TSTP Solution File: SCT088-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SCT088-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 22:00:45 EDT 2023
% Result : Unsatisfiable 4.93s 1.23s
% Output : Refutation 4.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1284
% Syntax : Number of formulae : 2459 ( 755 unt; 0 def)
% Number of atoms : 5836 (1369 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 5936 (2559 ~;2637 |; 0 &)
% ( 740 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 783 ( 781 usr; 742 prp; 0-3 aty)
% Number of functors : 60 ( 60 usr; 14 con; 0-5 aty)
% Number of variables : 4118 (;4118 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17370,plain,
$false,
inference(avatar_sat_refutation,[],[f717,f722,f727,f732,f737,f742,f747,f752,f757,f762,f767,f772,f777,f782,f787,f792,f797,f802,f807,f812,f817,f822,f827,f832,f837,f842,f847,f852,f857,f862,f867,f872,f877,f882,f887,f892,f897,f902,f907,f912,f917,f922,f927,f932,f937,f942,f947,f952,f957,f962,f967,f972,f977,f982,f987,f992,f997,f1002,f1007,f1012,f1017,f1021,f1025,f1029,f1033,f1037,f1041,f1045,f1049,f1053,f1057,f1061,f1065,f1069,f1073,f1077,f1081,f1086,f1090,f1094,f1098,f1102,f1106,f1110,f1119,f1123,f1127,f1131,f1135,f1139,f1143,f1147,f1151,f1155,f1159,f1163,f1167,f1171,f1175,f1179,f1183,f1187,f1191,f1196,f1200,f1204,f1208,f1219,f1223,f1227,f1231,f1235,f1239,f1243,f1247,f1251,f1255,f1259,f1263,f1267,f1271,f1275,f1279,f1283,f1287,f1291,f1295,f1299,f1303,f1307,f1311,f1315,f1319,f1323,f1327,f1331,f1335,f1339,f1343,f1347,f1361,f1383,f1402,f1406,f1410,f1414,f1419,f1423,f1427,f1431,f1435,f1439,f1443,f1447,f1451,f1455,f1459,f1463,f1467,f1471,f1475,f1479,f1483,f1487,f1491,f1495,f1499,f1503,f1507,f1511,f1515,f1519,f1523,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1559,f1702,f1706,f1710,f1714,f1718,f1722,f1726,f1730,f1734,f1738,f1742,f1746,f1750,f1754,f1758,f1762,f1766,f1770,f1774,f1778,f1782,f1786,f1790,f1794,f1798,f1802,f1806,f1810,f1814,f1818,f1822,f1827,f1831,f2014,f2036,f2040,f2044,f2048,f2052,f2056,f2060,f2064,f2068,f2072,f2081,f2085,f2089,f2093,f2097,f2101,f2105,f2109,f2113,f2117,f2121,f2125,f2129,f2133,f2137,f2141,f2145,f2149,f2153,f2157,f2161,f2165,f2169,f2173,f2177,f2311,f2395,f2419,f2434,f2438,f2442,f2446,f2450,f2454,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2538,f2542,f2546,f2550,f2554,f2559,f2563,f2568,f2572,f2576,f2580,f2584,f2588,f2592,f2773,f2896,f2900,f2904,f2908,f2913,f2917,f2921,f2925,f2929,f2933,f2937,f2941,f2945,f2949,f2953,f2957,f2961,f2965,f2969,f2973,f2977,f2981,f2985,f2989,f2993,f2997,f3001,f3005,f3009,f3013,f3018,f3022,f3100,f3415,f3535,f3579,f3583,f3587,f3591,f3595,f3599,f3603,f3607,f3611,f3615,f3619,f3623,f3627,f3631,f3635,f3639,f3643,f3647,f3651,f3655,f3659,f3663,f3667,f3671,f3675,f3679,f3692,f3696,f3700,f3704,f3708,f3712,f3716,f3720,f3724,f3728,f3742,f3746,f3750,f3754,f3758,f3762,f3767,f4139,f4446,f4464,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4521,f4525,f4529,f4533,f4537,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4597,f4606,f4610,f4614,f4618,f4622,f4626,f4631,f4635,f4639,f4643,f4647,f4651,f5858,f5933,f6040,f6044,f6048,f6052,f6076,f6080,f6084,f6088,f6092,f6096,f6100,f6104,f6108,f6112,f6120,f6124,f6128,f6132,f6136,f6140,f6144,f6148,f6152,f6633,f6951,f6962,f6966,f6970,f6974,f6978,f6982,f6986,f6990,f7012,f7016,f7020,f7024,f7028,f7032,f7036,f7040,f7044,f7048,f7052,f7056,f7060,f7065,f7069,f7073,f7077,f7170,f7457,f7505,f7568,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7670,f7705,f7709,f7713,f7717,f7721,f7725,f7729,f7733,f7737,f7741,f7745,f7749,f7754,f7758,f7763,f7768,f7837,f8391,f8551,f8582,f8586,f8666,f8676,f8680,f8684,f8688,f8692,f8696,f8700,f8709,f8976,f8980,f8984,f8988,f8992,f8996,f9000,f9004,f9008,f9012,f9016,f9020,f9024,f9028,f9032,f9036,f9040,f9044,f9048,f9052,f9056,f9060,f9064,f9068,f9072,f9076,f9080,f9084,f9088,f9092,f9096,f9100,f9105,f9110,f9116,f9123,f9138,f9499,f9766,f9920,f9924,f9928,f9932,f9936,f10052,f10056,f10060,f10064,f10073,f10077,f10081,f10085,f10089,f10093,f10097,f10102,f10375,f10379,f10452,f10456,f10460,f10464,f10468,f10472,f10476,f10508,f10597,f10601,f10605,f10609,f10613,f10683,f10687,f10691,f10695,f11119,f11123,f11127,f11388,f11429,f11433,f11437,f11441,f11445,f11449,f11453,f11734,f11738,f11742,f11869,f11917,f11921,f11978,f12040,f12044,f12160,f12542,f12546,f12550,f12554,f12558,f12593,f12597,f12601,f12605,f12609,f12613,f12617,f12621,f12625,f12629,f12633,f12637,f12660,f12664,f12668,f12672,f12676,f12680,f12684,f12688,f12692,f12700,f13510,f13532,f13536,f13540,f13544,f13548,f13552,f13556,f13604,f13608,f13612,f13616,f13620,f13624,f13628,f13632,f13636,f13640,f13644,f13648,f13652,f13656,f13660,f13664,f13668,f13672,f13677,f13681,f13685,f13709,f13713,f13717,f13721,f13725,f13729,f13733,f13737,f13741,f13745,f13749,f13753,f14200,f14575,f14645,f14963,f14988,f15014,f15038,f15042,f15046,f15050,f15074,f15078,f15082,f15086,f15090,f15094,f15098,f15102,f15106,f15110,f15114,f15118,f15122,f15126,f15131,f15135,f15139,f15143,f15147,f15183,f15187,f15191,f15195,f15217,f15253,f15289,f15294,f15303,f15318,f15322,f15326,f15330,f15334,f15338,f15342,f15346,f15350,f15354,f15400,f15404,f15408,f15412,f15416,f15420,f15424,f16825,f17331,f17335,f17339,f17368,f17369]) ).
fof(f17369,plain,
( spl0_61
| ~ spl0_505
| ~ spl0_736 ),
inference(avatar_split_clause,[],[f17224,f16823,f8580,f1014]) ).
fof(f1014,plain,
( spl0_61
<=> v_c____ = v_d____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f8580,plain,
( spl0_505
<=> ! [X9,X1] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f16823,plain,
( spl0_736
<=> ! [X135] : ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X135,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f17224,plain,
( v_c____ = v_d____
| ~ spl0_505
| ~ spl0_736 ),
inference(resolution,[],[f16824,f8581]) ).
fof(f8581,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f8580]) ).
fof(f16824,plain,
( ! [X135] : ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X135,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_736 ),
inference(avatar_component_clause,[],[f16823]) ).
fof(f17368,plain,
( ~ spl0_20
| spl0_740
| ~ spl0_184
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1894,f1724,f1704,f17366,f809]) ).
fof(f809,plain,
( spl0_20
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f17366,plain,
( spl0_740
<=> ! [X16,X17] :
( c_Divides_Odiv__class_Omod(X16,X17,tc_nat) = X16
| c_lessequals(X17,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1704,plain,
( spl0_184
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1724,plain,
( spl0_189
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1894,plain,
( ! [X16,X17] :
( c_Divides_Odiv__class_Omod(X16,X17,tc_nat) = X16
| c_lessequals(X17,X16,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_184
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1705]) ).
fof(f1705,plain,
( ! [X0,X8,X5] :
( c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1704]) ).
fof(f1725,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1724]) ).
fof(f17339,plain,
( ~ spl0_20
| spl0_739
| ~ spl0_184
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1877,f1720,f1704,f17337,f809]) ).
fof(f17337,plain,
( spl0_739
<=> ! [X13,X12] :
( c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_lessequals(c_Suc(X13),c_Suc(X12),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1720,plain,
( spl0_188
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1877,plain,
( ! [X12,X13] :
( c_HOL_Oord__class_Oless(X12,X13,tc_nat)
| c_lessequals(c_Suc(X13),c_Suc(X12),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_184
| ~ spl0_188 ),
inference(resolution,[],[f1721,f1705]) ).
fof(f1721,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1720]) ).
fof(f17335,plain,
( spl0_738
| ~ spl0_134
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1398,f1341,f1321,f17333]) ).
fof(f17333,plain,
( spl0_738
<=> ! [X6,X5] :
( c_List_Orotate1(X5,X6) = c_List_Oremdups(c_List_Orotate1(X5,X6),X6)
| ~ c_List_Odistinct(X5,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f1321,plain,
( spl0_134
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1341,plain,
( spl0_139
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1398,plain,
( ! [X6,X5] :
( c_List_Orotate1(X5,X6) = c_List_Oremdups(c_List_Orotate1(X5,X6),X6)
| ~ c_List_Odistinct(X5,X6) )
| ~ spl0_134
| ~ spl0_139 ),
inference(resolution,[],[f1342,f1322]) ).
fof(f1322,plain,
( ! [X0,X12] :
( c_List_Odistinct(c_List_Orotate1(X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1321]) ).
fof(f1342,plain,
( ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f17331,plain,
( spl0_737
| ~ spl0_136
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1396,f1341,f1329,f17329]) ).
fof(f17329,plain,
( spl0_737
<=> ! [X2,X1] :
( c_List_Orev(X1,X2) = c_List_Oremdups(c_List_Orev(X1,X2),X2)
| ~ c_List_Odistinct(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f1329,plain,
( spl0_136
<=> ! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1396,plain,
( ! [X2,X1] :
( c_List_Orev(X1,X2) = c_List_Oremdups(c_List_Orev(X1,X2),X2)
| ~ c_List_Odistinct(X1,X2) )
| ~ spl0_136
| ~ spl0_139 ),
inference(resolution,[],[f1342,f1330]) ).
fof(f1330,plain,
( ! [X0,X12] :
( c_List_Odistinct(c_List_Orev(X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f16825,plain,
( spl0_736
| ~ spl0_62
| ~ spl0_718 ),
inference(avatar_split_clause,[],[f16680,f15301,f1019,f16823]) ).
fof(f1019,plain,
( spl0_62
<=> ! [X5] : ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f15301,plain,
( spl0_718
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f16680,plain,
( ! [X135] : ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X135,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_62
| ~ spl0_718 ),
inference(superposition,[],[f1020,f15302]) ).
fof(f15302,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f15301]) ).
fof(f1020,plain,
( ! [X5] : ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1019]) ).
fof(f15424,plain,
( spl0_735
| ~ spl0_79
| ~ spl0_568 ),
inference(avatar_split_clause,[],[f10270,f10083,f1088,f15422]) ).
fof(f15422,plain,
( spl0_735
<=> ! [X2,X0,X1] :
( ~ c_List_Onull(c_List_Otake(c_Suc(X2),X0,X1),X1)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f1088,plain,
( spl0_79
<=> ! [X5,X0,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f10083,plain,
( spl0_568
<=> ! [X0,X12,X3] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_Suc(X3),X12,X0) = c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f10270,plain,
( ! [X2,X0,X1] :
( ~ c_List_Onull(c_List_Otake(c_Suc(X2),X0,X1),X1)
| c_List_Olist_ONil(X1) = X0 )
| ~ spl0_79
| ~ spl0_568 ),
inference(superposition,[],[f1089,f10084]) ).
fof(f10084,plain,
( ! [X3,X0,X12] :
( c_List_Otake(c_Suc(X3),X12,X0) = c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_568 ),
inference(avatar_component_clause,[],[f10083]) ).
fof(f1089,plain,
( ! [X0,X5,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f15420,plain,
( spl0_734
| ~ spl0_107
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f10115,f10100,f1206,f15418]) ).
fof(f15418,plain,
( spl0_734
<=> ! [X13,X14,X12,X15] : c_List_Olist_ONil(X14) != c_List_Oappend(c_List_Oreplicate(c_Suc(X13),X12,X14),X15,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f1206,plain,
( spl0_107
<=> ! [X5,X0,X27] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X5,X27,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f10100,plain,
( spl0_572
<=> ! [X0,X12,X5,X3] : c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0) = c_List_Oappend(c_List_Oreplicate(c_Suc(X3),X5,X0),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f10115,plain,
( ! [X14,X15,X12,X13] : c_List_Olist_ONil(X14) != c_List_Oappend(c_List_Oreplicate(c_Suc(X13),X12,X14),X15,X14)
| ~ spl0_107
| ~ spl0_572 ),
inference(superposition,[],[f1207,f10101]) ).
fof(f10101,plain,
( ! [X3,X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0) = c_List_Oappend(c_List_Oreplicate(c_Suc(X3),X5,X0),X12,X0)
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f10100]) ).
fof(f1207,plain,
( ! [X0,X27,X5] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X5,X27,X0)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1206]) ).
fof(f15416,plain,
( spl0_733
| ~ spl0_92
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f10114,f10100,f1145,f15414]) ).
fof(f15414,plain,
( spl0_733
<=> ! [X10,X11,X9,X8] : c_List_Omember(X8,c_List_Oappend(c_List_Oreplicate(c_Suc(X9),X8,X10),X11,X10),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f1145,plain,
( spl0_92
<=> ! [X13,X0,X5] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f10114,plain,
( ! [X10,X11,X8,X9] : c_List_Omember(X8,c_List_Oappend(c_List_Oreplicate(c_Suc(X9),X8,X10),X11,X10),X10)
| ~ spl0_92
| ~ spl0_572 ),
inference(superposition,[],[f1146,f10101]) ).
fof(f1146,plain,
( ! [X0,X5,X13] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f1145]) ).
fof(f15412,plain,
( spl0_732
| ~ spl0_109
| ~ spl0_482 ),
inference(avatar_split_clause,[],[f8002,f7655,f1221,f15410]) ).
fof(f15410,plain,
( spl0_732
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f1221,plain,
( spl0_109
<=> ! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Oplus__class_Oplus(X4,X6,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f7655,plain,
( spl0_482
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f8002,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_109
| ~ spl0_482 ),
inference(superposition,[],[f1222,f7656]) ).
fof(f7656,plain,
( ! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat))
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_482 ),
inference(avatar_component_clause,[],[f7655]) ).
fof(f1222,plain,
( ! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Oplus__class_Oplus(X4,X6,tc_nat)),tc_nat)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1221]) ).
fof(f15408,plain,
( spl0_731
| ~ spl0_393
| ~ spl0_394
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f7390,f7046,f4539,f4535,f15406]) ).
fof(f15406,plain,
( spl0_731
<=> ! [X0,X1] : c_List_Otl(c_List_Obutlast(X0,X1),X1) = c_List_Obutlast(c_List_Otl(X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f4535,plain,
( spl0_393
<=> ! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f4539,plain,
( spl0_394
<=> ! [X0,X12] : c_List_Obutlast(X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f7046,plain,
( spl0_465
<=> ! [X0,X12,X3] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f7390,plain,
( ! [X0,X1] : c_List_Otl(c_List_Obutlast(X0,X1),X1) = c_List_Obutlast(c_List_Otl(X0,X1),X1)
| ~ spl0_393
| ~ spl0_394
| ~ spl0_465 ),
inference(forward_demodulation,[],[f7371,f5091]) ).
fof(f5091,plain,
( ! [X0,X1] : c_List_Obutlast(X0,X1) = c_List_Otake(c_Nat_Osize__class_Osize(c_List_Otl(X0,X1),tc_List_Olist(X1)),X0,X1)
| ~ spl0_393
| ~ spl0_394 ),
inference(superposition,[],[f4540,f4536]) ).
fof(f4536,plain,
( ! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0))
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f4535]) ).
fof(f4540,plain,
( ! [X0,X12] : c_List_Obutlast(X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0)
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f4539]) ).
fof(f7371,plain,
( ! [X0,X1] : c_List_Obutlast(c_List_Otl(X0,X1),X1) = c_List_Otl(c_List_Otake(c_Nat_Osize__class_Osize(c_List_Otl(X0,X1),tc_List_Olist(X1)),X0,X1),X1)
| ~ spl0_394
| ~ spl0_465 ),
inference(superposition,[],[f7047,f4540]) ).
fof(f7047,plain,
( ! [X3,X0,X12] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0)
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f7046]) ).
fof(f15404,plain,
( spl0_730
| ~ spl0_175
| ~ spl0_421 ),
inference(avatar_split_clause,[],[f6009,f5856,f1529,f15402]) ).
fof(f15402,plain,
( spl0_730
<=> ! [X4,X5,X3] :
( ~ c_List_Odistinct(c_List_Orotate1(c_List_Olist_OCons(X4,X3,X5),X5),X5)
| c_List_Odistinct(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f1529,plain,
( spl0_175
<=> ! [X13,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f5856,plain,
( spl0_421
<=> ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X36),X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f6009,plain,
( ! [X3,X4,X5] :
( ~ c_List_Odistinct(c_List_Orotate1(c_List_Olist_OCons(X4,X3,X5),X5),X5)
| c_List_Odistinct(X3,X5) )
| ~ spl0_175
| ~ spl0_421 ),
inference(superposition,[],[f1530,f5857]) ).
fof(f5857,plain,
( ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X36),X36)
| ~ spl0_421 ),
inference(avatar_component_clause,[],[f5856]) ).
fof(f1530,plain,
( ! [X0,X12,X13] :
( ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0)
| c_List_Odistinct(X12,X0) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f15400,plain,
( spl0_729
| ~ spl0_124
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5756,f4604,f1281,f15398]) ).
fof(f15398,plain,
( spl0_729
<=> ! [X18,X17,X16,X19] : c_List_Ohd(c_List_Oappend(c_List_Olist_OCons(X16,X17,X19),X18,X19),X19) = X16 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f1281,plain,
( spl0_124
<=> ! [X12,X5,X0] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f4604,plain,
( spl0_409
<=> ! [X5,X13,X0,X12] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f5756,plain,
( ! [X18,X19,X16,X17] : c_List_Ohd(c_List_Oappend(c_List_Olist_OCons(X16,X17,X19),X18,X19),X19) = X16
| ~ spl0_124
| ~ spl0_409 ),
inference(superposition,[],[f1282,f4605]) ).
fof(f4605,plain,
( ! [X0,X5,X12,X13] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0)
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f4604]) ).
fof(f1282,plain,
( ! [X0,X5,X12] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f15354,plain,
( spl0_728
| ~ spl0_110
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f5593,f4575,f1225,f15352]) ).
fof(f15352,plain,
( spl0_728
<=> ! [X6,X7,X8] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f1225,plain,
( spl0_110
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f4575,plain,
( spl0_403
<=> ! [X4,X3,X14] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f5593,plain,
( ! [X8,X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X7,X8,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),tc_nat)
| ~ spl0_110
| ~ spl0_403 ),
inference(superposition,[],[f1226,f4576]) ).
fof(f4576,plain,
( ! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat)
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f4575]) ).
fof(f1226,plain,
( ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_Suc(X4),tc_nat)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1225]) ).
fof(f15350,plain,
( spl0_727
| ~ spl0_110
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5541,f4571,f1225,f15348]) ).
fof(f15348,plain,
( spl0_727
<=> ! [X6,X7,X8] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f4571,plain,
( spl0_402
<=> ! [X3,X4,X14] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f5541,plain,
( ! [X8,X6,X7] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,X8,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),tc_nat)
| ~ spl0_110
| ~ spl0_402 ),
inference(superposition,[],[f1226,f4572]) ).
fof(f4572,plain,
( ! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat)
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f4571]) ).
fof(f15346,plain,
( spl0_726
| ~ spl0_109
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5380,f4563,f1221,f15344]) ).
fof(f15344,plain,
( spl0_726
<=> ! [X9,X11,X10] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f4563,plain,
( spl0_400
<=> ! [X3,X4,X14] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5380,plain,
( ! [X10,X11,X9] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X10,X11,tc_nat),tc_nat)),tc_nat)
| ~ spl0_109
| ~ spl0_400 ),
inference(superposition,[],[f1222,f4564]) ).
fof(f4564,plain,
( ! [X3,X14,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat)
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f4563]) ).
fof(f15342,plain,
( spl0_725
| ~ spl0_125
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f4426,f3756,f1285,f15340]) ).
fof(f15340,plain,
( spl0_725
<=> ! [X11,X10] :
( c_List_Otl(X10,X11) = c_List_Osko__List__Xneq__Nil__conv__1__2(X10,X11)
| c_List_Olist_ONil(X11) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1285,plain,
( spl0_125
<=> ! [X5,X0,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f3756,plain,
( spl0_372
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f4426,plain,
( ! [X10,X11] :
( c_List_Otl(X10,X11) = c_List_Osko__List__Xneq__Nil__conv__1__2(X10,X11)
| c_List_Olist_ONil(X11) = X10 )
| ~ spl0_125
| ~ spl0_372 ),
inference(superposition,[],[f1286,f3757]) ).
fof(f3757,plain,
( ! [X0,X12] :
( c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f3756]) ).
fof(f1286,plain,
( ! [X0,X5,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1285]) ).
fof(f15338,plain,
( spl0_724
| ~ spl0_124
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f4425,f3756,f1281,f15336]) ).
fof(f15336,plain,
( spl0_724
<=> ! [X9,X8] :
( c_List_Ohd(X8,X9) = c_List_Osko__List__Xneq__Nil__conv__1__1(X8,X9)
| c_List_Olist_ONil(X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f4425,plain,
( ! [X8,X9] :
( c_List_Ohd(X8,X9) = c_List_Osko__List__Xneq__Nil__conv__1__1(X8,X9)
| c_List_Olist_ONil(X9) = X8 )
| ~ spl0_124
| ~ spl0_372 ),
inference(superposition,[],[f1282,f3757]) ).
fof(f15334,plain,
( spl0_723
| ~ spl0_125
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4404,f3752,f1285,f15332]) ).
fof(f15332,plain,
( spl0_723
<=> ! [X11,X10] :
( c_List_Otl(X10,X11) = c_List_Osko__List__Xlist__Xexhaust__1__2(X10,X11)
| c_List_Olist_ONil(X11) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f3752,plain,
( spl0_371
<=> ! [X0,X8] :
( c_List_Olist_ONil(X0) = X8
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f4404,plain,
( ! [X10,X11] :
( c_List_Otl(X10,X11) = c_List_Osko__List__Xlist__Xexhaust__1__2(X10,X11)
| c_List_Olist_ONil(X11) = X10 )
| ~ spl0_125
| ~ spl0_371 ),
inference(superposition,[],[f1286,f3753]) ).
fof(f3753,plain,
( ! [X0,X8] :
( c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8
| c_List_Olist_ONil(X0) = X8 )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f3752]) ).
fof(f15330,plain,
( spl0_722
| ~ spl0_124
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4403,f3752,f1281,f15328]) ).
fof(f15328,plain,
( spl0_722
<=> ! [X9,X8] :
( c_List_Ohd(X8,X9) = c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X9)
| c_List_Olist_ONil(X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f4403,plain,
( ! [X8,X9] :
( c_List_Ohd(X8,X9) = c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X9)
| c_List_Olist_ONil(X9) = X8 )
| ~ spl0_124
| ~ spl0_371 ),
inference(superposition,[],[f1282,f3753]) ).
fof(f15326,plain,
( spl0_721
| ~ spl0_125
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4382,f3748,f1285,f15324]) ).
fof(f15324,plain,
( spl0_721
<=> ! [X11,X10] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X10,X11) = c_List_Otl(X10,X11)
| c_List_Olist_ONil(X11) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f3748,plain,
( spl0_370
<=> ! [X18,X0] :
( c_List_Olist_ONil(X0) = X18
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4382,plain,
( ! [X10,X11] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X10,X11) = c_List_Otl(X10,X11)
| c_List_Olist_ONil(X11) = X10 )
| ~ spl0_125
| ~ spl0_370 ),
inference(superposition,[],[f1286,f3749]) ).
fof(f3749,plain,
( ! [X0,X18] :
( c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18
| c_List_Olist_ONil(X0) = X18 )
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f3748]) ).
fof(f15322,plain,
( spl0_720
| ~ spl0_124
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4381,f3748,f1281,f15320]) ).
fof(f15320,plain,
( spl0_720
<=> ! [X9,X8] :
( c_List_Osko__List__Xlist__Xnchotomy__1__1(X8,X9) = c_List_Ohd(X8,X9)
| c_List_Olist_ONil(X9) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f4381,plain,
( ! [X8,X9] :
( c_List_Osko__List__Xlist__Xnchotomy__1__1(X8,X9) = c_List_Ohd(X8,X9)
| c_List_Olist_ONil(X9) = X8 )
| ~ spl0_124
| ~ spl0_370 ),
inference(superposition,[],[f1282,f3749]) ).
fof(f15318,plain,
( spl0_719
| ~ spl0_218
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f4052,f3617,f2038,f15316]) ).
fof(f15316,plain,
( spl0_719
<=> ! [X9,X8,X7] :
( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2038,plain,
( spl0_218
<=> ! [X6,X14,X15] :
( c_HOL_Oord__class_Oless(X6,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f3617,plain,
( spl0_342
<=> ! [X4,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f4052,plain,
( ! [X8,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X7,X8,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X9,X8,tc_nat),tc_nat) )
| ~ spl0_218
| ~ spl0_342 ),
inference(resolution,[],[f3618,f2039]) ).
fof(f2039,plain,
( ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat)
| c_HOL_Oord__class_Oless(X6,X14,tc_nat) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2038]) ).
fof(f3618,plain,
( ! [X3,X14,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f3617]) ).
fof(f15303,plain,
( spl0_718
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3524,f2987,f1289,f1083,f15301]) ).
fof(f1083,plain,
( spl0_78
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1289,plain,
( spl0_126
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f2987,plain,
( spl0_320
<=> ! [X5,X0,X3] : c_List_Oreplicate(c_Suc(X3),X5,X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f3524,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320 ),
inference(forward_demodulation,[],[f3504,f1085]) ).
fof(f1085,plain,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1083]) ).
fof(f3504,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil(X1),X1) = c_List_Oreplicate(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_126
| ~ spl0_320 ),
inference(superposition,[],[f2988,f1290]) ).
fof(f1290,plain,
( ! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1289]) ).
fof(f2988,plain,
( ! [X3,X0,X5] : c_List_Oreplicate(c_Suc(X3),X5,X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0)
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f2987]) ).
fof(f15294,plain,
( spl0_717
| ~ spl0_320
| ~ spl0_421
| ~ spl0_476
| ~ spl0_716 ),
inference(avatar_split_clause,[],[f15290,f15287,f7566,f5856,f2987,f15292]) ).
fof(f15292,plain,
( spl0_717
<=> ! [X38,X37,X39] : c_List_Olast(c_List_Oreplicate(c_Suc(X38),X37,X39),X39) = X37 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f7566,plain,
( spl0_476
<=> ! [X5,X0,X6] : c_List_Oreplicate(c_Suc(X6),X5,X0) = c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f15287,plain,
( spl0_716
<=> ! [X38,X37,X39] : c_List_Olast(c_List_Orotate1(c_List_Oreplicate(c_Suc(X38),X37,X39),X39),X39) = X37 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f15290,plain,
( ! [X38,X39,X37] : c_List_Olast(c_List_Oreplicate(c_Suc(X38),X37,X39),X39) = X37
| ~ spl0_320
| ~ spl0_421
| ~ spl0_476
| ~ spl0_716 ),
inference(forward_demodulation,[],[f15288,f7628]) ).
fof(f7628,plain,
( ! [X3,X4,X5] : c_List_Oreplicate(c_Suc(X3),X4,X5) = c_List_Orotate1(c_List_Oreplicate(c_Suc(X3),X4,X5),X5)
| ~ spl0_320
| ~ spl0_421
| ~ spl0_476 ),
inference(forward_demodulation,[],[f7607,f2988]) ).
fof(f7607,plain,
( ! [X3,X4,X5] : c_List_Orotate1(c_List_Olist_OCons(X4,c_List_Oreplicate(X3,X4,X5),X5),X5) = c_List_Oreplicate(c_Suc(X3),X4,X5)
| ~ spl0_421
| ~ spl0_476 ),
inference(superposition,[],[f7567,f5857]) ).
fof(f7567,plain,
( ! [X0,X6,X5] : c_List_Oreplicate(c_Suc(X6),X5,X0) = c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f7566]) ).
fof(f15288,plain,
( ! [X38,X39,X37] : c_List_Olast(c_List_Orotate1(c_List_Oreplicate(c_Suc(X38),X37,X39),X39),X39) = X37
| ~ spl0_716 ),
inference(avatar_component_clause,[],[f15287]) ).
fof(f15289,plain,
( spl0_716
| ~ spl0_286
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3517,f2987,f2557,f15287]) ).
fof(f2557,plain,
( spl0_286
<=> ! [X12,X5,X0] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3517,plain,
( ! [X38,X39,X37] : c_List_Olast(c_List_Orotate1(c_List_Oreplicate(c_Suc(X38),X37,X39),X39),X39) = X37
| ~ spl0_286
| ~ spl0_320 ),
inference(superposition,[],[f2558,f2988]) ).
fof(f2558,plain,
( ! [X0,X5,X12] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X5
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f15253,plain,
( spl0_715
| ~ spl0_44
| ~ spl0_58
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3475,f2967,f999,f929,f15251]) ).
fof(f15251,plain,
( spl0_715
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(X1),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f929,plain,
( spl0_44
<=> class_Ring__and__Field_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f999,plain,
( spl0_58
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2967,plain,
( spl0_315
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f3475,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Osemiring__0(tc_Int_Oint)
| c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Int_Oint),c_Suc(X1),tc_Int_Oint) )
| ~ spl0_58
| ~ spl0_315 ),
inference(resolution,[],[f2968,f1001]) ).
fof(f1001,plain,
( class_Power_Opower(tc_Int_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f999]) ).
fof(f2968,plain,
( ! [X3,X0] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Osemiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X3),X0) )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f2967]) ).
fof(f15217,plain,
( spl0_714
| ~ spl0_14
| ~ spl0_22
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f3474,f2967,f819,f779,f15215]) ).
fof(f15215,plain,
( spl0_714
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f779,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f819,plain,
( spl0_22
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3474,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) )
| ~ spl0_22
| ~ spl0_315 ),
inference(resolution,[],[f2968,f821]) ).
fof(f821,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f819]) ).
fof(f15195,plain,
( ~ spl0_20
| spl0_713
| ~ spl0_115
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f3403,f2951,f1245,f15193,f809]) ).
fof(f15193,plain,
( spl0_713
<=> ! [X2,X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1245,plain,
( spl0_115
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2951,plain,
( spl0_311
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f3403,plain,
( ! [X2,X3] :
( ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_lessequals(X3,X2,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_115
| ~ spl0_311 ),
inference(superposition,[],[f2952,f1246]) ).
fof(f1246,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1245]) ).
fof(f2952,plain,
( ! [X0,X1,X9,X5] :
( ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0)
| c_lessequals(X5,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f2951]) ).
fof(f15191,plain,
( spl0_712
| ~ spl0_176
| ~ spl0_633 ),
inference(avatar_split_clause,[],[f13465,f12670,f1533,f15189]) ).
fof(f15189,plain,
( spl0_712
<=> ! [X4,X5] :
( c_List_Odistinct(c_List_Otl(X4,X5),X5)
| ~ c_List_Odistinct(X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1533,plain,
( spl0_176
<=> ! [X6,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f12670,plain,
( spl0_633
<=> ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f13465,plain,
( ! [X4,X5] :
( c_List_Odistinct(c_List_Otl(X4,X5),X5)
| ~ c_List_Odistinct(X4,X5) )
| ~ spl0_176
| ~ spl0_633 ),
inference(superposition,[],[f1534,f12671]) ).
fof(f12671,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_633 ),
inference(avatar_component_clause,[],[f12670]) ).
fof(f1534,plain,
( ! [X0,X6,X12] :
( c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f15187,plain,
( spl0_711
| ~ spl0_251
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f2835,f2528,f2175,f15185]) ).
fof(f15185,plain,
( spl0_711
<=> ! [X22,X21,X23] :
( c_List_Olist_ONil(X23) != X22
| c_List_Otake(X21,X22,X23) = c_List_Olist_ONil(X23) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2175,plain,
( spl0_251
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2528,plain,
( spl0_279
<=> ! [X0,X12,X3] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2835,plain,
( ! [X21,X22,X23] :
( c_List_Olist_ONil(X23) != X22
| c_List_Otake(X21,X22,X23) = c_List_Olist_ONil(X23) )
| ~ spl0_251
| ~ spl0_279 ),
inference(superposition,[],[f2176,f2529]) ).
fof(f2529,plain,
( ! [X3,X0,X12] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12
| ~ spl0_279 ),
inference(avatar_component_clause,[],[f2528]) ).
fof(f2176,plain,
( ! [X0,X12,X13] :
( c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2175]) ).
fof(f15183,plain,
( spl0_710
| ~ spl0_250
| ~ spl0_279 ),
inference(avatar_split_clause,[],[f2834,f2528,f2171,f15181]) ).
fof(f15181,plain,
( spl0_710
<=> ! [X20,X18,X19] :
( c_List_Olist_ONil(X20) != X19
| c_List_Odrop(X18,X19,X20) = c_List_Olist_ONil(X20) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f2171,plain,
( spl0_250
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2834,plain,
( ! [X18,X19,X20] :
( c_List_Olist_ONil(X20) != X19
| c_List_Odrop(X18,X19,X20) = c_List_Olist_ONil(X20) )
| ~ spl0_250
| ~ spl0_279 ),
inference(superposition,[],[f2172,f2529]) ).
fof(f2172,plain,
( ! [X0,X12,X13] :
( c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0)
| c_List_Olist_ONil(X0) = X13 )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2171]) ).
fof(f15147,plain,
( ~ spl0_20
| spl0_709
| ~ spl0_155
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2796,f2508,f1449,f15145,f809]) ).
fof(f15145,plain,
( spl0_709
<=> ! [X4,X3] : c_lessequals(c_Suc(c_Orderings_Oord__class_Omin(X3,X4,tc_nat)),c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1449,plain,
( spl0_155
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2508,plain,
( spl0_274
<=> ! [X4,X3] : c_Orderings_Oord__class_Omin(c_Suc(X4),c_Suc(X3),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X4,X3,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2796,plain,
( ! [X3,X4] :
( c_lessequals(c_Suc(c_Orderings_Oord__class_Omin(X3,X4,tc_nat)),c_Suc(X4),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_155
| ~ spl0_274 ),
inference(superposition,[],[f1450,f2509]) ).
fof(f2509,plain,
( ! [X3,X4] : c_Orderings_Oord__class_Omin(c_Suc(X4),c_Suc(X3),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X4,X3,tc_nat))
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2508]) ).
fof(f1450,plain,
( ! [X0,X8,X5] :
( c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1449]) ).
fof(f15143,plain,
( spl0_708
| ~ spl0_121
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2779,f2504,f1269,f15141]) ).
fof(f15141,plain,
( spl0_708
<=> ! [X13,X14] :
( c_Suc(X13) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat)
| X13 = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1269,plain,
( spl0_121
<=> ! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f2504,plain,
( spl0_273
<=> ! [X4,X3,X14] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2779,plain,
( ! [X14,X13] :
( c_Suc(X13) != c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X14,tc_nat)
| X13 = X14 )
| ~ spl0_121
| ~ spl0_273 ),
inference(superposition,[],[f2505,f1270]) ).
fof(f1270,plain,
( ! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1269]) ).
fof(f2505,plain,
( ! [X3,X14,X4] :
( c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X4,tc_nat)
| X3 = X4 )
| ~ spl0_273 ),
inference(avatar_component_clause,[],[f2504]) ).
fof(f15139,plain,
( spl0_707
| ~ spl0_122
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2776,f2504,f1273,f15137]) ).
fof(f15137,plain,
( spl0_707
<=> ! [X6,X7] :
( c_Suc(X6) != c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1273,plain,
( spl0_122
<=> ! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f2776,plain,
( ! [X6,X7] :
( c_Suc(X6) != c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X7 )
| ~ spl0_122
| ~ spl0_273 ),
inference(superposition,[],[f2505,f1274]) ).
fof(f1274,plain,
( ! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f15135,plain,
( spl0_706
| ~ spl0_121
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2754,f2500,f1269,f15133]) ).
fof(f15133,plain,
( spl0_706
<=> ! [X13,X14] :
( c_Suc(X13) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f2500,plain,
( spl0_272
<=> ! [X4,X3,X14] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2754,plain,
( ! [X14,X13] :
( c_Suc(X13) != c_HOL_Oplus__class_Oplus(X14,X13,tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X14 )
| ~ spl0_121
| ~ spl0_272 ),
inference(superposition,[],[f2501,f1270]) ).
fof(f2501,plain,
( ! [X3,X14,X4] :
( c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat)
| X3 = X4 )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2500]) ).
fof(f15131,plain,
( spl0_705
| ~ spl0_122
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2751,f2500,f1273,f15129]) ).
fof(f15129,plain,
( spl0_705
<=> ! [X6,X7] :
( c_Suc(X6) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| X6 = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f2751,plain,
( ! [X6,X7] :
( c_Suc(X6) != c_HOL_Oplus__class_Oplus(X7,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| X6 = X7 )
| ~ spl0_122
| ~ spl0_272 ),
inference(superposition,[],[f2501,f1274]) ).
fof(f15126,plain,
( ~ spl0_20
| spl0_704
| ~ spl0_115
| ~ spl0_267 ),
inference(avatar_split_clause,[],[f2707,f2480,f1245,f15124,f809]) ).
fof(f15124,plain,
( spl0_704
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2480,plain,
( spl0_267
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2707,plain,
( ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X1
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_115
| ~ spl0_267 ),
inference(superposition,[],[f2481,f1246]) ).
fof(f2481,plain,
( ! [X0,X8,X5] :
( c_Orderings_Oord__class_Omin(X5,X8,X0) != X5
| c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_267 ),
inference(avatar_component_clause,[],[f2480]) ).
fof(f15122,plain,
( spl0_703
| ~ spl0_121
| ~ spl0_624 ),
inference(avatar_split_clause,[],[f13094,f12615,f1269,f15120]) ).
fof(f15120,plain,
( spl0_703
<=> ! [X14] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X14)),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f12615,plain,
( spl0_624
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f13094,plain,
( ! [X14] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X14)),c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_121
| ~ spl0_624 ),
inference(superposition,[],[f12616,f1270]) ).
fof(f12616,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat)
| ~ spl0_624 ),
inference(avatar_component_clause,[],[f12615]) ).
fof(f15118,plain,
( spl0_702
| ~ spl0_145
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2637,f2452,f1408,f15116]) ).
fof(f15116,plain,
( spl0_702
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1408,plain,
( spl0_145
<=> ! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f2452,plain,
( spl0_260
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2637,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) )
| ~ spl0_145
| ~ spl0_260 ),
inference(resolution,[],[f2453,f1409]) ).
fof(f1409,plain,
( ! [X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1408]) ).
fof(f2453,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2452]) ).
fof(f15114,plain,
( spl0_701
| ~ spl0_159
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2390,f2099,f1465,f15112]) ).
fof(f15112,plain,
( spl0_701
<=> ! [X6,X5,X7] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X5
| c_List_Oreplicate(X5,X6,X7) = c_List_Olist_ONil(X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1465,plain,
( spl0_159
<=> ! [X5,X0,X3] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2099,plain,
( spl0_232
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2390,plain,
( ! [X6,X7,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X5
| c_List_Oreplicate(X5,X6,X7) = c_List_Olist_ONil(X7) )
| ~ spl0_159
| ~ spl0_232 ),
inference(superposition,[],[f2100,f1466]) ).
fof(f1466,plain,
( ! [X3,X0,X5] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1465]) ).
fof(f2100,plain,
( ! [X0,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0))
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2099]) ).
fof(f15110,plain,
( spl0_700
| ~ spl0_204
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2352,f2070,f1784,f15108]) ).
fof(f15108,plain,
( spl0_700
<=> ! [X18,X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_Suc(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1784,plain,
( spl0_204
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f2070,plain,
( spl0_226
<=> ! [X4,X3] : c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)) = c_HOL_Oplus__class_Oplus(X4,c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2352,plain,
( ! [X18,X19] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X18,c_Suc(c_HOL_Oplus__class_Oplus(X18,X19,tc_nat)),tc_nat)
| ~ spl0_204
| ~ spl0_226 ),
inference(superposition,[],[f1785,f2071]) ).
fof(f2071,plain,
( ! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)) = c_HOL_Oplus__class_Oplus(X4,c_Suc(X3),tc_nat)
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2070]) ).
fof(f1785,plain,
( ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat)
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f1784]) ).
fof(f15106,plain,
( spl0_699
| ~ spl0_167
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2350,f2070,f1497,f15104]) ).
fof(f15104,plain,
( spl0_699
<=> ! [X14,X15] : c_Suc(X15) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X14,X15,tc_nat)),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1497,plain,
( spl0_167
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f2350,plain,
( ! [X14,X15] : c_Suc(X15) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X14,X15,tc_nat)),X14,tc_nat)
| ~ spl0_167
| ~ spl0_226 ),
inference(superposition,[],[f1498,f2071]) ).
fof(f1498,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1497]) ).
fof(f15102,plain,
( spl0_698
| ~ spl0_166
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2349,f2070,f1493,f15100]) ).
fof(f15100,plain,
( spl0_698
<=> ! [X13,X12] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),c_Suc(X13),tc_nat) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1493,plain,
( spl0_166
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2349,plain,
( ! [X12,X13] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),c_Suc(X13),tc_nat) = X12
| ~ spl0_166
| ~ spl0_226 ),
inference(superposition,[],[f1494,f2071]) ).
fof(f1494,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1493]) ).
fof(f15098,plain,
( spl0_697
| ~ spl0_151
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2338,f2070,f1433,f15096]) ).
fof(f15096,plain,
( spl0_697
<=> ! [X2,X3] : c_Suc(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1433,plain,
( spl0_151
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f2338,plain,
( ! [X2,X3] : c_Suc(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X2,tc_nat)
| ~ spl0_151
| ~ spl0_226 ),
inference(superposition,[],[f2071,f1434]) ).
fof(f1434,plain,
( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1433]) ).
fof(f15094,plain,
( spl0_696
| ~ spl0_167
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2326,f2066,f1497,f15092]) ).
fof(f15092,plain,
( spl0_696
<=> ! [X14,X15] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X14,X15,tc_nat)),c_Suc(X14),tc_nat) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f2066,plain,
( spl0_225
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2326,plain,
( ! [X14,X15] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X14,X15,tc_nat)),c_Suc(X14),tc_nat) = X15
| ~ spl0_167
| ~ spl0_225 ),
inference(superposition,[],[f1498,f2067]) ).
fof(f2067,plain,
( ! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat))
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f15090,plain,
( spl0_695
| ~ spl0_166
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2325,f2066,f1493,f15088]) ).
fof(f15088,plain,
( spl0_695
<=> ! [X13,X12] : c_Suc(X12) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2325,plain,
( ! [X12,X13] : c_Suc(X12) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),X13,tc_nat)
| ~ spl0_166
| ~ spl0_225 ),
inference(superposition,[],[f1494,f2067]) ).
fof(f15086,plain,
( spl0_694
| ~ spl0_151
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2317,f2066,f1433,f15084]) ).
fof(f15084,plain,
( spl0_694
<=> ! [X4,X5] : c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2317,plain,
( ! [X4,X5] : c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)) = c_HOL_Oplus__class_Oplus(X5,c_Suc(X4),tc_nat)
| ~ spl0_151
| ~ spl0_225 ),
inference(superposition,[],[f2067,f1434]) ).
fof(f15082,plain,
( spl0_693
| ~ spl0_151
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2212,f2038,f1433,f15080]) ).
fof(f15080,plain,
( spl0_693
<=> ! [X6,X8,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(X6,X8,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f2212,plain,
( ! [X8,X6,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(X6,X8,tc_nat) )
| ~ spl0_151
| ~ spl0_218 ),
inference(superposition,[],[f2039,f1434]) ).
fof(f15078,plain,
( spl0_692
| ~ spl0_226
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f12583,f12556,f2070,f15076]) ).
fof(f15076,plain,
( spl0_692
<=> ! [X13,X12] : c_lessequals(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f12556,plain,
( spl0_617
<=> ! [X13,X12] : c_lessequals(X12,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f12583,plain,
( ! [X12,X13] : c_lessequals(X12,c_Suc(c_HOL_Oplus__class_Oplus(X12,X13,tc_nat)),tc_nat)
| ~ spl0_226
| ~ spl0_617 ),
inference(superposition,[],[f12557,f2071]) ).
fof(f12557,plain,
( ! [X12,X13] : c_lessequals(X12,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat)
| ~ spl0_617 ),
inference(avatar_component_clause,[],[f12556]) ).
fof(f15074,plain,
( spl0_691
| ~ spl0_109
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2205,f2038,f1221,f15072]) ).
fof(f15072,plain,
( spl0_691
<=> ! [X16,X17,X15] : c_HOL_Oord__class_Oless(X15,c_Suc(c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X15,X17,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2205,plain,
( ! [X16,X17,X15] : c_HOL_Oord__class_Oless(X15,c_Suc(c_HOL_Oplus__class_Oplus(X16,c_HOL_Oplus__class_Oplus(X15,X17,tc_nat),tc_nat)),tc_nat)
| ~ spl0_109
| ~ spl0_218 ),
inference(resolution,[],[f2039,f1222]) ).
fof(f15050,plain,
( spl0_690
| ~ spl0_21
| ~ spl0_147
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1898,f1728,f1417,f814,f15048]) ).
fof(f15048,plain,
( spl0_690
<=> ! [X4,X5] :
( c_lessequals(X4,c_Suc(X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f814,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1417,plain,
( spl0_147
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1728,plain,
( spl0_190
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1898,plain,
( ! [X4,X5] :
( ~ class_Orderings_Oorder(tc_nat)
| c_lessequals(X4,c_Suc(X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) )
| ~ spl0_147
| ~ spl0_190 ),
inference(resolution,[],[f1729,f1418]) ).
fof(f1418,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f1729,plain,
( ! [X0,X8,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X8,X0) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1728]) ).
fof(f15046,plain,
( spl0_689
| ~ spl0_144
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1886,f1724,f1404,f15044]) ).
fof(f15044,plain,
( spl0_689
<=> ! [X6,X7] :
( c_Divides_Odiv__class_Omod(X6,c_Suc(X7),tc_nat) = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1404,plain,
( spl0_144
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1886,plain,
( ! [X6,X7] :
( c_Divides_Odiv__class_Omod(X6,c_Suc(X7),tc_nat) = X6
| c_HOL_Oord__class_Oless(X7,X6,tc_nat) )
| ~ spl0_144
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1405]) ).
fof(f1405,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1404]) ).
fof(f15042,plain,
( spl0_688
| ~ spl0_147
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1885,f1724,f1417,f15040]) ).
fof(f15040,plain,
( spl0_688
<=> ! [X4,X5] :
( c_Divides_Odiv__class_Omod(X4,c_Suc(X5),tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1885,plain,
( ! [X4,X5] :
( c_Divides_Odiv__class_Omod(X4,c_Suc(X5),tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,X5,tc_nat) )
| ~ spl0_147
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1418]) ).
fof(f15038,plain,
( spl0_687
| ~ spl0_78
| ~ spl0_188 ),
inference(avatar_split_clause,[],[f1878,f1720,f1083,f15036]) ).
fof(f15036,plain,
( spl0_687
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1878,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_78
| ~ spl0_188 ),
inference(superposition,[],[f1721,f1085]) ).
fof(f15014,plain,
( ~ spl0_20
| spl0_686
| ~ spl0_146
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1843,f1704,f1412,f15012,f809]) ).
fof(f15012,plain,
( spl0_686
<=> ! [X18,X17] :
( c_lessequals(X17,c_Suc(X18),tc_nat)
| c_HOL_Oord__class_Oless(X18,X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1412,plain,
( spl0_146
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1843,plain,
( ! [X18,X17] :
( c_lessequals(X17,c_Suc(X18),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_HOL_Oord__class_Oless(X18,X17,tc_nat) )
| ~ spl0_146
| ~ spl0_184 ),
inference(resolution,[],[f1705,f1413]) ).
fof(f1413,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1412]) ).
fof(f14988,plain,
( ~ spl0_20
| spl0_685
| ~ spl0_143
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1835,f1704,f1400,f14986,f809]) ).
fof(f14986,plain,
( spl0_685
<=> ! [X4,X3] :
( c_lessequals(c_Suc(X3),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1400,plain,
( spl0_143
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1835,plain,
( ! [X3,X4] :
( c_lessequals(c_Suc(X3),X4,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_143
| ~ spl0_184 ),
inference(resolution,[],[f1705,f1401]) ).
fof(f1401,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1400]) ).
fof(f14963,plain,
( ~ spl0_20
| spl0_684
| ~ spl0_182
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1833,f1704,f1557,f14961,f809]) ).
fof(f14961,plain,
( spl0_684
<=> ! [X1] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1557,plain,
( spl0_182
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1833,plain,
( ! [X1] :
( c_lessequals(c_HOL_Oone__class_Oone(tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_182
| ~ spl0_184 ),
inference(resolution,[],[f1705,f1558]) ).
fof(f1558,plain,
( ! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1557]) ).
fof(f14645,plain,
( spl0_683
| ~ spl0_181
| ~ spl0_666 ),
inference(avatar_split_clause,[],[f14607,f13674,f1553,f14642]) ).
fof(f14642,plain,
( spl0_683
<=> c_List_Odistinct(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1553,plain,
( spl0_181
<=> ! [X5,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f13674,plain,
( spl0_666
<=> c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f14607,plain,
( c_List_Odistinct(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_181
| ~ spl0_666 ),
inference(resolution,[],[f13676,f1554]) ).
fof(f1554,plain,
( ! [X0,X5,X12] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0)
| c_List_Odistinct(X12,X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1553]) ).
fof(f13676,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f13674]) ).
fof(f14575,plain,
( spl0_682
| ~ spl0_78
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f12529,f9930,f1083,f14573]) ).
fof(f14573,plain,
( spl0_682
<=> ! [X0,X1] : c_List_Olist_ONil(X0) != c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f9930,plain,
( spl0_558
<=> ! [X9,X11,X10] : c_List_Olist_ONil(X11) != c_List_Oreplicate(c_Suc(X10),X9,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f12529,plain,
( ! [X0,X1] : c_List_Olist_ONil(X0) != c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X1,X0)
| ~ spl0_78
| ~ spl0_558 ),
inference(superposition,[],[f9931,f1085]) ).
fof(f9931,plain,
( ! [X10,X11,X9] : c_List_Olist_ONil(X11) != c_List_Oreplicate(c_Suc(X10),X9,X11)
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f9930]) ).
fof(f14200,plain,
( spl0_681
| ~ spl0_78
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f12525,f9764,f1083,f14198]) ).
fof(f14198,plain,
( spl0_681
<=> ! [X0,X1] : c_List_Omember(X0,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f9764,plain,
( spl0_554
<=> ! [X6,X8,X7] : c_List_Omember(X6,c_List_Oreplicate(c_Suc(X7),X6,X8),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f12525,plain,
( ! [X0,X1] : c_List_Omember(X0,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_78
| ~ spl0_554 ),
inference(superposition,[],[f9765,f1085]) ).
fof(f9765,plain,
( ! [X8,X6,X7] : c_List_Omember(X6,c_List_Oreplicate(c_Suc(X7),X6,X8),X8)
| ~ spl0_554 ),
inference(avatar_component_clause,[],[f9764]) ).
fof(f13753,plain,
( spl0_680
| ~ spl0_79
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f10112,f10100,f1088,f13751]) ).
fof(f13751,plain,
( spl0_680
<=> ! [X2,X0,X1,X3] : ~ c_List_Onull(c_List_Oappend(c_List_Oreplicate(c_Suc(X1),X0,X2),X3,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f10112,plain,
( ! [X2,X3,X0,X1] : ~ c_List_Onull(c_List_Oappend(c_List_Oreplicate(c_Suc(X1),X0,X2),X3,X2),X2)
| ~ spl0_79
| ~ spl0_572 ),
inference(superposition,[],[f1089,f10101]) ).
fof(f13749,plain,
( spl0_679
| ~ spl0_229
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f3872,f2163,f2087,f13747]) ).
fof(f13747,plain,
( spl0_679
<=> ! [X11,X10] : ~ c_HOL_Oord__class_Oless(c_Suc(X10),c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f2087,plain,
( spl0_229
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X4),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2163,plain,
( spl0_248
<=> ! [X2,X3] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3872,plain,
( ! [X10,X11] : ~ c_HOL_Oord__class_Oless(c_Suc(X10),c_HOL_Ominus__class_Ominus(X10,X11,tc_nat),tc_nat)
| ~ spl0_229
| ~ spl0_248 ),
inference(superposition,[],[f2164,f2088]) ).
fof(f2088,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X4),c_Suc(X3),tc_nat)
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2087]) ).
fof(f2164,plain,
( ! [X2,X3] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2163]) ).
fof(f13745,plain,
( spl0_678
| ~ spl0_90
| ~ spl0_127
| ~ spl0_492 ),
inference(avatar_split_clause,[],[f8420,f7727,f1293,f1137,f13743]) ).
fof(f13743,plain,
( spl0_678
<=> ! [X32,X31,X33] : c_List_Olist_ONil(X33) = c_List_Odrop(X31,c_List_Otake(X31,X32,X33),X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f1137,plain,
( spl0_90
<=> ! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1293,plain,
( spl0_127
<=> ! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f7727,plain,
( spl0_492
<=> ! [X4,X0,X12,X3] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f8420,plain,
( ! [X31,X32,X33] : c_List_Olist_ONil(X33) = c_List_Odrop(X31,c_List_Otake(X31,X32,X33),X33)
| ~ spl0_90
| ~ spl0_127
| ~ spl0_492 ),
inference(forward_demodulation,[],[f8400,f1294]) ).
fof(f1294,plain,
( ! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1293]) ).
fof(f8400,plain,
( ! [X31,X32,X33] : c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Odrop(X31,X32,X33),X33) = c_List_Odrop(X31,c_List_Otake(X31,X32,X33),X33)
| ~ spl0_90
| ~ spl0_492 ),
inference(superposition,[],[f7728,f1138]) ).
fof(f1138,plain,
( ! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1137]) ).
fof(f7728,plain,
( ! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0)
| ~ spl0_492 ),
inference(avatar_component_clause,[],[f7727]) ).
fof(f13741,plain,
( spl0_677
| ~ spl0_89
| ~ spl0_115
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f8247,f7707,f1245,f1133,f13739]) ).
fof(f13739,plain,
( spl0_677
<=> ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X2,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f1133,plain,
( spl0_89
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f7707,plain,
( spl0_487
<=> ! [X6,X4,X3] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f8247,plain,
( ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X2,tc_nat),X2,tc_nat)
| ~ spl0_89
| ~ spl0_115
| ~ spl0_487 ),
inference(forward_demodulation,[],[f8206,f1246]) ).
fof(f8206,plain,
( ! [X2,X3] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X3,X2,tc_nat),X2,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_89
| ~ spl0_487 ),
inference(superposition,[],[f7708,f1134]) ).
fof(f1134,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1133]) ).
fof(f7708,plain,
( ! [X3,X6,X4] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat)
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f7707]) ).
fof(f13737,plain,
( spl0_676
| ~ spl0_89
| ~ spl0_113
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f8241,f7707,f1237,f1133,f13735]) ).
fof(f13735,plain,
( spl0_676
<=> ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1237,plain,
( spl0_113
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f8241,plain,
( ! [X2,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,tc_nat),X2,tc_nat)
| ~ spl0_89
| ~ spl0_113
| ~ spl0_487 ),
inference(forward_demodulation,[],[f8189,f1238]) ).
fof(f1238,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f1237]) ).
fof(f8189,plain,
( ! [X2,X3] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X3,tc_nat),X2,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X2,tc_nat),tc_nat)
| ~ spl0_89
| ~ spl0_487 ),
inference(superposition,[],[f7708,f1134]) ).
fof(f13733,plain,
( spl0_675
| ~ spl0_433
| ~ spl0_434 ),
inference(avatar_split_clause,[],[f6675,f6102,f6098,f13731]) ).
fof(f13731,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f6098,plain,
( spl0_433
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f6102,plain,
( spl0_434
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f6675,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) )
| ~ spl0_433
| ~ spl0_434 ),
inference(duplicate_literal_removal,[],[f6634]) ).
fof(f6634,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_433
| ~ spl0_434 ),
inference(resolution,[],[f6103,f6099]) ).
fof(f6099,plain,
( ! [X10,X0,X1,X9] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f6098]) ).
fof(f6103,plain,
( ! [X10,X0,X1,X9] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0)
| ~ c_lessequals(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_434 ),
inference(avatar_component_clause,[],[f6102]) ).
fof(f13729,plain,
( spl0_674
| ~ spl0_427
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f6471,f6082,f6074,f13727]) ).
fof(f13727,plain,
( spl0_674
<=> ! [X12,X11,X10] :
( ~ c_HOL_Oord__class_Oless(X10,X10,X11)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X11)
| c_HOL_Oord__class_Oless(X12,X12,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f6074,plain,
( spl0_427
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f6082,plain,
( spl0_429
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f6471,plain,
( ! [X10,X11,X12] :
( ~ c_HOL_Oord__class_Oless(X10,X10,X11)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X11)
| c_HOL_Oord__class_Oless(X12,X12,X11) )
| ~ spl0_427
| ~ spl0_429 ),
inference(duplicate_literal_removal,[],[f6431]) ).
fof(f6431,plain,
( ! [X10,X11,X12] :
( ~ c_HOL_Oord__class_Oless(X10,X10,X11)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X11)
| c_HOL_Oord__class_Oless(X12,X12,X11)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X11) )
| ~ spl0_427
| ~ spl0_429 ),
inference(resolution,[],[f6083,f6075]) ).
fof(f6075,plain,
( ! [X10,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f6074]) ).
fof(f6083,plain,
( ! [X10,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f6082]) ).
fof(f13725,plain,
( spl0_673
| ~ spl0_107
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5755,f4604,f1206,f13723]) ).
fof(f13723,plain,
( spl0_673
<=> ! [X13,X14,X12,X15] : c_List_Olist_ONil(X15) != c_List_Oappend(c_List_Olist_OCons(X12,X13,X15),X14,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f5755,plain,
( ! [X14,X15,X12,X13] : c_List_Olist_ONil(X15) != c_List_Oappend(c_List_Olist_OCons(X12,X13,X15),X14,X15)
| ~ spl0_107
| ~ spl0_409 ),
inference(superposition,[],[f1207,f4605]) ).
fof(f13721,plain,
( spl0_672
| ~ spl0_92
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5754,f4604,f1145,f13719]) ).
fof(f13719,plain,
( spl0_672
<=> ! [X10,X11,X9,X8] : c_List_Omember(X8,c_List_Oappend(c_List_Olist_OCons(X8,X9,X11),X10,X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f5754,plain,
( ! [X10,X11,X8,X9] : c_List_Omember(X8,c_List_Oappend(c_List_Olist_OCons(X8,X9,X11),X10,X11),X11)
| ~ spl0_92
| ~ spl0_409 ),
inference(superposition,[],[f1146,f4605]) ).
fof(f13717,plain,
( spl0_671
| ~ spl0_242
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f5098,f4539,f2139,f13715]) ).
fof(f13715,plain,
( spl0_671
<=> ! [X6,X5] :
( c_List_Olinorder__class_Osorted(c_List_Obutlast(X5,X6),X6)
| ~ c_List_Olinorder__class_Osorted(X5,X6)
| ~ class_Orderings_Olinorder(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2139,plain,
( spl0_242
<=> ! [X0,X12,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Otake(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f5098,plain,
( ! [X6,X5] :
( c_List_Olinorder__class_Osorted(c_List_Obutlast(X5,X6),X6)
| ~ c_List_Olinorder__class_Osorted(X5,X6)
| ~ class_Orderings_Olinorder(X6) )
| ~ spl0_242
| ~ spl0_394 ),
inference(superposition,[],[f2140,f4540]) ).
fof(f2140,plain,
( ! [X3,X0,X12] :
( c_List_Olinorder__class_Osorted(c_List_Otake(X3,X12,X0),X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2139]) ).
fof(f13713,plain,
( spl0_670
| ~ spl0_92
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f4423,f3756,f1145,f13711]) ).
fof(f13711,plain,
( spl0_670
<=> ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xneq__Nil__conv__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f4423,plain,
( ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xneq__Nil__conv__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 )
| ~ spl0_92
| ~ spl0_372 ),
inference(superposition,[],[f1146,f3757]) ).
fof(f13709,plain,
( spl0_669
| ~ spl0_92
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4401,f3752,f1145,f13707]) ).
fof(f13707,plain,
( spl0_669
<=> ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xlist__Xexhaust__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f4401,plain,
( ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xlist__Xexhaust__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 )
| ~ spl0_92
| ~ spl0_371 ),
inference(superposition,[],[f1146,f3753]) ).
fof(f13685,plain,
( spl0_668
| ~ spl0_92
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4379,f3748,f1145,f13683]) ).
fof(f13683,plain,
( spl0_668
<=> ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xlist__Xnchotomy__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f4379,plain,
( ! [X4,X5] :
( c_List_Omember(c_List_Osko__List__Xlist__Xnchotomy__1__1(X4,X5),X4,X5)
| c_List_Olist_ONil(X5) = X4 )
| ~ spl0_92
| ~ spl0_370 ),
inference(superposition,[],[f1146,f3749]) ).
fof(f13681,plain,
( spl0_667
| ~ spl0_78
| ~ spl0_127
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f4357,f3722,f1293,f1083,f13679]) ).
fof(f13679,plain,
( spl0_667
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f3722,plain,
( spl0_366
<=> ! [X0,X12,X3] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_Suc(X3),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f4357,plain,
( ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_78
| ~ spl0_127
| ~ spl0_366 ),
inference(forward_demodulation,[],[f4354,f1294]) ).
fof(f4354,plain,
( ! [X0,X1] : c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Otl(X0,X1),X1) = c_List_Otl(c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_78
| ~ spl0_366 ),
inference(superposition,[],[f3723,f1085]) ).
fof(f3723,plain,
( ! [X3,X0,X12] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_Suc(X3),X12,X0),X0)
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f3722]) ).
fof(f13677,plain,
( spl0_666
| ~ spl0_78
| ~ spl0_126
| ~ spl0_181
| ~ spl0_320
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f3563,f3015,f2987,f1553,f1289,f1083,f13674]) ).
fof(f3015,plain,
( spl0_327
<=> c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f3563,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xalt3__3,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_181
| ~ spl0_320
| ~ spl0_327 ),
inference(forward_demodulation,[],[f3560,f3524]) ).
fof(f3560,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_181
| ~ spl0_327 ),
inference(resolution,[],[f3017,f1554]) ).
fof(f3017,plain,
( c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f3015]) ).
fof(f13672,plain,
( spl0_665
| ~ spl0_81
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3506,f2987,f1096,f13670]) ).
fof(f13670,plain,
( spl0_665
<=> ! [X4,X5,X3] : c_List_Oreplicate(X4,X3,X5) != c_List_Oreplicate(c_Suc(X4),X3,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f1096,plain,
( spl0_81
<=> ! [X5,X0,X12] : c_List_Olist_OCons(X5,X12,X0) != X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f3506,plain,
( ! [X3,X4,X5] : c_List_Oreplicate(X4,X3,X5) != c_List_Oreplicate(c_Suc(X4),X3,X5)
| ~ spl0_81
| ~ spl0_320 ),
inference(superposition,[],[f1097,f2988]) ).
fof(f1097,plain,
( ! [X0,X5,X12] : c_List_Olist_OCons(X5,X12,X0) != X12
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f13668,plain,
( spl0_664
| ~ spl0_102
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f2855,f2544,f1185,f13666]) ).
fof(f13666,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f1185,plain,
( spl0_102
<=> ! [X13,X0] : c_List_Oappend(c_List_Olist_ONil(X0),X13,X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2544,plain,
( spl0_283
<=> ! [X13,X0,X12,X28] :
( X13 = X28
| c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2855,plain,
( ! [X2,X0,X1] :
( c_List_Oappend(c_List_Olist_ONil(X0),X2,X0) != X1
| X1 = X2 )
| ~ spl0_102
| ~ spl0_283 ),
inference(superposition,[],[f2545,f1186]) ).
fof(f1186,plain,
( ! [X0,X13] : c_List_Oappend(c_List_Olist_ONil(X0),X13,X0) = X13
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1185]) ).
fof(f2545,plain,
( ! [X28,X0,X12,X13] :
( c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0)
| X13 = X28 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2544]) ).
fof(f13664,plain,
( spl0_663
| ~ spl0_103
| ~ spl0_282 ),
inference(avatar_split_clause,[],[f2849,f2540,f1189,f13662]) ).
fof(f13662,plain,
( spl0_663
<=> ! [X4,X5,X3] :
( c_List_Oappend(X5,c_List_Olist_ONil(X4),X4) != X3
| X3 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f1189,plain,
( spl0_103
<=> ! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2540,plain,
( spl0_282
<=> ! [X13,X0,X12,X28] :
( X13 = X28
| c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2849,plain,
( ! [X3,X4,X5] :
( c_List_Oappend(X5,c_List_Olist_ONil(X4),X4) != X3
| X3 = X5 )
| ~ spl0_103
| ~ spl0_282 ),
inference(superposition,[],[f2541,f1190]) ).
fof(f1190,plain,
( ! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f1189]) ).
fof(f2541,plain,
( ! [X28,X0,X12,X13] :
( c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0)
| X13 = X28 )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2540]) ).
fof(f13660,plain,
( spl0_662
| ~ spl0_90
| ~ spl0_273 ),
inference(avatar_split_clause,[],[f2780,f2504,f1137,f13658]) ).
fof(f13658,plain,
( spl0_662
<=> ! [X16,X15] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) != X15
| X15 = X16 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2780,plain,
( ! [X16,X15] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X16,tc_nat) != X15
| X15 = X16 )
| ~ spl0_90
| ~ spl0_273 ),
inference(superposition,[],[f2505,f1138]) ).
fof(f13656,plain,
( spl0_661
| ~ spl0_91
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2752,f2500,f1141,f13654]) ).
fof(f13654,plain,
( spl0_661
<=> ! [X9,X8] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X8
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f1141,plain,
( spl0_91
<=> ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f2752,plain,
( ! [X8,X9] :
( c_HOL_Oplus__class_Oplus(X9,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X8
| X8 = X9 )
| ~ spl0_91
| ~ spl0_272 ),
inference(superposition,[],[f2501,f1142]) ).
fof(f1142,plain,
( ! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1141]) ).
fof(f13652,plain,
( spl0_660
| ~ spl0_103
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2684,f2468,f1189,f13650]) ).
fof(f13650,plain,
( spl0_660
<=> ! [X2,X3] : c_List_Olist_ONil(X3) = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2468,plain,
( spl0_264
<=> ! [X13,X0,X12] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2684,plain,
( ! [X2,X3] : c_List_Olist_ONil(X3) = c_List_Odrop(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X2,X3)
| ~ spl0_103
| ~ spl0_264 ),
inference(superposition,[],[f2469,f1190]) ).
fof(f2469,plain,
( ! [X0,X12,X13] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f13648,plain,
( spl0_659
| ~ spl0_109
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2346,f2070,f1221,f13646]) ).
fof(f13646,plain,
( spl0_659
<=> ! [X6,X7] : c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2346,plain,
( ! [X6,X7] : c_HOL_Oord__class_Oless(c_Suc(X7),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat))),tc_nat)
| ~ spl0_109
| ~ spl0_226 ),
inference(superposition,[],[f1222,f2071]) ).
fof(f13644,plain,
( spl0_658
| ~ spl0_114
| ~ spl0_647 ),
inference(avatar_split_clause,[],[f13581,f13554,f1241,f13642]) ).
fof(f13642,plain,
( spl0_658
<=> ! [X17] : c_lessequals(X17,c_Suc(c_Suc(X17)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f1241,plain,
( spl0_114
<=> ! [X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f13554,plain,
( spl0_647
<=> ! [X2,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),c_Suc(X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f13581,plain,
( ! [X17] : c_lessequals(X17,c_Suc(c_Suc(X17)),tc_nat)
| ~ spl0_114
| ~ spl0_647 ),
inference(superposition,[],[f13555,f1242]) ).
fof(f1242,plain,
( ! [X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1241]) ).
fof(f13555,plain,
( ! [X2,X3] : c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),c_Suc(X2),tc_nat)
| ~ spl0_647 ),
inference(avatar_component_clause,[],[f13554]) ).
fof(f13640,plain,
( spl0_657
| ~ spl0_108
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2321,f2066,f1217,f13638]) ).
fof(f13638,plain,
( spl0_657
<=> ! [X4,X5] : c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f1217,plain,
( spl0_108
<=> ! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2321,plain,
( ! [X4,X5] : c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat))),tc_nat)
| ~ spl0_108
| ~ spl0_225 ),
inference(superposition,[],[f1218,f2067]) ).
fof(f1218,plain,
( ! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)),tc_nat)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1217]) ).
fof(f13636,plain,
( spl0_656
| ~ spl0_87
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2228,f2042,f1125,f13634]) ).
fof(f13634,plain,
( spl0_656
<=> ! [X29,X30,X31] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X30,X31,tc_nat),tc_nat),X31,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f1125,plain,
( spl0_87
<=> ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f2042,plain,
( spl0_219
<=> ! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2228,plain,
( ! [X31,X29,X30] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X30,X31,tc_nat),tc_nat),X31,tc_nat)
| ~ spl0_87
| ~ spl0_219 ),
inference(resolution,[],[f2043,f1126]) ).
fof(f1126,plain,
( ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1125]) ).
fof(f2043,plain,
( ! [X6,X4,X15] :
( c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2042]) ).
fof(f13632,plain,
( spl0_655
| ~ spl0_121
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2214,f2038,f1269,f13630]) ).
fof(f13630,plain,
( spl0_655
<=> ! [X13,X12] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X12),X13,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2214,plain,
( ! [X12,X13] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X12),X13,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),X13,tc_nat) )
| ~ spl0_121
| ~ spl0_218 ),
inference(superposition,[],[f2039,f1270]) ).
fof(f13628,plain,
( spl0_654
| ~ spl0_121
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2198,f2034,f1269,f13626]) ).
fof(f13626,plain,
( spl0_654
<=> ! [X13,X12] :
( c_HOL_Oord__class_Oless(X13,c_Suc(X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2034,plain,
( spl0_217
<=> ! [X5,X8,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X8,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f2198,plain,
( ! [X12,X13] :
( c_HOL_Oord__class_Oless(X13,c_Suc(X12),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_121
| ~ spl0_217 ),
inference(superposition,[],[f2035,f1270]) ).
fof(f2035,plain,
( ! [X8,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X8,tc_nat) )
| ~ spl0_217 ),
inference(avatar_component_clause,[],[f2034]) ).
fof(f13624,plain,
( spl0_653
| ~ spl0_87
| ~ spl0_217 ),
inference(avatar_split_clause,[],[f2189,f2034,f1125,f13622]) ).
fof(f13622,plain,
( spl0_653
<=> ! [X29,X30,X31] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X30,X31,tc_nat),tc_nat),X30,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2189,plain,
( ! [X31,X29,X30] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X29,c_HOL_Oplus__class_Oplus(X30,X31,tc_nat),tc_nat),X30,tc_nat)
| ~ spl0_87
| ~ spl0_217 ),
inference(resolution,[],[f2035,f1126]) ).
fof(f13620,plain,
( spl0_652
| ~ spl0_95
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2028,f1816,f1157,f13618]) ).
fof(f13618,plain,
( spl0_652
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) != X0
| c_List_Olist_ONil(X1) = c_List_Orev(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f1157,plain,
( spl0_95
<=> ! [X13,X0] : c_List_Orev(c_List_Orev(X13,X0),X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1816,plain,
( spl0_212
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orev(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2028,plain,
( ! [X0,X1] :
( c_List_Olist_ONil(X1) != X0
| c_List_Olist_ONil(X1) = c_List_Orev(X0,X1) )
| ~ spl0_95
| ~ spl0_212 ),
inference(superposition,[],[f1817,f1158]) ).
fof(f1158,plain,
( ! [X0,X13] : c_List_Orev(c_List_Orev(X13,X0),X0) = X13
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f1157]) ).
fof(f1817,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) != c_List_Orev(X12,X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1816]) ).
fof(f13616,plain,
( spl0_651
| ~ spl0_95
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2016,f1792,f1157,f13614]) ).
fof(f13614,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f1792,plain,
( spl0_206
<=> ! [X13,X0,X12] :
( X12 = X13
| c_List_Orev(X12,X0) != c_List_Orev(X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2016,plain,
( ! [X2,X0,X1] :
( c_List_Orev(X2,X1) != X0
| c_List_Orev(X0,X1) = X2 )
| ~ spl0_95
| ~ spl0_206 ),
inference(superposition,[],[f1793,f1158]) ).
fof(f1793,plain,
( ! [X0,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Orev(X13,X0)
| X12 = X13 )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1792]) ).
fof(f13612,plain,
( spl0_650
| ~ spl0_151
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2007,f1784,f1433,f13610]) ).
fof(f13610,plain,
( spl0_650
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2007,plain,
( ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
| ~ spl0_151
| ~ spl0_204 ),
inference(superposition,[],[f1785,f1434]) ).
fof(f13608,plain,
( spl0_649
| ~ spl0_151
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f1982,f1756,f1433,f13606]) ).
fof(f13606,plain,
( spl0_649
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f1756,plain,
( spl0_197
<=> ! [X5,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1982,plain,
( ! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_151
| ~ spl0_197 ),
inference(superposition,[],[f1757,f1434]) ).
fof(f1757,plain,
( ! [X1,X5] :
( c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f1756]) ).
fof(f13604,plain,
( spl0_648
| ~ spl0_184
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f1964,f1748,f1704,f13602]) ).
fof(f13602,plain,
( spl0_648
<=> ! [X4,X5,X3] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_lessequals(X4,X5,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f1748,plain,
( spl0_195
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1964,plain,
( ! [X3,X4,X5] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_lessequals(X4,X5,X3) )
| ~ spl0_184
| ~ spl0_195 ),
inference(duplicate_literal_removal,[],[f1952]) ).
fof(f1952,plain,
( ! [X3,X4,X5] :
( ~ class_Orderings_Olinorder(X3)
| ~ c_HOL_Oord__class_Oless(X4,X5,X3)
| c_lessequals(X4,X5,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_184
| ~ spl0_195 ),
inference(resolution,[],[f1749,f1705]) ).
fof(f1749,plain,
( ! [X0,X8,X5] :
( ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f1748]) ).
fof(f13556,plain,
( spl0_647
| ~ spl0_21
| ~ spl0_110
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1897,f1728,f1225,f814,f13554]) ).
fof(f1897,plain,
( ! [X2,X3] :
( ~ class_Orderings_Oorder(tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),c_Suc(X2),tc_nat) )
| ~ spl0_110
| ~ spl0_190 ),
inference(resolution,[],[f1729,f1226]) ).
fof(f13552,plain,
( spl0_646
| ~ spl0_109
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1889,f1724,f1221,f13550]) ).
fof(f13550,plain,
( spl0_646
<=> ! [X13,X12] : c_Divides_Odiv__class_Omod(X12,c_Suc(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat)),tc_nat) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f1889,plain,
( ! [X12,X13] : c_Divides_Odiv__class_Omod(X12,c_Suc(c_HOL_Oplus__class_Oplus(X13,X12,tc_nat)),tc_nat) = X12
| ~ spl0_109
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1222]) ).
fof(f13548,plain,
( spl0_645
| ~ spl0_108
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1888,f1724,f1217,f13546]) ).
fof(f13546,plain,
( spl0_645
<=> ! [X11,X10] : c_Divides_Odiv__class_Omod(X10,c_Suc(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat)),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1888,plain,
( ! [X10,X11] : c_Divides_Odiv__class_Omod(X10,c_Suc(c_HOL_Oplus__class_Oplus(X10,X11,tc_nat)),tc_nat) = X10
| ~ spl0_108
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1218]) ).
fof(f13544,plain,
( spl0_644
| ~ spl0_146
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1600,f1417,f1412,f13542]) ).
fof(f13542,plain,
( spl0_644
<=> ! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f1600,plain,
( ! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_Suc(X12),tc_nat) )
| ~ spl0_146
| ~ spl0_147 ),
inference(resolution,[],[f1418,f1413]) ).
fof(f13540,plain,
( spl0_643
| ~ spl0_144
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1585,f1412,f1404,f13538]) ).
fof(f13538,plain,
( spl0_643
<=> ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f1585,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X1,c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) )
| ~ spl0_144
| ~ spl0_146 ),
inference(resolution,[],[f1413,f1405]) ).
fof(f13536,plain,
( spl0_642
| ~ spl0_78
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1575,f1404,f1083,f13534]) ).
fof(f13534,plain,
( spl0_642
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1575,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_78
| ~ spl0_144 ),
inference(superposition,[],[f1405,f1085]) ).
fof(f13532,plain,
( spl0_641
| ~ spl0_78
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1566,f1400,f1083,f13530]) ).
fof(f13530,plain,
( spl0_641
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f1566,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_78
| ~ spl0_143 ),
inference(superposition,[],[f1401,f1085]) ).
fof(f13510,plain,
( spl0_640
| ~ spl0_141
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1890,f1724,f1359,f13508]) ).
fof(f13508,plain,
( spl0_640
<=> ! [X14] : c_Divides_Odiv__class_Omod(X14,c_Suc(c_Suc(X14)),tc_nat) = X14 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f1359,plain,
( spl0_141
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1890,plain,
( ! [X14] : c_Divides_Odiv__class_Omod(X14,c_Suc(c_Suc(X14)),tc_nat) = X14
| ~ spl0_141
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1360]) ).
fof(f1360,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f12700,plain,
( spl0_639
| ~ spl0_151
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f12577,f12556,f1433,f12698]) ).
fof(f12698,plain,
( spl0_639
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f12577,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| ~ spl0_151
| ~ spl0_617 ),
inference(superposition,[],[f12557,f1434]) ).
fof(f12692,plain,
( spl0_638
| ~ spl0_79
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5752,f4604,f1088,f12690]) ).
fof(f12690,plain,
( spl0_638
<=> ! [X2,X0,X1,X3] : ~ c_List_Onull(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f5752,plain,
( ! [X2,X3,X0,X1] : ~ c_List_Onull(c_List_Oappend(c_List_Olist_OCons(X0,X1,X3),X2,X3),X3)
| ~ spl0_79
| ~ spl0_409 ),
inference(superposition,[],[f1089,f4605]) ).
fof(f12688,plain,
( spl0_637
| ~ spl0_81
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f4422,f3756,f1096,f12686]) ).
fof(f12686,plain,
( spl0_637
<=> ! [X2,X3] :
( c_List_Osko__List__Xneq__Nil__conv__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f4422,plain,
( ! [X2,X3] :
( c_List_Osko__List__Xneq__Nil__conv__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 )
| ~ spl0_81
| ~ spl0_372 ),
inference(superposition,[],[f1097,f3757]) ).
fof(f12684,plain,
( spl0_636
| ~ spl0_81
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f4400,f3752,f1096,f12682]) ).
fof(f12682,plain,
( spl0_636
<=> ! [X2,X3] :
( c_List_Osko__List__Xlist__Xexhaust__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f4400,plain,
( ! [X2,X3] :
( c_List_Osko__List__Xlist__Xexhaust__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 )
| ~ spl0_81
| ~ spl0_371 ),
inference(superposition,[],[f1097,f3753]) ).
fof(f12680,plain,
( spl0_635
| ~ spl0_81
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f4378,f3748,f1096,f12678]) ).
fof(f12678,plain,
( spl0_635
<=> ! [X2,X3] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f4378,plain,
( ! [X2,X3] :
( c_List_Osko__List__Xlist__Xnchotomy__1__2(X2,X3) != X2
| c_List_Olist_ONil(X3) = X2 )
| ~ spl0_81
| ~ spl0_370 ),
inference(superposition,[],[f1097,f3749]) ).
fof(f12676,plain,
( spl0_634
| ~ spl0_124
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3509,f2987,f1281,f12674]) ).
fof(f12674,plain,
( spl0_634
<=> ! [X13,X12,X14] : c_List_Ohd(c_List_Oreplicate(c_Suc(X13),X12,X14),X14) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f3509,plain,
( ! [X14,X12,X13] : c_List_Ohd(c_List_Oreplicate(c_Suc(X13),X12,X14),X14) = X12
| ~ spl0_124
| ~ spl0_320 ),
inference(superposition,[],[f1282,f2988]) ).
fof(f12672,plain,
( spl0_633
| ~ spl0_78
| ~ spl0_93
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2810,f2512,f1149,f1083,f12670]) ).
fof(f1149,plain,
( spl0_93
<=> ! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2512,plain,
( spl0_275
<=> ! [X0,X12,X3] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Odrop(X3,c_List_Otl(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2810,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_78
| ~ spl0_93
| ~ spl0_275 ),
inference(forward_demodulation,[],[f2805,f1085]) ).
fof(f2805,plain,
( ! [X0,X1] : c_List_Otl(X0,X1) = c_List_Odrop(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_93
| ~ spl0_275 ),
inference(superposition,[],[f2513,f1150]) ).
fof(f1150,plain,
( ! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1149]) ).
fof(f2513,plain,
( ! [X3,X0,X12] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Odrop(X3,c_List_Otl(X12,X0),X0)
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2512]) ).
fof(f12668,plain,
( spl0_632
| ~ spl0_78
| ~ spl0_113
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f2799,f2508,f1237,f1083,f12666]) ).
fof(f12666,plain,
( spl0_632
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2799,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_78
| ~ spl0_113
| ~ spl0_274 ),
inference(forward_demodulation,[],[f2798,f1085]) ).
fof(f2798,plain,
( ! [X0] : c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Orderings_Oord__class_Omin(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_78
| ~ spl0_113
| ~ spl0_274 ),
inference(forward_demodulation,[],[f2791,f1238]) ).
fof(f2791,plain,
( ! [X0] : c_Suc(c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)) = c_Orderings_Oord__class_Omin(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_78
| ~ spl0_274 ),
inference(superposition,[],[f2509,f1085]) ).
fof(f12664,plain,
( spl0_631
| ~ spl0_103
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2674,f2464,f1189,f12662]) ).
fof(f12662,plain,
( spl0_631
<=> ! [X2,X3] : c_List_Otake(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X2,X3) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2464,plain,
( spl0_263
<=> ! [X13,X0,X12] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2674,plain,
( ! [X2,X3] : c_List_Otake(c_Nat_Osize__class_Osize(X2,tc_List_Olist(X3)),X2,X3) = X2
| ~ spl0_103
| ~ spl0_263 ),
inference(superposition,[],[f2465,f1190]) ).
fof(f2465,plain,
( ! [X0,X12,X13] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2464]) ).
fof(f12660,plain,
( spl0_630
| ~ spl0_49
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2400,f2123,f954,f12658]) ).
fof(f12658,plain,
( spl0_630
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f954,plain,
( spl0_49
<=> class_OrderedGroup_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2123,plain,
( spl0_238
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2400,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_49
| ~ spl0_238 ),
inference(resolution,[],[f2124,f956]) ).
fof(f956,plain,
( class_OrderedGroup_Ogroup__add(tc_Int_Oint)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f954]) ).
fof(f2124,plain,
( ! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2123]) ).
fof(f12637,plain,
( spl0_629
| ~ spl0_53
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2398,f2111,f974,f12635]) ).
fof(f12635,plain,
( spl0_629
<=> ! [X2,X3] : c_Orderings_Oord__class_Omin(X2,X3,tc_Int_Oint) = c_Orderings_Oord__class_Omin(X3,X2,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f974,plain,
( spl0_53
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f2111,plain,
( spl0_235
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2398,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Omin(X2,X3,tc_Int_Oint) = c_Orderings_Oord__class_Omin(X3,X2,tc_Int_Oint)
| ~ spl0_53
| ~ spl0_235 ),
inference(resolution,[],[f2112,f976]) ).
fof(f976,plain,
( class_Orderings_Olinorder(tc_Int_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f974]) ).
fof(f2112,plain,
( ! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2111]) ).
fof(f12633,plain,
( spl0_628
| ~ spl0_20
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2397,f2111,f809,f12631]) ).
fof(f12631,plain,
( spl0_628
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2397,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat)
| ~ spl0_20
| ~ spl0_235 ),
inference(resolution,[],[f2112,f811]) ).
fof(f811,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f809]) ).
fof(f12629,plain,
( spl0_627
| ~ spl0_49
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2391,f2103,f954,f12627]) ).
fof(f12627,plain,
( spl0_627
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2103,plain,
( spl0_233
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2391,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Int_Oint),X1,tc_Int_Oint) = X0
| ~ spl0_49
| ~ spl0_233 ),
inference(resolution,[],[f2104,f956]) ).
fof(f2104,plain,
( ! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2103]) ).
fof(f12625,plain,
( spl0_626
| ~ spl0_110
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f2383,f2087,f1225,f12623]) ).
fof(f12623,plain,
( spl0_626
<=> ! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),c_Suc(c_Suc(X4)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2383,plain,
( ! [X4,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X5,tc_nat),c_Suc(c_Suc(X4)),tc_nat)
| ~ spl0_110
| ~ spl0_229 ),
inference(superposition,[],[f1226,f2088]) ).
fof(f12621,plain,
( spl0_625
| ~ spl0_87
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2344,f2070,f1125,f12619]) ).
fof(f12619,plain,
( spl0_625
<=> ! [X2,X3] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2344,plain,
( ! [X2,X3] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X2,X3,tc_nat)),c_Suc(X3),tc_nat)
| ~ spl0_87
| ~ spl0_226 ),
inference(superposition,[],[f1126,f2071]) ).
fof(f12617,plain,
( spl0_624
| ~ spl0_86
| ~ spl0_225 ),
inference(avatar_split_clause,[],[f2319,f2066,f1121,f12615]) ).
fof(f1121,plain,
( spl0_86
<=> ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f2319,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat)
| ~ spl0_86
| ~ spl0_225 ),
inference(superposition,[],[f1122,f2067]) ).
fof(f1122,plain,
( ! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1121]) ).
fof(f12613,plain,
( spl0_623
| ~ spl0_41
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2307,f2058,f914,f12611]) ).
fof(f12611,plain,
( spl0_623
<=> ! [X2,X3] : c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X3,X2,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f914,plain,
( spl0_41
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2058,plain,
( spl0_223
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2307,plain,
( ! [X2,X3] : c_HOL_Oplus__class_Oplus(X2,X3,tc_Int_Oint) = c_HOL_Oplus__class_Oplus(X3,X2,tc_Int_Oint)
| ~ spl0_41
| ~ spl0_223 ),
inference(resolution,[],[f2059,f916]) ).
fof(f916,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f914]) ).
fof(f2059,plain,
( ! [X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2058]) ).
fof(f12609,plain,
( spl0_622
| ~ spl0_90
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2209,f2038,f1137,f12607]) ).
fof(f12607,plain,
( spl0_622
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2209,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
| ~ spl0_90
| ~ spl0_218 ),
inference(superposition,[],[f2039,f1138]) ).
fof(f12605,plain,
( spl0_621
| ~ spl0_121
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2009,f1784,f1269,f12603]) ).
fof(f12603,plain,
( spl0_621
<=> ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X7),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2009,plain,
( ! [X7] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X7),tc_nat)
| ~ spl0_121
| ~ spl0_204 ),
inference(superposition,[],[f1785,f1270]) ).
fof(f12601,plain,
( spl0_620
| ~ spl0_154
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1853,f1708,f1445,f12599]) ).
fof(f12599,plain,
( spl0_620
<=> ! [X6,X8,X7] :
( ~ class_Orderings_Olinorder(X6)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X7,X8,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1445,plain,
( spl0_154
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1708,plain,
( spl0_185
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1853,plain,
( ! [X8,X6,X7] :
( ~ class_Orderings_Olinorder(X6)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X7,X8,X6),X6) )
| ~ spl0_154
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1850]) ).
fof(f1850,plain,
( ! [X8,X6,X7] :
( ~ class_Orderings_Olinorder(X6)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X7,X8,X6),X6)
| ~ class_Orderings_Olinorder(X6) )
| ~ spl0_154
| ~ spl0_185 ),
inference(resolution,[],[f1709,f1446]) ).
fof(f1446,plain,
( ! [X0,X8,X5] :
( c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1445]) ).
fof(f1709,plain,
( ! [X0,X8,X5] :
( ~ c_lessequals(X5,X8,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1708]) ).
fof(f12597,plain,
( spl0_619
| ~ spl0_121
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f12584,f12556,f1269,f12595]) ).
fof(f12595,plain,
( spl0_619
<=> ! [X14] : c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X14),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f12584,plain,
( ! [X14] : c_lessequals(c_HOL_Oone__class_Oone(tc_nat),c_Suc(X14),tc_nat)
| ~ spl0_121
| ~ spl0_617 ),
inference(superposition,[],[f12557,f1270]) ).
fof(f12593,plain,
( spl0_618
| ~ spl0_155
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1852,f1708,f1449,f12591]) ).
fof(f12591,plain,
( spl0_618
<=> ! [X9,X11,X10] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X10,c_Orderings_Oord__class_Omin(X11,X10,X9),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1852,plain,
( ! [X10,X11,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X10,c_Orderings_Oord__class_Omin(X11,X10,X9),X9) )
| ~ spl0_155
| ~ spl0_185 ),
inference(duplicate_literal_removal,[],[f1851]) ).
fof(f1851,plain,
( ! [X10,X11,X9] :
( ~ class_Orderings_Olinorder(X9)
| ~ c_HOL_Oord__class_Oless(X10,c_Orderings_Oord__class_Omin(X11,X10,X9),X9)
| ~ class_Orderings_Olinorder(X9) )
| ~ spl0_155
| ~ spl0_185 ),
inference(resolution,[],[f1709,f1450]) ).
fof(f12558,plain,
( ~ spl0_20
| spl0_617
| ~ spl0_86
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1840,f1704,f1121,f12556,f809]) ).
fof(f1840,plain,
( ! [X12,X13] :
( c_lessequals(X12,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_86
| ~ spl0_184 ),
inference(resolution,[],[f1705,f1122]) ).
fof(f12554,plain,
( spl0_616
| ~ spl0_109
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1591,f1412,f1221,f12552]) ).
fof(f12552,plain,
( spl0_616
<=> ! [X6,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1591,plain,
( ! [X6,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat))),tc_nat)
| ~ spl0_109
| ~ spl0_146 ),
inference(forward_demodulation,[],[f1587,f197]) ).
fof(f197,axiom,
! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)) = c_HOL_Oplus__class_Oplus(X4,c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__Suc__right_0) ).
fof(f1587,plain,
( ! [X6,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X6,c_Suc(X5),tc_nat)),tc_nat)
| ~ spl0_109
| ~ spl0_146 ),
inference(resolution,[],[f1413,f1222]) ).
fof(f12550,plain,
( spl0_615
| ~ spl0_108
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1590,f1412,f1217,f12548]) ).
fof(f12548,plain,
( spl0_615
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1590,plain,
( ! [X3,X4] : c_HOL_Oord__class_Oless(X3,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat))),tc_nat)
| ~ spl0_108
| ~ spl0_146 ),
inference(forward_demodulation,[],[f1586,f196]) ).
fof(f196,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(c_Suc(X4),X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__Suc_0) ).
fof(f1586,plain,
( ! [X3,X4] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat)),tc_nat)
| ~ spl0_108
| ~ spl0_146 ),
inference(resolution,[],[f1413,f1218]) ).
fof(f12546,plain,
( spl0_614
| ~ spl0_71
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1397,f1341,f1055,f12544]) ).
fof(f12544,plain,
( spl0_614
<=> ! [X4,X3] : c_List_Oremdups(X3,X4) = c_List_Oremdups(c_List_Oremdups(X3,X4),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1055,plain,
( spl0_71
<=> ! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1397,plain,
( ! [X3,X4] : c_List_Oremdups(X3,X4) = c_List_Oremdups(c_List_Oremdups(X3,X4),X4)
| ~ spl0_71
| ~ spl0_139 ),
inference(resolution,[],[f1342,f1056]) ).
fof(f1056,plain,
( ! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1055]) ).
fof(f12542,plain,
( spl0_613
| ~ spl0_78
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f1362,f1249,f1083,f12540]) ).
fof(f12540,plain,
( spl0_613
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1249,plain,
( spl0_116
<=> ! [X5,X8] :
( X5 = X8
| c_Suc(X5) != c_Suc(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f1362,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_nat) != c_Suc(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_116 ),
inference(superposition,[],[f1250,f1085]) ).
fof(f1250,plain,
( ! [X8,X5] :
( c_Suc(X5) != c_Suc(X8)
| X5 = X8 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1249]) ).
fof(f12160,plain,
spl0_612,
inference(avatar_split_clause,[],[f425,f12158]) ).
fof(f12158,plain,
( spl0_612
<=> ! [X31,X0,X29,X30] :
( c_List_Otake(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0) != X29
| c_List_Otake(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0) != X30
| c_List_Oappend(X30,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) = c_List_Oappend(X29,X31,X0)
| c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) != X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f425,axiom,
! [X31,X29,X0,X30] :
( c_List_Otake(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0) != X29
| c_List_Otake(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0) != X30
| c_List_Oappend(X30,c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) = c_List_Oappend(X29,X31,X0)
| c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X29,tc_List_Olist(X0)),X30,X0),c_List_Oappend(c_List_Odrop(c_Nat_Osize__class_Osize(X30,tc_List_Olist(X0)),X29,X0),X31,X0),X0) != X31 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__append__conv__if_6) ).
fof(f12044,plain,
spl0_611,
inference(avatar_split_clause,[],[f235,f12042]) ).
fof(f12042,plain,
( spl0_611
<=> ! [X24,X23,X9,X0,X10,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X24,X23,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f235,axiom,
! [X10,X0,X1,X9,X24,X23] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X24,X23,X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__diff__cong_0) ).
fof(f12040,plain,
spl0_610,
inference(avatar_split_clause,[],[f218,f12038]) ).
fof(f12038,plain,
( spl0_610
<=> ! [X24,X23,X9,X0,X10,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X24,X23,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f218,axiom,
! [X10,X0,X1,X9,X24,X23] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X10,X0) != c_Divides_Odiv__class_Omod(X24,X10,X0)
| c_Divides_Odiv__class_Omod(X9,X10,X0) != c_Divides_Odiv__class_Omod(X23,X10,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X24,X23,X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__add__cong_0) ).
fof(f11978,plain,
spl0_609,
inference(avatar_split_clause,[],[f160,f11976]) ).
fof(f11976,plain,
( spl0_609
<=> ! [X0,X13,X12,X5,X3] :
( c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(X12,c_List_Olist__update(X13,c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f160,axiom,
! [X3,X0,X5,X12,X13] :
( c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X3,X5,X0) = c_List_Oappend(X12,c_List_Olist__update(X13,c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X5,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__append_1) ).
fof(f11921,plain,
spl0_608,
inference(avatar_split_clause,[],[f696,f11919]) ).
fof(f11919,plain,
( spl0_608
<=> ! [X0,X14,X12,X8] :
( c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Suc(X14),tc_nat),X8,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f696,plain,
! [X0,X8,X14,X12] :
( c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Suc(X14),tc_nat),X8,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
inference(forward_demodulation,[],[f695,f314]) ).
fof(f314,axiom,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__eq__plus1_0) ).
fof(f695,plain,
! [X0,X8,X14,X12] :
( c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oplus__class_Oplus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_nat),X8,X0)
| ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
inference(forward_demodulation,[],[f162,f355]) ).
fof(f355,axiom,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__diff__left_0) ).
fof(f162,axiom,
! [X0,X8,X14,X12] :
( ~ c_HOL_Oord__class_Oless(X14,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Orev(c_List_Olist__update(X12,X14,X8,X0),X0) = c_List_Olist__update(c_List_Orev(X12,X0),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X14,tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__update_0) ).
fof(f11917,plain,
spl0_607,
inference(avatar_split_clause,[],[f156,f11915]) ).
fof(f11915,plain,
( spl0_607
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X9,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f156,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X9,X3,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__eq__imp__eq__base_0) ).
fof(f11869,plain,
( spl0_606
| ~ spl0_93
| ~ spl0_103
| ~ spl0_127
| ~ spl0_254
| ~ spl0_385
| ~ spl0_604 ),
inference(avatar_split_clause,[],[f11856,f11736,f4500,f2417,f1293,f1189,f1149,f11867]) ).
fof(f11867,plain,
( spl0_606
<=> ! [X0,X1] : c_List_Orotate(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2417,plain,
( spl0_254
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f4500,plain,
( spl0_385
<=> ! [X0,X12,X3] : c_List_Orotate(X3,X12,X0) = c_List_Orotate(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f11736,plain,
( spl0_604
<=> ! [X0,X12,X3] : c_List_Orotate(X3,X12,X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f11856,plain,
( ! [X0,X1] : c_List_Orotate(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = X0
| ~ spl0_93
| ~ spl0_103
| ~ spl0_127
| ~ spl0_254
| ~ spl0_385
| ~ spl0_604 ),
inference(forward_demodulation,[],[f11855,f1150]) ).
fof(f11855,plain,
( ! [X0,X1] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = c_List_Orotate(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1)
| ~ spl0_103
| ~ spl0_127
| ~ spl0_254
| ~ spl0_385
| ~ spl0_604 ),
inference(forward_demodulation,[],[f11854,f4784]) ).
fof(f4784,plain,
( ! [X0,X1] : c_List_Orotate(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = c_List_Orotate(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1)
| ~ spl0_254
| ~ spl0_385 ),
inference(superposition,[],[f4501,f2418]) ).
fof(f2418,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2417]) ).
fof(f4501,plain,
( ! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Orotate(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0)
| ~ spl0_385 ),
inference(avatar_component_clause,[],[f4500]) ).
fof(f11854,plain,
( ! [X0,X1] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1) = c_List_Orotate(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1)
| ~ spl0_103
| ~ spl0_127
| ~ spl0_254
| ~ spl0_604 ),
inference(forward_demodulation,[],[f11853,f1190]) ).
fof(f11853,plain,
( ! [X0,X1] : c_List_Orotate(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = c_List_Oappend(c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1),c_List_Olist_ONil(X1),X1)
| ~ spl0_127
| ~ spl0_254
| ~ spl0_604 ),
inference(forward_demodulation,[],[f11803,f1294]) ).
fof(f11803,plain,
( ! [X0,X1] : c_List_Orotate(c_Nat_Osize__class_Osize(X0,tc_List_Olist(X1)),X0,X1) = c_List_Oappend(c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1),c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X0,X1),X1)
| ~ spl0_254
| ~ spl0_604 ),
inference(superposition,[],[f11737,f2418]) ).
fof(f11737,plain,
( ! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0)
| ~ spl0_604 ),
inference(avatar_component_clause,[],[f11736]) ).
fof(f11742,plain,
spl0_605,
inference(avatar_split_clause,[],[f694,f11740]) ).
fof(f11740,plain,
( spl0_605
<=> ! [X0,X12,X3] :
( c_List_Otake(c_Suc(X3),X12,X0) = c_List_Orotate1(c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Otake(X3,X12,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f694,plain,
! [X3,X0,X12] :
( c_List_Otake(c_Suc(X3),X12,X0) = c_List_Orotate1(c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Otake(X3,X12,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
inference(forward_demodulation,[],[f205,f521]) ).
fof(f521,axiom,
! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__simps_1) ).
fof(f205,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Olist_OCons(c_List_Ohd(c_List_Odrop(X3,X12,X0),X0),c_List_Olist_ONil(X0),X0),X0) = c_List_Otake(c_Suc(X3),X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__hd__drop_0) ).
fof(f11738,plain,
spl0_604,
inference(avatar_split_clause,[],[f413,f11736]) ).
fof(f413,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Oappend(c_List_Odrop(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),c_List_Otake(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__drop__take_0) ).
fof(f11734,plain,
spl0_603,
inference(avatar_split_clause,[],[f206,f11732]) ).
fof(f11732,plain,
( spl0_603
<=> ! [X0,X12,X6,X1] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X12,X6,X1,X0) = c_List_Oappend(c_List_Otake(X6,X12,X0),c_List_Olist_OCons(X1,c_List_Odrop(c_Suc(X6),X12,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f206,axiom,
! [X0,X1,X6,X12] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X12,X6,X1,X0) = c_List_Oappend(c_List_Otake(X6,X12,X0),c_List_Olist_OCons(X1,c_List_Odrop(c_Suc(X6),X12,X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_upd__conv__take__nth__drop_0) ).
fof(f11453,plain,
spl0_602,
inference(avatar_split_clause,[],[f493,f11451]) ).
fof(f11451,plain,
( spl0_602
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f493,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Cons__eq__append__conv_3) ).
fof(f11449,plain,
spl0_601,
inference(avatar_split_clause,[],[f492,f11447]) ).
fof(f11447,plain,
( spl0_601
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f492,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__Cons__conv_2) ).
fof(f11445,plain,
spl0_600,
inference(avatar_split_clause,[],[f467,f11443]) ).
fof(f11443,plain,
( spl0_600
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f467,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Cons__eq__append__conv_2) ).
fof(f11441,plain,
spl0_599,
inference(avatar_split_clause,[],[f466,f11439]) ).
fof(f11439,plain,
( spl0_599
<=> ! [X0,X13,X12,X5,X28] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f466,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_OCons(X5,X12,X0) = X28
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__Cons__conv_3) ).
fof(f11437,plain,
spl0_598,
inference(avatar_split_clause,[],[f433,f11435]) ).
fof(f11435,plain,
( spl0_598
<=> ! [X5,X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(c_List_Ohd(X13,X0),c_List_Osplice(X12,c_List_Otl(X13,X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f433,axiom,
! [X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(c_List_Ohd(X13,X0),c_List_Osplice(X12,c_List_Otl(X13,X0),X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_splice_Osimps_I2_J_1) ).
fof(f11433,plain,
spl0_597,
inference(avatar_split_clause,[],[f390,f11431]) ).
fof(f11431,plain,
( spl0_597
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X3),X0) != c_Power_Opower__class_Opower(X9,c_Suc(X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f390,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X1 = X9
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X3),X0) != c_Power_Opower__class_Opower(X9,c_Suc(X3),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__inject__base_0) ).
fof(f11429,plain,
spl0_596,
inference(avatar_split_clause,[],[f26,f11427]) ).
fof(f11427,plain,
( spl0_596
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f26,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__strict__mono_0) ).
fof(f11388,plain,
spl0_595,
inference(avatar_split_clause,[],[f1,f11386]) ).
fof(f11386,plain,
( spl0_595
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__strict__decreasing_0) ).
fof(f11127,plain,
spl0_594,
inference(avatar_split_clause,[],[f414,f11125]) ).
fof(f11125,plain,
( spl0_594
<=> ! [X0,X14,X12,X5] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist__update(X12,X14,X5,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f414,axiom,
! [X0,X14,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist__update(X12,X14,X5,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__list__update_1) ).
fof(f11123,plain,
spl0_593,
inference(avatar_split_clause,[],[f323,f11121]) ).
fof(f11121,plain,
( spl0_593
<=> ! [X0,X12,X3] : c_List_Orotate(X3,c_List_Orev(X12,X0),X0) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f323,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,c_List_Orev(X12,X0),X0) = c_List_Orev(c_List_Orotate(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),tc_nat),X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__rev_0) ).
fof(f11119,plain,
spl0_592,
inference(avatar_split_clause,[],[f284,f11117]) ).
fof(f11117,plain,
( spl0_592
<=> ! [X0,X14,X12,X5] :
( c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Obutlast(c_List_Olist__update(X12,X14,X5,X0),X0) = c_List_Olist__update(c_List_Obutlast(X12,X0),X14,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f284,axiom,
! [X0,X14,X5,X12] :
( c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X14
| c_List_Obutlast(c_List_Olist__update(X12,X14,X5,X0),X0) = c_List_Olist__update(c_List_Obutlast(X12,X0),X14,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast__list__update_1) ).
fof(f10695,plain,
spl0_591,
inference(avatar_split_clause,[],[f517,f10693]) ).
fof(f10693,plain,
( spl0_591
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f517,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Cons__eq__append__conv_0) ).
fof(f10691,plain,
spl0_590,
inference(avatar_split_clause,[],[f516,f10689]) ).
fof(f10689,plain,
( spl0_590
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f516,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__Cons__conv_1) ).
fof(f10687,plain,
spl0_589,
inference(avatar_split_clause,[],[f509,f10685]) ).
fof(f10685,plain,
( spl0_589
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f509,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Olist_OCons(X5,c_List_Osko__List__Xappend__eq__Cons__conv__1__1(X5,X12,X13,X28,X0),X0) = X13 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__Cons__conv_0) ).
fof(f10683,plain,
spl0_588,
inference(avatar_split_clause,[],[f508,f10681]) ).
fof(f10681,plain,
( spl0_588
<=> ! [X5,X13,X0,X12,X28] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f508,axiom,
! [X28,X0,X5,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_OCons(X5,X12,X0) != c_List_Oappend(X13,X28,X0)
| c_List_Oappend(c_List_Osko__List__XCons__eq__append__conv__1__1(X5,X12,X13,X28,X0),X28,X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Cons__eq__append__conv_1) ).
fof(f10613,plain,
spl0_587,
inference(avatar_split_clause,[],[f387,f10611]) ).
fof(f10611,plain,
( spl0_587
<=> ! [X18,X0,X25] :
( ~ class_Int_Onumber(X0)
| ~ class_HOL_Oord(X0)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X25,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f387,axiom,
! [X0,X18,X25] :
( ~ class_Int_Onumber(X0)
| ~ class_HOL_Oord(X0)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X25,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__number__of_0) ).
fof(f10609,plain,
spl0_586,
inference(avatar_split_clause,[],[f309,f10607]) ).
fof(f10607,plain,
( spl0_586
<=> ! [X13,X0,X12,X3] : c_List_Odrop(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Odrop(X3,X12,X0),c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f309,axiom,
! [X3,X0,X12,X13] : c_List_Odrop(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Odrop(X3,X12,X0),c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__append_0) ).
fof(f10605,plain,
spl0_585,
inference(avatar_split_clause,[],[f269,f10603]) ).
fof(f10603,plain,
( spl0_585
<=> ! [X18,X0,X25] :
( ~ class_Int_Onumber(X0)
| ~ class_HOL_Oord(X0)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X18,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f269,axiom,
! [X0,X18,X25] :
( ~ class_Int_Onumber(X0)
| ~ class_HOL_Oord(X0)
| c_lessequals(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0)
| c_Int_Onumber__class_Onumber__of(X18,X0) = c_Orderings_Oord__class_Omin(c_Int_Onumber__class_Onumber__of(X25,X0),c_Int_Onumber__class_Onumber__of(X18,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__number__of_1) ).
fof(f10601,plain,
spl0_584,
inference(avatar_split_clause,[],[f251,f10599]) ).
fof(f10599,plain,
( spl0_584
<=> ! [X13,X0,X12,X3] : c_List_Otake(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f251,axiom,
! [X3,X0,X12,X13] : c_List_Otake(X3,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__append_0) ).
fof(f10597,plain,
spl0_583,
inference(avatar_split_clause,[],[f59,f10595]) ).
fof(f10595,plain,
( spl0_583
<=> ! [X5,X0,X13,X12,X6] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X6,X5,X0) = c_List_Oappend(c_List_Olist__update(X12,X6,X5,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f59,axiom,
! [X0,X6,X5,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X6,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Oappend(X12,X13,X0),X6,X5,X0) = c_List_Oappend(c_List_Olist__update(X12,X6,X5,X0),X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__append1_0) ).
fof(f10508,plain,
( spl0_582
| ~ spl0_177
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f5099,f4539,f1537,f10506]) ).
fof(f10506,plain,
( spl0_582
<=> ! [X8,X7] :
( c_List_Odistinct(c_List_Obutlast(X7,X8),X8)
| ~ c_List_Odistinct(X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1537,plain,
( spl0_177
<=> ! [X6,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Otake(X6,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f5099,plain,
( ! [X8,X7] :
( c_List_Odistinct(c_List_Obutlast(X7,X8),X8)
| ~ c_List_Odistinct(X7,X8) )
| ~ spl0_177
| ~ spl0_394 ),
inference(superposition,[],[f1538,f4540]) ).
fof(f1538,plain,
( ! [X0,X6,X12] :
( c_List_Odistinct(c_List_Otake(X6,X12,X0),X0)
| ~ c_List_Odistinct(X12,X0) )
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f10476,plain,
spl0_581,
inference(avatar_split_clause,[],[f430,f10474]) ).
fof(f10474,plain,
( spl0_581
<=> ! [X0,X12,X5,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otake(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f430,axiom,
! [X3,X0,X5,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otake(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__Cons_H_1) ).
fof(f10472,plain,
spl0_580,
inference(avatar_split_clause,[],[f386,f10470]) ).
fof(f10470,plain,
( spl0_580
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f386,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f10468,plain,
spl0_579,
inference(avatar_split_clause,[],[f380,f10466]) ).
fof(f10466,plain,
( spl0_579
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f380,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__diff__eq_0) ).
fof(f10464,plain,
spl0_578,
inference(avatar_split_clause,[],[f329,f10462]) ).
fof(f10462,plain,
( spl0_578
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f329,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__add__eq_0) ).
fof(f10460,plain,
spl0_577,
inference(avatar_split_clause,[],[f248,f10458]) ).
fof(f10458,plain,
( spl0_577
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_Power_Opower__class_Opower(X9,c_Suc(X3),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f248,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_lessequals(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_Power_Opower__class_Opower(X9,c_Suc(X3),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__le__imp__le__base_0) ).
fof(f10456,plain,
spl0_576,
inference(avatar_split_clause,[],[f209,f10454]) ).
fof(f10454,plain,
( spl0_576
<=> ! [X5,X0,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f209,axiom,
! [X0,X8,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X5
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonneg__eq__0__iff_0) ).
fof(f10452,plain,
spl0_575,
inference(avatar_split_clause,[],[f208,f10450]) ).
fof(f10450,plain,
( spl0_575
<=> ! [X5,X0,X8] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f208,axiom,
! [X0,X8,X5] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X8
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X5,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonneg__eq__0__iff_1) ).
fof(f10379,plain,
spl0_574,
inference(avatar_split_clause,[],[f496,f10377]) ).
fof(f10377,plain,
( spl0_574
<=> ! [X5,X33,X0,X12,X6,X19] :
( X6 = X33
| c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X33,X19,X0) = c_List_Olist__update(c_List_Olist__update(X12,X33,X19,X0),X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f496,axiom,
! [X0,X6,X19,X5,X12,X33] :
( X6 = X33
| c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X33,X19,X0) = c_List_Olist__update(c_List_Olist__update(X12,X33,X19,X0),X6,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__swap_0) ).
fof(f10375,plain,
spl0_573,
inference(avatar_split_clause,[],[f423,f10373]) ).
fof(f10373,plain,
( spl0_573
<=> ! [X5,X13,X0,X12,X8] : c_List_Olist__update(c_List_Oappend(X12,c_List_Olist_OCons(X5,X13,X0),X0),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X8,X0) = c_List_Oappend(X12,c_List_Olist_OCons(X8,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f423,axiom,
! [X0,X8,X5,X12,X13] : c_List_Olist__update(c_List_Oappend(X12,c_List_Olist_OCons(X5,X13,X0),X0),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X8,X0) = c_List_Oappend(X12,c_List_Olist_OCons(X8,X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__length_0) ).
fof(f10102,plain,
( spl0_572
| ~ spl0_205
| ~ spl0_279
| ~ spl0_377
| ~ spl0_413
| ~ spl0_476
| ~ spl0_571 ),
inference(avatar_split_clause,[],[f10098,f10095,f7566,f4620,f4444,f2528,f1788,f10100]) ).
fof(f1788,plain,
( spl0_205
<=> ! [X5,X0,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f4444,plain,
( spl0_377
<=> ! [X5,X0,X12] : c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f4620,plain,
( spl0_413
<=> ! [X34,X0,X12,X32] : c_List_Oappend(X12,c_List_Oappend(X32,X34,X0),X0) = c_List_Oappend(c_List_Oappend(X12,X32,X0),X34,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f10095,plain,
( spl0_571
<=> ! [X0,X12,X5,X3] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f10098,plain,
( ! [X3,X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0) = c_List_Oappend(c_List_Oreplicate(c_Suc(X3),X5,X0),X12,X0)
| ~ spl0_205
| ~ spl0_279
| ~ spl0_377
| ~ spl0_413
| ~ spl0_476
| ~ spl0_571 ),
inference(forward_demodulation,[],[f10096,f7633]) ).
fof(f7633,plain,
( ! [X59,X62,X60,X61] : c_List_Oappend(c_List_Oreplicate(c_Suc(X59),X60,X61),X62,X61) = c_List_Oappend(c_List_Oreplicate(X59,X60,X61),c_List_Olist_OCons(X60,X62,X61),X61)
| ~ spl0_205
| ~ spl0_279
| ~ spl0_377
| ~ spl0_413
| ~ spl0_476 ),
inference(forward_demodulation,[],[f7626,f4460]) ).
fof(f4460,plain,
( ! [X2,X0,X1] : c_List_Olist_OCons(X0,X1,X2) = c_List_Oappend(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X2),X1,X2)
| ~ spl0_205
| ~ spl0_279
| ~ spl0_377 ),
inference(forward_demodulation,[],[f4457,f1789]) ).
fof(f1789,plain,
( ! [X0,X5,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f4457,plain,
( ! [X2,X0,X1] : c_List_Olist_OCons(X0,X1,X2) = c_List_Oappend(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X2),c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X0,X1,X2),X2),X2)
| ~ spl0_279
| ~ spl0_377 ),
inference(superposition,[],[f2529,f4445]) ).
fof(f4445,plain,
( ! [X0,X5,X12] : c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0)
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4444]) ).
fof(f7626,plain,
( ! [X59,X62,X60,X61] : c_List_Oappend(c_List_Oreplicate(X59,X60,X61),c_List_Oappend(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X60,X61),X62,X61),X61) = c_List_Oappend(c_List_Oreplicate(c_Suc(X59),X60,X61),X62,X61)
| ~ spl0_413
| ~ spl0_476 ),
inference(superposition,[],[f4621,f7567]) ).
fof(f4621,plain,
( ! [X0,X34,X12,X32] : c_List_Oappend(X12,c_List_Oappend(X32,X34,X0),X0) = c_List_Oappend(c_List_Oappend(X12,X32,X0),X34,X0)
| ~ spl0_413 ),
inference(avatar_component_clause,[],[f4620]) ).
fof(f10096,plain,
( ! [X3,X0,X5,X12] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0)
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f10095]) ).
fof(f10097,plain,
spl0_571,
inference(avatar_split_clause,[],[f498,f10095]) ).
fof(f498,axiom,
! [X3,X0,X5,X12] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Oappend(c_List_Oreplicate(X3,X5,X0),X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__app__Cons__same_0) ).
fof(f10093,plain,
spl0_570,
inference(avatar_split_clause,[],[f444,f10091]) ).
fof(f10091,plain,
( spl0_570
<=> ! [X5,X13,X0,X12,X8] : c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),c_List_Olist_OCons(X8,X13,X0),X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,c_List_Osplice(X12,X13,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f444,axiom,
! [X0,X8,X5,X12,X13] : c_List_Osplice(c_List_Olist_OCons(X5,X12,X0),c_List_Olist_OCons(X8,X13,X0),X0) = c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,c_List_Osplice(X12,X13,X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_splice__Cons__Cons_0) ).
fof(f10089,plain,
spl0_569,
inference(avatar_split_clause,[],[f424,f10087]) ).
fof(f10087,plain,
( spl0_569
<=> ! [X0,X12,X28] :
( c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0) != X12
| c_List_Oappend(X12,c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0),X0) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f424,axiom,
! [X28,X0,X12] :
( c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0) != X12
| c_List_Oappend(X12,c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X28,X0),X0) = X28 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__conv__conj_2) ).
fof(f10085,plain,
spl0_568,
inference(avatar_split_clause,[],[f410,f10083]) ).
fof(f410,axiom,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otake(c_Suc(X3),X12,X0) = c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Otake(X3,c_List_Otl(X12,X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__Suc_0) ).
fof(f10081,plain,
spl0_567,
inference(avatar_split_clause,[],[f408,f10079]) ).
fof(f10079,plain,
( spl0_567
<=> ! [X0,X8,X5,X28] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X8,X28,X0),X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f408,axiom,
! [X28,X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X8,X28,X0),X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted_Osimps_I3_J_2) ).
fof(f10077,plain,
spl0_566,
inference(avatar_split_clause,[],[f356,f10075]) ).
fof(f10075,plain,
( spl0_566
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f356,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__mono_0) ).
fof(f10073,plain,
( ~ spl0_564
| spl0_296
| ~ spl0_565
| ~ spl0_123
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f4266,f3702,f1277,f10070,f2771,f10066]) ).
fof(f10066,plain,
( spl0_564
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2771,plain,
( spl0_296
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f10070,plain,
( spl0_565
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1277,plain,
( spl0_123
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f3702,plain,
( spl0_361
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f4266,plain,
( ! [X4] :
( ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_123
| ~ spl0_361 ),
inference(trivial_inequality_removal,[],[f4261]) ).
fof(f4261,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Int_Onumber__ring(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_Ring__and__Field_Oidom(tc_nat) )
| ~ spl0_123
| ~ spl0_361 ),
inference(superposition,[],[f3703,f1278]) ).
fof(f1278,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f3703,plain,
( ! [X0,X8,X5] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3702]) ).
fof(f10064,plain,
spl0_563,
inference(avatar_split_clause,[],[f157,f10062]) ).
fof(f10062,plain,
( spl0_563
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f157,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__Suc__less__one_0) ).
fof(f10060,plain,
spl0_562,
inference(avatar_split_clause,[],[f115,f10058]) ).
fof(f10058,plain,
( spl0_562
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f115,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X4,X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__less__imp__less__exp_0) ).
fof(f10056,plain,
spl0_561,
inference(avatar_split_clause,[],[f114,f10054]) ).
fof(f10054,plain,
( spl0_561
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f114,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X1,X2,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__strict__increasing_0) ).
fof(f10052,plain,
spl0_560,
inference(avatar_split_clause,[],[f53,f10050]) ).
fof(f10050,plain,
( spl0_560
<=> ! [X3,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f53,axiom,
! [X3,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X3,X0),c_Power_Opower__class_Opower(X9,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__less__imp__less__base_0) ).
fof(f9936,plain,
( spl0_559
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f9118,f9114,f2987,f1289,f1083,f9934]) ).
fof(f9934,plain,
( spl0_559
<=> ! [X0,X13,X12,X5,X8] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X12 = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f9114,plain,
( spl0_550
<=> ! [X5,X13,X0,X12,X8] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f9118,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X12 = X13 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_550 ),
inference(forward_demodulation,[],[f9117,f3524]) ).
fof(f9117,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0)
| X12 = X13 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_550 ),
inference(forward_demodulation,[],[f9115,f3524]) ).
fof(f9115,plain,
( ! [X0,X8,X5,X12,X13] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f9114]) ).
fof(f9932,plain,
( spl0_558
| ~ spl0_107
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3508,f2987,f1206,f9930]) ).
fof(f3508,plain,
( ! [X10,X11,X9] : c_List_Olist_ONil(X11) != c_List_Oreplicate(c_Suc(X10),X9,X11)
| ~ spl0_107
| ~ spl0_320 ),
inference(superposition,[],[f1207,f2988]) ).
fof(f9928,plain,
( spl0_557
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_549 ),
inference(avatar_split_clause,[],[f9112,f9108,f2987,f1289,f1083,f9926]) ).
fof(f9926,plain,
( spl0_557
<=> ! [X0,X13,X12,X5,X8] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X5 = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f9108,plain,
( spl0_549
<=> ! [X13,X0,X12,X5,X8] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f9112,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) != c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| X5 = X8 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_549 ),
inference(forward_demodulation,[],[f9111,f3524]) ).
fof(f9111,plain,
( ! [X0,X8,X5,X12,X13] :
( c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0)
| X5 = X8 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_549 ),
inference(forward_demodulation,[],[f9109,f3524]) ).
fof(f9109,plain,
( ! [X0,X8,X5,X12,X13] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_549 ),
inference(avatar_component_clause,[],[f9108]) ).
fof(f9924,plain,
( spl0_556
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f9106,f9103,f2987,f1289,f1083,f9922]) ).
fof(f9922,plain,
( spl0_556
<=> ! [X13,X0,X12,X8] :
( c_List_Oappend(c_List_Orev(X13,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f9103,plain,
( spl0_548
<=> ! [X13,X0,X12,X8] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f9106,plain,
( ! [X0,X8,X12,X13] :
( c_List_Oappend(c_List_Orev(X13,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X8,X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0) )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_548 ),
inference(forward_demodulation,[],[f9104,f3524]) ).
fof(f9104,plain,
( ! [X0,X8,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 )
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f9103]) ).
fof(f9920,plain,
( spl0_555
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_547 ),
inference(avatar_split_clause,[],[f9101,f9098,f2987,f1289,f1083,f9918]) ).
fof(f9918,plain,
( spl0_555
<=> ! [X0,X12] :
( c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Ohd(X12,X0),X0),X0)
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f9098,plain,
( spl0_547
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f9101,plain,
( ! [X0,X12] :
( c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Ohd(X12,X0),X0),X0)
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_547 ),
inference(forward_demodulation,[],[f9099,f3524]) ).
fof(f9099,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) )
| ~ spl0_547 ),
inference(avatar_component_clause,[],[f9098]) ).
fof(f9766,plain,
( spl0_554
| ~ spl0_92
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3507,f2987,f1145,f9764]) ).
fof(f3507,plain,
( ! [X8,X6,X7] : c_List_Omember(X6,c_List_Oreplicate(c_Suc(X7),X6,X8),X8)
| ~ spl0_92
| ~ spl0_320 ),
inference(superposition,[],[f1146,f2988]) ).
fof(f9499,plain,
( spl0_553
| ~ spl0_122
| ~ spl0_204 ),
inference(avatar_split_clause,[],[f2006,f1784,f1273,f9497]) ).
fof(f9497,plain,
( spl0_553
<=> ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_Suc(X2),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2006,plain,
( ! [X2] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X2,c_Suc(X2),tc_nat)
| ~ spl0_122
| ~ spl0_204 ),
inference(superposition,[],[f1785,f1274]) ).
fof(f9138,plain,
( spl0_552
| ~ spl0_47
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2003,f1780,f944,f9136]) ).
fof(f9136,plain,
( spl0_552
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X1,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f944,plain,
( spl0_47
<=> class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1780,plain,
( spl0_203
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f2003,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Int_Oint),X1,tc_Int_Oint)
| ~ spl0_47
| ~ spl0_203 ),
inference(resolution,[],[f1781,f946]) ).
fof(f946,plain,
( class_OrderedGroup_Omonoid__mult(tc_Int_Oint)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f944]) ).
fof(f1781,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f1780]) ).
fof(f9123,plain,
spl0_551,
inference(avatar_split_clause,[],[f608,f9120]) ).
fof(f9120,plain,
( spl0_551
<=> c_in(c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),v_h____,v_n____,tc_Arrow__Order__Mirabelle_Oindi,tc_nat)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f608,axiom,
c_in(c_Pair(v_c____,v_d____,tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_P____,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_bool)),v_h____,v_n____,tc_Arrow__Order__Mirabelle_Oindi,tc_nat)),tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_CHAINED_0_01) ).
fof(f9116,plain,
spl0_550,
inference(avatar_split_clause,[],[f583,f9114]) ).
fof(f583,axiom,
! [X0,X8,X5,X12,X13] :
( X12 = X13
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append1__eq__conv_0) ).
fof(f9110,plain,
spl0_549,
inference(avatar_split_clause,[],[f582,f9108]) ).
fof(f582,axiom,
! [X0,X8,X5,X12,X13] :
( X5 = X8
| c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) != c_List_Oappend(X13,c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append1__eq__conv_1) ).
fof(f9105,plain,
spl0_548,
inference(avatar_split_clause,[],[f519,f9103]) ).
fof(f519,axiom,
! [X0,X8,X12,X13] :
( c_List_Orev(X12,X0) != c_List_Olist_OCons(X8,X13,X0)
| c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__eq__Cons__iff_0) ).
fof(f9100,plain,
spl0_547,
inference(avatar_split_clause,[],[f434,f9098]) ).
fof(f434,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Orotate1(X12,X0) = c_List_Oappend(c_List_Otl(X12,X0),c_List_Olist_OCons(c_List_Ohd(X12,X0),c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate1__hd__tl_0) ).
fof(f9096,plain,
spl0_546,
inference(avatar_split_clause,[],[f431,f9094]) ).
fof(f9094,plain,
( spl0_546
<=> ! [X0,X12,X5,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Odrop(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f431,axiom,
! [X3,X0,X5,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Odrop(X3,c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__Cons_H_1) ).
fof(f9092,plain,
spl0_545,
inference(avatar_split_clause,[],[f415,f9090]) ).
fof(f9090,plain,
( spl0_545
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f415,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__list__update_0) ).
fof(f9088,plain,
spl0_544,
inference(avatar_split_clause,[],[f379,f9086]) ).
fof(f9086,plain,
( spl0_544
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f379,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X5,X7,X0),c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__add__distrib__left_0) ).
fof(f9084,plain,
spl0_543,
inference(avatar_split_clause,[],[f349,f9082]) ).
fof(f9082,plain,
( spl0_543
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f349,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__add__left__eq_0) ).
fof(f9080,plain,
( spl0_542
| ~ spl0_16
| ~ spl0_203 ),
inference(avatar_split_clause,[],[f2002,f1780,f789,f9078]) ).
fof(f9078,plain,
( spl0_542
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f789,plain,
( spl0_16
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f2002,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_16
| ~ spl0_203 ),
inference(resolution,[],[f1781,f791]) ).
fof(f791,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f9076,plain,
spl0_541,
inference(avatar_split_clause,[],[f344,f9074]) ).
fof(f9074,plain,
( spl0_541
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f344,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__diff__right__eq_0) ).
fof(f9072,plain,
spl0_540,
inference(avatar_split_clause,[],[f343,f9070]) ).
fof(f9070,plain,
( spl0_540
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f343,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X10,X0),X9,X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__diff__left__eq_0) ).
fof(f9068,plain,
spl0_539,
inference(avatar_split_clause,[],[f342,f9066]) ).
fof(f9066,plain,
( spl0_539
<=> ! [X0,X8,X5,X25,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X25
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X8,X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f342,axiom,
! [X0,X8,X7,X5,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,X7,X0) = X25
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) != c_HOL_Oplus__class_Oplus(X8,X25,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__cancel__21_0) ).
fof(f9064,plain,
spl0_538,
inference(avatar_split_clause,[],[f330,f9062]) ).
fof(f9062,plain,
( spl0_538
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f330,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonneg__nonneg_0) ).
fof(f9060,plain,
spl0_537,
inference(avatar_split_clause,[],[f324,f9058]) ).
fof(f9058,plain,
( spl0_537
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X10,X11,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f324,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_lessequals(X10,X11,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__mono_0) ).
fof(f9056,plain,
spl0_536,
inference(avatar_split_clause,[],[f308,f9054]) ).
fof(f9054,plain,
( spl0_536
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ominus__class_Ominus(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f308,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X7,X0),c_HOL_Ominus__class_Ominus(X8,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__diff__distrib__left_0) ).
fof(f9052,plain,
spl0_535,
inference(avatar_split_clause,[],[f287,f9050]) ).
fof(f9050,plain,
( spl0_535
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f287,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__eq__0__iff_2) ).
fof(f9048,plain,
spl0_534,
inference(avatar_split_clause,[],[f276,f9046]) ).
fof(f9046,plain,
( spl0_534
<=> ! [X10,X0,X9,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f276,axiom,
! [X10,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X9,X10,X0),X0),X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zmod__simps_I2_J_0) ).
fof(f9044,plain,
spl0_533,
inference(avatar_split_clause,[],[f266,f9042]) ).
fof(f9042,plain,
( spl0_533
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f266,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_le__add__right__mono_0) ).
fof(f9040,plain,
spl0_532,
inference(avatar_split_clause,[],[f262,f9038]) ).
fof(f9038,plain,
( spl0_532
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f262,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonpos__nonpos_0) ).
fof(f9036,plain,
( spl0_531
| ~ spl0_50
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2001,f1776,f959,f9034]) ).
fof(f9034,plain,
( spl0_531
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f959,plain,
( spl0_50
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1776,plain,
( spl0_202
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2001,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint)
| ~ spl0_50
| ~ spl0_202 ),
inference(resolution,[],[f1777,f961]) ).
fof(f961,plain,
( class_Divides_Osemiring__div(tc_Int_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f959]) ).
fof(f1777,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f1776]) ).
fof(f9032,plain,
spl0_530,
inference(avatar_split_clause,[],[f191,f9030]) ).
fof(f9030,plain,
( spl0_530
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f191,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__increasing_0) ).
fof(f9028,plain,
spl0_529,
inference(avatar_split_clause,[],[f190,f9026]) ).
fof(f9026,plain,
( spl0_529
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f190,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X10,X0)
| c_lessequals(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__increasing2_0) ).
fof(f9024,plain,
spl0_528,
inference(avatar_split_clause,[],[f96,f9022]) ).
fof(f9022,plain,
( spl0_528
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f96,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__strict__mono_0) ).
fof(f9020,plain,
spl0_527,
inference(avatar_split_clause,[],[f88,f9018]) ).
fof(f9018,plain,
( spl0_527
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f88,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__pos__pos_0) ).
fof(f9016,plain,
spl0_526,
inference(avatar_split_clause,[],[f51,f9014]) ).
fof(f9014,plain,
( spl0_526
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f51,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__pos__nonneg_0) ).
fof(f9012,plain,
spl0_525,
inference(avatar_split_clause,[],[f50,f9010]) ).
fof(f9010,plain,
( spl0_525
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f50,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonneg__pos_0) ).
fof(f9008,plain,
spl0_524,
inference(avatar_split_clause,[],[f49,f9006]) ).
fof(f9006,plain,
( spl0_524
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f49,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__strict__increasing2_0) ).
fof(f9004,plain,
spl0_523,
inference(avatar_split_clause,[],[f48,f9002]) ).
fof(f9002,plain,
( spl0_523
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f48,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__strict__increasing_0) ).
fof(f9000,plain,
spl0_522,
inference(avatar_split_clause,[],[f47,f8998]) ).
fof(f8998,plain,
( spl0_522
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f47,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonpos__neg_0) ).
fof(f8996,plain,
spl0_521,
inference(avatar_split_clause,[],[f46,f8994]) ).
fof(f8994,plain,
( spl0_521
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f46,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__neg__nonpos_0) ).
fof(f8992,plain,
( spl0_520
| ~ spl0_18
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2000,f1776,f799,f8990]) ).
fof(f8990,plain,
( spl0_520
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f799,plain,
( spl0_18
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f2000,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_18
| ~ spl0_202 ),
inference(resolution,[],[f1777,f801]) ).
fof(f801,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f799]) ).
fof(f8988,plain,
spl0_519,
inference(avatar_split_clause,[],[f38,f8986]) ).
fof(f8986,plain,
( spl0_519
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f38,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X10,X11,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__le__mono_0) ).
fof(f8984,plain,
spl0_518,
inference(avatar_split_clause,[],[f37,f8982]) ).
fof(f8982,plain,
( spl0_518
<=> ! [X10,X11,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f37,axiom,
! [X10,X0,X11,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(X10,X11,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__le__less__mono_0) ).
fof(f8980,plain,
spl0_517,
inference(avatar_split_clause,[],[f25,f8978]) ).
fof(f8978,plain,
( spl0_517
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f25,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__neg__neg_0) ).
fof(f8976,plain,
spl0_516,
inference(avatar_split_clause,[],[f24,f8974]) ).
fof(f8974,plain,
( spl0_516
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f24,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_one__less__power_0) ).
fof(f8709,plain,
( spl0_515
| ~ spl0_58
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1997,f1768,f999,f8707]) ).
fof(f8707,plain,
( spl0_515
<=> ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f1768,plain,
( spl0_200
<=> ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1997,plain,
( ! [X1] : c_HOL_Oone__class_Oone(tc_Int_Oint) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_Int_Oint)
| ~ spl0_58
| ~ spl0_200 ),
inference(resolution,[],[f1769,f1001]) ).
fof(f1769,plain,
( ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f1768]) ).
fof(f8700,plain,
spl0_514,
inference(avatar_split_clause,[],[f432,f8698]) ).
fof(f8698,plain,
( spl0_514
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f432,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Otl(c_List_Oreplicate(X3,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_tl__replicate_0) ).
fof(f8696,plain,
spl0_513,
inference(avatar_split_clause,[],[f281,f8694]) ).
fof(f8694,plain,
( spl0_513
<=> ! [X6,X0,X12] : c_List_Orev(c_List_Otake(X6,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f281,axiom,
! [X0,X6,X12] : c_List_Orev(c_List_Otake(X6,X12,X0),X0) = c_List_Odrop(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__take_0) ).
fof(f8692,plain,
spl0_512,
inference(avatar_split_clause,[],[f280,f8690]) ).
fof(f8690,plain,
( spl0_512
<=> ! [X6,X0,X12] : c_List_Orev(c_List_Odrop(X6,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f280,axiom,
! [X0,X6,X12] : c_List_Orev(c_List_Odrop(X6,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X6,tc_nat),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__drop_0) ).
fof(f8688,plain,
spl0_511,
inference(avatar_split_clause,[],[f273,f8686]) ).
fof(f8686,plain,
( spl0_511
<=> ! [X19,X0,X5,X8,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X5,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f273,axiom,
! [X0,X8,X19,X5,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X5,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_le__eqI_0) ).
fof(f8684,plain,
spl0_510,
inference(avatar_split_clause,[],[f250,f8682]) ).
fof(f8682,plain,
( spl0_510
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f250,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__eq__0__iff_0) ).
fof(f8680,plain,
spl0_509,
inference(avatar_split_clause,[],[f140,f8678]) ).
fof(f8678,plain,
( spl0_509
<=> ! [X19,X20,X0,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f140,axiom,
! [X0,X8,X19,X5,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Ominus__class_Ominus(X5,X8,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__eqI_1) ).
fof(f8676,plain,
spl0_508,
inference(avatar_split_clause,[],[f106,f8674]) ).
fof(f8674,plain,
( spl0_508
<=> ! [X4,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X1,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f106,axiom,
! [X3,X0,X1,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X3,X0) != c_Power_Opower__class_Opower(X1,X4,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__inject__exp_0) ).
fof(f8666,plain,
( spl0_507
| ~ spl0_22
| ~ spl0_200 ),
inference(avatar_split_clause,[],[f1996,f1768,f819,f8664]) ).
fof(f8664,plain,
( spl0_507
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f1996,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_200 ),
inference(resolution,[],[f1769,f821]) ).
fof(f8586,plain,
( spl0_506
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f7764,f7761,f2987,f1289,f1083,f8584]) ).
fof(f8584,plain,
( spl0_506
<=> ! [X9,X1] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__CHAINED__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f7761,plain,
( spl0_500
<=> ! [X9,X1] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f7764,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__CHAINED__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_500 ),
inference(forward_demodulation,[],[f7762,f3524]) ).
fof(f7762,plain,
( ! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f7761]) ).
fof(f8582,plain,
( spl0_505
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_499 ),
inference(avatar_split_clause,[],[f7759,f7756,f2987,f1289,f1083,f8580]) ).
fof(f7756,plain,
( spl0_499
<=> ! [X9,X1] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f7759,plain,
( ! [X1,X9] :
( c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt)
| X1 = X9 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_499 ),
inference(forward_demodulation,[],[f7757,f3524]) ).
fof(f7757,plain,
( ! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) )
| ~ spl0_499 ),
inference(avatar_component_clause,[],[f7756]) ).
fof(f8551,plain,
( spl0_504
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f7750,f7747,f2987,f1289,f1083,f8549]) ).
fof(f8549,plain,
( spl0_504
<=> ! [X0,X12] :
( c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Olast(X12,X0),X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f7747,plain,
( spl0_497
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f7750,plain,
( ! [X0,X12] :
( c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),c_List_Olast(X12,X0),X0),X0) = X12
| c_List_Olist_ONil(X0) = X12 )
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_497 ),
inference(forward_demodulation,[],[f7748,f3524]) ).
fof(f7748,plain,
( ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 )
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f7747]) ).
fof(f8391,plain,
( spl0_503
| ~ spl0_50
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f1995,f1764,f959,f8389]) ).
fof(f8389,plain,
( spl0_503
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f1764,plain,
( spl0_199
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1995,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_Int_Oint),tc_Int_Oint)
| ~ spl0_50
| ~ spl0_199 ),
inference(resolution,[],[f1765,f961]) ).
fof(f1765,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f1764]) ).
fof(f7837,plain,
( spl0_502
| ~ spl0_121
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1665,f1493,f1269,f7835]) ).
fof(f7835,plain,
( spl0_502
<=> ! [X7] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X7),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f1665,plain,
( ! [X7] : c_HOL_Oone__class_Oone(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X7),X7,tc_nat)
| ~ spl0_121
| ~ spl0_166 ),
inference(superposition,[],[f1494,f1270]) ).
fof(f7768,plain,
spl0_501,
inference(avatar_split_clause,[],[f689,f7766]) ).
fof(f7766,plain,
( spl0_501
<=> ! [X0,X14,X5,X3] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f689,plain,
! [X3,X0,X14,X5] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),X5,X0),
inference(forward_demodulation,[],[f485,f409]) ).
fof(f409,axiom,
! [X3,X0,X4,X5] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X5,X0) = c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X4,X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__add_0) ).
fof(f485,axiom,
! [X3,X0,X14,X5] : c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oappend(c_List_Oreplicate(X14,X5,X0),c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__replicate__commute_0) ).
fof(f7763,plain,
spl0_500,
inference(avatar_split_clause,[],[f607,f7761]) ).
fof(f607,axiom,
! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__CHAINED__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_CHAINED_0) ).
fof(f7758,plain,
spl0_499,
inference(avatar_split_clause,[],[f596,f7756]) ).
fof(f596,axiom,
! [X1,X9] :
( X1 = X9
| c_List_Odistinct(c_List_Olist_OCons(X1,c_List_Olist_OCons(X9,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xthird__alt__1(X1,X9),c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_third__alt_0) ).
fof(f7754,plain,
spl0_498,
inference(avatar_split_clause,[],[f482,f7752]) ).
fof(f7752,plain,
( spl0_498
<=> ! [X5,X13,X0,X12] : c_List_OremoveAll(X5,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_OremoveAll(X5,X12,X0),c_List_OremoveAll(X5,X13,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f482,axiom,
! [X0,X5,X12,X13] : c_List_OremoveAll(X5,c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_OremoveAll(X5,X12,X0),c_List_OremoveAll(X5,X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_removeAll__append_0) ).
fof(f7749,plain,
spl0_497,
inference(avatar_split_clause,[],[f478,f7747]) ).
fof(f478,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(c_List_Obutlast(X12,X0),c_List_Olist_OCons(c_List_Olast(X12,X0),c_List_Olist_ONil(X0),X0),X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__butlast__last__id_0) ).
fof(f7745,plain,
spl0_496,
inference(avatar_split_clause,[],[f443,f7743]) ).
fof(f7743,plain,
( spl0_496
<=> ! [X5,X0,X12,X8] :
( X5 = X8
| c_List_Oremove1(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_Oremove1(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f443,axiom,
! [X0,X8,X5,X12] :
( X5 = X8
| c_List_Oremove1(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_Oremove1(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remove1_Osimps_I2_J_1) ).
fof(f7741,plain,
spl0_495,
inference(avatar_split_clause,[],[f442,f7739]) ).
fof(f7739,plain,
( spl0_495
<=> ! [X5,X0,X12,X8] :
( X5 = X8
| c_List_OremoveAll(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_OremoveAll(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f442,axiom,
! [X0,X8,X5,X12] :
( X5 = X8
| c_List_OremoveAll(X5,c_List_Olist_OCons(X8,X12,X0),X0) = c_List_Olist_OCons(X8,c_List_OremoveAll(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_removeAll_Osimps_I2_J_1) ).
fof(f7737,plain,
spl0_494,
inference(avatar_split_clause,[],[f412,f7735]) ).
fof(f7735,plain,
( spl0_494
<=> ! [X4,X0,X12,X3] : c_List_Odrop(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_List_Odrop(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f412,axiom,
! [X3,X0,X4,X12] : c_List_Odrop(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_List_Odrop(X3,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__take_0) ).
fof(f7733,plain,
( spl0_493
| ~ spl0_87
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1603,f1417,f1125,f7731]) ).
fof(f7731,plain,
( spl0_493
<=> ! [X9,X8] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X8,X9,tc_nat)),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f1603,plain,
( ! [X8,X9] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X8,X9,tc_nat)),X9,tc_nat)
| ~ spl0_87
| ~ spl0_147 ),
inference(forward_demodulation,[],[f1598,f197]) ).
fof(f1598,plain,
( ! [X8,X9] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,c_Suc(X9),tc_nat),X9,tc_nat)
| ~ spl0_87
| ~ spl0_147 ),
inference(resolution,[],[f1418,f1126]) ).
fof(f7729,plain,
spl0_492,
inference(avatar_split_clause,[],[f411,f7727]) ).
fof(f411,axiom,
! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(X4,c_List_Otake(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__drop_0) ).
fof(f7725,plain,
spl0_491,
inference(avatar_split_clause,[],[f409,f7723]) ).
fof(f7723,plain,
( spl0_491
<=> ! [X4,X0,X5,X3] : c_List_Oreplicate(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X5,X0) = c_List_Oappend(c_List_Oreplicate(X3,X5,X0),c_List_Oreplicate(X4,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f7721,plain,
spl0_490,
inference(avatar_split_clause,[],[f322,f7719]) ).
fof(f7719,plain,
( spl0_490
<=> ! [X4,X3] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) = X3
| c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f322,axiom,
! [X3,X4] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) = X3
| c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__Suc_1) ).
fof(f7717,plain,
spl0_489,
inference(avatar_split_clause,[],[f305,f7715]) ).
fof(f7715,plain,
( spl0_489
<=> ! [X5,X0,X12,X6,X8] : c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_Suc(X6),X8,X0) = c_List_Olist_OCons(X5,c_List_Olist__update(X12,X6,X8,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f305,axiom,
! [X0,X8,X6,X5,X12] : c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_Suc(X6),X8,X0) = c_List_Olist_OCons(X5,c_List_Olist__update(X12,X6,X8,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__code_I3_J_0) ).
fof(f7713,plain,
spl0_488,
inference(avatar_split_clause,[],[f283,f7711]) ).
fof(f7711,plain,
( spl0_488
<=> ! [X5,X0,X12] : c_List_Obutlast(X12,X0) = c_List_Obutlast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f283,axiom,
! [X0,X5,X12] : c_List_Obutlast(X12,X0) = c_List_Obutlast(c_List_Olist__update(X12,c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast__list__update_0) ).
fof(f7709,plain,
spl0_487,
inference(avatar_split_clause,[],[f267,f7707]) ).
fof(f267,axiom,
! [X3,X6,X4] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X4,X6,tc_nat),c_HOL_Ominus__class_Ominus(X3,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X4,X3,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__diff_0) ).
fof(f7705,plain,
spl0_486,
inference(avatar_split_clause,[],[f238,f7703]) ).
fof(f7703,plain,
( spl0_486
<=> ! [X13,X0,X12] : c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f238,axiom,
! [X0,X12,X13] : c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__splice_0) ).
fof(f7670,plain,
( spl0_485
| ~ spl0_484 ),
inference(avatar_split_clause,[],[f7666,f7663,f7668]) ).
fof(f7668,plain,
( spl0_485
<=> ! [X13,X0,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f7663,plain,
( spl0_484
<=> ! [X13,X0,X12] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f7666,plain,
( ! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Osplice(X12,X13,X0),tc_List_Olist(X0))
| ~ spl0_484 ),
inference(forward_demodulation,[],[f7664,f238]) ).
fof(f7664,plain,
( ! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat)
| ~ spl0_484 ),
inference(avatar_component_clause,[],[f7663]) ).
fof(f7665,plain,
spl0_484,
inference(avatar_split_clause,[],[f229,f7663]) ).
fof(f229,axiom,
! [X0,X12,X13] : c_Nat_Osize__class_Osize(c_List_Oappend(X12,X13,X0),tc_List_Olist(X0)) = c_HOL_Oplus__class_Oplus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_Nat_Osize__class_Osize(X13,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__append_0) ).
fof(f7661,plain,
( spl0_483
| ~ spl0_86
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1602,f1417,f1121,f7659]) ).
fof(f7659,plain,
( spl0_483
<=> ! [X6,X7] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f1602,plain,
( ! [X6,X7] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)),X6,tc_nat)
| ~ spl0_86
| ~ spl0_147 ),
inference(forward_demodulation,[],[f1597,f196]) ).
fof(f1597,plain,
( ! [X6,X7] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(X6),X7,tc_nat),X6,tc_nat)
| ~ spl0_86
| ~ spl0_147 ),
inference(resolution,[],[f1418,f1122]) ).
fof(f7657,plain,
spl0_482,
inference(avatar_split_clause,[],[f223,f7655]) ).
fof(f223,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__eq__if_1) ).
fof(f7653,plain,
spl0_481,
inference(avatar_split_clause,[],[f111,f7651]) ).
fof(f7651,plain,
( spl0_481
<=> ! [X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f111,axiom,
! [X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_pos__add__strict_0) ).
fof(f7649,plain,
spl0_480,
inference(avatar_split_clause,[],[f97,f7647]) ).
fof(f7647,plain,
( spl0_480
<=> ! [X15,X14,X6,X16] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f97,axiom,
! [X6,X16,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__mono_0) ).
fof(f7645,plain,
spl0_479,
inference(avatar_split_clause,[],[f69,f7643]) ).
fof(f7643,plain,
( spl0_479
<=> ! [X4,X16,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X16,X3,tc_nat),c_HOL_Ominus__class_Ominus(X16,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f69,axiom,
! [X3,X16,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,X16,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X16,X3,tc_nat),c_HOL_Ominus__class_Ominus(X16,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__less__mono2_0) ).
fof(f7641,plain,
spl0_478,
inference(avatar_split_clause,[],[f61,f7639]) ).
fof(f7639,plain,
( spl0_478
<=> ! [X0,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Otake(X3,c_List_Obutlast(X12,X0),X0) = c_List_Otake(X3,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f61,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Otake(X3,c_List_Obutlast(X12,X0),X0) = c_List_Otake(X3,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__butlast_0) ).
fof(f7637,plain,
spl0_477,
inference(avatar_split_clause,[],[f10,f7635]) ).
fof(f7635,plain,
( spl0_477
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f10,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__gr__0_0) ).
fof(f7568,plain,
( spl0_476
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f7078,f7075,f2987,f1289,f1083,f7566]) ).
fof(f7075,plain,
( spl0_472
<=> ! [X5,X0,X6] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Oreplicate(c_Suc(X6),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f7078,plain,
( ! [X0,X6,X5] : c_List_Oreplicate(c_Suc(X6),X5,X0) = c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_472 ),
inference(forward_demodulation,[],[f7076,f3524]) ).
fof(f7076,plain,
( ! [X0,X6,X5] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Oreplicate(c_Suc(X6),X5,X0)
| ~ spl0_472 ),
inference(avatar_component_clause,[],[f7075]) ).
fof(f7505,plain,
( spl0_475
| ~ spl0_143
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1592,f1417,f1400,f7503]) ).
fof(f7503,plain,
( spl0_475
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f1592,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_143
| ~ spl0_147 ),
inference(resolution,[],[f1418,f1401]) ).
fof(f7457,plain,
( spl0_474
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_468 ),
inference(avatar_split_clause,[],[f7061,f7058,f2987,f1289,f1083,f7455]) ).
fof(f7455,plain,
( spl0_474
<=> ! [X5,X0,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f7058,plain,
( spl0_468
<=> ! [X5,X0,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f7061,plain,
( ! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0),X0)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_468 ),
inference(forward_demodulation,[],[f7059,f3524]) ).
fof(f7059,plain,
( ! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0)
| ~ spl0_468 ),
inference(avatar_component_clause,[],[f7058]) ).
fof(f7170,plain,
( spl0_473
| ~ spl0_147
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f2074,f1700,f1417,f7168]) ).
fof(f7168,plain,
( spl0_473
<=> ! [X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X1))),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f1700,plain,
( spl0_183
<=> ! [X10] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X10)),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f2074,plain,
( ! [X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X1))),X1,tc_nat)
| ~ spl0_147
| ~ spl0_183 ),
inference(resolution,[],[f1701,f1418]) ).
fof(f1701,plain,
( ! [X10] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X10)),X10,tc_nat)
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1700]) ).
fof(f7077,plain,
spl0_472,
inference(avatar_split_clause,[],[f688,f7075]) ).
fof(f688,plain,
! [X0,X6,X5] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Oreplicate(c_Suc(X6),X5,X0),
inference(forward_demodulation,[],[f522,f306]) ).
fof(f306,axiom,
! [X3,X0,X5] : c_List_Oreplicate(c_Suc(X3),X5,X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__Suc_0) ).
fof(f522,axiom,
! [X0,X6,X5] : c_List_Oappend(c_List_Oreplicate(X6,X5,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = c_List_Olist_OCons(X5,c_List_Oreplicate(X6,X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__append__same_0) ).
fof(f7073,plain,
spl0_471,
inference(avatar_split_clause,[],[f687,f7071]) ).
fof(f7071,plain,
( spl0_471
<=> ! [X3,X4,X14] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f687,plain,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
inference(forward_demodulation,[],[f384,f355]) ).
fof(f384,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X4),X3,tc_nat),c_Suc(X14),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X14,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__diff__diff_0) ).
fof(f7069,plain,
spl0_470,
inference(avatar_split_clause,[],[f675,f7067]) ).
fof(f7067,plain,
( spl0_470
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f675,plain,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
inference(duplicate_literal_removal,[],[f328]) ).
fof(f328,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__nonneg__eq__0__iff_2) ).
fof(f7065,plain,
spl0_469,
inference(avatar_split_clause,[],[f585,f7063]) ).
fof(f7063,plain,
( spl0_469
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Obutlast(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Obutlast(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f585,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Obutlast(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Obutlast(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast_Osimps_I2_J_1) ).
fof(f7060,plain,
spl0_468,
inference(avatar_split_clause,[],[f518,f7058]) ).
fof(f518,axiom,
! [X0,X5,X12] : c_List_Orev(c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oappend(c_List_Orev(X12,X0),c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev_Osimps_I2_J_0) ).
fof(f7056,plain,
spl0_467,
inference(avatar_split_clause,[],[f499,f7054]) ).
fof(f7054,plain,
( spl0_467
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Obutlast(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Obutlast(X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f499,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Obutlast(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(X12,c_List_Obutlast(X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast__append_1) ).
fof(f7052,plain,
spl0_466,
inference(avatar_split_clause,[],[f481,f7050]) ).
fof(f7050,plain,
( spl0_466
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otl(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otl(X12,X0),X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f481,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Otl(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Otl(X12,X0),X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_tl__append2_0) ).
fof(f7048,plain,
spl0_465,
inference(avatar_split_clause,[],[f428,f7046]) ).
fof(f428,axiom,
! [X3,X0,X12] : c_List_Otl(c_List_Otake(X3,X12,X0),X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),c_List_Otl(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_tl__take_0) ).
fof(f7044,plain,
spl0_464,
inference(avatar_split_clause,[],[f352,f7042]) ).
fof(f7042,plain,
( spl0_464
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) = c_Orderings_Oord__class_Omin(X8,c_Orderings_Oord__class_Omin(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f352,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) = c_Orderings_Oord__class_Omin(X8,c_Orderings_Oord__class_Omin(X5,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__left__commute_0) ).
fof(f7040,plain,
spl0_463,
inference(avatar_split_clause,[],[f351,f7038]) ).
fof(f7038,plain,
( spl0_463
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f351,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__assoc_0) ).
fof(f7036,plain,
spl0_462,
inference(avatar_split_clause,[],[f340,f7034]) ).
fof(f7034,plain,
( spl0_462
<=> ! [X11,X0,X10,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X1,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f340,axiom,
! [X10,X0,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X10,X11,X0),X0) = c_HOL_Oplus__class_Oplus(X10,c_HOL_Oplus__class_Oplus(X1,X11,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f7032,plain,
spl0_461,
inference(avatar_split_clause,[],[f339,f7030]) ).
fof(f7030,plain,
( spl0_461
<=> ! [X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f339,axiom,
! [X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X10,X0),X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f7028,plain,
spl0_460,
inference(avatar_split_clause,[],[f337,f7026]) ).
fof(f7026,plain,
( spl0_460
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f337,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f7024,plain,
spl0_459,
inference(avatar_split_clause,[],[f336,f7022]) ).
fof(f7022,plain,
( spl0_459
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f336,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f7020,plain,
spl0_458,
inference(avatar_split_clause,[],[f335,f7018]) ).
fof(f7018,plain,
( spl0_458
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f335,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X10,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f7016,plain,
spl0_457,
inference(avatar_split_clause,[],[f332,f7014]) ).
fof(f7014,plain,
( spl0_457
<=> ! [X0,X5,X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f332,axiom,
! [X0,X8,X7,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__cancel__21_1) ).
fof(f7012,plain,
spl0_456,
inference(avatar_split_clause,[],[f331,f7010]) ).
fof(f7010,plain,
( spl0_456
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f331,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Oadd__a_0) ).
fof(f6990,plain,
spl0_455,
inference(avatar_split_clause,[],[f231,f6988]) ).
fof(f6988,plain,
( spl0_455
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f231,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diffs0__imp__equal_0) ).
fof(f6986,plain,
spl0_454,
inference(avatar_split_clause,[],[f217,f6984]) ).
fof(f6984,plain,
( spl0_454
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| c_lessequals(X8,X7,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f217,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| c_lessequals(X8,X7,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__le__iff__disj_0) ).
fof(f6982,plain,
spl0_453,
inference(avatar_split_clause,[],[f203,f6980]) ).
fof(f6980,plain,
( spl0_453
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f203,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Ole__inf__iff_2) ).
fof(f6978,plain,
spl0_452,
inference(avatar_split_clause,[],[f138,f6976]) ).
fof(f6976,plain,
( spl0_452
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f138,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__less_0) ).
fof(f6974,plain,
spl0_451,
inference(avatar_split_clause,[],[f76,f6972]) ).
fof(f6972,plain,
( spl0_451
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f76,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0)
| c_HOL_Oord__class_Oless(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__less__iff__disj_0) ).
fof(f6970,plain,
spl0_450,
inference(avatar_split_clause,[],[f68,f6968]) ).
fof(f6968,plain,
( spl0_450
<=> ! [X4,X14,X3,X16] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,X16,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f68,axiom,
! [X3,X16,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X14,X16,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,X16,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__add__eq__less_0) ).
fof(f6966,plain,
spl0_449,
inference(avatar_split_clause,[],[f62,f6964]) ).
fof(f6964,plain,
( spl0_449
<=> ! [X0,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(c_List_Odrop(X3,X12,X0),X0) = c_List_Olast(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f62,axiom,
! [X3,X0,X12] :
( ~ c_HOL_Oord__class_Oless(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(c_List_Odrop(X3,X12,X0),X0) = c_List_Olast(X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__drop_0) ).
fof(f6962,plain,
spl0_448,
inference(avatar_split_clause,[],[f5,f6960]) ).
fof(f6960,plain,
( spl0_448
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f5,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__less__iff__conj_2) ).
fof(f6951,plain,
( spl0_447
| ~ spl0_78
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f6163,f5931,f1083,f6949]) ).
fof(f6949,plain,
( spl0_447
<=> ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f5931,plain,
( spl0_422
<=> ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_Suc(X1),X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f6163,plain,
( ! [X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X0,X1),X1)
| ~ spl0_78
| ~ spl0_422 ),
inference(superposition,[],[f5932,f1085]) ).
fof(f5932,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_Suc(X1),X0,X2),X2)
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f5931]) ).
fof(f6633,plain,
( spl0_446
| ~ spl0_141
| ~ spl0_146 ),
inference(avatar_split_clause,[],[f1588,f1412,f1359,f6631]) ).
fof(f6631,plain,
( spl0_446
<=> ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(c_Suc(c_Suc(X7))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1588,plain,
( ! [X7] : c_HOL_Oord__class_Oless(X7,c_Suc(c_Suc(c_Suc(X7))),tc_nat)
| ~ spl0_141
| ~ spl0_146 ),
inference(resolution,[],[f1413,f1360]) ).
fof(f6152,plain,
spl0_445,
inference(avatar_split_clause,[],[f590,f6150]) ).
fof(f6150,plain,
( spl0_445
<=> ! [X5,X0,X12] :
( c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f590,axiom,
! [X0,X5,X12] :
( c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = X12
| c_List_Orev(X12,X0) != c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_singleton__rev__conv_0) ).
fof(f6148,plain,
spl0_444,
inference(avatar_split_clause,[],[f452,f6146]) ).
fof(f6146,plain,
( spl0_444
<=> ! [X3,X4,X0,X5,X8] :
( X5 = X8
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f452,axiom,
! [X3,X0,X8,X4,X5] :
( X5 = X8
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__eq__replicate_1) ).
fof(f6144,plain,
spl0_443,
inference(avatar_split_clause,[],[f375,f6142]) ).
fof(f6142,plain,
( spl0_443
<=> ! [X0,X5,X8,X7] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X8,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f375,axiom,
! [X0,X8,X7,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X7 = X8
| c_HOL_Oplus__class_Oplus(X5,X8,X0) != c_HOL_Oplus__class_Oplus(X5,X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__ringb_Oadd__cancel_0) ).
fof(f6140,plain,
spl0_442,
inference(avatar_split_clause,[],[f371,f6138]) ).
fof(f6138,plain,
( spl0_442
<=> ! [X0,X12,X3] :
( c_List_Orotate(X3,X12,X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f371,axiom,
! [X3,X0,X12] :
( c_List_Orotate(X3,X12,X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__id_0) ).
fof(f6136,plain,
spl0_441,
inference(avatar_split_clause,[],[f300,f6134]) ).
fof(f6134,plain,
( spl0_441
<=> ! [X0,X12,X5,X3] : c_List_Otake(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f300,axiom,
! [X3,X0,X5,X12] : c_List_Otake(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Olist_OCons(X5,c_List_Otake(X3,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__Suc__Cons_0) ).
fof(f6132,plain,
spl0_440,
inference(avatar_split_clause,[],[f286,f6130]) ).
fof(f6130,plain,
( spl0_440
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f286,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__0__left_1) ).
fof(f6128,plain,
spl0_439,
inference(avatar_split_clause,[],[f285,f6126]) ).
fof(f6126,plain,
( spl0_439
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f285,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__eq__0__iff_1) ).
fof(f6124,plain,
spl0_438,
inference(avatar_split_clause,[],[f271,f6122]) ).
fof(f6122,plain,
( spl0_438
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Suc(c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f271,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Suc(c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Nitpick_Olist__size__simp_I2_J_1) ).
fof(f6120,plain,
spl0_437,
inference(avatar_split_clause,[],[f246,f6118]) ).
fof(f6118,plain,
( spl0_437
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f246,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__left__mono_0) ).
fof(f6112,plain,
spl0_436,
inference(avatar_split_clause,[],[f245,f6110]) ).
fof(f6110,plain,
( spl0_436
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f245,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__right__mono_0) ).
fof(f6108,plain,
spl0_435,
inference(avatar_split_clause,[],[f244,f6106]) ).
fof(f6106,plain,
( spl0_435
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f244,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__le__cancel__left_0) ).
fof(f6104,plain,
spl0_434,
inference(avatar_split_clause,[],[f243,f6102]) ).
fof(f243,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__le__cancel__left_1) ).
fof(f6100,plain,
spl0_433,
inference(avatar_split_clause,[],[f242,f6098]) ).
fof(f242,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__le__cancel__right_0) ).
fof(f6096,plain,
spl0_432,
inference(avatar_split_clause,[],[f241,f6094]) ).
fof(f6094,plain,
( spl0_432
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f241,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__le__cancel__right_1) ).
fof(f6092,plain,
spl0_431,
inference(avatar_split_clause,[],[f193,f6090]) ).
fof(f6090,plain,
( spl0_431
<=> ! [X0,X12] :
( c_List_Oremdups(X12,X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) != c_Nat_Osize__class_Osize(c_List_Oremdups(X12,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f193,axiom,
! [X0,X12] :
( c_List_Oremdups(X12,X0) = X12
| c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) != c_Nat_Osize__class_Osize(c_List_Oremdups(X12,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__remdups__eq_0) ).
fof(f6088,plain,
spl0_430,
inference(avatar_split_clause,[],[f126,f6086]) ).
fof(f6086,plain,
( spl0_430
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f126,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__cancel__left_0) ).
fof(f6084,plain,
spl0_429,
inference(avatar_split_clause,[],[f125,f6082]) ).
fof(f125,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__cancel__left_1) ).
fof(f6080,plain,
spl0_428,
inference(avatar_split_clause,[],[f124,f6078]) ).
fof(f6078,plain,
( spl0_428
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f124,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X1,X0),c_HOL_Oplus__class_Oplus(X10,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__strict__left__mono_0) ).
fof(f6076,plain,
spl0_427,
inference(avatar_split_clause,[],[f123,f6074]) ).
fof(f123,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__cancel__right_0) ).
fof(f6052,plain,
spl0_426,
inference(avatar_split_clause,[],[f122,f6050]) ).
fof(f6050,plain,
( spl0_426
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f122,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__cancel__right_1) ).
fof(f6048,plain,
spl0_425,
inference(avatar_split_clause,[],[f121,f6046]) ).
fof(f6046,plain,
( spl0_425
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f121,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X10,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__strict__right__mono_0) ).
fof(f6044,plain,
spl0_424,
inference(avatar_split_clause,[],[f118,f6042]) ).
fof(f6042,plain,
( spl0_424
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f118,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__if_1) ).
fof(f6040,plain,
spl0_423,
inference(avatar_split_clause,[],[f54,f6038]) ).
fof(f6038,plain,
( spl0_423
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f54,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X3),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__gt1_0) ).
fof(f5933,plain,
( spl0_422
| ~ spl0_79
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f3505,f2987,f1088,f5931]) ).
fof(f3505,plain,
( ! [X2,X0,X1] : ~ c_List_Onull(c_List_Oreplicate(c_Suc(X1),X0,X2),X2)
| ~ spl0_79
| ~ spl0_320 ),
inference(superposition,[],[f1089,f2988]) ).
fof(f5858,plain,
( spl0_421
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f4627,f4624,f2987,f1289,f1083,f5856]) ).
fof(f4624,plain,
( spl0_414
<=> ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f4627,plain,
( ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X36),X36)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_414 ),
inference(forward_demodulation,[],[f4625,f3524]) ).
fof(f4625,plain,
( ! [X36,X5,X12] : c_List_Orotate1(c_List_Olist_OCons(X5,X12,X36),X36) = c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X36),X36),X36)
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f4624]) ).
fof(f4651,plain,
spl0_420,
inference(avatar_split_clause,[],[f709,f4649]) ).
fof(f4649,plain,
( spl0_420
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f709,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4 ),
inference(forward_demodulation,[],[f708,f297]) ).
fof(f297,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_One__nat__def_0) ).
fof(f708,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
inference(forward_demodulation,[],[f707,f297]) ).
fof(f707,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
inference(forward_demodulation,[],[f277,f297]) ).
fof(f277,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__is__1_1) ).
fof(f4647,plain,
spl0_419,
inference(avatar_split_clause,[],[f704,f4645]) ).
fof(f4645,plain,
( spl0_419
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f704,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f703,f297]) ).
fof(f703,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
inference(forward_demodulation,[],[f383,f297]) ).
fof(f383,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__is__1_0) ).
fof(f4643,plain,
spl0_418,
inference(avatar_split_clause,[],[f700,f4641]) ).
fof(f4641,plain,
( spl0_418
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f700,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f699,f297]) ).
fof(f699,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
inference(forward_demodulation,[],[f359,f297]) ).
fof(f359,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_one__is__add_3) ).
fof(f4639,plain,
spl0_417,
inference(avatar_split_clause,[],[f697,f4637]) ).
fof(f4637,plain,
( spl0_417
<=> ! [X4,X3] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f697,plain,
! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f278,f297]) ).
fof(f278,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__is__1_2) ).
fof(f4635,plain,
spl0_416,
inference(avatar_split_clause,[],[f684,f4633]) ).
fof(f4633,plain,
( spl0_416
<=> ! [X13,X0,X8] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X8,c_List_Orev(X13,X0),X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f684,plain,
! [X0,X8,X13] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Orotate1(c_List_Olist_OCons(X8,c_List_Orev(X13,X0),X0),X0),X0),
inference(forward_demodulation,[],[f520,f521]) ).
fof(f520,axiom,
! [X0,X8,X13] : c_List_Olist_OCons(X8,X13,X0) = c_List_Orev(c_List_Oappend(c_List_Orev(X13,X0),c_List_Olist_OCons(X8,c_List_Olist_ONil(X0),X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__eq__Cons__iff_1) ).
fof(f4631,plain,
spl0_415,
inference(avatar_split_clause,[],[f683,f4629]) ).
fof(f4629,plain,
( spl0_415
<=> ! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f683,plain,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X14,X15,tc_nat),tc_nat),
inference(forward_demodulation,[],[f370,f355]) ).
fof(f370,axiom,
! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X14,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__commute_0) ).
fof(f4626,plain,
spl0_414,
inference(avatar_split_clause,[],[f521,f4624]) ).
fof(f4622,plain,
spl0_413,
inference(avatar_split_clause,[],[f503,f4620]) ).
fof(f503,axiom,
! [X0,X34,X12,X32] : c_List_Oappend(X12,c_List_Oappend(X32,X34,X0),X0) = c_List_Oappend(c_List_Oappend(X12,X32,X0),X34,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__appendI_0) ).
fof(f4618,plain,
spl0_412,
inference(avatar_split_clause,[],[f501,f4616]) ).
fof(f4616,plain,
( spl0_412
<=> ! [X5,X0,X12,X6,X8] : c_List_Olist__update(X12,X6,X8,X0) = c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X6,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f501,axiom,
! [X0,X8,X6,X5,X12] : c_List_Olist__update(X12,X6,X8,X0) = c_List_Olist__update(c_List_Olist__update(X12,X6,X5,X0),X6,X8,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__overwrite_0) ).
fof(f4614,plain,
spl0_411,
inference(avatar_split_clause,[],[f461,f4612]) ).
fof(f4612,plain,
( spl0_411
<=> ! [X0,X12,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Otake(X3,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f461,axiom,
! [X3,X0,X12] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Otake(X3,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__eq__Nil_0) ).
fof(f4610,plain,
spl0_410,
inference(avatar_split_clause,[],[f451,f4608]) ).
fof(f4608,plain,
( spl0_410
<=> ! [X13,X0,X12] : c_List_Orev(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Orev(X13,X0),c_List_Orev(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f451,axiom,
! [X0,X12,X13] : c_List_Orev(c_List_Oappend(X12,X13,X0),X0) = c_List_Oappend(c_List_Orev(X13,X0),c_List_Orev(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__append_0) ).
fof(f4606,plain,
spl0_409,
inference(avatar_split_clause,[],[f439,f4604]) ).
fof(f439,axiom,
! [X0,X5,X12,X13] : c_List_Oappend(c_List_Olist_OCons(X5,X12,X0),X13,X0) = c_List_Olist_OCons(X5,c_List_Oappend(X12,X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__Cons_0) ).
fof(f4597,plain,
spl0_408,
inference(avatar_split_clause,[],[f417,f4595]) ).
fof(f4595,plain,
( spl0_408
<=> ! [X6,X0,X14,X5] : c_List_Odrop(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X14,X6,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f417,axiom,
! [X0,X6,X14,X5] : c_List_Odrop(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_HOL_Ominus__class_Ominus(X14,X6,tc_nat),X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__replicate_0) ).
fof(f4593,plain,
spl0_407,
inference(avatar_split_clause,[],[f416,f4591]) ).
fof(f4591,plain,
( spl0_407
<=> ! [X6,X0,X14,X5] : c_List_Otake(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_Orderings_Oord__class_Omin(X6,X14,tc_nat),X5,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f416,axiom,
! [X0,X6,X14,X5] : c_List_Otake(X6,c_List_Oreplicate(X14,X5,X0),X0) = c_List_Oreplicate(c_Orderings_Oord__class_Omin(X6,X14,tc_nat),X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__replicate_0) ).
fof(f4589,plain,
spl0_406,
inference(avatar_split_clause,[],[f407,f4587]) ).
fof(f4587,plain,
( spl0_406
<=> ! [X0,X8,X5,X28] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f407,axiom,
! [X28,X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_OCons(X8,X28,X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted_Osimps_I3_J_0) ).
fof(f4585,plain,
spl0_405,
inference(avatar_split_clause,[],[f405,f4583]) ).
fof(f4583,plain,
( spl0_405
<=> ! [X4,X0,X12,X3] : c_List_Orotate(X4,c_List_Orotate(X3,X12,X0),X0) = c_List_Orotate(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f405,axiom,
! [X3,X0,X4,X12] : c_List_Orotate(X4,c_List_Orotate(X3,X12,X0),X0) = c_List_Orotate(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__rotate_0) ).
fof(f4581,plain,
spl0_404,
inference(avatar_split_clause,[],[f381,f4579]) ).
fof(f4579,plain,
( spl0_404
<=> ! [X4,X3] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f381,axiom,
! [X3,X4] :
( c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__Suc_0) ).
fof(f4577,plain,
spl0_403,
inference(avatar_split_clause,[],[f365,f4575]) ).
fof(f365,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__cancel_0) ).
fof(f4573,plain,
spl0_402,
inference(avatar_split_clause,[],[f364,f4571]) ).
fof(f364,axiom,
! [X3,X14,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X14,tc_nat),c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__cancel2_0) ).
fof(f4569,plain,
spl0_401,
inference(avatar_split_clause,[],[f355,f4567]) ).
fof(f4567,plain,
( spl0_401
<=> ! [X6,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X6,X15,tc_nat),X14,tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f4565,plain,
spl0_400,
inference(avatar_split_clause,[],[f334,f4563]) ).
fof(f334,axiom,
! [X3,X14,X4] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X14,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__assoc_0) ).
fof(f4561,plain,
spl0_399,
inference(avatar_split_clause,[],[f333,f4559]) ).
fof(f4559,plain,
( spl0_399
<=> ! [X5,X7,X8] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f333,axiom,
! [X8,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__left__commute_0) ).
fof(f4557,plain,
spl0_398,
inference(avatar_split_clause,[],[f321,f4555]) ).
fof(f4555,plain,
( spl0_398
<=> ! [X4,X0,X12,X3] : c_List_Otake(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_Orderings_Oord__class_Omin(X3,X4,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f321,axiom,
! [X3,X0,X4,X12] : c_List_Otake(X3,c_List_Otake(X4,X12,X0),X0) = c_List_Otake(c_Orderings_Oord__class_Omin(X3,X4,tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__take_0) ).
fof(f4553,plain,
spl0_397,
inference(avatar_split_clause,[],[f317,f4551]) ).
fof(f4551,plain,
( spl0_397
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f317,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__le__double__add__iff__zero__le__single__add_1) ).
fof(f4549,plain,
spl0_396,
inference(avatar_split_clause,[],[f316,f4547]) ).
fof(f4547,plain,
( spl0_396
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f316,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__le__double__add__iff__zero__le__single__add_0) ).
fof(f4545,plain,
spl0_395,
inference(avatar_split_clause,[],[f307,f4543]) ).
fof(f4543,plain,
( spl0_395
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f307,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__le__power_0) ).
fof(f4541,plain,
spl0_394,
inference(avatar_split_clause,[],[f282,f4539]) ).
fof(f282,axiom,
! [X0,X12] : c_List_Obutlast(X12,X0) = c_List_Otake(c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast__conv__take_0) ).
fof(f4537,plain,
spl0_393,
inference(avatar_split_clause,[],[f270,f4535]) ).
fof(f270,axiom,
! [X0,X12] : c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = c_Nat_Osize__class_Osize(c_List_Otl(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__tl_0) ).
fof(f4533,plain,
spl0_392,
inference(avatar_split_clause,[],[f257,f4531]) ).
fof(f4531,plain,
( spl0_392
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f257,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__add__le__zero__iff__single__add__le__zero_0) ).
fof(f4529,plain,
spl0_391,
inference(avatar_split_clause,[],[f256,f4527]) ).
fof(f4527,plain,
( spl0_391
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f256,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__add__le__zero__iff__single__add__le__zero_1) ).
fof(f4525,plain,
spl0_390,
inference(avatar_split_clause,[],[f252,f4523]) ).
fof(f4523,plain,
( spl0_390
<=> ! [X0,X12] : c_Nat_Osize__class_Osize(c_List_Obutlast(X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f252,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(c_List_Obutlast(X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_HOL_Oone__class_Oone(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__butlast_0) ).
fof(f4521,plain,
spl0_389,
inference(avatar_split_clause,[],[f247,f4519]) ).
fof(f4519,plain,
( spl0_389
<=> ! [X4,X0,X12,X3] : c_List_Odrop(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f247,axiom,
! [X3,X0,X4,X12] : c_List_Odrop(X3,c_List_Odrop(X4,X12,X0),X0) = c_List_Odrop(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__drop_0) ).
fof(f4514,plain,
spl0_388,
inference(avatar_split_clause,[],[f230,f4512]) ).
fof(f4512,plain,
( spl0_388
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f230,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(c_List_Odrop(X3,X12,X0),tc_List_Olist(X0)) = c_HOL_Ominus__class_Ominus(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__drop_0) ).
fof(f4510,plain,
spl0_387,
inference(avatar_split_clause,[],[f224,f4508]) ).
fof(f4508,plain,
( spl0_387
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(c_List_Otake(X3,X12,X0),tc_List_Olist(X0)) = c_Orderings_Oord__class_Omin(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f224,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(c_List_Otake(X3,X12,X0),tc_List_Olist(X0)) = c_Orderings_Oord__class_Omin(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__take_0) ).
fof(f4506,plain,
spl0_386,
inference(avatar_split_clause,[],[f199,f4504]) ).
fof(f4504,plain,
( spl0_386
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f199,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_lessequals(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_one__le__power_0) ).
fof(f4502,plain,
spl0_385,
inference(avatar_split_clause,[],[f182,f4500]) ).
fof(f182,axiom,
! [X3,X0,X12] : c_List_Orotate(X3,X12,X0) = c_List_Orotate(c_Divides_Odiv__class_Omod(X3,c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__conv__mod_0) ).
fof(f4498,plain,
spl0_384,
inference(avatar_split_clause,[],[f75,f4496]) ).
fof(f4496,plain,
( spl0_384
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f75,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X3,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__power_0) ).
fof(f4494,plain,
spl0_383,
inference(avatar_split_clause,[],[f74,f4492]) ).
fof(f4492,plain,
( spl0_383
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f74,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_even__less__0__iff_1) ).
fof(f4490,plain,
spl0_382,
inference(avatar_split_clause,[],[f73,f4488]) ).
fof(f4488,plain,
( spl0_382
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f73,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_even__less__0__iff_0) ).
fof(f4486,plain,
spl0_381,
inference(avatar_split_clause,[],[f72,f4484]) ).
fof(f4484,plain,
( spl0_381
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f72,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f4482,plain,
spl0_380,
inference(avatar_split_clause,[],[f71,f4480]) ).
fof(f4480,plain,
( spl0_380
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f71,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f4478,plain,
spl0_379,
inference(avatar_split_clause,[],[f45,f4476]) ).
fof(f4476,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f45,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f4464,plain,
spl0_378,
inference(avatar_split_clause,[],[f44,f4462]) ).
fof(f4462,plain,
( spl0_378
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f44,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f4446,plain,
( spl0_377
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f3763,f3760,f2987,f1289,f1083,f4444]) ).
fof(f3760,plain,
( spl0_373
<=> ! [X5,X0,X12] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f3763,plain,
( ! [X0,X5,X12] : c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = c_List_Oreplicate(c_HOL_Oone__class_Oone(tc_nat),X5,X0)
| ~ spl0_78
| ~ spl0_126
| ~ spl0_320
| ~ spl0_373 ),
inference(forward_demodulation,[],[f3761,f3524]) ).
fof(f3761,plain,
( ! [X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0)
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f3760]) ).
fof(f4139,plain,
( ~ spl0_375
| spl0_376
| ~ spl0_67
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f3901,f3597,f1039,f4137,f4133]) ).
fof(f4133,plain,
( spl0_375
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f4137,plain,
( spl0_376
<=> ! [X27,X26] : ~ c_HOL_Oord__class_Oless(X26,X27,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f1039,plain,
( spl0_67
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f3597,plain,
( spl0_337
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f3901,plain,
( ! [X26,X27] :
( ~ c_HOL_Oord__class_Oless(X26,X27,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_67
| ~ spl0_337 ),
inference(resolution,[],[f3598,f1040]) ).
fof(f1040,plain,
( ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_67 ),
inference(avatar_component_clause,[],[f1039]) ).
fof(f3598,plain,
( ! [X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f3597]) ).
fof(f3767,plain,
spl0_374,
inference(avatar_split_clause,[],[f592,f3765]) ).
fof(f3765,plain,
( spl0_374
<=> ! [X5,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f592,axiom,
! [X0,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Olast(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last_Osimps_1) ).
fof(f3762,plain,
spl0_373,
inference(avatar_split_clause,[],[f515,f3760]) ).
fof(f515,axiom,
! [X0,X5,X12] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Otake(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__1__Cons_0) ).
fof(f3758,plain,
spl0_372,
inference(avatar_split_clause,[],[f514,f3756]) ).
fof(f514,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_OCons(c_List_Osko__List__Xneq__Nil__conv__1__1(X12,X0),c_List_Osko__List__Xneq__Nil__conv__1__2(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_neq__Nil__conv_0) ).
fof(f3754,plain,
spl0_371,
inference(avatar_split_clause,[],[f512,f3752]) ).
fof(f512,axiom,
! [X0,X8] :
( c_List_Olist_ONil(X0) = X8
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xexhaust__1__1(X8,X0),c_List_Osko__List__Xlist__Xexhaust__1__2(X8,X0),X0) = X8 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list_Oexhaust_0) ).
fof(f3750,plain,
spl0_370,
inference(avatar_split_clause,[],[f507,f3748]) ).
fof(f507,axiom,
! [X0,X18] :
( c_List_Olist_ONil(X0) = X18
| c_List_Olist_OCons(c_List_Osko__List__Xlist__Xnchotomy__1__1(X18,X0),c_List_Osko__List__Xlist__Xnchotomy__1__2(X18,X0),X0) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list_Onchotomy_0) ).
fof(f3746,plain,
spl0_369,
inference(avatar_split_clause,[],[f484,f3744]) ).
fof(f3744,plain,
( spl0_369
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olast(c_List_Oappend(X12,X13,X0),X0) = c_List_Olast(X13,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f484,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olast(c_List_Oappend(X12,X13,X0),X0) = c_List_Olast(X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__append_1) ).
fof(f3742,plain,
spl0_368,
inference(avatar_split_clause,[],[f453,f3740]) ).
fof(f3740,plain,
( spl0_368
<=> ! [X0,X12,X5,X8] : c_List_Olist_OCons(X8,X12,X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_nat),X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f453,axiom,
! [X0,X8,X5,X12] : c_List_Olist_OCons(X8,X12,X0) = c_List_Olist__update(c_List_Olist_OCons(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_nat),X8,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__code_I2_J_0) ).
fof(f3728,plain,
spl0_367,
inference(avatar_split_clause,[],[f450,f3726]) ).
fof(f3726,plain,
( spl0_367
<=> ! [X13,X0,X5,X8] :
( X5 = X8
| c_List_Omember(X5,X13,X0)
| ~ c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f450,axiom,
! [X0,X8,X5,X13] :
( X5 = X8
| c_List_Omember(X5,X13,X0)
| ~ c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_List_Omember_Osimps_I2_J_0) ).
fof(f3724,plain,
spl0_366,
inference(avatar_split_clause,[],[f418,f3722]) ).
fof(f418,axiom,
! [X3,X0,X12] : c_List_Otake(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Otake(c_Suc(X3),X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__tl_0) ).
fof(f3720,plain,
spl0_365,
inference(avatar_split_clause,[],[f385,f3718]) ).
fof(f3718,plain,
( spl0_365
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X4,c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f385,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X4,c_Suc(X3),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__Suc__eq__diff__pred_0) ).
fof(f3716,plain,
spl0_364,
inference(avatar_split_clause,[],[f378,f3714]) ).
fof(f3714,plain,
( spl0_364
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X10,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f378,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X10,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__right__cancel_0) ).
fof(f3712,plain,
spl0_363,
inference(avatar_split_clause,[],[f377,f3710]) ).
fof(f3710,plain,
( spl0_363
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f377,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__left__cancel_0) ).
fof(f3708,plain,
spl0_362,
inference(avatar_split_clause,[],[f376,f3706]) ).
fof(f3706,plain,
( spl0_362
<=> ! [X10,X0,X9,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f376,axiom,
! [X10,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X9 = X10
| c_HOL_Oplus__class_Oplus(X1,X9,X0) != c_HOL_Oplus__class_Oplus(X1,X10,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__imp__eq_0) ).
fof(f3704,plain,
spl0_361,
inference(avatar_split_clause,[],[f367,f3702]) ).
fof(f367,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__ringb_Osubr0__iff_0) ).
fof(f3700,plain,
spl0_360,
inference(avatar_split_clause,[],[f362,f3698]) ).
fof(f3698,plain,
( spl0_360
<=> ! [X5,X0,X8] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f362,axiom,
! [X0,X8,X5] :
( ~ class_Int_Oring__char__0(X0)
| ~ class_Int_Onumber__ring(X0)
| X5 = X8
| c_Int_Onumber__class_Onumber__of(X5,X0) != c_Int_Onumber__class_Onumber__of(X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_eq__number__of_0) ).
fof(f3696,plain,
spl0_359,
inference(avatar_split_clause,[],[f358,f3694]) ).
fof(f3694,plain,
( spl0_359
<=> ! [X20,X0,X5,X19] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f358,axiom,
! [X0,X19,X5,X20] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_eq__eqI_0) ).
fof(f3692,plain,
spl0_358,
inference(avatar_split_clause,[],[f318,f3690]) ).
fof(f3690,plain,
( spl0_358
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f318,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X5,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__left__idem_0) ).
fof(f3679,plain,
spl0_357,
inference(avatar_split_clause,[],[f312,f3677]) ).
fof(f3677,plain,
( spl0_357
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X9,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f312,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X9,X0),X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__mod__trivial_0) ).
fof(f3675,plain,
spl0_356,
inference(avatar_split_clause,[],[f295,f3673]) ).
fof(f3673,plain,
( spl0_356
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(c_List_Oappend(X12,X13,X0),X0) = c_List_Ohd(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f295,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(c_List_Oappend(X12,X13,X0),X0) = c_List_Ohd(X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_hd__append_1) ).
fof(f3671,plain,
spl0_355,
inference(avatar_split_clause,[],[f263,f3669]) ).
fof(f3669,plain,
( spl0_355
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f263,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(X5,X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__trans_0) ).
fof(f3667,plain,
spl0_354,
inference(avatar_split_clause,[],[f261,f3665]) ).
fof(f3665,plain,
( spl0_354
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X7,X8,X0)
| c_lessequals(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f261,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_lessequals(X7,X8,X0)
| c_lessequals(X7,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_xt1_I6_J_0) ).
fof(f3663,plain,
spl0_353,
inference(avatar_split_clause,[],[f260,f3661]) ).
fof(f3661,plain,
( spl0_353
<=> ! [X4,X3] : c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)),X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f260,axiom,
! [X3,X4] : c_Divides_Odiv__class_Omod(c_Suc(X4),X3,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X4,X3,tc_nat)),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f3659,plain,
spl0_352,
inference(avatar_split_clause,[],[f254,f3657]) ).
fof(f3657,plain,
( spl0_352
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X1,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f254,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X9,X1,X0),X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__add__self1_0) ).
fof(f3655,plain,
spl0_351,
inference(avatar_split_clause,[],[f253,f3653]) ).
fof(f3653,plain,
( spl0_351
<=> ! [X9,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = c_Divides_Odiv__class_Omod(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f253,axiom,
! [X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = c_Divides_Odiv__class_Omod(X1,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__add__self2_0) ).
fof(f3651,plain,
spl0_350,
inference(avatar_split_clause,[],[f237,f3649]) ).
fof(f3649,plain,
( spl0_350
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f237,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X1,X9,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_le__iff__diff__le__0_0) ).
fof(f3647,plain,
spl0_349,
inference(avatar_split_clause,[],[f236,f3645]) ).
fof(f3645,plain,
( spl0_349
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f236,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,X9,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_le__iff__diff__le__0_1) ).
fof(f3643,plain,
spl0_348,
inference(avatar_split_clause,[],[f181,f3641]) ).
fof(f3641,plain,
( spl0_348
<=> ! [X5,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f181,axiom,
! [X0,X1,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,X0) != X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3639,plain,
( spl0_347
| ~ spl0_21
| ~ spl0_68
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1895,f1728,f1043,f814,f3637]) ).
fof(f3637,plain,
( spl0_347
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1043,plain,
( spl0_68
<=> ! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1895,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_nat)
| c_lessequals(X0,c_Suc(X0),tc_nat) )
| ~ spl0_68
| ~ spl0_190 ),
inference(resolution,[],[f1729,f1044]) ).
fof(f1044,plain,
( ! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f1043]) ).
fof(f3635,plain,
spl0_346,
inference(avatar_split_clause,[],[f133,f3633]) ).
fof(f3633,plain,
( spl0_346
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f133,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__le__trans_0) ).
fof(f3631,plain,
spl0_345,
inference(avatar_split_clause,[],[f132,f3629]) ).
fof(f3629,plain,
( spl0_345
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f132,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__le__less__trans_0) ).
fof(f3627,plain,
spl0_344,
inference(avatar_split_clause,[],[f131,f3625]) ).
fof(f3625,plain,
( spl0_344
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f131,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_xt1_I8_J_0) ).
fof(f3623,plain,
spl0_343,
inference(avatar_split_clause,[],[f130,f3621]) ).
fof(f3621,plain,
( spl0_343
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f130,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_xt1_I7_J_0) ).
fof(f3619,plain,
spl0_342,
inference(avatar_split_clause,[],[f129,f3617]) ).
fof(f129,axiom,
! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__left__cancel__less_1) ).
fof(f3615,plain,
spl0_341,
inference(avatar_split_clause,[],[f128,f3613]) ).
fof(f3613,plain,
( spl0_341
<=> ! [X4,X3,X14] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f128,axiom,
! [X3,X14,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X14,X4,tc_nat),c_HOL_Oplus__class_Oplus(X14,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__left__cancel__less_0) ).
fof(f3611,plain,
spl0_340,
inference(avatar_split_clause,[],[f127,f3609]) ).
fof(f3609,plain,
( spl0_340
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f127,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),c_HOL_Oplus__class_Oplus(X15,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__less__mono1_0) ).
fof(f3607,plain,
spl0_339,
inference(avatar_split_clause,[],[f120,f3605]) ).
fof(f3605,plain,
( spl0_339
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f120,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__diff__conv_1) ).
fof(f3603,plain,
spl0_338,
inference(avatar_split_clause,[],[f119,f3601]) ).
fof(f3601,plain,
( spl0_338
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f119,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ominus__class_Ominus(X15,X14,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X14,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__diff__conv_0) ).
fof(f3599,plain,
spl0_337,
inference(avatar_split_clause,[],[f101,f3597]) ).
fof(f101,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__iff__diff__less__0_0) ).
fof(f3595,plain,
( spl0_336
| ~ spl0_68
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1882,f1724,f1043,f3593]) ).
fof(f3593,plain,
( spl0_336
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1882,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_68
| ~ spl0_189 ),
inference(resolution,[],[f1725,f1044]) ).
fof(f3591,plain,
spl0_335,
inference(avatar_split_clause,[],[f100,f3589]) ).
fof(f3589,plain,
( spl0_335
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f100,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X9,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__iff__diff__less__0_1) ).
fof(f3587,plain,
spl0_334,
inference(avatar_split_clause,[],[f82,f3585]) ).
fof(f3585,plain,
( spl0_334
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f82,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__le__not__le_2) ).
fof(f3583,plain,
spl0_333,
inference(avatar_split_clause,[],[f9,f3581]) ).
fof(f3581,plain,
( spl0_333
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f9,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X8,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_xt1_I10_J_0) ).
fof(f3579,plain,
spl0_332,
inference(avatar_split_clause,[],[f8,f3577]) ).
fof(f3577,plain,
( spl0_332
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f8,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__trans_0) ).
fof(f3535,plain,
( spl0_331
| ~ spl0_41
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f1651,f1473,f914,f3533]) ).
fof(f3533,plain,
( spl0_331
<=> ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f1473,plain,
( spl0_161
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1651,plain,
( ! [X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X1
| ~ spl0_41
| ~ spl0_161 ),
inference(resolution,[],[f1474,f916]) ).
fof(f1474,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f3415,plain,
( spl0_330
| ~ spl0_41
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1647,f1469,f914,f3413]) ).
fof(f3413,plain,
( spl0_330
<=> ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f1469,plain,
( spl0_160
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1647,plain,
( ! [X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Int_Oint),X1,tc_Int_Oint) = X1
| ~ spl0_41
| ~ spl0_160 ),
inference(resolution,[],[f1470,f916]) ).
fof(f1470,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1469]) ).
fof(f3100,plain,
( spl0_329
| ~ spl0_39
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1642,f1453,f904,f3098]) ).
fof(f3098,plain,
( spl0_329
<=> ! [X1] : c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f904,plain,
( spl0_39
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1453,plain,
( spl0_156
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1642,plain,
( ! [X1] : c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),tc_Int_Oint) = X1
| ~ spl0_39
| ~ spl0_156 ),
inference(resolution,[],[f1454,f906]) ).
fof(f906,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f1454,plain,
( ! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1453]) ).
fof(f3022,plain,
spl0_328,
inference(avatar_split_clause,[],[f591,f3020]) ).
fof(f3020,plain,
( spl0_328
<=> ! [X5,X0] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f591,axiom,
! [X0,X5] : c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0) = c_List_Orev(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__singleton__conv_1) ).
fof(f3018,plain,
spl0_327,
inference(avatar_split_clause,[],[f581,f3015]) ).
fof(f581,axiom,
c_List_Odistinct(c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__1,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__2,c_List_Olist_OCons(v_sko__Arrow__Order__Mirabelle__Xalt3__3,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_alt3_0) ).
fof(f3013,plain,
spl0_326,
inference(avatar_split_clause,[],[f463,f3011]) ).
fof(f3011,plain,
( spl0_326
<=> ! [X0,X12,X3] : c_List_Obutlast(c_List_Odrop(X3,X12,X0),X0) = c_List_Odrop(X3,c_List_Obutlast(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f463,axiom,
! [X3,X0,X12] : c_List_Obutlast(c_List_Odrop(X3,X12,X0),X0) = c_List_Odrop(X3,c_List_Obutlast(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__butlast_0) ).
fof(f3009,plain,
spl0_325,
inference(avatar_split_clause,[],[f427,f3007]) ).
fof(f3007,plain,
( spl0_325
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Ohd(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f427,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olast(X12,X0) = c_List_Ohd(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_hd__rev_0) ).
fof(f3005,plain,
spl0_324,
inference(avatar_split_clause,[],[f426,f3003]) ).
fof(f3003,plain,
( spl0_324
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(X12,X0) = c_List_Olast(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f426,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Ohd(X12,X0) = c_List_Olast(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__rev_0) ).
fof(f3001,plain,
spl0_323,
inference(avatar_split_clause,[],[f389,f2999]) ).
fof(f2999,plain,
( spl0_323
<=> ! [X6,X0,X12,X5] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X12,X6,X5,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f389,axiom,
! [X0,X6,X5,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Olist__update(X12,X6,X5,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__list__update_0) ).
fof(f2997,plain,
( spl0_322
| ~ spl0_10
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1641,f1453,f759,f2995]) ).
fof(f2995,plain,
( spl0_322
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f759,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1641,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_10
| ~ spl0_156 ),
inference(resolution,[],[f1454,f761]) ).
fof(f761,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f759]) ).
fof(f2993,plain,
spl0_321,
inference(avatar_split_clause,[],[f320,f2991]) ).
fof(f2991,plain,
( spl0_321
<=> ! [X5,X0,X27] : c_Suc(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f320,axiom,
! [X0,X27,X5] : c_Suc(c_Nat_Osize__class_Osize(X27,tc_List_Olist(X0))) = c_Nat_Osize__class_Osize(c_List_Olist_OCons(X5,X27,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__length__conv_2) ).
fof(f2989,plain,
spl0_320,
inference(avatar_split_clause,[],[f306,f2987]) ).
fof(f2985,plain,
spl0_319,
inference(avatar_split_clause,[],[f301,f2983]) ).
fof(f2983,plain,
( spl0_319
<=> ! [X0,X12,X5,X3] : c_List_Odrop(X3,X12,X0) = c_List_Odrop(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f301,axiom,
! [X3,X0,X5,X12] : c_List_Odrop(X3,X12,X0) = c_List_Odrop(c_Suc(X3),c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__Suc__Cons_0) ).
fof(f2981,plain,
spl0_318,
inference(avatar_split_clause,[],[f249,f2979]) ).
fof(f2979,plain,
( spl0_318
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f249,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X3,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_field__power__not__zero_0) ).
fof(f2977,plain,
spl0_317,
inference(avatar_split_clause,[],[f232,f2975]) ).
fof(f2975,plain,
( spl0_317
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f232,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| ~ c_lessequals(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__eq__iff_2) ).
fof(f2973,plain,
spl0_316,
inference(avatar_split_clause,[],[f212,f2971]) ).
fof(f2971,plain,
( spl0_316
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f212,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__eq__0__iff_0) ).
fof(f2969,plain,
spl0_315,
inference(avatar_split_clause,[],[f198,f2967]) ).
fof(f198,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X3),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__0__Suc_0) ).
fof(f2965,plain,
spl0_314,
inference(avatar_split_clause,[],[f171,f2963]) ).
fof(f2963,plain,
( spl0_314
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f171,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X7,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X8,X7,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Ole__inf__iff_1) ).
fof(f2961,plain,
spl0_313,
inference(avatar_split_clause,[],[f169,f2959]) ).
fof(f2959,plain,
( spl0_313
<=> ! [X5,X0,X7,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f169,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__le__iff__disj_2) ).
fof(f2957,plain,
spl0_312,
inference(avatar_split_clause,[],[f168,f2955]) ).
fof(f2955,plain,
( spl0_312
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f168,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X7,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X7,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__le__iff__disj_1) ).
fof(f2953,plain,
spl0_311,
inference(avatar_split_clause,[],[f164,f2951]) ).
fof(f164,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X1,X0)
| ~ c_lessequals(X5,c_Orderings_Oord__class_Omin(X1,X9,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Ole__infE_0) ).
fof(f2949,plain,
spl0_310,
inference(avatar_split_clause,[],[f159,f2947]) ).
fof(f2947,plain,
( spl0_310
<=> ! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f159,axiom,
! [X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X3 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__pred_H_0) ).
fof(f2945,plain,
spl0_309,
inference(avatar_split_clause,[],[f148,f2943]) ).
fof(f2943,plain,
( spl0_309
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f148,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__antisym__conv1_0) ).
fof(f2941,plain,
spl0_308,
inference(avatar_split_clause,[],[f144,f2939]) ).
fof(f2939,plain,
( spl0_308
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f144,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Oorder(X0)
| X5 = X8
| ~ c_lessequals(X5,X8,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__le__less_0) ).
fof(f2937,plain,
spl0_307,
inference(avatar_split_clause,[],[f141,f2935]) ).
fof(f2935,plain,
( spl0_307
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f141,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) = X4 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__diff__inverse_0) ).
fof(f2933,plain,
spl0_306,
inference(avatar_split_clause,[],[f104,f2931]) ).
fof(f2931,plain,
( spl0_306
<=> ! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X6),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f104,axiom,
! [X6,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X6),X14,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__trans__Suc_0) ).
fof(f2929,plain,
spl0_305,
inference(avatar_split_clause,[],[f90,f2927]) ).
fof(f2927,plain,
( spl0_305
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f90,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__less__iff__gr__or__eq_0) ).
fof(f2925,plain,
spl0_304,
inference(avatar_split_clause,[],[f89,f2923]) ).
fof(f2923,plain,
( spl0_304
<=> ! [X5,X0,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f89,axiom,
! [X0,X8,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X5 = X8
| c_HOL_Oord__class_Oless(X5,X8,X0)
| c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__neqE__ordered__idom_0) ).
fof(f2921,plain,
spl0_303,
inference(avatar_split_clause,[],[f55,f2919]) ).
fof(f2919,plain,
( spl0_303
<=> ! [X6,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,c_Suc(X6),tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f55,axiom,
! [X3,X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,c_Suc(X6),tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__Suc__less_0) ).
fof(f2917,plain,
spl0_302,
inference(avatar_split_clause,[],[f33,f2915]) ).
fof(f2915,plain,
( spl0_302
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Suc(X4) = X3
| c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f33,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Suc(X4) = X3
| c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__lessI_0) ).
fof(f2913,plain,
( ~ spl0_301
| spl0_296
| ~ spl0_123
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2747,f2496,f1277,f2771,f2910]) ).
fof(f2910,plain,
( spl0_301
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2496,plain,
( spl0_271
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2747,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_123
| ~ spl0_271 ),
inference(trivial_inequality_removal,[],[f2742]) ).
fof(f2742,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_123
| ~ spl0_271 ),
inference(superposition,[],[f2497,f1278]) ).
fof(f2497,plain,
( ! [X0,X1,X9] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0)
| X1 = X9
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f2908,plain,
spl0_300,
inference(avatar_split_clause,[],[f30,f2906]) ).
fof(f2906,plain,
( spl0_300
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f30,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X8,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__less__iff__conj_1) ).
fof(f2904,plain,
spl0_299,
inference(avatar_split_clause,[],[f29,f2902]) ).
fof(f2902,plain,
( spl0_299
<=> ! [X0,X5,X8,X7] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f29,axiom,
! [X0,X8,X7,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X7,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,c_Orderings_Oord__class_Omin(X5,X8,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__less__iff__conj_0) ).
fof(f2900,plain,
spl0_298,
inference(avatar_split_clause,[],[f28,f2898]) ).
fof(f2898,plain,
( spl0_298
<=> ! [X5,X9,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f28,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oless__infI2_0) ).
fof(f2896,plain,
spl0_297,
inference(avatar_split_clause,[],[f27,f2894]) ).
fof(f2894,plain,
( spl0_297
<=> ! [X9,X0,X5,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f27,axiom,
! [X0,X1,X9,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X5,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X9,X0),X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oless__infI1_0) ).
fof(f2773,plain,
( ~ spl0_295
| spl0_296
| ~ spl0_123
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f2737,f2488,f1277,f2771,f2767]) ).
fof(f2767,plain,
( spl0_295
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2488,plain,
( spl0_269
<=> ! [X9,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2737,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_123
| ~ spl0_269 ),
inference(trivial_inequality_removal,[],[f2732]) ).
fof(f2732,plain,
( ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_123
| ~ spl0_269 ),
inference(superposition,[],[f2489,f1278]) ).
fof(f2489,plain,
( ! [X0,X1,X9] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0)
| X1 = X9
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2488]) ).
fof(f2592,plain,
spl0_294,
inference(avatar_split_clause,[],[f681,f2590]) ).
fof(f2590,plain,
( spl0_294
<=> ! [X0,X12,X3] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f681,plain,
! [X3,X0,X12] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0),
inference(forward_demodulation,[],[f470,f419]) ).
fof(f419,axiom,
! [X3,X0,X12] : c_List_Odrop(c_Suc(X3),X12,X0) = c_List_Odrop(X3,c_List_Otl(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__Suc_0) ).
fof(f470,axiom,
! [X3,X0,X12] : c_List_Odrop(X3,c_List_Otl(X12,X0),X0) = c_List_Otl(c_List_Odrop(X3,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__tl_0) ).
fof(f2588,plain,
spl0_293,
inference(avatar_split_clause,[],[f680,f2586]) ).
fof(f2586,plain,
( spl0_293
<=> ! [X0,X12,X3] : c_List_Orotate(c_Suc(X3),X12,X0) = c_List_Orotate(X3,c_List_Orotate1(X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f680,plain,
! [X3,X0,X12] : c_List_Orotate(c_Suc(X3),X12,X0) = c_List_Orotate(X3,c_List_Orotate1(X12,X0),X0),
inference(forward_demodulation,[],[f500,f420]) ).
fof(f420,axiom,
! [X3,X0,X12] : c_List_Orotate(c_Suc(X3),X12,X0) = c_List_Orotate1(c_List_Orotate(X3,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__Suc_0) ).
fof(f500,axiom,
! [X3,X0,X12] : c_List_Orotate1(c_List_Orotate(X3,X12,X0),X0) = c_List_Orotate(X3,c_List_Orotate1(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate1__rotate__swap_0) ).
fof(f2584,plain,
spl0_292,
inference(avatar_split_clause,[],[f598,f2582]) ).
fof(f2582,plain,
( spl0_292
<=> ! [X26,X38,X0,X1,X24] :
( X1 = X24
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f598,axiom,
! [X38,X0,X1,X26,X24] :
( X1 = X24
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list_Oinject_0) ).
fof(f2580,plain,
spl0_291,
inference(avatar_split_clause,[],[f597,f2578]) ).
fof(f2578,plain,
( spl0_291
<=> ! [X1,X38,X0,X26,X24] :
( X26 = X38
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f597,axiom,
! [X38,X0,X1,X26,X24] :
( X26 = X38
| c_List_Olist_OCons(X1,X26,X0) != c_List_Olist_OCons(X24,X38,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list_Oinject_1) ).
fof(f2576,plain,
( ~ spl0_20
| spl0_290
| ~ spl0_115
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1636,f1445,f1245,f2574,f809]) ).
fof(f2574,plain,
( spl0_290
<=> ! [X1] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f1636,plain,
( ! [X1] :
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_115
| ~ spl0_154 ),
inference(superposition,[],[f1446,f1246]) ).
fof(f2572,plain,
spl0_289,
inference(avatar_split_clause,[],[f566,f2570]) ).
fof(f2570,plain,
( spl0_289
<=> ! [X0,X14,X12,X5] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Olist__update(X12,X14,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f566,axiom,
! [X0,X14,X5,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Olist__update(X12,X14,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__nonempty_0) ).
fof(f2568,plain,
( spl0_288
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2564,f2561,f2566]) ).
fof(f2566,plain,
( spl0_288
<=> ! [X5,X0,X12] : c_List_Obutlast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2561,plain,
( spl0_287
<=> ! [X5,X0,X12] : c_List_Obutlast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2564,plain,
( ! [X0,X5,X12] : c_List_Obutlast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X12
| ~ spl0_287 ),
inference(forward_demodulation,[],[f2562,f521]) ).
fof(f2562,plain,
( ! [X0,X5,X12] : c_List_Obutlast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f2561]) ).
fof(f2563,plain,
spl0_287,
inference(avatar_split_clause,[],[f511,f2561]) ).
fof(f511,axiom,
! [X0,X5,X12] : c_List_Obutlast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast__snoc_0) ).
fof(f2559,plain,
( spl0_286
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f2555,f2552,f2557]) ).
fof(f2552,plain,
( spl0_285
<=> ! [X12,X5,X0] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2555,plain,
( ! [X0,X5,X12] : c_List_Olast(c_List_Orotate1(c_List_Olist_OCons(X5,X12,X0),X0),X0) = X5
| ~ spl0_285 ),
inference(forward_demodulation,[],[f2553,f521]) ).
fof(f2553,plain,
( ! [X0,X5,X12] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2552]) ).
fof(f2554,plain,
spl0_285,
inference(avatar_split_clause,[],[f510,f2552]) ).
fof(f510,axiom,
! [X0,X5,X12] : c_List_Olast(c_List_Oappend(X12,c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),X0) = X5,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__snoc_0) ).
fof(f2550,plain,
spl0_284,
inference(avatar_split_clause,[],[f486,f2548]) ).
fof(f2548,plain,
( spl0_284
<=> ! [X5,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_OremoveAll(X5,X12,X0) = c_List_Oremove1(X5,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f486,axiom,
! [X0,X5,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_OremoveAll(X5,X12,X0) = c_List_Oremove1(X5,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__remove1__removeAll_0) ).
fof(f2546,plain,
spl0_283,
inference(avatar_split_clause,[],[f473,f2544]) ).
fof(f473,axiom,
! [X28,X0,X12,X13] :
( X13 = X28
| c_List_Oappend(X12,X13,X0) != c_List_Oappend(X12,X28,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_same__append__eq_0) ).
fof(f2542,plain,
spl0_282,
inference(avatar_split_clause,[],[f472,f2540]) ).
fof(f472,axiom,
! [X28,X0,X12,X13] :
( X13 = X28
| c_List_Oappend(X13,X12,X0) != c_List_Oappend(X28,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__same__eq_0) ).
fof(f2538,plain,
( spl0_281
| ~ spl0_50
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1634,f1441,f959,f2536]) ).
fof(f2536,plain,
( spl0_281
<=> ! [X1] : c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1441,plain,
( spl0_153
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1634,plain,
( ! [X1] : c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X1
| ~ spl0_50
| ~ spl0_153 ),
inference(resolution,[],[f1442,f961]) ).
fof(f1442,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1441]) ).
fof(f2534,plain,
spl0_280,
inference(avatar_split_clause,[],[f471,f2532]) ).
fof(f2532,plain,
( spl0_280
<=> ! [X5,X4,X0,X3,X8] :
( X3 = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f471,axiom,
! [X3,X0,X8,X4,X5] :
( X3 = X4
| c_List_Oreplicate(X4,X5,X0) != c_List_Oreplicate(X3,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__eq__replicate_0) ).
fof(f2530,plain,
spl0_279,
inference(avatar_split_clause,[],[f459,f2528]) ).
fof(f459,axiom,
! [X3,X0,X12] : c_List_Oappend(c_List_Otake(X3,X12,X0),c_List_Odrop(X3,X12,X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__take__drop__id_0) ).
fof(f2526,plain,
spl0_278,
inference(avatar_split_clause,[],[f457,f2524]) ).
fof(f2524,plain,
( spl0_278
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olast(c_List_Oreplicate(X3,X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f457,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olast(c_List_Oreplicate(X3,X5,X0),X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last__replicate_0) ).
fof(f2522,plain,
spl0_277,
inference(avatar_split_clause,[],[f448,f2520]) ).
fof(f2520,plain,
( spl0_277
<=> ! [X5,X0,X12] : c_List_OremoveAll(X5,X12,X0) = c_List_OremoveAll(X5,c_List_Olist_OCons(X5,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f448,axiom,
! [X0,X5,X12] : c_List_OremoveAll(X5,X12,X0) = c_List_OremoveAll(X5,c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_removeAll_Osimps_I2_J_0) ).
fof(f2518,plain,
spl0_276,
inference(avatar_split_clause,[],[f420,f2516]) ).
fof(f2516,plain,
( spl0_276
<=> ! [X0,X12,X3] : c_List_Orotate(c_Suc(X3),X12,X0) = c_List_Orotate1(c_List_Orotate(X3,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2514,plain,
spl0_275,
inference(avatar_split_clause,[],[f419,f2512]) ).
fof(f2510,plain,
spl0_274,
inference(avatar_split_clause,[],[f388,f2508]) ).
fof(f388,axiom,
! [X3,X4] : c_Orderings_Oord__class_Omin(c_Suc(X4),c_Suc(X3),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X4,X3,tc_nat)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__Suc__Suc_0) ).
fof(f2506,plain,
spl0_273,
inference(avatar_split_clause,[],[f374,f2504]) ).
fof(f374,axiom,
! [X3,X14,X4] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X14,X3,tc_nat) != c_HOL_Oplus__class_Oplus(X14,X4,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__left__cancel_0) ).
fof(f2502,plain,
spl0_272,
inference(avatar_split_clause,[],[f373,f2500]) ).
fof(f373,axiom,
! [X3,X14,X4] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X4,X14,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__right__cancel_0) ).
fof(f2498,plain,
spl0_271,
inference(avatar_split_clause,[],[f369,f2496]) ).
fof(f369,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_eq__iff__diff__eq__0_1) ).
fof(f2494,plain,
( spl0_270
| ~ spl0_18
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f1633,f1441,f799,f2492]) ).
fof(f2492,plain,
( spl0_270
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1633,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_18
| ~ spl0_153 ),
inference(resolution,[],[f1442,f801]) ).
fof(f2490,plain,
spl0_269,
inference(avatar_split_clause,[],[f368,f2488]) ).
fof(f368,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X9
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_right__minus__eq_0) ).
fof(f2486,plain,
spl0_268,
inference(avatar_split_clause,[],[f348,f2484]) ).
fof(f2484,plain,
( spl0_268
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X5,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f348,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X8,X5,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X8 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__absorb2_0) ).
fof(f2482,plain,
spl0_267,
inference(avatar_split_clause,[],[f347,f2480]) ).
fof(f347,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) != X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Ole__iff__inf_1) ).
fof(f2478,plain,
spl0_266,
inference(avatar_split_clause,[],[f346,f2476]) ).
fof(f2476,plain,
( spl0_266
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f346,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Ole__iff__inf_0) ).
fof(f2474,plain,
spl0_265,
inference(avatar_split_clause,[],[f304,f2472]) ).
fof(f2472,plain,
( spl0_265
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Ohd(c_List_Oreplicate(X3,X5,X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f304,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Ohd(c_List_Oreplicate(X3,X5,X0),X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_hd__replicate_0) ).
fof(f2470,plain,
spl0_264,
inference(avatar_split_clause,[],[f303,f2468]) ).
fof(f303,axiom,
! [X0,X12,X13] : c_List_Odrop(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X13,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__conv__conj_1) ).
fof(f2466,plain,
spl0_263,
inference(avatar_split_clause,[],[f302,f2464]) ).
fof(f302,axiom,
! [X0,X12,X13] : c_List_Otake(c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),c_List_Oappend(X12,X13,X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__eq__conv__conj_0) ).
fof(f2462,plain,
spl0_262,
inference(avatar_split_clause,[],[f225,f2460]) ).
fof(f2460,plain,
( spl0_262
<=> ! [X0,X12,X3] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate(X3,X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f225,axiom,
! [X3,X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate(X3,X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__rotate_0) ).
fof(f2458,plain,
spl0_261,
inference(avatar_split_clause,[],[f135,f2456]) ).
fof(f2456,plain,
( spl0_261
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f135,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__diff_1) ).
fof(f2454,plain,
spl0_260,
inference(avatar_split_clause,[],[f134,f2452]) ).
fof(f134,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__diff_0) ).
fof(f2450,plain,
( spl0_259
| ~ spl0_50
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1632,f1437,f959,f2448]) ).
fof(f2448,plain,
( spl0_259
<=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X1,X1,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1437,plain,
( spl0_152
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1632,plain,
( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(X1,X1,tc_Int_Oint)
| ~ spl0_50
| ~ spl0_152 ),
inference(resolution,[],[f1438,f961]) ).
fof(f1438,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) )
| ~ spl0_152 ),
inference(avatar_component_clause,[],[f1437]) ).
fof(f2446,plain,
spl0_258,
inference(avatar_split_clause,[],[f78,f2444]) ).
fof(f2444,plain,
( spl0_258
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f78,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__antisym_0) ).
fof(f2442,plain,
spl0_257,
inference(avatar_split_clause,[],[f57,f2440]) ).
fof(f2440,plain,
( spl0_257
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f57,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__greater__0__conv_1) ).
fof(f2438,plain,
spl0_256,
inference(avatar_split_clause,[],[f52,f2436]) ).
fof(f2436,plain,
( spl0_256
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f52,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__two_0) ).
fof(f2434,plain,
spl0_255,
inference(avatar_split_clause,[],[f13,f2432]) ).
fof(f2432,plain,
( spl0_255
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f13,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X4,X3,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__less__divisor_0) ).
fof(f2419,plain,
( spl0_254
| ~ spl0_18
| ~ spl0_152 ),
inference(avatar_split_clause,[],[f1631,f1437,f799,f2417]) ).
fof(f1631,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_18
| ~ spl0_152 ),
inference(resolution,[],[f1438,f801]) ).
fof(f2395,plain,
( spl0_253
| ~ spl0_49
| ~ spl0_149 ),
inference(avatar_split_clause,[],[f1605,f1425,f954,f2393]) ).
fof(f2393,plain,
( spl0_253
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1425,plain,
( spl0_149
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1605,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Int_Oint),tc_Int_Oint) = X0
| ~ spl0_49
| ~ spl0_149 ),
inference(resolution,[],[f1426,f956]) ).
fof(f1426,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f2311,plain,
( spl0_252
| ~ spl0_49
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1604,f1421,f954,f2309]) ).
fof(f2309,plain,
( spl0_252
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1421,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1604,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Int_Oint) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Int_Oint)
| ~ spl0_49
| ~ spl0_148 ),
inference(resolution,[],[f1422,f956]) ).
fof(f1422,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f2177,plain,
spl0_251,
inference(avatar_split_clause,[],[f543,f2175]) ).
fof(f543,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Nil__is__append__conv_0) ).
fof(f2173,plain,
spl0_250,
inference(avatar_split_clause,[],[f540,f2171]) ).
fof(f540,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Olist_ONil(X0) != c_List_Oappend(X12,X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__is__Nil__conv_1) ).
fof(f2169,plain,
spl0_249,
inference(avatar_split_clause,[],[f537,f2167]) ).
fof(f2167,plain,
( spl0_249
<=> ! [X0,X12,X3] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate(X3,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f537,axiom,
! [X3,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate(X3,X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__is__Nil__conv_0) ).
fof(f2165,plain,
( spl0_248
| ~ spl0_110
| ~ spl0_143 ),
inference(avatar_split_clause,[],[f1562,f1400,f1225,f2163]) ).
fof(f1562,plain,
( ! [X2,X3] : ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(X2,X3,tc_nat),tc_nat)
| ~ spl0_110
| ~ spl0_143 ),
inference(resolution,[],[f1401,f1226]) ).
fof(f2161,plain,
spl0_247,
inference(avatar_split_clause,[],[f506,f2159]) ).
fof(f2159,plain,
( spl0_247
<=> ! [X0,X12,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X1,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f506,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremove1(X1,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__remove1_0) ).
fof(f2157,plain,
spl0_246,
inference(avatar_split_clause,[],[f495,f2155]) ).
fof(f2155,plain,
( spl0_246
<=> ! [X13,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X13,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f495,axiom,
! [X0,X12,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X13,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__append_1) ).
fof(f2153,plain,
spl0_245,
inference(avatar_split_clause,[],[f494,f2151]) ).
fof(f2151,plain,
( spl0_245
<=> ! [X13,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f494,axiom,
! [X0,X12,X13] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__append_0) ).
fof(f2149,plain,
spl0_244,
inference(avatar_split_clause,[],[f490,f2147]) ).
fof(f2147,plain,
( spl0_244
<=> ! [X5,X0,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X3,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f490,axiom,
! [X3,X0,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_List_Olist_ONil(X0) != c_List_Oreplicate(X3,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_replicate__empty_0) ).
fof(f2145,plain,
spl0_243,
inference(avatar_split_clause,[],[f479,f2143]) ).
fof(f2143,plain,
( spl0_243
<=> ! [X5,X0,X3] : c_List_Oreplicate(X3,X5,X0) = c_List_Orev(c_List_Oreplicate(X3,X5,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f479,axiom,
! [X3,X0,X5] : c_List_Oreplicate(X3,X5,X0) = c_List_Orev(c_List_Oreplicate(X3,X5,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__replicate_0) ).
fof(f2141,plain,
spl0_242,
inference(avatar_split_clause,[],[f474,f2139]) ).
fof(f474,axiom,
! [X3,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Otake(X3,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__take_0) ).
fof(f2137,plain,
spl0_241,
inference(avatar_split_clause,[],[f469,f2135]) ).
fof(f2135,plain,
( spl0_241
<=> ! [X0,X12,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f469,axiom,
! [X3,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X12,X0)
| c_List_Olinorder__class_Osorted(c_List_Odrop(X3,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__drop_0) ).
fof(f2133,plain,
spl0_240,
inference(avatar_split_clause,[],[f445,f2131]) ).
fof(f2131,plain,
( spl0_240
<=> ! [X13,X0,X5,X8] :
( ~ c_List_Omember(X5,X13,X0)
| c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f445,axiom,
! [X0,X8,X5,X13] :
( ~ c_List_Omember(X5,X13,X0)
| c_List_Omember(X5,c_List_Olist_OCons(X8,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_List_Omember_Osimps_I2_J_2) ).
fof(f2129,plain,
spl0_239,
inference(avatar_split_clause,[],[f435,f2127]) ).
fof(f2127,plain,
( spl0_239
<=> ! [X5,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f435,axiom,
! [X0,X5,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(X12,X0)
| ~ c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__Cons_0) ).
fof(f2125,plain,
spl0_238,
inference(avatar_split_clause,[],[f404,f2123]) ).
fof(f404,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X9,X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__diff__cancel_0) ).
fof(f2121,plain,
( spl0_237
| ~ spl0_108
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1369,f1269,f1217,f2119]) ).
fof(f2119,plain,
( spl0_237
<=> ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_Suc(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1369,plain,
( ! [X1] : c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_Suc(c_Suc(X1)),tc_nat)
| ~ spl0_108
| ~ spl0_121 ),
inference(superposition,[],[f1218,f1270]) ).
fof(f2117,plain,
spl0_236,
inference(avatar_split_clause,[],[f396,f2115]) ).
fof(f2115,plain,
( spl0_236
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f396,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2113,plain,
spl0_235,
inference(avatar_split_clause,[],[f366,f2111]) ).
fof(f366,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X8,X0) = c_Orderings_Oord__class_Omin(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__commute_0) ).
fof(f2109,plain,
spl0_234,
inference(avatar_split_clause,[],[f326,f2107]) ).
fof(f2107,plain,
( spl0_234
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f326,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_double__eq__0__iff_1) ).
fof(f2105,plain,
spl0_233,
inference(avatar_split_clause,[],[f319,f2103]) ).
fof(f319,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X9,X0),X9,X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__add__cancel_0) ).
fof(f2101,plain,
spl0_232,
inference(avatar_split_clause,[],[f294,f2099]) ).
fof(f294,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__0__conv_0) ).
fof(f2097,plain,
spl0_231,
inference(avatar_split_clause,[],[f272,f2095]) ).
fof(f2095,plain,
( spl0_231
<=> ! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f272,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orev(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__rev_0) ).
fof(f2093,plain,
spl0_230,
inference(avatar_split_clause,[],[f227,f2091]) ).
fof(f2091,plain,
( spl0_230
<=> ! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f227,axiom,
! [X0,X12] : c_Nat_Osize__class_Osize(X12,tc_List_Olist(X0)) = c_Nat_Osize__class_Osize(c_List_Orotate1(X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__rotate1_0) ).
fof(f2089,plain,
spl0_229,
inference(avatar_split_clause,[],[f221,f2087]) ).
fof(f221,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X4),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__Suc__Suc_0) ).
fof(f2085,plain,
spl0_228,
inference(avatar_split_clause,[],[f211,f2083]) ).
fof(f2083,plain,
( spl0_228
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f211,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__is__0_1) ).
fof(f2081,plain,
spl0_227,
inference(avatar_split_clause,[],[f210,f2079]) ).
fof(f2079,plain,
( spl0_227
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f210,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__is__0_0) ).
fof(f2072,plain,
spl0_226,
inference(avatar_split_clause,[],[f197,f2070]) ).
fof(f2068,plain,
spl0_225,
inference(avatar_split_clause,[],[f196,f2066]) ).
fof(f2064,plain,
spl0_224,
inference(avatar_split_clause,[],[f186,f2062]) ).
fof(f2062,plain,
( spl0_224
<=> ! [X0,X1,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X10,X0) = c_HOL_Oplus__class_Oplus(X10,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f186,axiom,
! [X10,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X10,X0) = c_HOL_Oplus__class_Oplus(X10,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2060,plain,
spl0_223,
inference(avatar_split_clause,[],[f185,f2058]) ).
fof(f185,axiom,
! [X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2056,plain,
spl0_222,
inference(avatar_split_clause,[],[f174,f2054]) ).
fof(f2054,plain,
( spl0_222
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f174,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__ringb_Osubr0__iff_1) ).
fof(f2052,plain,
spl0_221,
inference(avatar_split_clause,[],[f91,f2050]) ).
fof(f2050,plain,
( spl0_221
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f91,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__neq__iff_0) ).
fof(f2048,plain,
spl0_220,
inference(avatar_split_clause,[],[f80,f2046]) ).
fof(f2046,plain,
( spl0_220
<=> ! [X3,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f80,axiom,
! [X3,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X15,X3,tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__imp__diff__less_0) ).
fof(f2044,plain,
spl0_219,
inference(avatar_split_clause,[],[f67,f2042]) ).
fof(f67,axiom,
! [X6,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X6,X15,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Oplus__class_Oplus(X4,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_trans__less__add2_0) ).
fof(f2040,plain,
spl0_218,
inference(avatar_split_clause,[],[f65,f2038]) ).
fof(f65,axiom,
! [X6,X14,X15] :
( c_HOL_Oord__class_Oless(X6,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X14,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__lessD1_0) ).
fof(f2036,plain,
spl0_217,
inference(avatar_split_clause,[],[f63,f2034]) ).
fof(f63,axiom,
! [X8,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X8,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X8,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_termination__basic__simps_I1_J_0) ).
fof(f2014,plain,
( spl0_216
| ~ spl0_74
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1845,f1704,f1067,f2012]) ).
fof(f2012,plain,
( spl0_216
<=> ! [X8,X7] :
( c_lessequals(X7,X7,X8)
| ~ class_Orderings_Olinorder(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1067,plain,
( spl0_74
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1845,plain,
( ! [X8,X7] :
( c_lessequals(X7,X7,X8)
| ~ class_Orderings_Olinorder(X8) )
| ~ spl0_74
| ~ spl0_184 ),
inference(duplicate_literal_removal,[],[f1837]) ).
fof(f1837,plain,
( ! [X8,X7] :
( c_lessequals(X7,X7,X8)
| ~ class_Orderings_Olinorder(X8)
| ~ class_Orderings_Olinorder(X8) )
| ~ spl0_74
| ~ spl0_184 ),
inference(resolution,[],[f1705,f1068]) ).
fof(f1068,plain,
( ! [X0,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X5,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1067]) ).
fof(f1831,plain,
( ~ spl0_53
| spl0_215
| ~ spl0_155
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f1648,f1501,f1449,f1829,f974]) ).
fof(f1829,plain,
( spl0_215
<=> ! [X0] : c_lessequals(X0,X0,tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1501,plain,
( spl0_168
<=> ! [X1] : c_Orderings_Oord__class_Omin(X1,X1,tc_Int_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1648,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_Int_Oint)
| ~ class_Orderings_Olinorder(tc_Int_Oint) )
| ~ spl0_155
| ~ spl0_168 ),
inference(superposition,[],[f1450,f1502]) ).
fof(f1502,plain,
( ! [X1] : c_Orderings_Oord__class_Omin(X1,X1,tc_Int_Oint) = X1
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f1827,plain,
spl0_214,
inference(avatar_split_clause,[],[f610,f1824]) ).
fof(f1824,plain,
( spl0_214
<=> c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f610,axiom,
c_in(v_P____,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_bool))),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_CHAINED_0_03) ).
fof(f1822,plain,
spl0_213,
inference(avatar_split_clause,[],[f587,f1820]) ).
fof(f1820,plain,
( spl0_213
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f587,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast_Osimps_I2_J_0) ).
fof(f1818,plain,
spl0_212,
inference(avatar_split_clause,[],[f562,f1816]) ).
fof(f562,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orev(X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__is__Nil__conv_0) ).
fof(f1814,plain,
spl0_211,
inference(avatar_split_clause,[],[f557,f1812]) ).
fof(f1812,plain,
( spl0_211
<=> ! [X5,X0] :
( c_List_Olist_ONil(X0) = X5
| c_List_Olist_ONil(X0) != c_List_Oremdups(X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f557,axiom,
! [X0,X5] :
( c_List_Olist_ONil(X0) = X5
| c_List_Olist_ONil(X0) != c_List_Oremdups(X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remdups__eq__nil__right__iff_0) ).
fof(f1810,plain,
spl0_210,
inference(avatar_split_clause,[],[f552,f1808]) ).
fof(f1808,plain,
( spl0_210
<=> ! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate1(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f552,axiom,
! [X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Olist_ONil(X0) != c_List_Orotate1(X12,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate1__is__Nil__conv_0) ).
fof(f1806,plain,
spl0_209,
inference(avatar_split_clause,[],[f532,f1804]) ).
fof(f1804,plain,
( spl0_209
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X13
| c_List_Oappend(X12,X13,X0) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f532,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X13
| c_List_Oappend(X12,X13,X0) != X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__self__conv_0) ).
fof(f1802,plain,
spl0_208,
inference(avatar_split_clause,[],[f530,f1800]) ).
fof(f1800,plain,
( spl0_208
<=> ! [X13,X0,X12] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X12,X13,X0) != X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f530,axiom,
! [X0,X12,X13] :
( c_List_Olist_ONil(X0) = X12
| c_List_Oappend(X12,X13,X0) != X13 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__self__conv2_0) ).
fof(f1798,plain,
spl0_207,
inference(avatar_split_clause,[],[f497,f1796]) ).
fof(f1796,plain,
( spl0_207
<=> ! [X0,X16] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X16,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f497,axiom,
! [X0,X16] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_List_Olinorder__class_Osorted(X16,X0)
| c_List_Olinorder__class_Osorted(c_List_Oremdups(X16,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted__remdups_0) ).
fof(f1794,plain,
spl0_206,
inference(avatar_split_clause,[],[f488,f1792]) ).
fof(f488,axiom,
! [X0,X12,X13] :
( X12 = X13
| c_List_Orev(X12,X0) != c_List_Orev(X13,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__is__rev__conv_0) ).
fof(f1790,plain,
spl0_205,
inference(avatar_split_clause,[],[f460,f1788]) ).
fof(f460,axiom,
! [X0,X5,X12] : c_List_Odrop(c_HOL_Oone__class_Oone(tc_nat),c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__1__Cons_0) ).
fof(f1786,plain,
spl0_204,
inference(avatar_split_clause,[],[f354,f1784]) ).
fof(f354,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__add__0_0) ).
fof(f1782,plain,
spl0_203,
inference(avatar_split_clause,[],[f345,f1780]) ).
fof(f345,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X3,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__one_0) ).
fof(f1778,plain,
spl0_202,
inference(avatar_split_clause,[],[f315,f1776]) ).
fof(f315,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__0_0) ).
fof(f1774,plain,
spl0_201,
inference(avatar_split_clause,[],[f292,f1772]) ).
fof(f1772,plain,
( spl0_201
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f292,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Opwr__0_0) ).
fof(f1770,plain,
spl0_200,
inference(avatar_split_clause,[],[f291,f1768]) ).
fof(f291,axiom,
! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__0_0) ).
fof(f1766,plain,
spl0_199,
inference(avatar_split_clause,[],[f289,f1764]) ).
fof(f289,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__by__1_0) ).
fof(f1762,plain,
spl0_198,
inference(avatar_split_clause,[],[f279,f1760]) ).
fof(f1760,plain,
( spl0_198
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f279,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X5,X8,X0)
| c_lessequals(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__linear_0) ).
fof(f1758,plain,
spl0_197,
inference(avatar_split_clause,[],[f179,f1756]) ).
fof(f179,axiom,
! [X1,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_HOL_Oplus__class_Oplus(X5,X1,tc_nat) != X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_natgb_Oadd__r0__iff_0) ).
fof(f1754,plain,
spl0_196,
inference(avatar_split_clause,[],[f152,f1752]) ).
fof(f1752,plain,
( spl0_196
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f152,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__asym_0) ).
fof(f1750,plain,
spl0_195,
inference(avatar_split_clause,[],[f151,f1748]) ).
fof(f151,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__less__iff__gr__or__eq_1) ).
fof(f1746,plain,
( ~ spl0_20
| spl0_194
| ~ spl0_154
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1637,f1457,f1445,f1744,f809]) ).
fof(f1744,plain,
( spl0_194
<=> ! [X2] : c_lessequals(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1457,plain,
( spl0_157
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1637,plain,
( ! [X2] :
( c_lessequals(X2,X2,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_154
| ~ spl0_157 ),
inference(superposition,[],[f1446,f1458]) ).
fof(f1458,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1457]) ).
fof(f1742,plain,
spl0_193,
inference(avatar_split_clause,[],[f150,f1740]) ).
fof(f1740,plain,
( spl0_193
<=> ! [X9,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f150,axiom,
! [X0,X1,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X9,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X9,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_xt1_I9_J_0) ).
fof(f1738,plain,
spl0_192,
inference(avatar_split_clause,[],[f105,f1736]) ).
fof(f1736,plain,
( spl0_192
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f105,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__add__one_0) ).
fof(f1734,plain,
spl0_191,
inference(avatar_split_clause,[],[f99,f1732]) ).
fof(f1732,plain,
( spl0_191
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f99,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__imp__le_0) ).
fof(f1730,plain,
spl0_190,
inference(avatar_split_clause,[],[f98,f1728]) ).
fof(f98,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0)
| c_lessequals(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__le__less_1) ).
fof(f1726,plain,
spl0_189,
inference(avatar_split_clause,[],[f81,f1724]) ).
fof(f81,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_Divides_Odiv__class_Omod(X4,X3,tc_nat) = X4 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__if_0) ).
fof(f1722,plain,
spl0_188,
inference(avatar_split_clause,[],[f40,f1720]) ).
fof(f40,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__less__eq_0) ).
fof(f1718,plain,
spl0_187,
inference(avatar_split_clause,[],[f39,f1716]) ).
fof(f1716,plain,
( spl0_187
<=> ! [X5,X3] :
( ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f39,axiom,
! [X3,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__Suc__eq__0__disj_3) ).
fof(f1714,plain,
spl0_186,
inference(avatar_split_clause,[],[f21,f1712]) ).
fof(f1712,plain,
( spl0_186
<=> ! [X5,X0,X8] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f21,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X8,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__le__not__le_1) ).
fof(f1710,plain,
spl0_185,
inference(avatar_split_clause,[],[f19,f1708]) ).
fof(f19,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X5,X8,X0)
| ~ c_HOL_Oord__class_Oless(X8,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__not__le_1) ).
fof(f1706,plain,
spl0_184,
inference(avatar_split_clause,[],[f18,f1704]) ).
fof(f18,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X8,X5,X0)
| c_HOL_Oord__class_Oless(X5,X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__not__less_0) ).
fof(f1702,plain,
( spl0_183
| ~ spl0_142
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1599,f1417,f1381,f1700]) ).
fof(f1381,plain,
( spl0_142
<=> ! [X2] : ~ c_HOL_Oord__class_Oless(c_Suc(X2),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1599,plain,
( ! [X10] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X10)),X10,tc_nat)
| ~ spl0_142
| ~ spl0_147 ),
inference(resolution,[],[f1418,f1382]) ).
fof(f1382,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(c_Suc(X2),X2,tc_nat)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f1559,plain,
spl0_182,
inference(avatar_split_clause,[],[f690,f1557]) ).
fof(f690,plain,
! [X3] :
( ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f6,f297]) ).
fof(f6,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__Suc0_0) ).
fof(f1555,plain,
spl0_181,
inference(avatar_split_clause,[],[f606,f1553]) ).
fof(f606,axiom,
! [X0,X5,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Olist_OCons(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct_Osimps_I2_J_1) ).
fof(f1551,plain,
spl0_180,
inference(avatar_split_clause,[],[f595,f1549]) ).
fof(f1549,plain,
( spl0_180
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f595,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted_Osimps_I2_J_0) ).
fof(f1547,plain,
( spl0_179
| ~ spl0_86
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1371,f1269,f1121,f1545]) ).
fof(f1545,plain,
( spl0_179
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1371,plain,
( ! [X3] : ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_86
| ~ spl0_121 ),
inference(superposition,[],[f1122,f1270]) ).
fof(f1543,plain,
spl0_178,
inference(avatar_split_clause,[],[f586,f1541]) ).
fof(f1541,plain,
( spl0_178
<=> ! [X5,X0] : c_List_Olast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f586,axiom,
! [X0,X5] : c_List_Olast(c_List_Olist_OCons(X5,c_List_Olist_ONil(X0),X0),X0) = X5,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_last_Osimps_0) ).
fof(f1539,plain,
spl0_177,
inference(avatar_split_clause,[],[f580,f1537]) ).
fof(f580,axiom,
! [X0,X6,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Otake(X6,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__take_0) ).
fof(f1535,plain,
spl0_176,
inference(avatar_split_clause,[],[f575,f1533]) ).
fof(f575,axiom,
! [X0,X6,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Odrop(X6,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__drop_0) ).
fof(f1531,plain,
spl0_175,
inference(avatar_split_clause,[],[f572,f1529]) ).
fof(f572,axiom,
! [X0,X12,X13] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__append_0) ).
fof(f1527,plain,
spl0_174,
inference(avatar_split_clause,[],[f571,f1525]) ).
fof(f1525,plain,
( spl0_174
<=> ! [X13,X0,X12] :
( c_List_Odistinct(X13,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f571,axiom,
! [X0,X12,X13] :
( c_List_Odistinct(X13,X0)
| ~ c_List_Odistinct(c_List_Oappend(X12,X13,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__append_1) ).
fof(f1523,plain,
spl0_173,
inference(avatar_split_clause,[],[f570,f1521]) ).
fof(f1521,plain,
( spl0_173
<=> ! [X5,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oremove1(X5,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f570,axiom,
! [X0,X5,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Oremove1(X5,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__remove1_0) ).
fof(f1519,plain,
spl0_172,
inference(avatar_split_clause,[],[f569,f1517]) ).
fof(f1517,plain,
( spl0_172
<=> ! [X0,X12,X3] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f569,axiom,
! [X3,X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__rotate_0) ).
fof(f1515,plain,
spl0_171,
inference(avatar_split_clause,[],[f568,f1513]) ).
fof(f1513,plain,
( spl0_171
<=> ! [X0,X12,X3] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f568,axiom,
! [X3,X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate(X3,X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__rotate_1) ).
fof(f1511,plain,
spl0_170,
inference(avatar_split_clause,[],[f559,f1509]) ).
fof(f1509,plain,
( spl0_170
<=> ! [X6,X0,X8] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X6,X8,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f559,axiom,
! [X0,X8,X6] : c_List_Olist_ONil(X0) = c_List_Olist__update(c_List_Olist_ONil(X0),X6,X8,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__update__code_I1_J_0) ).
fof(f1507,plain,
spl0_169,
inference(avatar_split_clause,[],[f438,f1505]) ).
fof(f1505,plain,
( spl0_169
<=> ! [X5,X0,X12] : c_List_Oremove1(X5,c_List_Olist_OCons(X5,X12,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f438,axiom,
! [X0,X5,X12] : c_List_Oremove1(X5,c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remove1_Osimps_I2_J_0) ).
fof(f1503,plain,
( spl0_168
| ~ spl0_53
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1366,f1253,f974,f1501]) ).
fof(f1253,plain,
( spl0_117
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1366,plain,
( ! [X1] : c_Orderings_Oord__class_Omin(X1,X1,tc_Int_Oint) = X1
| ~ spl0_53
| ~ spl0_117 ),
inference(resolution,[],[f1254,f976]) ).
fof(f1254,plain,
( ! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 )
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f1499,plain,
spl0_167,
inference(avatar_split_clause,[],[f403,f1497]) ).
fof(f403,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X3,tc_nat) = X4,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__add__inverse_0) ).
fof(f1495,plain,
spl0_166,
inference(avatar_split_clause,[],[f402,f1493]) ).
fof(f402,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X3,tc_nat) = X4,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__add__inverse2_0) ).
fof(f1491,plain,
spl0_165,
inference(avatar_split_clause,[],[f401,f1489]) ).
fof(f1489,plain,
( spl0_165
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f401,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1487,plain,
spl0_164,
inference(avatar_split_clause,[],[f400,f1485]) ).
fof(f1485,plain,
( spl0_164
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f400,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1483,plain,
spl0_163,
inference(avatar_split_clause,[],[f399,f1481]) ).
fof(f1481,plain,
( spl0_163
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f399,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1479,plain,
spl0_162,
inference(avatar_split_clause,[],[f398,f1477]) ).
fof(f1477,plain,
( spl0_162
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f398,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_add__0__left_0) ).
fof(f1475,plain,
spl0_161,
inference(avatar_split_clause,[],[f397,f1473]) ).
fof(f397,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1471,plain,
spl0_160,
inference(avatar_split_clause,[],[f392,f1469]) ).
fof(f392,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_comm__monoid__add_Omult__1_0) ).
fof(f1467,plain,
spl0_159,
inference(avatar_split_clause,[],[f255,f1465]) ).
fof(f255,axiom,
! [X3,X0,X5] : c_Nat_Osize__class_Osize(c_List_Oreplicate(X3,X5,X0),tc_List_Olist(X0)) = X3,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__replicate_0) ).
fof(f1463,plain,
spl0_158,
inference(avatar_split_clause,[],[f216,f1461]) ).
fof(f1461,plain,
( spl0_158
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f216,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Oone__class_Oone(tc_nat),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_power__one__right_0) ).
fof(f1459,plain,
( spl0_157
| ~ spl0_20
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1365,f1253,f809,f1457]) ).
fof(f1365,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_20
| ~ spl0_117 ),
inference(resolution,[],[f1254,f811]) ).
fof(f1455,plain,
spl0_156,
inference(avatar_split_clause,[],[f215,f1453]) ).
fof(f215,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X5,c_HOL_Oone__class_Oone(tc_nat),X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_class__semiring_Osemiring__rules_I33_J_0) ).
fof(f1451,plain,
spl0_155,
inference(avatar_split_clause,[],[f201,f1449]) ).
fof(f201,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X8,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__le2_0) ).
fof(f1447,plain,
spl0_154,
inference(avatar_split_clause,[],[f200,f1445]) ).
fof(f200,axiom,
! [X0,X8,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X5,X8,X0),X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__le1_0) ).
fof(f1443,plain,
spl0_153,
inference(avatar_split_clause,[],[f188,f1441]) ).
fof(f188,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__by__0_0) ).
fof(f1439,plain,
spl0_152,
inference(avatar_split_clause,[],[f187,f1437]) ).
fof(f187,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__self_0) ).
fof(f1435,plain,
spl0_151,
inference(avatar_split_clause,[],[f184,f1433]) ).
fof(f184,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) = c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__add__commute_0) ).
fof(f1431,plain,
spl0_150,
inference(avatar_split_clause,[],[f178,f1429]) ).
fof(f1429,plain,
( spl0_150
<=> ! [X5,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f178,axiom,
! [X0,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_eq__iff__diff__eq__0_0) ).
fof(f1427,plain,
spl0_149,
inference(avatar_split_clause,[],[f176,f1425]) ).
fof(f176,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__0__right_0) ).
fof(f1423,plain,
spl0_148,
inference(avatar_split_clause,[],[f175,f1421]) ).
fof(f175,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__self_0) ).
fof(f1419,plain,
spl0_147,
inference(avatar_split_clause,[],[f137,f1417]) ).
fof(f137,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__SucI_0) ).
fof(f1414,plain,
spl0_146,
inference(avatar_split_clause,[],[f136,f1412]) ).
fof(f136,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X4),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__lessD_0) ).
fof(f1410,plain,
spl0_145,
inference(avatar_split_clause,[],[f109,f1408]) ).
fof(f109,axiom,
! [X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_gr0I_0) ).
fof(f1406,plain,
spl0_144,
inference(avatar_split_clause,[],[f36,f1404]) ).
fof(f36,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__less__eq_0) ).
fof(f1402,plain,
spl0_143,
inference(avatar_split_clause,[],[f35,f1400]) ).
fof(f35,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__less__eq_1) ).
fof(f1383,plain,
( spl0_142
| ~ spl0_87
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1370,f1269,f1125,f1381]) ).
fof(f1370,plain,
( ! [X2] : ~ c_HOL_Oord__class_Oless(c_Suc(X2),X2,tc_nat)
| ~ spl0_87
| ~ spl0_121 ),
inference(superposition,[],[f1126,f1270]) ).
fof(f1361,plain,
( spl0_141
| ~ spl0_110
| ~ spl0_114 ),
inference(avatar_split_clause,[],[f1357,f1241,f1225,f1359]) ).
fof(f1357,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_110
| ~ spl0_114 ),
inference(superposition,[],[f1226,f1242]) ).
fof(f1347,plain,
spl0_140,
inference(avatar_split_clause,[],[f677,f1345]) ).
fof(f1345,plain,
( spl0_140
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f677,plain,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),
inference(forward_demodulation,[],[f222,f297]) ).
fof(f222,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_mod__1_0) ).
fof(f1343,plain,
spl0_139,
inference(avatar_split_clause,[],[f579,f1341]) ).
fof(f579,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__remdups__id_0) ).
fof(f1339,plain,
spl0_138,
inference(avatar_split_clause,[],[f578,f1337]) ).
fof(f1337,plain,
( spl0_138
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) != X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f578,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| c_List_Oremdups(X12,X0) != X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remdups__id__iff__distinct_0) ).
fof(f1335,plain,
spl0_137,
inference(avatar_split_clause,[],[f577,f1333]) ).
fof(f1333,plain,
( spl0_137
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orev(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f577,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__rev_0) ).
fof(f1331,plain,
spl0_136,
inference(avatar_split_clause,[],[f576,f1329]) ).
fof(f576,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orev(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__rev_1) ).
fof(f1327,plain,
spl0_135,
inference(avatar_split_clause,[],[f574,f1325]) ).
fof(f1325,plain,
( spl0_135
<=> ! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f574,axiom,
! [X0,X12] :
( c_List_Odistinct(X12,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct1__rotate_0) ).
fof(f1323,plain,
spl0_134,
inference(avatar_split_clause,[],[f573,f1321]) ).
fof(f573,axiom,
! [X0,X12] :
( ~ c_List_Odistinct(X12,X0)
| c_List_Odistinct(c_List_Orotate1(X12,X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct1__rotate_1) ).
fof(f1319,plain,
spl0_133,
inference(avatar_split_clause,[],[f563,f1317]) ).
fof(f1317,plain,
( spl0_133
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Orotate(X3,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f563,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Orotate(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__is__Nil__conv_1) ).
fof(f1315,plain,
spl0_132,
inference(avatar_split_clause,[],[f561,f1313]) ).
fof(f1313,plain,
( spl0_132
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_Oremove1(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f561,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oremove1(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remove1_Osimps_I1_J_0) ).
fof(f1311,plain,
spl0_131,
inference(avatar_split_clause,[],[f553,f1309]) ).
fof(f1309,plain,
( spl0_131
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Otake(X3,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f553,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Otake(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__eq__Nil_2) ).
fof(f1307,plain,
spl0_130,
inference(avatar_split_clause,[],[f546,f1305]) ).
fof(f1305,plain,
( spl0_130
<=> ! [X0,X37] : c_List_Olist_ONil(X0) = c_List_Olist__inter(c_List_Olist_ONil(X0),X37,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f546,axiom,
! [X0,X37] : c_List_Olist_ONil(X0) = c_List_Olist__inter(c_List_Olist_ONil(X0),X37,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_list__inter_Osimps_I1_J_0) ).
fof(f1303,plain,
spl0_129,
inference(avatar_split_clause,[],[f545,f1301]) ).
fof(f1301,plain,
( spl0_129
<=> ! [X0,X3] : c_List_Olist_ONil(X0) = c_List_Odrop(X3,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f545,axiom,
! [X3,X0] : c_List_Olist_ONil(X0) = c_List_Odrop(X3,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__Nil_0) ).
fof(f1299,plain,
spl0_128,
inference(avatar_split_clause,[],[f525,f1297]) ).
fof(f1297,plain,
( spl0_128
<=> ! [X5,X0] : c_List_Olist_ONil(X0) = c_List_OremoveAll(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f525,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_OremoveAll(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_removeAll_Osimps_I1_J_0) ).
fof(f1295,plain,
spl0_127,
inference(avatar_split_clause,[],[f487,f1293]) ).
fof(f487,axiom,
! [X0,X12] : c_List_Olist_ONil(X0) = c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_take__0_0) ).
fof(f1291,plain,
spl0_126,
inference(avatar_split_clause,[],[f483,f1289]) ).
fof(f483,axiom,
! [X0,X5] : c_List_Olist_ONil(X0) = c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),X5,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_empty__replicate_1) ).
fof(f1287,plain,
spl0_125,
inference(avatar_split_clause,[],[f446,f1285]) ).
fof(f446,axiom,
! [X0,X5,X12] : c_List_Otl(c_List_Olist_OCons(X5,X12,X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_tl_Osimps_I2_J_0) ).
fof(f1283,plain,
spl0_124,
inference(avatar_split_clause,[],[f406,f1281]) ).
fof(f406,axiom,
! [X0,X5,X12] : c_List_Ohd(c_List_Olist_OCons(X5,X12,X0),X0) = X5,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_hd_Osimps_0) ).
fof(f1279,plain,
spl0_123,
inference(avatar_split_clause,[],[f363,f1277]) ).
fof(f363,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__0__eq__0_0) ).
fof(f1275,plain,
spl0_122,
inference(avatar_split_clause,[],[f314,f1273]) ).
fof(f1271,plain,
spl0_121,
inference(avatar_split_clause,[],[f313,f1269]) ).
fof(f313,axiom,
! [X3] : c_Suc(X3) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__eq__plus1__left_0) ).
fof(f1267,plain,
spl0_120,
inference(avatar_split_clause,[],[f293,f1265]) ).
fof(f1265,plain,
( spl0_120
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f293,axiom,
! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osize__class_Osize(c_List_Olist_ONil(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_length__0__conv_1) ).
fof(f1263,plain,
spl0_119,
inference(avatar_split_clause,[],[f290,f1261]) ).
fof(f1261,plain,
( spl0_119
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f290,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__one__le__zero_0) ).
fof(f1259,plain,
spl0_118,
inference(avatar_split_clause,[],[f288,f1257]) ).
fof(f1257,plain,
( spl0_118
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f288,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__le__one_0) ).
fof(f1255,plain,
spl0_117,
inference(avatar_split_clause,[],[f228,f1253]) ).
fof(f228,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X5,X5,X0) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__max_Oinf__idem_0) ).
fof(f1251,plain,
spl0_116,
inference(avatar_split_clause,[],[f213,f1249]) ).
fof(f213,axiom,
! [X8,X5] :
( X5 = X8
| c_Suc(X5) != c_Suc(X8) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__inject_0) ).
fof(f1247,plain,
spl0_115,
inference(avatar_split_clause,[],[f207,f1245]) ).
fof(f207,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__0R_0) ).
fof(f1243,plain,
spl0_114,
inference(avatar_split_clause,[],[f189,f1241]) ).
fof(f189,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(c_Suc(X3),c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__Suc__1_0) ).
fof(f1239,plain,
spl0_113,
inference(avatar_split_clause,[],[f163,f1237]) ).
fof(f163,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_min__0L_0) ).
fof(f1235,plain,
spl0_112,
inference(avatar_split_clause,[],[f155,f1233]) ).
fof(f1233,plain,
( spl0_112
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f155,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__one_0) ).
fof(f1231,plain,
spl0_111,
inference(avatar_split_clause,[],[f154,f1229]) ).
fof(f1229,plain,
( spl0_111
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f154,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__one__less__zero_0) ).
fof(f1227,plain,
spl0_110,
inference(avatar_split_clause,[],[f7,f1225]) ).
fof(f7,axiom,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__less__Suc_0) ).
fof(f1223,plain,
spl0_109,
inference(avatar_split_clause,[],[f3,f1221]) ).
fof(f3,axiom,
! [X6,X4] : c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Oplus__class_Oplus(X4,X6,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__add__Suc2_0) ).
fof(f1219,plain,
spl0_108,
inference(avatar_split_clause,[],[f2,f1217]) ).
fof(f2,axiom,
! [X4,X5] : c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Oplus__class_Oplus(X4,X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_less__iff__Suc__add_1) ).
fof(f1208,plain,
spl0_107,
inference(avatar_split_clause,[],[f602,f1206]) ).
fof(f602,axiom,
! [X0,X27,X5] : c_List_Olist_ONil(X0) != c_List_Olist_OCons(X5,X27,X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_neq__Nil__conv_1) ).
fof(f1204,plain,
spl0_106,
inference(avatar_split_clause,[],[f565,f1202]) ).
fof(f1202,plain,
( spl0_106
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f565,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orev(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__is__Nil__conv_1) ).
fof(f1200,plain,
spl0_105,
inference(avatar_split_clause,[],[f554,f1198]) ).
fof(f1198,plain,
( spl0_105
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f554,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Orotate1(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rotate__simps_0) ).
fof(f1196,plain,
( spl0_104
| ~ spl0_72
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f1111,f1083,f1059,f1193]) ).
fof(f1193,plain,
( spl0_104
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1059,plain,
( spl0_72
<=> ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1111,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_72
| ~ spl0_78 ),
inference(superposition,[],[f1060,f1085]) ).
fof(f1060,plain,
( ! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat)
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1191,plain,
spl0_103,
inference(avatar_split_clause,[],[f551,f1189]) ).
fof(f551,axiom,
! [X0,X12] : c_List_Oappend(X12,c_List_Olist_ONil(X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__Nil2_0) ).
fof(f1187,plain,
spl0_102,
inference(avatar_split_clause,[],[f548,f1185]) ).
fof(f548,axiom,
! [X0,X13] : c_List_Oappend(c_List_Olist_ONil(X0),X13,X0) = X13,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_append__Nil_0) ).
fof(f1183,plain,
spl0_101,
inference(avatar_split_clause,[],[f536,f1181]) ).
fof(f1181,plain,
( spl0_101
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Otl(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f536,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Otl(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_tl_Osimps_I1_J_0) ).
fof(f1179,plain,
spl0_100,
inference(avatar_split_clause,[],[f535,f1177]) ).
fof(f1177,plain,
( spl0_100
<=> ! [X13,X0] : c_List_Osplice(c_List_Olist_ONil(X0),X13,X0) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f535,axiom,
! [X0,X13] : c_List_Osplice(c_List_Olist_ONil(X0),X13,X0) = X13,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_splice_Osimps_I1_J_0) ).
fof(f1175,plain,
spl0_99,
inference(avatar_split_clause,[],[f534,f1173]) ).
fof(f1173,plain,
( spl0_99
<=> ! [X0,X12] : c_List_Osplice(X12,c_List_Olist_ONil(X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f534,axiom,
! [X0,X12] : c_List_Osplice(X12,c_List_Olist_ONil(X0),X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_splice__Nil2_0) ).
fof(f1171,plain,
spl0_98,
inference(avatar_split_clause,[],[f528,f1169]) ).
fof(f1169,plain,
( spl0_98
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f528,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_remdups__eq__nil__right__iff_1) ).
fof(f1167,plain,
spl0_97,
inference(avatar_split_clause,[],[f527,f1165]) ).
fof(f1165,plain,
( spl0_97
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f527,axiom,
! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_butlast_Osimps_I1_J_0) ).
fof(f1163,plain,
spl0_96,
inference(avatar_split_clause,[],[f524,f1161]) ).
fof(f1161,plain,
( spl0_96
<=> ! [X0,X12] :
( ~ c_List_Onull(X12,X0)
| c_List_Olist_ONil(X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f524,axiom,
! [X0,X12] :
( ~ c_List_Onull(X12,X0)
| c_List_Olist_ONil(X0) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_empty__null_1) ).
fof(f1159,plain,
spl0_95,
inference(avatar_split_clause,[],[f476,f1157]) ).
fof(f476,axiom,
! [X0,X13] : c_List_Orev(c_List_Orev(X13,X0),X0) = X13,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_rev__swap_1) ).
fof(f1155,plain,
spl0_94,
inference(avatar_split_clause,[],[f465,f1153]) ).
fof(f1153,plain,
( spl0_94
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f465,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__neq__one_0) ).
fof(f1151,plain,
spl0_93,
inference(avatar_split_clause,[],[f464,f1149]) ).
fof(f464,axiom,
! [X0,X12] : c_List_Odrop(c_HOL_Ozero__class_Ozero(tc_nat),X12,X0) = X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_drop__0_0) ).
fof(f1147,plain,
spl0_92,
inference(avatar_split_clause,[],[f447,f1145]) ).
fof(f447,axiom,
! [X0,X5,X13] : c_List_Omember(X5,c_List_Olist_OCons(X5,X13,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_List_Omember_Osimps_I2_J_1) ).
fof(f1143,plain,
spl0_91,
inference(avatar_split_clause,[],[f395,f1141]) ).
fof(f395,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Nat_Oadd__0__right_0) ).
fof(f1139,plain,
spl0_90,
inference(avatar_split_clause,[],[f394,f1137]) ).
fof(f394,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) = X3,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_plus__nat_Oadd__0_0) ).
fof(f1135,plain,
spl0_89,
inference(avatar_split_clause,[],[f173,f1133]) ).
fof(f173,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,X4,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_diff__self__eq__0_0) ).
fof(f1131,plain,
spl0_88,
inference(avatar_split_clause,[],[f172,f1129]) ).
fof(f1129,plain,
( spl0_88
<=> ! [X4] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f172,axiom,
! [X4] : c_HOL_Ominus__class_Ominus(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X4,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_minus__nat_Odiff__0_0) ).
fof(f1127,plain,
spl0_87,
inference(avatar_split_clause,[],[f117,f1125]) ).
fof(f117,axiom,
! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X15,X6,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__add__less2_0) ).
fof(f1123,plain,
spl0_86,
inference(avatar_split_clause,[],[f116,f1121]) ).
fof(f116,axiom,
! [X6,X15] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X6,X15,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__add__less1_0) ).
fof(f1119,plain,
( ~ spl0_85
| ~ spl0_69
| ~ spl0_78 ),
inference(avatar_split_clause,[],[f1112,f1083,f1047,f1116]) ).
fof(f1116,plain,
( spl0_85
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1047,plain,
( spl0_69
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1112,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_69
| ~ spl0_78 ),
inference(superposition,[],[f1048,f1085]) ).
fof(f1048,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X4)
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f1047]) ).
fof(f1110,plain,
spl0_84,
inference(avatar_split_clause,[],[f615,f1108]) ).
fof(f1108,plain,
( spl0_84
<=> ! [X41,X42] :
( ~ class_HOL_Oord(X42)
| class_HOL_Oord(tc_fun(X41,X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f615,axiom,
! [X41,X42] :
( ~ class_HOL_Oord(X42)
| class_HOL_Oord(tc_fun(X41,X42)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_fun__HOL_Oord) ).
fof(f1106,plain,
spl0_83,
inference(avatar_split_clause,[],[f614,f1104]) ).
fof(f1104,plain,
( spl0_83
<=> ! [X41,X42] :
( ~ class_Orderings_Oorder(X42)
| class_Orderings_Oorder(tc_fun(X41,X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f614,axiom,
! [X41,X42] :
( ~ class_Orderings_Oorder(X42)
| class_Orderings_Oorder(tc_fun(X41,X42)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_fun__Orderings_Oorder) ).
fof(f1102,plain,
spl0_82,
inference(avatar_split_clause,[],[f613,f1100]) ).
fof(f1100,plain,
( spl0_82
<=> ! [X41,X42] :
( ~ class_Orderings_Opreorder(X42)
| class_Orderings_Opreorder(tc_fun(X41,X42)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f613,axiom,
! [X41,X42] :
( ~ class_Orderings_Opreorder(X42)
| class_Orderings_Opreorder(tc_fun(X41,X42)) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_fun__Orderings_Opreorder) ).
fof(f1098,plain,
spl0_81,
inference(avatar_split_clause,[],[f605,f1096]) ).
fof(f605,axiom,
! [X0,X5,X12] : c_List_Olist_OCons(X5,X12,X0) != X12,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__Cons__self_0) ).
fof(f1094,plain,
spl0_80,
inference(avatar_split_clause,[],[f556,f1092]) ).
fof(f1092,plain,
( spl0_80
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f556,axiom,
! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_List_Olinorder__class_Osorted(c_List_Olist_ONil(X0),X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_sorted_Osimps_I1_J_0) ).
fof(f1090,plain,
spl0_79,
inference(avatar_split_clause,[],[f449,f1088]) ).
fof(f449,axiom,
! [X0,X5,X12] : ~ c_List_Onull(c_List_Olist_OCons(X5,X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_List_Onull_Osimps_I2_J_0) ).
fof(f1086,plain,
spl0_78,
inference(avatar_split_clause,[],[f297,f1083]) ).
fof(f1081,plain,
spl0_77,
inference(avatar_split_clause,[],[f265,f1079]) ).
fof(f1079,plain,
( spl0_77
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f265,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__eq__refl_0) ).
fof(f1077,plain,
spl0_76,
inference(avatar_split_clause,[],[f264,f1075]) ).
fof(f1075,plain,
( spl0_76
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f264,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__eq__iff_0) ).
fof(f1073,plain,
spl0_75,
inference(avatar_split_clause,[],[f87,f1071]) ).
fof(f1071,plain,
( spl0_75
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f87,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__irrefl_0) ).
fof(f1069,plain,
spl0_74,
inference(avatar_split_clause,[],[f86,f1067]) ).
fof(f86,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_linorder__neq__iff_1) ).
fof(f1065,plain,
spl0_73,
inference(avatar_split_clause,[],[f85,f1063]) ).
fof(f1063,plain,
( spl0_73
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f85,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_order__less__le_1) ).
fof(f1061,plain,
spl0_72,
inference(avatar_split_clause,[],[f22,f1059]) ).
fof(f22,axiom,
! [X3] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_zero__less__Suc_0) ).
fof(f1057,plain,
spl0_71,
inference(avatar_split_clause,[],[f567,f1055]) ).
fof(f567,axiom,
! [X0,X12] : c_List_Odistinct(c_List_Oremdups(X12,X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct__remdups_0) ).
fof(f1053,plain,
spl0_70,
inference(avatar_split_clause,[],[f539,f1051]) ).
fof(f1051,plain,
( spl0_70
<=> ! [X5,X0] : ~ c_List_Omember(X5,c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f539,axiom,
! [X0,X5] : ~ c_List_Omember(X5,c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_List_Omember_Osimps_I1_J_0) ).
fof(f1049,plain,
spl0_69,
inference(avatar_split_clause,[],[f240,f1047]) ).
fof(f240,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X4),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_Suc__neq__Zero_0) ).
fof(f1045,plain,
spl0_68,
inference(avatar_split_clause,[],[f102,f1043]) ).
fof(f102,axiom,
! [X3] : c_HOL_Oord__class_Oless(X3,c_Suc(X3),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_lessI_0) ).
fof(f1041,plain,
spl0_67,
inference(avatar_split_clause,[],[f12,f1039]) ).
fof(f12,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_not__less0_0) ).
fof(f1037,plain,
spl0_66,
inference(avatar_split_clause,[],[f600,f1035]) ).
fof(f1035,plain,
( spl0_66
<=> ! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f600,axiom,
! [X0] : c_List_Odistinct(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_distinct_Osimps_I1_J_0) ).
fof(f1033,plain,
spl0_65,
inference(avatar_split_clause,[],[f555,f1031]) ).
fof(f1031,plain,
( spl0_65
<=> ! [X0] : c_List_Onull(c_List_Olist_ONil(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f555,axiom,
! [X0] : c_List_Onull(c_List_Olist_ONil(X0),X0),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_empty__null_0) ).
fof(f1029,plain,
spl0_64,
inference(avatar_split_clause,[],[f259,f1027]) ).
fof(f1027,plain,
( spl0_64
<=> ! [X3] : c_Suc(X3) != X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f259,axiom,
! [X3] : c_Suc(X3) != X3,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_n__not__Suc__n_0) ).
fof(f1025,plain,
spl0_63,
inference(avatar_split_clause,[],[f83,f1023]) ).
fof(f1023,plain,
( spl0_63
<=> ! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f83,axiom,
! [X5] : ~ c_HOL_Oord__class_Oless(X5,X5,tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_nat__less__le_1) ).
fof(f1021,plain,
( spl0_62
| spl0_1 ),
inference(avatar_split_clause,[],[f612,f714,f1019]) ).
fof(f714,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f612,axiom,
! [X5] :
( v_thesis____
| ~ c_List_Odistinct(c_List_Olist_OCons(v_c____,c_List_Olist_OCons(v_d____,c_List_Olist_OCons(X5,c_List_Olist_ONil(tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt) ),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_conjecture_1) ).
fof(f1017,plain,
~ spl0_61,
inference(avatar_split_clause,[],[f609,f1014]) ).
fof(f609,axiom,
v_c____ != v_d____,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_CHAINED_0_02) ).
fof(f1012,plain,
spl0_60,
inference(avatar_split_clause,[],[f674,f1009]) ).
fof(f1009,plain,
( spl0_60
<=> class_HOL_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f674,axiom,
class_HOL_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__HOL_Oord) ).
fof(f1007,plain,
spl0_59,
inference(avatar_split_clause,[],[f673,f1004]) ).
fof(f1004,plain,
( spl0_59
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f673,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Int_Onumber) ).
fof(f1002,plain,
spl0_58,
inference(avatar_split_clause,[],[f672,f999]) ).
fof(f672,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Power_Opower) ).
fof(f997,plain,
spl0_57,
inference(avatar_split_clause,[],[f671,f994]) ).
fof(f994,plain,
( spl0_57
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f671,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Int_Onumber__ring) ).
fof(f992,plain,
spl0_56,
inference(avatar_split_clause,[],[f670,f989]) ).
fof(f989,plain,
( spl0_56
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f670,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Int_Oring__char__0) ).
fof(f987,plain,
spl0_55,
inference(avatar_split_clause,[],[f669,f984]) ).
fof(f984,plain,
( spl0_55
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f669,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Orderings_Oorder) ).
fof(f982,plain,
spl0_54,
inference(avatar_split_clause,[],[f668,f979]) ).
fof(f979,plain,
( spl0_54
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f668,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Divides_Oring__div) ).
fof(f977,plain,
spl0_53,
inference(avatar_split_clause,[],[f667,f974]) ).
fof(f667,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Orderings_Olinorder) ).
fof(f972,plain,
spl0_52,
inference(avatar_split_clause,[],[f666,f969]) ).
fof(f969,plain,
( spl0_52
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f666,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Orderings_Opreorder) ).
fof(f967,plain,
spl0_51,
inference(avatar_split_clause,[],[f665,f964]) ).
fof(f964,plain,
( spl0_51
<=> class_Ring__and__Field_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f665,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Oidom) ).
fof(f962,plain,
spl0_50,
inference(avatar_split_clause,[],[f664,f959]) ).
fof(f664,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Divides_Osemiring__div) ).
fof(f957,plain,
spl0_49,
inference(avatar_split_clause,[],[f663,f954]) ).
fof(f663,axiom,
class_OrderedGroup_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).
fof(f952,plain,
spl0_48,
inference(avatar_split_clause,[],[f662,f949]) ).
fof(f949,plain,
( spl0_48
<=> class_OrderedGroup_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f662,axiom,
class_OrderedGroup_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Omonoid__add) ).
fof(f947,plain,
spl0_47,
inference(avatar_split_clause,[],[f661,f944]) ).
fof(f661,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Omonoid__mult) ).
fof(f942,plain,
spl0_46,
inference(avatar_split_clause,[],[f660,f939]) ).
fof(f939,plain,
( spl0_46
<=> class_Ring__and__Field_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f660,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).
fof(f937,plain,
spl0_45,
inference(avatar_split_clause,[],[f659,f934]) ).
fof(f934,plain,
( spl0_45
<=> class_OrderedGroup_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f659,axiom,
class_OrderedGroup_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).
fof(f932,plain,
spl0_44,
inference(avatar_split_clause,[],[f658,f929]) ).
fof(f658,axiom,
class_Ring__and__Field_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Osemiring__0) ).
fof(f927,plain,
spl0_43,
inference(avatar_split_clause,[],[f657,f924]) ).
fof(f924,plain,
( spl0_43
<=> class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f657,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).
fof(f922,plain,
spl0_42,
inference(avatar_split_clause,[],[f656,f919]) ).
fof(f919,plain,
( spl0_42
<=> class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f656,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one) ).
fof(f917,plain,
spl0_41,
inference(avatar_split_clause,[],[f655,f914]) ).
fof(f655,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__add) ).
fof(f912,plain,
spl0_40,
inference(avatar_split_clause,[],[f654,f909]) ).
fof(f909,plain,
( spl0_40
<=> class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f654,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__add) ).
fof(f907,plain,
spl0_39,
inference(avatar_split_clause,[],[f653,f904]) ).
fof(f653,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).
fof(f902,plain,
spl0_38,
inference(avatar_split_clause,[],[f652,f899]) ).
fof(f899,plain,
( spl0_38
<=> class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f652,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Oordered__semidom) ).
fof(f897,plain,
spl0_37,
inference(avatar_split_clause,[],[f651,f894]) ).
fof(f894,plain,
( spl0_37
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f651,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).
fof(f892,plain,
spl0_36,
inference(avatar_split_clause,[],[f650,f889]) ).
fof(f889,plain,
( spl0_36
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f650,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Ocancel__semigroup__add) ).
fof(f887,plain,
spl0_35,
inference(avatar_split_clause,[],[f649,f884]) ).
fof(f884,plain,
( spl0_35
<=> class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f649,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).
fof(f882,plain,
spl0_34,
inference(avatar_split_clause,[],[f648,f879]) ).
fof(f879,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f648,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).
fof(f877,plain,
spl0_33,
inference(avatar_split_clause,[],[f647,f874]) ).
fof(f874,plain,
( spl0_33
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f647,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f872,plain,
spl0_32,
inference(avatar_split_clause,[],[f646,f869]) ).
fof(f869,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f646,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f867,plain,
spl0_31,
inference(avatar_split_clause,[],[f645,f864]) ).
fof(f864,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f645,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f862,plain,
spl0_30,
inference(avatar_split_clause,[],[f644,f859]) ).
fof(f859,plain,
( spl0_30
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f644,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f857,plain,
spl0_29,
inference(avatar_split_clause,[],[f643,f854]) ).
fof(f854,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f643,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f852,plain,
spl0_28,
inference(avatar_split_clause,[],[f642,f849]) ).
fof(f849,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f642,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_Int__Oint__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f847,plain,
spl0_27,
inference(avatar_split_clause,[],[f641,f844]) ).
fof(f844,plain,
( spl0_27
<=> class_HOL_Oord(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f641,axiom,
class_HOL_Oord(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_bool__HOL_Oord) ).
fof(f842,plain,
spl0_26,
inference(avatar_split_clause,[],[f640,f839]) ).
fof(f839,plain,
( spl0_26
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f640,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_bool__Orderings_Oorder) ).
fof(f837,plain,
spl0_25,
inference(avatar_split_clause,[],[f639,f834]) ).
fof(f834,plain,
( spl0_25
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f639,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_bool__Orderings_Opreorder) ).
fof(f832,plain,
spl0_24,
inference(avatar_split_clause,[],[f638,f829]) ).
fof(f829,plain,
( spl0_24
<=> class_HOL_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f638,axiom,
class_HOL_Oord(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__HOL_Oord) ).
fof(f827,plain,
spl0_23,
inference(avatar_split_clause,[],[f637,f824]) ).
fof(f824,plain,
( spl0_23
<=> class_Int_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f637,axiom,
class_Int_Onumber(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Int_Onumber) ).
fof(f822,plain,
spl0_22,
inference(avatar_split_clause,[],[f636,f819]) ).
fof(f636,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Power_Opower) ).
fof(f817,plain,
spl0_21,
inference(avatar_split_clause,[],[f635,f814]) ).
fof(f635,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Orderings_Oorder) ).
fof(f812,plain,
spl0_20,
inference(avatar_split_clause,[],[f634,f809]) ).
fof(f634,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Orderings_Olinorder) ).
fof(f807,plain,
spl0_19,
inference(avatar_split_clause,[],[f633,f804]) ).
fof(f804,plain,
( spl0_19
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f633,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Orderings_Opreorder) ).
fof(f802,plain,
spl0_18,
inference(avatar_split_clause,[],[f632,f799]) ).
fof(f632,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Divides_Osemiring__div) ).
fof(f797,plain,
spl0_17,
inference(avatar_split_clause,[],[f631,f794]) ).
fof(f794,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f631,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f792,plain,
spl0_16,
inference(avatar_split_clause,[],[f630,f789]) ).
fof(f630,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f787,plain,
spl0_15,
inference(avatar_split_clause,[],[f629,f784]) ).
fof(f784,plain,
( spl0_15
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f629,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f782,plain,
spl0_14,
inference(avatar_split_clause,[],[f628,f779]) ).
fof(f628,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f777,plain,
spl0_13,
inference(avatar_split_clause,[],[f627,f774]) ).
fof(f774,plain,
( spl0_13
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f627,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f772,plain,
spl0_12,
inference(avatar_split_clause,[],[f626,f769]) ).
fof(f769,plain,
( spl0_12
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f626,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f767,plain,
spl0_11,
inference(avatar_split_clause,[],[f625,f764]) ).
fof(f764,plain,
( spl0_11
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f625,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f762,plain,
spl0_10,
inference(avatar_split_clause,[],[f624,f759]) ).
fof(f624,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f757,plain,
spl0_9,
inference(avatar_split_clause,[],[f623,f754]) ).
fof(f754,plain,
( spl0_9
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f623,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f752,plain,
spl0_8,
inference(avatar_split_clause,[],[f622,f749]) ).
fof(f749,plain,
( spl0_8
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f622,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f747,plain,
spl0_7,
inference(avatar_split_clause,[],[f621,f744]) ).
fof(f744,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f621,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f742,plain,
spl0_6,
inference(avatar_split_clause,[],[f620,f739]) ).
fof(f739,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f620,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f737,plain,
spl0_5,
inference(avatar_split_clause,[],[f619,f734]) ).
fof(f734,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f619,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f732,plain,
spl0_4,
inference(avatar_split_clause,[],[f618,f729]) ).
fof(f729,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f618,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f727,plain,
spl0_3,
inference(avatar_split_clause,[],[f617,f724]) ).
fof(f724,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f617,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f722,plain,
spl0_2,
inference(avatar_split_clause,[],[f616,f719]) ).
fof(f719,plain,
( spl0_2
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f616,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f717,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f611,f714]) ).
fof(f611,axiom,
~ v_thesis____,
file('/export/starexec/sandbox2/tmp/tmp.lG1LcqGMxE/Vampire---4.8_28517',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SCT088-1 : TPTP v8.1.2. Released v4.1.0.
% 0.16/0.16 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.16/0.38 % Computer : n013.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Wed Aug 30 14:35:32 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.45 % (28707)Running in auto input_syntax mode. Trying TPTP
% 0.23/0.47 % (28711)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on Vampire---4 for (569ds/0Mi)
% 0.23/0.48 % (28710)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.23/0.48 % (28713)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.23/0.48 % (28714)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on Vampire---4 for (531ds/0Mi)
% 0.23/0.48 % (28715)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on Vampire---4 for (522ds/0Mi)
% 0.23/0.48 % (28716)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on Vampire---4 for (497ds/0Mi)
% 0.23/0.49 % (28708)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.23/0.53 TRYING [1]
% 0.23/0.54 TRYING [2]
% 1.30/0.70 TRYING [3]
% 1.97/0.79 TRYING [1]
% 2.40/0.84 TRYING [2]
% 4.49/1.10 TRYING [1]
% 4.49/1.11 TRYING [2]
% 4.93/1.20 % (28714)First to succeed.
% 4.93/1.23 % (28714)Refutation found. Thanks to Tanya!
% 4.93/1.23 % SZS status Unsatisfiable for Vampire---4
% 4.93/1.23 % SZS output start Proof for Vampire---4
% See solution above
% 4.93/1.25 % (28714)------------------------------
% 4.93/1.25 % (28714)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 4.93/1.25 % (28714)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 4.93/1.25 % (28714)Termination reason: Refutation
% 4.93/1.25
% 4.93/1.25 % (28714)Memory used [KB]: 22643
% 4.93/1.25 % (28714)Time elapsed: 0.756 s
% 4.93/1.25 % (28714)------------------------------
% 4.93/1.25 % (28714)------------------------------
% 4.93/1.25 % (28707)Success in time 0.834 s
% 4.93/1.25 % Vampire---4.8 exiting
%------------------------------------------------------------------------------