0) )
| ~ spl41_161 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f1465,plain,
spl41_170,
inference(avatar_split_clause,[],[f469,f1463]) ).
fof(f1463,plain,
( spl41_170
<=> ! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_170])]) ).
fof(f469,plain,
! [X0] : plus(n3,X0) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f442,f439]) ).
fof(f442,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(f1461,plain,
spl41_169,
inference(avatar_split_clause,[],[f468,f1459]) ).
fof(f468,plain,
! [X0] : plus(X0,n3) = plus(plus(n2,X0),n1),
inference(forward_demodulation,[],[f441,f439]) ).
fof(f441,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(f1457,plain,
spl41_168,
inference(avatar_split_clause,[],[f440,f1455]) ).
fof(f1455,plain,
( spl41_168
<=> ! [X0] : plus(X0,n2) = plus(plus(X0,n1),n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_168])]) ).
fof(f440,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(f1453,plain,
spl41_167,
inference(avatar_split_clause,[],[f439,f1451]) ).
fof(f1449,plain,
spl41_166,
inference(avatar_split_clause,[],[f364,f1447]) ).
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(f1445,plain,
spl41_165,
inference(avatar_split_clause,[],[f363,f1443]) ).
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(f1441,plain,
spl41_164,
inference(avatar_split_clause,[],[f337,f1439]) ).
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(f1437,plain,
( ~ spl41_163
| ~ spl41_59
| spl41_160 ),
inference(avatar_split_clause,[],[f1421,f1417,f785,f1434]) ).
fof(f1434,plain,
( spl41_163
<=> init = a_select2(rho_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_163])]) ).
fof(f1417,plain,
( spl41_160
<=> init = a_select2(rho_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_160])]) ).
fof(f1421,plain,
( init != a_select2(rho_init,tptp_float_0_0)
| ~ spl41_59
| spl41_160 ),
inference(forward_demodulation,[],[f1418,f787]) ).
fof(f1418,plain,
( init != a_select2(rho_init,n0)
| spl41_160 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f1432,plain,
spl41_162,
inference(avatar_split_clause,[],[f330,f1430]) ).
fof(f1430,plain,
( spl41_162
<=> ! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_162])]) ).
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(f1425,plain,
spl41_161,
inference(avatar_split_clause,[],[f329,f1423]) ).
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(f1420,plain,
( spl41_160
| ~ spl41_125
| ~ spl41_7
| ~ spl41_43 ),
inference(avatar_split_clause,[],[f705,f689,f507,f1154,f1417]) ).
fof(f507,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(f705,plain,
( ~ leq(n0,n4)
| init = a_select2(rho_init,n0)
| ~ spl41_7
| ~ spl41_43 ),
inference(resolution,[],[f690,f508]) ).
fof(f508,plain,
( ! [X7] :
( ~ leq(n0,X7)
| ~ leq(X7,n4)
| init = a_select2(rho_init,X7) )
| ~ spl41_7 ),
inference(avatar_component_clause,[],[f507]) ).
fof(f1384,plain,
( ~ spl41_159
| ~ spl41_59
| spl41_156 ),
inference(avatar_split_clause,[],[f1287,f1283,f785,f1381]) ).
fof(f1381,plain,
( spl41_159
<=> init = a_select2(mu_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_159])]) ).
fof(f1283,plain,
( spl41_156
<=> init = a_select2(mu_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_156])]) ).
fof(f1287,plain,
( init != a_select2(mu_init,tptp_float_0_0)
| ~ spl41_59
| spl41_156 ),
inference(forward_demodulation,[],[f1284,f787]) ).
fof(f1284,plain,
( init != a_select2(mu_init,n0)
| spl41_156 ),
inference(avatar_component_clause,[],[f1283]) ).
fof(f1295,plain,
( spl41_158
| ~ spl41_59
| ~ spl41_119 ),
inference(avatar_split_clause,[],[f1132,f1129,f785,f1293]) ).
fof(f1293,plain,
( spl41_158
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_158])]) ).
fof(f1129,plain,
( spl41_119
<=> ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_119])]) ).
fof(f1132,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_59
| ~ spl41_119 ),
inference(forward_demodulation,[],[f1130,f787]) ).
fof(f1130,plain,
( ! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_119 ),
inference(avatar_component_clause,[],[f1129]) ).
fof(f1291,plain,
( spl41_157
| ~ spl41_59
| ~ spl41_117 ),
inference(avatar_split_clause,[],[f1123,f1120,f785,f1289]) ).
fof(f1289,plain,
( spl41_157
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_157])]) ).
fof(f1120,plain,
( spl41_117
<=> ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_117])]) ).
fof(f1123,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_59
| ~ spl41_117 ),
inference(forward_demodulation,[],[f1121,f787]) ).
fof(f1121,plain,
( ! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) )
| ~ spl41_117 ),
inference(avatar_component_clause,[],[f1120]) ).
fof(f1286,plain,
( spl41_156
| ~ spl41_125
| ~ spl41_8
| ~ spl41_43 ),
inference(avatar_split_clause,[],[f704,f689,f511,f1154,f1283]) ).
fof(f511,plain,
( spl41_8
<=> ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_8])]) ).
fof(f704,plain,
( ~ leq(n0,n4)
| init = a_select2(mu_init,n0)
| ~ spl41_8
| ~ spl41_43 ),
inference(resolution,[],[f690,f512]) ).
fof(f512,plain,
( ! [X6] :
( ~ leq(n0,X6)
| ~ leq(X6,n4)
| init = a_select2(mu_init,X6) )
| ~ spl41_8 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f1281,plain,
( spl41_155
| ~ spl41_59
| ~ spl41_115 ),
inference(avatar_split_clause,[],[f1114,f1111,f785,f1279]) ).
fof(f1279,plain,
( spl41_155
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_155])]) ).
fof(f1111,plain,
( spl41_115
<=> ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_115])]) ).
fof(f1114,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_59
| ~ spl41_115 ),
inference(forward_demodulation,[],[f1112,f787]) ).
fof(f1112,plain,
( ! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_115 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1277,plain,
( spl41_154
| ~ spl41_59
| ~ spl41_113 ),
inference(avatar_split_clause,[],[f1105,f1102,f785,f1275]) ).
fof(f1275,plain,
( spl41_154
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_154])]) ).
fof(f1102,plain,
( spl41_113
<=> ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_113])]) ).
fof(f1105,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_59
| ~ spl41_113 ),
inference(forward_demodulation,[],[f1103,f787]) ).
fof(f1103,plain,
( ! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) )
| ~ spl41_113 ),
inference(avatar_component_clause,[],[f1102]) ).
fof(f1273,plain,
( spl41_153
| ~ spl41_59
| ~ spl41_111 ),
inference(avatar_split_clause,[],[f1096,f1093,f785,f1271]) ).
fof(f1271,plain,
( spl41_153
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_153])]) ).
fof(f1093,plain,
( spl41_111
<=> ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_111])]) ).
fof(f1096,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_59
| ~ spl41_111 ),
inference(forward_demodulation,[],[f1094,f787]) ).
fof(f1094,plain,
( ! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_111 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f1269,plain,
( spl41_152
| ~ spl41_59
| ~ spl41_109 ),
inference(avatar_split_clause,[],[f1087,f1084,f785,f1267]) ).
fof(f1267,plain,
( spl41_152
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_152])]) ).
fof(f1084,plain,
( spl41_109
<=> ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_109])]) ).
fof(f1087,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_59
| ~ spl41_109 ),
inference(forward_demodulation,[],[f1085,f787]) ).
fof(f1085,plain,
( ! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) )
| ~ spl41_109 ),
inference(avatar_component_clause,[],[f1084]) ).
fof(f1265,plain,
( spl41_151
| ~ spl41_59
| ~ spl41_107 ),
inference(avatar_split_clause,[],[f1078,f1075,f785,f1263]) ).
fof(f1263,plain,
( spl41_151
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_151])]) ).
fof(f1075,plain,
( spl41_107
<=> ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_107])]) ).
fof(f1078,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_59
| ~ spl41_107 ),
inference(forward_demodulation,[],[f1076,f787]) ).
fof(f1076,plain,
( ! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_107 ),
inference(avatar_component_clause,[],[f1075]) ).
fof(f1261,plain,
( spl41_150
| ~ spl41_59
| ~ spl41_105 ),
inference(avatar_split_clause,[],[f1069,f1066,f785,f1259]) ).
fof(f1259,plain,
( spl41_150
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_150])]) ).
fof(f1066,plain,
( spl41_105
<=> ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_105])]) ).
fof(f1069,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_59
| ~ spl41_105 ),
inference(forward_demodulation,[],[f1067,f787]) ).
fof(f1067,plain,
( ! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) )
| ~ spl41_105 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f1257,plain,
( spl41_149
| ~ spl41_59
| ~ spl41_103 ),
inference(avatar_split_clause,[],[f1060,f1057,f785,f1255]) ).
fof(f1255,plain,
( spl41_149
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_149])]) ).
fof(f1057,plain,
( spl41_103
<=> ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_103])]) ).
fof(f1060,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_59
| ~ spl41_103 ),
inference(forward_demodulation,[],[f1058,f787]) ).
fof(f1058,plain,
( ! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_103 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f1253,plain,
( spl41_148
| ~ spl41_59
| ~ spl41_101 ),
inference(avatar_split_clause,[],[f1051,f1048,f785,f1251]) ).
fof(f1251,plain,
( spl41_148
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_148])]) ).
fof(f1048,plain,
( spl41_101
<=> ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_101])]) ).
fof(f1051,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_59
| ~ spl41_101 ),
inference(forward_demodulation,[],[f1049,f787]) ).
fof(f1049,plain,
( ! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) )
| ~ spl41_101 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f1249,plain,
( spl41_147
| ~ spl41_59
| ~ spl41_99 ),
inference(avatar_split_clause,[],[f1042,f1039,f785,f1247]) ).
fof(f1247,plain,
( spl41_147
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_147])]) ).
fof(f1039,plain,
( spl41_99
<=> ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_99])]) ).
fof(f1042,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_59
| ~ spl41_99 ),
inference(forward_demodulation,[],[f1040,f787]) ).
fof(f1040,plain,
( ! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_99 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f1245,plain,
( spl41_146
| ~ spl41_59
| ~ spl41_97 ),
inference(avatar_split_clause,[],[f1033,f1030,f785,f1243]) ).
fof(f1243,plain,
( spl41_146
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_146])]) ).
fof(f1030,plain,
( spl41_97
<=> ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_97])]) ).
fof(f1033,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_59
| ~ spl41_97 ),
inference(forward_demodulation,[],[f1031,f787]) ).
fof(f1031,plain,
( ! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) )
| ~ spl41_97 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f1241,plain,
( ~ spl41_145
| ~ spl41_59
| spl41_124 ),
inference(avatar_split_clause,[],[f1159,f1150,f785,f1238]) ).
fof(f1238,plain,
( spl41_145
<=> init = a_select2(sigma_init,tptp_float_0_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_145])]) ).
fof(f1150,plain,
( spl41_124
<=> init = a_select2(sigma_init,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_124])]) ).
fof(f1159,plain,
( init != a_select2(sigma_init,tptp_float_0_0)
| ~ spl41_59
| spl41_124 ),
inference(forward_demodulation,[],[f1151,f787]) ).
fof(f1151,plain,
( init != a_select2(sigma_init,n0)
| spl41_124 ),
inference(avatar_component_clause,[],[f1150]) ).
fof(f1236,plain,
( spl41_144
| ~ spl41_59
| ~ spl41_95 ),
inference(avatar_split_clause,[],[f1024,f1021,f785,f1234]) ).
fof(f1234,plain,
( spl41_144
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_144])]) ).
fof(f1021,plain,
( spl41_95
<=> ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_95])]) ).
fof(f1024,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_59
| ~ spl41_95 ),
inference(forward_demodulation,[],[f1022,f787]) ).
fof(f1022,plain,
( ! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_95 ),
inference(avatar_component_clause,[],[f1021]) ).
fof(f1232,plain,
( spl41_143
| ~ spl41_59
| ~ spl41_93 ),
inference(avatar_split_clause,[],[f1015,f1012,f785,f1230]) ).
fof(f1230,plain,
( spl41_143
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_143])]) ).
fof(f1012,plain,
( spl41_93
<=> ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_93])]) ).
fof(f1015,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_59
| ~ spl41_93 ),
inference(forward_demodulation,[],[f1013,f787]) ).
fof(f1013,plain,
( ! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) )
| ~ spl41_93 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1228,plain,
( spl41_142
| ~ spl41_59
| ~ spl41_91 ),
inference(avatar_split_clause,[],[f1006,f1003,f785,f1226]) ).
fof(f1226,plain,
( spl41_142
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_142])]) ).
fof(f1003,plain,
( spl41_91
<=> ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_91])]) ).
fof(f1006,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_59
| ~ spl41_91 ),
inference(forward_demodulation,[],[f1004,f787]) ).
fof(f1004,plain,
( ! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_91 ),
inference(avatar_component_clause,[],[f1003]) ).
fof(f1224,plain,
( spl41_141
| ~ spl41_59
| ~ spl41_89 ),
inference(avatar_split_clause,[],[f997,f994,f785,f1222]) ).
fof(f1222,plain,
( spl41_141
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_141])]) ).
fof(f994,plain,
( spl41_89
<=> ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_89])]) ).
fof(f997,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_59
| ~ spl41_89 ),
inference(forward_demodulation,[],[f995,f787]) ).
fof(f995,plain,
( ! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) )
| ~ spl41_89 ),
inference(avatar_component_clause,[],[f994]) ).
fof(f1220,plain,
( spl41_140
| ~ spl41_59
| ~ spl41_87 ),
inference(avatar_split_clause,[],[f988,f985,f785,f1218]) ).
fof(f1218,plain,
( spl41_140
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_140])]) ).
fof(f985,plain,
( spl41_87
<=> ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_87])]) ).
fof(f988,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_59
| ~ spl41_87 ),
inference(forward_demodulation,[],[f986,f787]) ).
fof(f986,plain,
( ! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_87 ),
inference(avatar_component_clause,[],[f985]) ).
fof(f1216,plain,
( spl41_139
| ~ spl41_59
| ~ spl41_85 ),
inference(avatar_split_clause,[],[f979,f976,f785,f1214]) ).
fof(f1214,plain,
( spl41_139
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_139])]) ).
fof(f976,plain,
( spl41_85
<=> ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_85])]) ).
fof(f979,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_59
| ~ spl41_85 ),
inference(forward_demodulation,[],[f977,f787]) ).
fof(f977,plain,
( ! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) )
| ~ spl41_85 ),
inference(avatar_component_clause,[],[f976]) ).
fof(f1212,plain,
( spl41_138
| ~ spl41_59
| ~ spl41_81 ),
inference(avatar_split_clause,[],[f961,f958,f785,f1210]) ).
fof(f1210,plain,
( spl41_138
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_138])]) ).
fof(f958,plain,
( spl41_81
<=> ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_81])]) ).
fof(f961,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_59
| ~ spl41_81 ),
inference(forward_demodulation,[],[f959,f787]) ).
fof(f959,plain,
( ! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_81 ),
inference(avatar_component_clause,[],[f958]) ).
fof(f1208,plain,
( spl41_137
| ~ spl41_59
| ~ spl41_79 ),
inference(avatar_split_clause,[],[f952,f949,f785,f1206]) ).
fof(f1206,plain,
( spl41_137
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_137])]) ).
fof(f949,plain,
( spl41_79
<=> ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_79])]) ).
fof(f952,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_59
| ~ spl41_79 ),
inference(forward_demodulation,[],[f950,f787]) ).
fof(f950,plain,
( ! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) )
| ~ spl41_79 ),
inference(avatar_component_clause,[],[f949]) ).
fof(f1204,plain,
( spl41_136
| ~ spl41_59
| ~ spl41_77 ),
inference(avatar_split_clause,[],[f943,f940,f785,f1202]) ).
fof(f1202,plain,
( spl41_136
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_136])]) ).
fof(f940,plain,
( spl41_77
<=> ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_77])]) ).
fof(f943,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_59
| ~ spl41_77 ),
inference(forward_demodulation,[],[f941,f787]) ).
fof(f941,plain,
( ! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_77 ),
inference(avatar_component_clause,[],[f940]) ).
fof(f1200,plain,
( spl41_135
| ~ spl41_59
| ~ spl41_75 ),
inference(avatar_split_clause,[],[f934,f931,f785,f1198]) ).
fof(f1198,plain,
( spl41_135
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_135])]) ).
fof(f931,plain,
( spl41_75
<=> ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_75])]) ).
fof(f934,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_59
| ~ spl41_75 ),
inference(forward_demodulation,[],[f932,f787]) ).
fof(f932,plain,
( ! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) )
| ~ spl41_75 ),
inference(avatar_component_clause,[],[f931]) ).
fof(f1196,plain,
( ~ spl41_134
| ~ spl41_59
| spl41_125 ),
inference(avatar_split_clause,[],[f1158,f1154,f785,f1193]) ).
fof(f1193,plain,
( spl41_134
<=> leq(tptp_float_0_0,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_134])]) ).
fof(f1158,plain,
( ~ leq(tptp_float_0_0,n4)
| ~ spl41_59
| spl41_125 ),
inference(forward_demodulation,[],[f1156,f787]) ).
fof(f1156,plain,
( ~ leq(n0,n4)
| spl41_125 ),
inference(avatar_component_clause,[],[f1154]) ).
fof(f1191,plain,
( spl41_133
| ~ spl41_59
| ~ spl41_73 ),
inference(avatar_split_clause,[],[f925,f922,f785,f1189]) ).
fof(f1189,plain,
( spl41_133
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_133])]) ).
fof(f922,plain,
( spl41_73
<=> ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_73])]) ).
fof(f925,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_59
| ~ spl41_73 ),
inference(forward_demodulation,[],[f923,f787]) ).
fof(f923,plain,
( ! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_73 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f1187,plain,
( spl41_132
| ~ spl41_59
| ~ spl41_70 ),
inference(avatar_split_clause,[],[f911,f908,f785,f1185]) ).
fof(f1185,plain,
( spl41_132
<=> ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_132])]) ).
fof(f908,plain,
( spl41_70
<=> ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_70])]) ).
fof(f911,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_59
| ~ spl41_70 ),
inference(forward_demodulation,[],[f909,f787]) ).
fof(f909,plain,
( ! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) )
| ~ spl41_70 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f1183,plain,
( spl41_131
| ~ spl41_59
| ~ spl41_69 ),
inference(avatar_split_clause,[],[f906,f903,f785,f1181]) ).
fof(f1181,plain,
( spl41_131
<=> ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_131])]) ).
fof(f903,plain,
( spl41_69
<=> ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_69])]) ).
fof(f906,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_59
| ~ spl41_69 ),
inference(forward_demodulation,[],[f904,f787]) ).
fof(f904,plain,
( ! [X0,X1] :
( leq(n0,X1)
| ~ leq(minus(X0,X1),X0) )
| ~ spl41_69 ),
inference(avatar_component_clause,[],[f903]) ).
fof(f1179,plain,
( spl41_130
| ~ spl41_59
| ~ spl41_68 ),
inference(avatar_split_clause,[],[f901,f898,f785,f1177]) ).
fof(f1177,plain,
( spl41_130
<=> ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_130])]) ).
fof(f898,plain,
( spl41_68
<=> ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_68])]) ).
fof(f901,plain,
( ! [X0,X1] :
( ~ leq(tptp_float_0_0,X0)
| leq(uniform_int_rnd(X1,X0),X0) )
| ~ spl41_59
| ~ spl41_68 ),
inference(forward_demodulation,[],[f899,f787]) ).
fof(f899,plain,
( ! [X0,X1] :
( leq(uniform_int_rnd(X1,X0),X0)
| ~ leq(n0,X0) )
| ~ spl41_68 ),
inference(avatar_component_clause,[],[f898]) ).
fof(f1175,plain,
( spl41_129
| ~ spl41_59
| ~ spl41_67 ),
inference(avatar_split_clause,[],[f896,f892,f785,f1173]) ).
fof(f1173,plain,
( spl41_129
<=> ! [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_129])]) ).
fof(f892,plain,
( spl41_67
<=> ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_67])]) ).
fof(f896,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,[],[f895,f787]) ).
fof(f895,plain,
( ! [X0,X1] :
( leq(tptp_float_0_0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_59
| ~ spl41_67 ),
inference(forward_demodulation,[],[f893,f787]) ).
fof(f893,plain,
( ! [X0,X1] :
( leq(n0,uniform_int_rnd(X1,X0))
| ~ leq(n0,X0) )
| ~ spl41_67 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f1171,plain,
spl41_128,
inference(avatar_split_clause,[],[f452,f1169]) ).
fof(f1169,plain,
( spl41_128
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_128])]) ).
fof(f452,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(f1167,plain,
spl41_127,
inference(avatar_split_clause,[],[f451,f1165]) ).
fof(f1165,plain,
( spl41_127
<=> ! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_127])]) ).
fof(f451,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(f1163,plain,
spl41_126,
inference(avatar_split_clause,[],[f450,f1161]) ).
fof(f1161,plain,
( spl41_126
<=> ! [X0,X1] :
( gt(plus(X1,n1),X0)
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_126])]) ).
fof(f450,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(f1157,plain,
( spl41_124
| ~ spl41_125
| ~ spl41_9
| ~ spl41_43 ),
inference(avatar_split_clause,[],[f703,f689,f515,f1154,f1150]) ).
fof(f515,plain,
( spl41_9
<=> ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_9])]) ).
fof(f703,plain,
( ~ leq(n0,n4)
| init = a_select2(sigma_init,n0)
| ~ spl41_9
| ~ spl41_43 ),
inference(resolution,[],[f690,f516]) ).
fof(f516,plain,
( ! [X5] :
( ~ leq(n0,X5)
| ~ leq(X5,n4)
| init = a_select2(sigma_init,X5) )
| ~ spl41_9 ),
inference(avatar_component_clause,[],[f515]) ).
fof(f1148,plain,
spl41_123,
inference(avatar_split_clause,[],[f449,f1146]) ).
fof(f1146,plain,
( spl41_123
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(plus(X1,n1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_123])]) ).
fof(f449,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(f1144,plain,
spl41_122,
inference(avatar_split_clause,[],[f448,f1142]) ).
fof(f1142,plain,
( spl41_122
<=> ! [X0,X1] :
( gt(X1,X0)
| ~ leq(plus(X0,n1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_122])]) ).
fof(f448,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(f1140,plain,
spl41_121,
inference(avatar_split_clause,[],[f447,f1138]) ).
fof(f1138,plain,
( spl41_121
<=> ! [X0,X1] :
( leq(X0,plus(X1,n1))
| ~ leq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_121])]) ).
fof(f447,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(f1136,plain,
spl41_120,
inference(avatar_split_clause,[],[f426,f1134]) ).
fof(f1134,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(f1131,plain,
spl41_119,
inference(avatar_split_clause,[],[f425,f1129]) ).
fof(f425,plain,
! [X0,X1] :
( leq(n0,sK40(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1127,plain,
spl41_118,
inference(avatar_split_clause,[],[f424,f1125]) ).
fof(f1125,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(f1122,plain,
spl41_117,
inference(avatar_split_clause,[],[f423,f1120]) ).
fof(f423,plain,
! [X0,X1] :
( leq(n0,sK39(X0,X1))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
fof(f1118,plain,
spl41_116,
inference(avatar_split_clause,[],[f421,f1116]) ).
fof(f1116,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(f1113,plain,
spl41_115,
inference(avatar_split_clause,[],[f420,f1111]) ).
fof(f420,plain,
! [X0,X1] :
( leq(n0,sK38(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1109,plain,
spl41_114,
inference(avatar_split_clause,[],[f419,f1107]) ).
fof(f1107,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(f1104,plain,
spl41_113,
inference(avatar_split_clause,[],[f418,f1102]) ).
fof(f418,plain,
! [X0,X1] :
( leq(n0,sK37(X0,X1))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f251]) ).
fof(f1100,plain,
spl41_112,
inference(avatar_split_clause,[],[f416,f1098]) ).
fof(f1098,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(f1095,plain,
spl41_111,
inference(avatar_split_clause,[],[f415,f1093]) ).
fof(f415,plain,
! [X0,X1] :
( leq(n0,sK36(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1091,plain,
spl41_110,
inference(avatar_split_clause,[],[f414,f1089]) ).
fof(f1089,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(f1086,plain,
spl41_109,
inference(avatar_split_clause,[],[f413,f1084]) ).
fof(f413,plain,
! [X0,X1] :
( leq(n0,sK35(X0,X1))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f247]) ).
fof(f1082,plain,
spl41_108,
inference(avatar_split_clause,[],[f401,f1080]) ).
fof(f1080,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(f1077,plain,
spl41_107,
inference(avatar_split_clause,[],[f400,f1075]) ).
fof(f400,plain,
! [X0,X1] :
( leq(n0,sK32(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1073,plain,
spl41_106,
inference(avatar_split_clause,[],[f399,f1071]) ).
fof(f1071,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(f1068,plain,
spl41_105,
inference(avatar_split_clause,[],[f398,f1066]) ).
fof(f398,plain,
! [X0,X1] :
( leq(n0,sK31(X0,X1))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f238]) ).
fof(f1064,plain,
spl41_104,
inference(avatar_split_clause,[],[f390,f1062]) ).
fof(f1062,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(f1059,plain,
spl41_103,
inference(avatar_split_clause,[],[f389,f1057]) ).
fof(f389,plain,
! [X0,X1] :
( leq(n0,sK29(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1055,plain,
spl41_102,
inference(avatar_split_clause,[],[f388,f1053]) ).
fof(f1053,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(f1050,plain,
spl41_101,
inference(avatar_split_clause,[],[f387,f1048]) ).
fof(f387,plain,
! [X0,X1] :
( leq(n0,sK28(X0,X1))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
fof(f1046,plain,
spl41_100,
inference(avatar_split_clause,[],[f384,f1044]) ).
fof(f1044,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(f1041,plain,
spl41_99,
inference(avatar_split_clause,[],[f383,f1039]) ).
fof(f383,plain,
! [X0,X1] :
( leq(n0,sK27(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1037,plain,
spl41_98,
inference(avatar_split_clause,[],[f382,f1035]) ).
fof(f1035,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(f1032,plain,
spl41_97,
inference(avatar_split_clause,[],[f381,f1030]) ).
fof(f381,plain,
! [X0,X1] :
( leq(n0,sK26(X0,X1))
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f226]) ).
fof(f1028,plain,
spl41_96,
inference(avatar_split_clause,[],[f379,f1026]) ).
fof(f1026,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(f1023,plain,
spl41_95,
inference(avatar_split_clause,[],[f378,f1021]) ).
fof(f378,plain,
! [X0,X1] :
( leq(n0,sK25(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1019,plain,
spl41_94,
inference(avatar_split_clause,[],[f377,f1017]) ).
fof(f1017,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(f1014,plain,
spl41_93,
inference(avatar_split_clause,[],[f376,f1012]) ).
fof(f376,plain,
! [X0,X1] :
( leq(n0,sK24(X0,X1))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f222]) ).
fof(f1010,plain,
spl41_92,
inference(avatar_split_clause,[],[f373,f1008]) ).
fof(f1008,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(f1005,plain,
spl41_91,
inference(avatar_split_clause,[],[f372,f1003]) ).
fof(f372,plain,
! [X0,X1] :
( leq(n0,sK23(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f1001,plain,
spl41_90,
inference(avatar_split_clause,[],[f371,f999]) ).
fof(f999,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(f996,plain,
spl41_89,
inference(avatar_split_clause,[],[f370,f994]) ).
fof(f370,plain,
! [X0,X1] :
( leq(n0,sK22(X0,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f217]) ).
fof(f992,plain,
spl41_88,
inference(avatar_split_clause,[],[f368,f990]) ).
fof(f990,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(f987,plain,
spl41_87,
inference(avatar_split_clause,[],[f367,f985]) ).
fof(f367,plain,
! [X0,X1] :
( leq(n0,sK21(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f983,plain,
spl41_86,
inference(avatar_split_clause,[],[f366,f981]) ).
fof(f981,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(f978,plain,
spl41_85,
inference(avatar_split_clause,[],[f365,f976]) ).
fof(f365,plain,
! [X0,X1] :
( leq(n0,sK20(X0,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f213]) ).
fof(f974,plain,
spl41_84,
inference(avatar_split_clause,[],[f362,f972]) ).
fof(f972,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(f970,plain,
( spl41_83
| ~ spl41_3
| ~ spl41_61 ),
inference(avatar_split_clause,[],[f849,f813,f487,f967]) ).
fof(f967,plain,
( spl41_83
<=> leq(n1,loopcounter) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_83])]) ).
fof(f813,plain,
( spl41_61
<=> ! [X0,X1] :
( leq(X0,X1)
| ~ gt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_61])]) ).
fof(f849,plain,
( leq(n1,loopcounter)
| ~ spl41_3
| ~ spl41_61 ),
inference(resolution,[],[f814,f489]) ).
fof(f814,plain,
( ! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) )
| ~ spl41_61 ),
inference(avatar_component_clause,[],[f813]) ).
fof(f965,plain,
spl41_82,
inference(avatar_split_clause,[],[f353,f963]) ).
fof(f963,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(f960,plain,
spl41_81,
inference(avatar_split_clause,[],[f352,f958]) ).
fof(f352,plain,
! [X0,X1] :
( leq(n0,sK19(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f956,plain,
spl41_80,
inference(avatar_split_clause,[],[f351,f954]) ).
fof(f954,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(f951,plain,
spl41_79,
inference(avatar_split_clause,[],[f350,f949]) ).
fof(f350,plain,
! [X0,X1] :
( leq(n0,sK18(X0,X1))
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
fof(f947,plain,
spl41_78,
inference(avatar_split_clause,[],[f347,f945]) ).
fof(f945,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(f942,plain,
spl41_77,
inference(avatar_split_clause,[],[f346,f940]) ).
fof(f346,plain,
! [X0,X1] :
( leq(n0,sK17(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f938,plain,
spl41_76,
inference(avatar_split_clause,[],[f345,f936]) ).
fof(f936,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(f933,plain,
spl41_75,
inference(avatar_split_clause,[],[f344,f931]) ).
fof(f344,plain,
! [X0,X1] :
( leq(n0,sK16(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f201]) ).
fof(f929,plain,
spl41_74,
inference(avatar_split_clause,[],[f341,f927]) ).
fof(f927,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(f924,plain,
spl41_73,
inference(avatar_split_clause,[],[f340,f922]) ).
fof(f340,plain,
! [X0,X1] :
( leq(n0,sK15(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f920,plain,
( spl41_72
| ~ spl41_4
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f790,f785,f492,f917]) ).
fof(f917,plain,
( spl41_72
<=> leq(tptp_float_0_0,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_72])]) ).
fof(f790,plain,
( leq(tptp_float_0_0,sK13)
| ~ spl41_4
| ~ spl41_59 ),
inference(superposition,[],[f494,f787]) ).
fof(f915,plain,
spl41_71,
inference(avatar_split_clause,[],[f339,f913]) ).
fof(f913,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(f910,plain,
spl41_70,
inference(avatar_split_clause,[],[f338,f908]) ).
fof(f338,plain,
! [X0,X1] :
( leq(n0,sK14(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f905,plain,
spl41_69,
inference(avatar_split_clause,[],[f336,f903]) ).
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(f900,plain,
spl41_68,
inference(avatar_split_clause,[],[f333,f898]) ).
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(f894,plain,
spl41_67,
inference(avatar_split_clause,[],[f332,f892]) ).
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(f873,plain,
spl41_66,
inference(avatar_split_clause,[],[f438,f871]) ).
fof(f871,plain,
( spl41_66
<=> ! [X0] : plus(X0,n1) = plus(n1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_66])]) ).
fof(f438,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(f869,plain,
spl41_65,
inference(avatar_split_clause,[],[f437,f867]) ).
fof(f867,plain,
( spl41_65
<=> ! [X0] : plus(minus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_65])]) ).
fof(f437,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(f865,plain,
( spl41_64
| ~ spl41_1
| ~ spl41_59 ),
inference(avatar_split_clause,[],[f789,f785,f477,f862]) ).
fof(f862,plain,
( spl41_64
<=> leq(tptp_float_0_0,pv10) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_64])]) ).
fof(f789,plain,
( leq(tptp_float_0_0,pv10)
| ~ spl41_1
| ~ spl41_59 ),
inference(superposition,[],[f479,f787]) ).
fof(f860,plain,
spl41_63,
inference(avatar_split_clause,[],[f436,f858]) ).
fof(f858,plain,
( spl41_63
<=> ! [X0] : minus(plus(X0,n1),n1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl41_63])]) ).
fof(f436,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(f819,plain,
( spl41_62
| ~ spl41_59
| ~ spl41_60 ),
inference(avatar_split_clause,[],[f811,f808,f785,f817]) ).
fof(f817,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(f808,plain,
( spl41_60
<=> ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_60])]) ).
fof(f811,plain,
( ! [X0] : tptp_float_0_0 = sum(tptp_float_0_0,tptp_minus_1,X0)
| ~ spl41_59
| ~ spl41_60 ),
inference(forward_demodulation,[],[f809,f787]) ).
fof(f809,plain,
( ! [X0] : tptp_float_0_0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_60 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f815,plain,
spl41_61,
inference(avatar_split_clause,[],[f334,f813]) ).
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(f810,plain,
spl41_60,
inference(avatar_split_clause,[],[f315,f808]) ).
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(f788,plain,
( spl41_59
| ~ spl41_58 ),
inference(avatar_split_clause,[],[f783,f780,f785]) ).
fof(f780,plain,
( spl41_58
<=> ! [X0] : n0 = sum(n0,tptp_minus_1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_58])]) ).
fof(f783,plain,
( n0 = tptp_float_0_0
| ~ spl41_58 ),
inference(forward_demodulation,[],[f781,f315]) ).
fof(f781,plain,
( ! [X0] : n0 = sum(n0,tptp_minus_1,X0)
| ~ spl41_58 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f782,plain,
spl41_58,
inference(avatar_split_clause,[],[f311,f780]) ).
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(f772,plain,
spl41_57,
inference(avatar_split_clause,[],[f467,f769]) ).
fof(f769,plain,
( spl41_57
<=> n5 = plus(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_57])]) ).
fof(f467,plain,
n5 = plus(n4,n1),
inference(forward_demodulation,[],[f466,f463]) ).
fof(f463,plain,
n4 = plus(n3,n1),
inference(forward_demodulation,[],[f462,f460]) ).
fof(f460,plain,
n3 = plus(n2,n1),
inference(forward_demodulation,[],[f459,f458]) ).
fof(f458,plain,
n2 = plus(n1,n1),
inference(forward_demodulation,[],[f431,f429]) ).
fof(f429,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(f431,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(f459,plain,
n3 = plus(plus(n1,n1),n1),
inference(forward_demodulation,[],[f432,f429]) ).
fof(f432,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(f462,plain,
n4 = plus(plus(n2,n1),n1),
inference(forward_demodulation,[],[f461,f458]) ).
fof(f461,plain,
n4 = plus(plus(plus(n1,n1),n1),n1),
inference(forward_demodulation,[],[f433,f429]) ).
fof(f433,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(f466,plain,
n5 = plus(plus(n3,n1),n1),
inference(forward_demodulation,[],[f465,f460]) ).
fof(f465,plain,
n5 = plus(plus(plus(n2,n1),n1),n1),
inference(forward_demodulation,[],[f464,f458]) ).
fof(f464,plain,
n5 = plus(plus(plus(plus(n1,n1),n1),n1),n1),
inference(forward_demodulation,[],[f434,f429]) ).
fof(f434,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(f767,plain,
spl41_56,
inference(avatar_split_clause,[],[f463,f764]) ).
fof(f764,plain,
( spl41_56
<=> n4 = plus(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_56])]) ).
fof(f762,plain,
spl41_55,
inference(avatar_split_clause,[],[f460,f759]) ).
fof(f759,plain,
( spl41_55
<=> n3 = plus(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_55])]) ).
fof(f757,plain,
spl41_54,
inference(avatar_split_clause,[],[f458,f754]) ).
fof(f754,plain,
( spl41_54
<=> n2 = plus(n1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_54])]) ).
fof(f752,plain,
( spl41_53
| ~ spl41_5
| ~ spl41_4
| ~ spl41_9 ),
inference(avatar_split_clause,[],[f523,f515,f492,f497,f749]) ).
fof(f749,plain,
( spl41_53
<=> init = a_select2(sigma_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_53])]) ).
fof(f523,plain,
( ~ leq(sK13,n4)
| init = a_select2(sigma_init,sK13)
| ~ spl41_4
| ~ spl41_9 ),
inference(resolution,[],[f516,f494]) ).
fof(f747,plain,
spl41_52,
inference(avatar_split_clause,[],[f435,f745]) ).
fof(f745,plain,
( spl41_52
<=> ! [X0] : gt(plus(X0,n1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_52])]) ).
fof(f435,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(f743,plain,
spl41_51,
inference(avatar_split_clause,[],[f430,f740]) ).
fof(f740,plain,
( spl41_51
<=> n0 = plus(tptp_minus_1,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_51])]) ).
fof(f430,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(f738,plain,
spl41_50,
inference(avatar_split_clause,[],[f429,f735]) ).
fof(f735,plain,
( spl41_50
<=> n1 = plus(n0,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_50])]) ).
fof(f730,plain,
spl41_49,
inference(avatar_split_clause,[],[f260,f728]) ).
fof(f728,plain,
( spl41_49
<=> ! [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_49])]) ).
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(rhoold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13)
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,n4)
| ~ 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(pv10,n135299)
& leq(n0,pv10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f192,f193]) ).
fof(f193,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
=> ( init != a_select2(rhoold_init,sK13)
& leq(sK13,n4)
& leq(n0,sK13) ) ),
introduced(choice_axiom,[]) ).
fof(f192,plain,
( ? [X0] :
( init != a_select2(rhoold_init,X0)
& leq(X0,n4)
& leq(n0,X0) )
& ( ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ( ! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
| ~ gt(loopcounter,n1) )
& ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) )
& ! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,n4)
| ~ 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(pv10,n135299)
& leq(n0,pv10) ),
inference(rectify,[],[f117]) ).
fof(f117,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(X9,n4)
& leq(n0,X9) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(sigma_init,X4)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(mu_init,X5)
| ~ leq(X5,n4)
| ~ 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(pv10,n135299)
& leq(n0,pv10) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
( ? [X9] :
( init != a_select2(rhoold_init,X9)
& leq(X9,n4)
& leq(n0,X9) )
& ( ! [X0] :
( init = a_select2(sigmaold_init,X0)
| ~ leq(X0,n4)
| ~ leq(n0,X0) )
| ~ gt(loopcounter,n1) )
& ( ! [X1] :
( init = a_select2(rhoold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1) )
| ~ gt(loopcounter,n1) )
& ( ! [X2] :
( init = a_select2(muold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2) )
| ~ gt(loopcounter,n1) )
& ! [X3] :
( init = a_select3(center_init,X3,n0)
| ~ leq(X3,n4)
| ~ leq(n0,X3) )
& ! [X4] :
( init = a_select2(sigma_init,X4)
| ~ leq(X4,n4)
| ~ leq(n0,X4) )
& ! [X5] :
( init = a_select2(mu_init,X5)
| ~ leq(X5,n4)
| ~ 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(pv10,n135299)
& leq(n0,pv10) ),
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,n4)
& leq(n0,X4) )
=> init = a_select2(sigma_init,X4) )
& ! [X5] :
( ( leq(X5,n4)
& 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(pv10,n135299)
& leq(n0,pv10) )
=> ! [X9] :
( ( leq(X9,n4)
& leq(n0,X9) )
=> init = a_select2(rhoold_init,X9) ) ),
inference(rectify,[],[f54]) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> init = a_select2(sigmaold_init,X4) ) )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(rhoold_init,X28) ) )
& ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(muold_init,X27) ) )
& ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select3(center_init,X21,n0) )
& ! [X20] :
( ( leq(X20,n4)
& leq(n0,X20) )
=> init = a_select2(sigma_init,X20) )
& ! [X19] :
( ( leq(X19,n4)
& 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(pv10,n135299)
& leq(n0,pv10) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(rhoold_init,X10) ) ),
inference(negated_conjecture,[],[f53]) ).
fof(f53,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> init = a_select2(sigmaold_init,X4) ) )
& ( gt(loopcounter,n1)
=> ! [X28] :
( ( leq(X28,n4)
& leq(n0,X28) )
=> init = a_select2(rhoold_init,X28) ) )
& ( gt(loopcounter,n1)
=> ! [X27] :
( ( leq(X27,n4)
& leq(n0,X27) )
=> init = a_select2(muold_init,X27) ) )
& ! [X21] :
( ( leq(X21,n4)
& leq(n0,X21) )
=> init = a_select3(center_init,X21,n0) )
& ! [X20] :
( ( leq(X20,n4)
& leq(n0,X20) )
=> init = a_select2(sigma_init,X20) )
& ! [X19] :
( ( leq(X19,n4)
& 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(pv10,n135299)
& leq(n0,pv10) )
=> ! [X10] :
( ( leq(X10,n4)
& leq(n0,X10) )
=> init = a_select2(rhoold_init,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0041) ).
fof(f723,plain,
( ~ spl41_3
| spl41_48 ),
inference(avatar_split_clause,[],[f267,f721,f487]) ).
fof(f721,plain,
( spl41_48
<=> ! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(n0,X1)
| ~ leq(X1,n4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_48])]) ).
fof(f267,plain,
! [X1] :
( init = a_select2(sigmaold_init,X1)
| ~ leq(X1,n4)
| ~ leq(n0,X1)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f716,plain,
( ~ spl41_3
| spl41_47 ),
inference(avatar_split_clause,[],[f266,f714,f487]) ).
fof(f266,plain,
! [X2] :
( init = a_select2(rhoold_init,X2)
| ~ leq(X2,n4)
| ~ leq(n0,X2)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f709,plain,
( ~ spl41_3
| spl41_46 ),
inference(avatar_split_clause,[],[f265,f707,f487]) ).
fof(f265,plain,
! [X3] :
( init = a_select2(muold_init,X3)
| ~ leq(X3,n4)
| ~ leq(n0,X3)
| ~ gt(loopcounter,n1) ),
inference(cnf_transformation,[],[f194]) ).
fof(f701,plain,
( spl41_45
| ~ spl41_5
| ~ spl41_4
| ~ spl41_8 ),
inference(avatar_split_clause,[],[f521,f511,f492,f497,f698]) ).
fof(f698,plain,
( spl41_45
<=> init = a_select2(mu_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_45])]) ).
fof(f521,plain,
( ~ leq(sK13,n4)
| init = a_select2(mu_init,sK13)
| ~ spl41_4
| ~ spl41_8 ),
inference(resolution,[],[f512,f494]) ).
fof(f696,plain,
( spl41_44
| ~ spl41_5
| ~ spl41_4
| ~ spl41_7 ),
inference(avatar_split_clause,[],[f519,f507,f492,f497,f693]) ).
fof(f693,plain,
( spl41_44
<=> init = a_select2(rho_init,sK13) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_44])]) ).
fof(f519,plain,
( ~ leq(sK13,n4)
| init = a_select2(rho_init,sK13)
| ~ spl41_4
| ~ spl41_7 ),
inference(resolution,[],[f508,f494]) ).
fof(f691,plain,
spl41_43,
inference(avatar_split_clause,[],[f307,f689]) ).
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(f687,plain,
spl41_42,
inference(avatar_split_clause,[],[f306,f685]) ).
fof(f685,plain,
( spl41_42
<=> ! [X0] : ~ gt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_42])]) ).
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(f683,plain,
spl41_41,
inference(avatar_split_clause,[],[f299,f680]) ).
fof(f680,plain,
( spl41_41
<=> gt(n0,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_41])]) ).
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(f678,plain,
spl41_40,
inference(avatar_split_clause,[],[f298,f675]) ).
fof(f675,plain,
( spl41_40
<=> gt(n4,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_40])]) ).
fof(f298,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(f673,plain,
spl41_39,
inference(avatar_split_clause,[],[f297,f670]) ).
fof(f670,plain,
( spl41_39
<=> gt(n4,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_39])]) ).
fof(f297,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(f668,plain,
spl41_38,
inference(avatar_split_clause,[],[f296,f665]) ).
fof(f665,plain,
( spl41_38
<=> gt(n4,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_38])]) ).
fof(f296,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(f663,plain,
spl41_37,
inference(avatar_split_clause,[],[f295,f660]) ).
fof(f660,plain,
( spl41_37
<=> gt(n4,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_37])]) ).
fof(f295,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(f658,plain,
spl41_36,
inference(avatar_split_clause,[],[f294,f655]) ).
fof(f655,plain,
( spl41_36
<=> gt(n4,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_36])]) ).
fof(f294,plain,
gt(n4,tptp_minus_1),
inference(cnf_transformation,[],[f58]) ).
fof(f58,axiom,
gt(n4,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_4_tptp_minus_1) ).
fof(f653,plain,
spl41_35,
inference(avatar_split_clause,[],[f293,f650]) ).
fof(f650,plain,
( spl41_35
<=> gt(n1,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_35])]) ).
fof(f293,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(f648,plain,
spl41_34,
inference(avatar_split_clause,[],[f292,f645]) ).
fof(f645,plain,
( spl41_34
<=> gt(n1,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_34])]) ).
fof(f292,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(f643,plain,
spl41_33,
inference(avatar_split_clause,[],[f291,f640]) ).
fof(f640,plain,
( spl41_33
<=> gt(n2,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_33])]) ).
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(f638,plain,
spl41_32,
inference(avatar_split_clause,[],[f290,f635]) ).
fof(f635,plain,
( spl41_32
<=> gt(n2,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_32])]) ).
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(f633,plain,
spl41_31,
inference(avatar_split_clause,[],[f289,f630]) ).
fof(f630,plain,
( spl41_31
<=> gt(n2,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_31])]) ).
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(f628,plain,
spl41_30,
inference(avatar_split_clause,[],[f288,f625]) ).
fof(f625,plain,
( spl41_30
<=> gt(n3,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_30])]) ).
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(f623,plain,
spl41_29,
inference(avatar_split_clause,[],[f287,f620]) ).
fof(f620,plain,
( spl41_29
<=> gt(n3,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_29])]) ).
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(f618,plain,
spl41_28,
inference(avatar_split_clause,[],[f286,f615]) ).
fof(f615,plain,
( spl41_28
<=> gt(n3,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_28])]) ).
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(f613,plain,
spl41_27,
inference(avatar_split_clause,[],[f285,f610]) ).
fof(f610,plain,
( spl41_27
<=> gt(n3,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_27])]) ).
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(f608,plain,
spl41_26,
inference(avatar_split_clause,[],[f284,f605]) ).
fof(f605,plain,
( spl41_26
<=> gt(n5,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_26])]) ).
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(f603,plain,
spl41_25,
inference(avatar_split_clause,[],[f283,f600]) ).
fof(f600,plain,
( spl41_25
<=> gt(n5,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_25])]) ).
fof(f283,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(f598,plain,
spl41_24,
inference(avatar_split_clause,[],[f282,f595]) ).
fof(f595,plain,
( spl41_24
<=> gt(n5,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_24])]) ).
fof(f282,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(f593,plain,
spl41_23,
inference(avatar_split_clause,[],[f281,f590]) ).
fof(f590,plain,
( spl41_23
<=> gt(n5,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_23])]) ).
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(f588,plain,
spl41_22,
inference(avatar_split_clause,[],[f280,f585]) ).
fof(f585,plain,
( spl41_22
<=> gt(n5,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_22])]) ).
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(f583,plain,
spl41_21,
inference(avatar_split_clause,[],[f279,f580]) ).
fof(f580,plain,
( spl41_21
<=> gt(n5,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_21])]) ).
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(f578,plain,
spl41_20,
inference(avatar_split_clause,[],[f278,f575]) ).
fof(f575,plain,
( spl41_20
<=> gt(n135299,n0) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_20])]) ).
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(f573,plain,
spl41_19,
inference(avatar_split_clause,[],[f277,f570]) ).
fof(f570,plain,
( spl41_19
<=> gt(n135299,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_19])]) ).
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(f568,plain,
spl41_18,
inference(avatar_split_clause,[],[f276,f565]) ).
fof(f565,plain,
( spl41_18
<=> gt(n135299,n1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_18])]) ).
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(f563,plain,
spl41_17,
inference(avatar_split_clause,[],[f275,f560]) ).
fof(f560,plain,
( spl41_17
<=> gt(n135299,n2) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_17])]) ).
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(f558,plain,
spl41_16,
inference(avatar_split_clause,[],[f274,f555]) ).
fof(f555,plain,
( spl41_16
<=> gt(n135299,n3) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_16])]) ).
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(f553,plain,
( spl41_14
| ~ spl41_15
| ~ spl41_1
| ~ spl41_7 ),
inference(avatar_split_clause,[],[f518,f507,f477,f550,f546]) ).
fof(f546,plain,
( spl41_14
<=> init = a_select2(rho_init,pv10) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_14])]) ).
fof(f550,plain,
( spl41_15
<=> leq(pv10,n4) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_15])]) ).
fof(f518,plain,
( ~ leq(pv10,n4)
| init = a_select2(rho_init,pv10)
| ~ spl41_1
| ~ spl41_7 ),
inference(resolution,[],[f508,f479]) ).
fof(f544,plain,
spl41_13,
inference(avatar_split_clause,[],[f273,f541]) ).
fof(f541,plain,
( spl41_13
<=> gt(n135299,n5) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_13])]) ).
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(f539,plain,
spl41_12,
inference(avatar_split_clause,[],[f272,f536]) ).
fof(f536,plain,
( spl41_12
<=> gt(n135299,tptp_minus_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_12])]) ).
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(f534,plain,
~ spl41_11,
inference(avatar_split_clause,[],[f271,f531]) ).
fof(f531,plain,
( spl41_11
<=> def = use ),
introduced(avatar_definition,[new_symbols(naming,[spl41_11])]) ).
fof(f271,plain,
def != use,
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
def != use,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defuse) ).
fof(f527,plain,
spl41_10,
inference(avatar_split_clause,[],[f264,f525]) ).
fof(f525,plain,
( spl41_10
<=> ! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl41_10])]) ).
fof(f264,plain,
! [X4] :
( init = a_select3(center_init,X4,n0)
| ~ leq(X4,n4)
| ~ leq(n0,X4) ),
inference(cnf_transformation,[],[f194]) ).
fof(f517,plain,
spl41_9,
inference(avatar_split_clause,[],[f263,f515]) ).
fof(f263,plain,
! [X5] :
( init = a_select2(sigma_init,X5)
| ~ leq(X5,n4)
| ~ leq(n0,X5) ),
inference(cnf_transformation,[],[f194]) ).
fof(f513,plain,
spl41_8,
inference(avatar_split_clause,[],[f262,f511]) ).
fof(f262,plain,
! [X6] :
( init = a_select2(mu_init,X6)
| ~ leq(X6,n4)
| ~ leq(n0,X6) ),
inference(cnf_transformation,[],[f194]) ).
fof(f509,plain,
spl41_7,
inference(avatar_split_clause,[],[f261,f507]) ).
fof(f261,plain,
! [X7] :
( init = a_select2(rho_init,X7)
| ~ leq(X7,n4)
| ~ leq(n0,X7) ),
inference(cnf_transformation,[],[f194]) ).
fof(f505,plain,
~ spl41_6,
inference(avatar_split_clause,[],[f270,f502]) ).
fof(f270,plain,
init != a_select2(rhoold_init,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f500,plain,
spl41_5,
inference(avatar_split_clause,[],[f269,f497]) ).
fof(f269,plain,
leq(sK13,n4),
inference(cnf_transformation,[],[f194]) ).
fof(f495,plain,
spl41_4,
inference(avatar_split_clause,[],[f268,f492]) ).
fof(f268,plain,
leq(n0,sK13),
inference(cnf_transformation,[],[f194]) ).
fof(f490,plain,
spl41_3,
inference(avatar_split_clause,[],[f259,f487]) ).
fof(f259,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f194]) ).
fof(f485,plain,
spl41_2,
inference(avatar_split_clause,[],[f258,f482]) ).
fof(f258,plain,
leq(pv10,n135299),
inference(cnf_transformation,[],[f194]) ).
fof(f480,plain,
spl41_1,
inference(avatar_split_clause,[],[f257,f477]) ).
fof(f257,plain,
leq(n0,pv10),
inference(cnf_transformation,[],[f194]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV173+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri May 3 21:09:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (4970)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (4973)WARNING: value z3 for option sas not known
% 0.13/0.37 % (4975)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)
% 0.13/0.37 % (4971)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (4972)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (4973)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)
% 0.13/0.37 % (4974)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (4976)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)
% 0.13/0.37 % (4977)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.47 % (4975)First to succeed.
% 0.21/0.48 TRYING [1]
% 0.21/0.48 % (4975)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4970"
% 0.21/0.49 % (4975)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (4975)------------------------------
% 0.21/0.49 % (4975)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.49 % (4975)Termination reason: Refutation
% 0.21/0.49
% 0.21/0.49 % (4975)Memory used [KB]: 3063
% 0.21/0.49 % (4975)Time elapsed: 0.113 s
% 0.21/0.49 % (4975)Instructions burned: 237 (million)
% 0.21/0.49 % (4970)Success in time 0.136 s
%------------------------------------------------------------------------------