TSTP Solution File: ALG428-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:30:23 EDT 2024
% Result : Unsatisfiable 23.49s 3.81s
% Output : Refutation 23.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1898
% Syntax : Number of formulae : 3961 ( 832 unt; 0 def)
% Number of atoms : 10657 (1438 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 12114 (5418 ~;5502 |; 0 &)
% (1194 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1246 (1244 usr;1196 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 3 con; 0-3 aty)
% Number of variables : 6667 (6667 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f54743,plain,
$false,
inference(avatar_sat_refutation,[],[f907,f911,f916,f921,f926,f931,f936,f941,f946,f951,f956,f961,f966,f971,f976,f981,f986,f991,f996,f1001,f1006,f1011,f1016,f1021,f1026,f1031,f1036,f1041,f1046,f1051,f1056,f1061,f1066,f1071,f1076,f1081,f1086,f1091,f1096,f1101,f1106,f1111,f1116,f1121,f1126,f1131,f1136,f1141,f1146,f1151,f1156,f1161,f1166,f1171,f1176,f1181,f1186,f1190,f1194,f1198,f1202,f1206,f1210,f1214,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,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1423,f1428,f1432,f1436,f1440,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1484,f1488,f1503,f1507,f1511,f1515,f1519,f1523,f1527,f1531,f1535,f1539,f1543,f1547,f1551,f1555,f1572,f1592,f1596,f1600,f1604,f1608,f1612,f1616,f1620,f1624,f1628,f1632,f1636,f1640,f1644,f1648,f1652,f1656,f1660,f1664,f1668,f1672,f1676,f1680,f1684,f1688,f1692,f1696,f1700,f1704,f1708,f1712,f1716,f1720,f1724,f1728,f1732,f1736,f1740,f1744,f1748,f1752,f1756,f1835,f1943,f1997,f2001,f2005,f2009,f2013,f2017,f2021,f2025,f2029,f2033,f2037,f2041,f2045,f2049,f2053,f2057,f2064,f2068,f2072,f2076,f2080,f2084,f2088,f2092,f2096,f2100,f2109,f2113,f2117,f2121,f2125,f2129,f2133,f2137,f2141,f2156,f2209,f2343,f2381,f2385,f2389,f2393,f2397,f2401,f2405,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2442,f2446,f2450,f2458,f2462,f2466,f2470,f2474,f2478,f2482,f2486,f2490,f2494,f2498,f2502,f2506,f2510,f2514,f2518,f2522,f2526,f2715,f2804,f2914,f2947,f2951,f2955,f2959,f2963,f2967,f2971,f2975,f2979,f2983,f2987,f2991,f2995,f2999,f3003,f3007,f3011,f3015,f3019,f3023,f3027,f3031,f3035,f3039,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3072,f3076,f3080,f3084,f3088,f3092,f3096,f3100,f3164,f3260,f3487,f3592,f3609,f3613,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3665,f3669,f3673,f3678,f3682,f3686,f3690,f3694,f3698,f3702,f3706,f3710,f3714,f3718,f3722,f3726,f3730,f3734,f3738,f3742,f3746,f3750,f3754,f3758,f3762,f3766,f3770,f3774,f3778,f3782,f3786,f3790,f3794,f3798,f3803,f3840,f3845,f3879,f3883,f3887,f3891,f3895,f3899,f4532,f4965,f4969,f4973,f4977,f4981,f4985,f4989,f4993,f4997,f5001,f5005,f5009,f5013,f5017,f5021,f5025,f5029,f5033,f5037,f5041,f5045,f5049,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5101,f5105,f5109,f5113,f5117,f5121,f5125,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5191,f5195,f5199,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5828,f6390,f6942,f6946,f6950,f6954,f6958,f6962,f6966,f6970,f6974,f6978,f6982,f6986,f6990,f6994,f7011,f7015,f7019,f7023,f7027,f7031,f7035,f7039,f7043,f7047,f7051,f7055,f7059,f7063,f7067,f7071,f7075,f7407,f8035,f8039,f8043,f8047,f8051,f8055,f8059,f8063,f8067,f8071,f8075,f8079,f8083,f8087,f8091,f8095,f8115,f8119,f8123,f8127,f8131,f8135,f8139,f8143,f8147,f8151,f8155,f8159,f8629,f8976,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9336,f9340,f9344,f9348,f9352,f9356,f9360,f9364,f9368,f9372,f9376,f9380,f9384,f9388,f9392,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9456,f9460,f9464,f9468,f9472,f9476,f9504,f9713,f9869,f10008,f10128,f10132,f10136,f10140,f10144,f10149,f10153,f10157,f10161,f10165,f10169,f10173,f10177,f10181,f10185,f10189,f10194,f10198,f10202,f10206,f10210,f10214,f10218,f10579,f11236,f11240,f11244,f11248,f11252,f11256,f11260,f11264,f11268,f11272,f11276,f11280,f11284,f11288,f11301,f11305,f11309,f11447,f11970,f11993,f11997,f12001,f12005,f12009,f12013,f12017,f12021,f12025,f12029,f12033,f12037,f12041,f12045,f12049,f12053,f12057,f12061,f12065,f12069,f12073,f12077,f12081,f12085,f12089,f12093,f12097,f12101,f12105,f12109,f12113,f12117,f12122,f12126,f12130,f12134,f12138,f12142,f12146,f12150,f12154,f12158,f12162,f12167,f12171,f12175,f12179,f12183,f12187,f12191,f12195,f12199,f12203,f12207,f12211,f12215,f12219,f12223,f12227,f12231,f12235,f12239,f12243,f12247,f12251,f12255,f12259,f12263,f12267,f12271,f12275,f12279,f12283,f12287,f12291,f12295,f12299,f12303,f12307,f12403,f12583,f12906,f13165,f13466,f14182,f14186,f14190,f14194,f14198,f14202,f14259,f14263,f14267,f14271,f14275,f14279,f14283,f14287,f14291,f14295,f14364,f14368,f14372,f14376,f14380,f14384,f14388,f14392,f14396,f14400,f14471,f14475,f14479,f14483,f14487,f14491,f14495,f14499,f16282,f16286,f16290,f16294,f16298,f16588,f16592,f16596,f16600,f16604,f16608,f16612,f16616,f16703,f16708,f16924,f16928,f16932,f17188,f17192,f17196,f17247,f17461,f17465,f17469,f17514,f17569,f17634,f17638,f17642,f17646,f17650,f17654,f17964,f17968,f17972,f17976,f18151,f18155,f18159,f18163,f18167,f18171,f19291,f19295,f19299,f19303,f19309,f19313,f19317,f19321,f20040,f20044,f20524,f20528,f20532,f20733,f21631,f21635,f21639,f21643,f21647,f21651,f21655,f21659,f21663,f21667,f21671,f21676,f21680,f21684,f21688,f21692,f21696,f21700,f21704,f21708,f21712,f21716,f21720,f21724,f21728,f21732,f21736,f21740,f21744,f21748,f21752,f21756,f21760,f21834,f21838,f21842,f21846,f21850,f21854,f23370,f23790,f23883,f23887,f23891,f23895,f23899,f23903,f23907,f23911,f23915,f23919,f23923,f23927,f23931,f23935,f23939,f23943,f23947,f23951,f23955,f23984,f23988,f23992,f23996,f24000,f24004,f24008,f24012,f24016,f24020,f24024,f24028,f24033,f24037,f24041,f24045,f24049,f24053,f24088,f24092,f24145,f24149,f24153,f24157,f25768,f26070,f26365,f26369,f26373,f26377,f26381,f26385,f26414,f26418,f26422,f26426,f26430,f26434,f26438,f26442,f26446,f26450,f26503,f26507,f26511,f26515,f26519,f26523,f26527,f26531,f26535,f26539,f26543,f26547,f26551,f26555,f26559,f26563,f26567,f26571,f26575,f26579,f26583,f26587,f26628,f26679,f26683,f26687,f26691,f26695,f26699,f26703,f26707,f26711,f26715,f26719,f26723,f26727,f26731,f26735,f26739,f26743,f26747,f26787,f26791,f26796,f26801,f26805,f26809,f26813,f26817,f26821,f26825,f26829,f26833,f26837,f26841,f26845,f26849,f26853,f26857,f26861,f26865,f26869,f26873,f26877,f26901,f27805,f28871,f29299,f29941,f30402,f31111,f31447,f31451,f31455,f31459,f31463,f31467,f31471,f31475,f31479,f31483,f31487,f31491,f31495,f31499,f31503,f31507,f31511,f31515,f31519,f31523,f31527,f31531,f31535,f31539,f31543,f31547,f31551,f31555,f31559,f31563,f31567,f31571,f31575,f31579,f31583,f31587,f31591,f31595,f31599,f31603,f31607,f31611,f31615,f31619,f31623,f31627,f31631,f31635,f31639,f31643,f31647,f31651,f31655,f31659,f31663,f31667,f31671,f31675,f31679,f31683,f31687,f31696,f31700,f31704,f31708,f31712,f31716,f31720,f31724,f31728,f31732,f31736,f31740,f31744,f31748,f31752,f31756,f31760,f31824,f31902,f31977,f31981,f31985,f31989,f31993,f32071,f32075,f32079,f32084,f32088,f32092,f32096,f32100,f32104,f32108,f32112,f32116,f32120,f32124,f32129,f32133,f32137,f32141,f32145,f32149,f32153,f32157,f32218,f32291,f32295,f32299,f32303,f32307,f32311,f35032,f36253,f37531,f38324,f41251,f41255,f41259,f41263,f41267,f41271,f41332,f41336,f41340,f41344,f41348,f41352,f41356,f41360,f41364,f41368,f41449,f41453,f41457,f41461,f41465,f41469,f41473,f41477,f41481,f41485,f41543,f41547,f41551,f41555,f41559,f41563,f41567,f41571,f41575,f41579,f41640,f41644,f41648,f41652,f41656,f41660,f41664,f41668,f41672,f41676,f41784,f41788,f41792,f41796,f41800,f42009,f42201,f42332,f42336,f42481,f42485,f42489,f42493,f42497,f42501,f42505,f42509,f42513,f42517,f42521,f42525,f42602,f42606,f42610,f42708,f42712,f42760,f42764,f42768,f42772,f42776,f42780,f42784,f42788,f42792,f42857,f42927,f42931,f42935,f42939,f42943,f42947,f42951,f42955,f42959,f42963,f42967,f42971,f42975,f42980,f42985,f42989,f42993,f42997,f43001,f43062,f43066,f43070,f43074,f43078,f43082,f43086,f43090,f43094,f43098,f43180,f43184,f43188,f43192,f43196,f43200,f43204,f43208,f43212,f43216,f43274,f43278,f43282,f43286,f43290,f43294,f43298,f43302,f43306,f49811,f52483,f54742]) ).
fof(f54742,plain,
( spl0_117
| ~ spl0_1194 ),
inference(avatar_split_clause,[],[f53860,f52481,f1425]) ).
fof(f1425,plain,
( spl0_117
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f52481,plain,
( spl0_1194
<=> ! [X0] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f53860,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| ~ spl0_1194 ),
inference(equality_resolution,[],[f52482]) ).
fof(f52482,plain,
( ! [X0] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f52481]) ).
fof(f52483,plain,
( spl0_1194
| ~ spl0_2
| ~ spl0_1155 ),
inference(avatar_split_clause,[],[f50843,f42965,f909,f52481]) ).
fof(f909,plain,
( spl0_2
<=> ! [X1] : c_Suc(X1) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f42965,plain,
( spl0_1155
<=> ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f50843,plain,
( ! [X0] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_2
| ~ spl0_1155 ),
inference(superposition,[],[f910,f42966]) ).
fof(f42966,plain,
( ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_1155 ),
inference(avatar_component_clause,[],[f42965]) ).
fof(f910,plain,
( ! [X1] : c_Suc(X1) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f909]) ).
fof(f49811,plain,
( spl0_1193
| ~ spl0_649
| ~ spl0_1000 ),
inference(avatar_split_clause,[],[f37075,f31669,f12209,f49809]) ).
fof(f49809,plain,
( spl0_1193
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f12209,plain,
( spl0_649
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f31669,plain,
( spl0_1000
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f37075,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat)),tc_nat)
| ~ spl0_649
| ~ spl0_1000 ),
inference(superposition,[],[f12210,f31670]) ).
fof(f31670,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat)
| ~ spl0_1000 ),
inference(avatar_component_clause,[],[f31669]) ).
fof(f12210,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat)
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f12209]) ).
fof(f43306,plain,
( ~ spl0_8
| spl0_1192
| ~ spl0_129
| ~ spl0_665 ),
inference(avatar_split_clause,[],[f13855,f12273,f1474,f43304,f938]) ).
fof(f938,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f43304,plain,
( spl0_1192
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1474,plain,
( spl0_129
<=> ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f12273,plain,
( spl0_665
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f13855,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) )
| ~ spl0_129
| ~ spl0_665 ),
inference(resolution,[],[f12274,f1475]) ).
fof(f1475,plain,
( ! [X10,X9] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X9,tc_nat)
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1474]) ).
fof(f12274,plain,
( ! [X3,X0,X18,X8,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
| ~ spl0_665 ),
inference(avatar_component_clause,[],[f12273]) ).
fof(f43302,plain,
( spl0_1191
| ~ spl0_123
| ~ spl0_571 ),
inference(avatar_split_clause,[],[f11079,f10204,f1450,f43300]) ).
fof(f43300,plain,
( spl0_1191
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1450,plain,
( spl0_123
<=> ! [X6,X5] : c_lessequals(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f10204,plain,
( spl0_571
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(X5,X6,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f11079,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_123
| ~ spl0_571 ),
inference(superposition,[],[f1451,f10205]) ).
fof(f10205,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(X5,X6,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f10204]) ).
fof(f1451,plain,
( ! [X6,X5] : c_lessequals(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X5,tc_nat)
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f43298,plain,
( spl0_1190
| ~ spl0_123
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f11051,f10200,f1450,f43296]) ).
fof(f43296,plain,
( spl0_1190
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f10200,plain,
( spl0_570
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f11051,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_123
| ~ spl0_570 ),
inference(superposition,[],[f1451,f10201]) ).
fof(f10201,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ spl0_570 ),
inference(avatar_component_clause,[],[f10200]) ).
fof(f43294,plain,
( spl0_1189
| ~ spl0_122
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f10925,f10187,f1446,f43292]) ).
fof(f43292,plain,
( spl0_1189
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f1446,plain,
( spl0_122
<=> ! [X6,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f10187,plain,
( spl0_567
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f10925,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_567 ),
inference(superposition,[],[f1447,f10188]) ).
fof(f10188,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f10187]) ).
fof(f1447,plain,
( ! [X6,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X5,tc_nat)
| ~ spl0_122 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f43290,plain,
( spl0_1188
| ~ spl0_122
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f10859,f10183,f1446,f43288]) ).
fof(f43288,plain,
( spl0_1188
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f10183,plain,
( spl0_566
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f10859,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_566 ),
inference(superposition,[],[f1447,f10184]) ).
fof(f10184,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ spl0_566 ),
inference(avatar_component_clause,[],[f10183]) ).
fof(f43286,plain,
( spl0_1187
| ~ spl0_130
| ~ spl0_555 ),
inference(avatar_split_clause,[],[f10470,f10138,f1478,f43284]) ).
fof(f43284,plain,
( spl0_1187
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1478,plain,
( spl0_130
<=> ! [X9,X10] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f10138,plain,
( spl0_555
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f10470,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_130
| ~ spl0_555 ),
inference(superposition,[],[f1479,f10139]) ).
fof(f10139,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ spl0_555 ),
inference(avatar_component_clause,[],[f10138]) ).
fof(f1479,plain,
( ! [X10,X9] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X9,tc_nat)
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f43282,plain,
( spl0_1186
| ~ spl0_129
| ~ spl0_555 ),
inference(avatar_split_clause,[],[f10469,f10138,f1474,f43280]) ).
fof(f43280,plain,
( spl0_1186
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f10469,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_555 ),
inference(superposition,[],[f1475,f10139]) ).
fof(f43278,plain,
( spl0_1185
| ~ spl0_128
| ~ spl0_555 ),
inference(avatar_split_clause,[],[f10468,f10138,f1470,f43276]) ).
fof(f43276,plain,
( spl0_1185
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1470,plain,
( spl0_128
<=> ! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f10468,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_555 ),
inference(superposition,[],[f1471,f10139]) ).
fof(f1471,plain,
( ! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f43274,plain,
( spl0_1184
| ~ spl0_127
| ~ spl0_555 ),
inference(avatar_split_clause,[],[f10467,f10138,f1466,f43272]) ).
fof(f43272,plain,
( spl0_1184
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1466,plain,
( spl0_127
<=> ! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f10467,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_555 ),
inference(superposition,[],[f1467,f10139]) ).
fof(f1467,plain,
( ! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1466]) ).
fof(f43216,plain,
( spl0_1183
| ~ spl0_130
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f10343,f10134,f1478,f43214]) ).
fof(f43214,plain,
( spl0_1183
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f10134,plain,
( spl0_554
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f10343,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_130
| ~ spl0_554 ),
inference(superposition,[],[f1479,f10135]) ).
fof(f10135,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ spl0_554 ),
inference(avatar_component_clause,[],[f10134]) ).
fof(f43212,plain,
( spl0_1182
| ~ spl0_129
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f10342,f10134,f1474,f43210]) ).
fof(f43210,plain,
( spl0_1182
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f10342,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_554 ),
inference(superposition,[],[f1475,f10135]) ).
fof(f43208,plain,
( spl0_1181
| ~ spl0_128
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f10341,f10134,f1470,f43206]) ).
fof(f43206,plain,
( spl0_1181
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f10341,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_554 ),
inference(superposition,[],[f1471,f10135]) ).
fof(f43204,plain,
( spl0_1180
| ~ spl0_127
| ~ spl0_554 ),
inference(avatar_split_clause,[],[f10340,f10134,f1466,f43202]) ).
fof(f43202,plain,
( spl0_1180
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f10340,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_554 ),
inference(superposition,[],[f1467,f10135]) ).
fof(f43200,plain,
( spl0_1179
| ~ spl0_136
| ~ spl0_205
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f10319,f10130,f2047,f1513,f43198]) ).
fof(f43198,plain,
( spl0_1179
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1513,plain,
( spl0_136
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f2047,plain,
( spl0_205
<=> ! [X6,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f10130,plain,
( spl0_553
<=> ! [X6,X9,X5] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X9,tc_nat),c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X6,tc_nat),X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f10319,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_136
| ~ spl0_205
| ~ spl0_553 ),
inference(forward_demodulation,[],[f10285,f1514]) ).
fof(f1514,plain,
( ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1513]) ).
fof(f10285,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_553 ),
inference(superposition,[],[f10131,f2048]) ).
fof(f2048,plain,
( ! [X6,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat)
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2047]) ).
fof(f10131,plain,
( ! [X6,X9,X5] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X9,tc_nat),c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X6,tc_nat),X9,tc_nat)
| ~ spl0_553 ),
inference(avatar_component_clause,[],[f10130]) ).
fof(f43196,plain,
( spl0_1178
| ~ spl0_135
| ~ spl0_205
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f10314,f10130,f2047,f1509,f43194]) ).
fof(f43194,plain,
( spl0_1178
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1509,plain,
( spl0_135
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f10314,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_135
| ~ spl0_205
| ~ spl0_553 ),
inference(forward_demodulation,[],[f10273,f1510]) ).
fof(f1510,plain,
( ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1509]) ).
fof(f10273,plain,
( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X2,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_553 ),
inference(superposition,[],[f10131,f2048]) ).
fof(f43192,plain,
( spl0_1177
| ~ spl0_115
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f10060,f9470,f1417,f43190]) ).
fof(f43190,plain,
( spl0_1177
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__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)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1417,plain,
( spl0_115
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f9470,plain,
( spl0_546
<=> ! [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_546])]) ).
fof(f10060,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__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)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_115
| ~ spl0_546 ),
inference(resolution,[],[f9471,f1418]) ).
fof(f1418,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f9471,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__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) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f9470]) ).
fof(f43188,plain,
( spl0_1176
| ~ spl0_116
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f10059,f9470,f1421,f43186]) ).
fof(f43186,plain,
( spl0_1176
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__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)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1421,plain,
( spl0_116
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f10059,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__comm__monoid__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)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_116
| ~ spl0_546 ),
inference(resolution,[],[f9471,f1422]) ).
fof(f1422,plain,
( ! [X0,X1] :
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f43184,plain,
( spl0_1175
| ~ spl0_48
| ~ spl0_356
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f10004,f9454,f3784,f1138,f43182]) ).
fof(f43182,plain,
( spl0_1175
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1138,plain,
( spl0_48
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f3784,plain,
( spl0_356
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f9454,plain,
( spl0_542
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f10004,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_356
| ~ spl0_542 ),
inference(forward_demodulation,[],[f10002,f4817]) ).
fof(f4817,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_356 ),
inference(resolution,[],[f3785,f1140]) ).
fof(f1140,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f3785,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f3784]) ).
fof(f10002,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_542 ),
inference(resolution,[],[f9455,f1140]) ).
fof(f9455,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f9454]) ).
fof(f43180,plain,
( spl0_1174
| ~ spl0_124
| ~ spl0_218
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f8698,f8073,f2107,f1454,f43178]) ).
fof(f43178,plain,
( spl0_1174
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f1454,plain,
( spl0_124
<=> ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f2107,plain,
( spl0_218
<=> ! [X18,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X1,tc_nat),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f8073,plain,
( spl0_485
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f8698,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat),X0,tc_nat)
| ~ spl0_124
| ~ spl0_218
| ~ spl0_485 ),
inference(forward_demodulation,[],[f8650,f2108]) ).
fof(f2108,plain,
( ! [X18,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X1,tc_nat),X18,tc_nat)
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f2107]) ).
fof(f8650,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat),X0,tc_nat)
| ~ spl0_124
| ~ spl0_485 ),
inference(resolution,[],[f8074,f1455]) ).
fof(f1455,plain,
( ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1454]) ).
fof(f8074,plain,
( ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X6,tc_nat) )
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f8073]) ).
fof(f43098,plain,
( spl0_1173
| ~ spl0_122
| ~ spl0_473 ),
inference(avatar_split_clause,[],[f7981,f7073,f1446,f43096]) ).
fof(f43096,plain,
( spl0_1173
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f7073,plain,
( spl0_473
<=> ! [X9,X7,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X7,X10,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f7981,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_473 ),
inference(superposition,[],[f1447,f7074]) ).
fof(f7074,plain,
( ! [X10,X9,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X7,X10,tc_nat),tc_nat)
| ~ spl0_473 ),
inference(avatar_component_clause,[],[f7073]) ).
fof(f43094,plain,
( spl0_1172
| ~ spl0_56
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f7962,f7069,f1178,f43092]) ).
fof(f43092,plain,
( spl0_1172
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,tc_Complex_Ocomplex) = c_Suc(c_Polynomial_Odegree(X0,tc_Complex_Ocomplex)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1178,plain,
( spl0_56
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f7069,plain,
( spl0_472
<=> ! [X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X15,X0) = c_Suc(c_Polynomial_Odegree(X15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f7962,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,tc_Complex_Ocomplex) = c_Suc(c_Polynomial_Odegree(X0,tc_Complex_Ocomplex)) )
| ~ spl0_56
| ~ spl0_472 ),
inference(resolution,[],[f7070,f1180]) ).
fof(f1180,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f7070,plain,
( ! [X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X15,X0) = c_Suc(c_Polynomial_Odegree(X15,X0)) )
| ~ spl0_472 ),
inference(avatar_component_clause,[],[f7069]) ).
fof(f43090,plain,
( spl0_1171
| ~ spl0_36
| ~ spl0_472 ),
inference(avatar_split_clause,[],[f7961,f7069,f1078,f43088]) ).
fof(f43088,plain,
( spl0_1171
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,tc_nat) = c_Suc(c_Polynomial_Odegree(X0,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1078,plain,
( spl0_36
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f7961,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = X0
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X0,tc_nat) = c_Suc(c_Polynomial_Odegree(X0,tc_nat)) )
| ~ spl0_36
| ~ spl0_472 ),
inference(resolution,[],[f7070,f1080]) ).
fof(f1080,plain,
( class_HOL_Ozero(tc_nat)
| ~ spl0_36 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f43086,plain,
( spl0_1170
| ~ spl0_123
| ~ spl0_470 ),
inference(avatar_split_clause,[],[f7945,f7061,f1450,f43084]) ).
fof(f43084,plain,
( spl0_1170
<=> ! [X2,X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f7061,plain,
( spl0_470
<=> ! [X6,X5,X7] : c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X5,tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f7945,plain,
( ! [X2,X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(X2,X1,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat),tc_nat)
| ~ spl0_123
| ~ spl0_470 ),
inference(superposition,[],[f1451,f7062]) ).
fof(f7062,plain,
( ! [X6,X7,X5] : c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X5,tc_nat),X6,tc_nat)
| ~ spl0_470 ),
inference(avatar_component_clause,[],[f7061]) ).
fof(f43082,plain,
( spl0_1169
| ~ spl0_122
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f7800,f7037,f1446,f43080]) ).
fof(f43080,plain,
( spl0_1169
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f7037,plain,
( spl0_464
<=> ! [X9,X7,X10] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f7800,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_464 ),
inference(superposition,[],[f1447,f7038]) ).
fof(f7038,plain,
( ! [X10,X9,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat)
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f7037]) ).
fof(f43078,plain,
( spl0_1168
| ~ spl0_205
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f7647,f7033,f2047,f43076]) ).
fof(f43076,plain,
( spl0_1168
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f7033,plain,
( spl0_463
<=> ! [X2,X21,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f7647,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_463 ),
inference(superposition,[],[f2048,f7034]) ).
fof(f7034,plain,
( ! [X2,X21,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat)
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f7033]) ).
fof(f43074,plain,
( spl0_1167
| ~ spl0_129
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f7638,f7033,f1474,f43072]) ).
fof(f43072,plain,
( spl0_1167
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f7638,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_463 ),
inference(superposition,[],[f1475,f7034]) ).
fof(f43070,plain,
( spl0_1166
| ~ spl0_127
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f7636,f7033,f1466,f43068]) ).
fof(f43068,plain,
( spl0_1166
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f7636,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_463 ),
inference(superposition,[],[f1467,f7034]) ).
fof(f43066,plain,
( spl0_1165
| ~ spl0_130
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f7520,f7029,f1478,f43064]) ).
fof(f43064,plain,
( spl0_1165
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f7029,plain,
( spl0_462
<=> ! [X6,X5,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f7520,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_130
| ~ spl0_462 ),
inference(superposition,[],[f1479,f7030]) ).
fof(f7030,plain,
( ! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat)
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f7029]) ).
fof(f43062,plain,
( spl0_1164
| ~ spl0_128
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f7518,f7029,f1470,f43060]) ).
fof(f43060,plain,
( spl0_1164
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f7518,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_462 ),
inference(superposition,[],[f1471,f7030]) ).
fof(f43001,plain,
( spl0_1163
| ~ spl0_142
| ~ spl0_461 ),
inference(avatar_split_clause,[],[f7494,f7025,f1537,f42999]) ).
fof(f42999,plain,
( spl0_1163
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(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_1163])]) ).
fof(f1537,plain,
( spl0_142
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f7025,plain,
( spl0_461
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f7494,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_142
| ~ spl0_461 ),
inference(superposition,[],[f7026,f1538]) ).
fof(f1538,plain,
( ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1537]) ).
fof(f7026,plain,
( ! [X6,X7,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) )
| ~ spl0_461 ),
inference(avatar_component_clause,[],[f7025]) ).
fof(f42997,plain,
( spl0_1162
| ~ spl0_141
| ~ spl0_460 ),
inference(avatar_split_clause,[],[f7458,f7021,f1533,f42995]) ).
fof(f42995,plain,
( spl0_1162
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(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_1162])]) ).
fof(f1533,plain,
( spl0_141
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f7021,plain,
( spl0_460
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f7458,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_141
| ~ spl0_460 ),
inference(superposition,[],[f7022,f1534]) ).
fof(f1534,plain,
( ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f7022,plain,
( ! [X6,X7,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat) )
| ~ spl0_460 ),
inference(avatar_component_clause,[],[f7021]) ).
fof(f42993,plain,
( spl0_1161
| ~ spl0_53
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f7289,f6984,f1163,f42991]) ).
fof(f42991,plain,
( spl0_1161
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f1163,plain,
( spl0_53
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f6984,plain,
( spl0_454
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f7289,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_53
| ~ spl0_454 ),
inference(resolution,[],[f6985,f1165]) ).
fof(f1165,plain,
( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1163]) ).
fof(f6985,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) )
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f6984]) ).
fof(f42989,plain,
( spl0_1160
| ~ spl0_53
| ~ spl0_444 ),
inference(avatar_split_clause,[],[f7078,f6944,f1163,f42987]) ).
fof(f42987,plain,
( spl0_1160
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f6944,plain,
( spl0_444
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f7078,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_53
| ~ spl0_444 ),
inference(resolution,[],[f6945,f1165]) ).
fof(f6945,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) )
| ~ spl0_444 ),
inference(avatar_component_clause,[],[f6944]) ).
fof(f42985,plain,
( spl0_1159
| ~ spl0_53
| ~ spl0_443 ),
inference(avatar_split_clause,[],[f7076,f6940,f1163,f42983]) ).
fof(f42983,plain,
( spl0_1159
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f6940,plain,
( spl0_443
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f7076,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_53
| ~ spl0_443 ),
inference(resolution,[],[f6941,f1165]) ).
fof(f6941,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) )
| ~ spl0_443 ),
inference(avatar_component_clause,[],[f6940]) ).
fof(f42980,plain,
( spl0_1158
| ~ spl0_128
| ~ spl0_167
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6070,f5123,f1666,f1470,f42978]) ).
fof(f42978,plain,
( spl0_1158
<=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f1666,plain,
( spl0_167
<=> ! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f5123,plain,
( spl0_410
<=> ! [X9,X7,X10] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f6070,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_167
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6038,f1667]) ).
fof(f1667,plain,
( ! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,X5,tc_nat)
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1666]) ).
fof(f6038,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_410 ),
inference(resolution,[],[f5124,f1471]) ).
fof(f5124,plain,
( ! [X10,X9,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat) )
| ~ spl0_410 ),
inference(avatar_component_clause,[],[f5123]) ).
fof(f42975,plain,
( spl0_1157
| ~ spl0_127
| ~ spl0_167
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6067,f5123,f1666,f1466,f42973]) ).
fof(f42973,plain,
( spl0_1157
<=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f6067,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_167
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6035,f1667]) ).
fof(f6035,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat),X2,tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_410 ),
inference(resolution,[],[f5124,f1467]) ).
fof(f42971,plain,
( spl0_1156
| ~ spl0_123
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5987,f5119,f1450,f42969]) ).
fof(f42969,plain,
( spl0_1156
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f5119,plain,
( spl0_409
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f5987,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat),X0,tc_nat)
| ~ spl0_123
| ~ spl0_409 ),
inference(resolution,[],[f5120,f1451]) ).
fof(f5120,plain,
( ! [X10,X9,X7] :
( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f5119]) ).
fof(f42967,plain,
( spl0_1155
| ~ spl0_179
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5545,f5015,f1714,f42965]) ).
fof(f1714,plain,
( spl0_179
<=> ! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f5015,plain,
( spl0_383
<=> ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f5545,plain,
( ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_179
| ~ spl0_383 ),
inference(resolution,[],[f5016,f1715]) ).
fof(f1715,plain,
( ! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X6 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f1714]) ).
fof(f5016,plain,
( ! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X6 )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f5015]) ).
fof(f42963,plain,
( spl0_1154
| ~ spl0_141
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f5537,f5011,f1533,f42961]) ).
fof(f42961,plain,
( spl0_1154
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f5011,plain,
( spl0_382
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f5537,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_141
| ~ spl0_382 ),
inference(superposition,[],[f5012,f1534]) ).
fof(f5012,plain,
( ! [X6,X7,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f5011]) ).
fof(f42959,plain,
( spl0_1153
| ~ spl0_63
| ~ spl0_905 ),
inference(avatar_split_clause,[],[f29427,f26713,f1208,f42957]) ).
fof(f42957,plain,
( spl0_1153
<=> ! [X0] : ~ c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f1208,plain,
( spl0_63
<=> ! [X6] : ~ c_lessequals(c_Suc(X6),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f26713,plain,
( spl0_905
<=> ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f29427,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat)),X0,tc_nat)
| ~ spl0_63
| ~ spl0_905 ),
inference(resolution,[],[f26714,f1209]) ).
fof(f1209,plain,
( ! [X6] : ~ c_lessequals(c_Suc(X6),X6,tc_nat)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1208]) ).
fof(f26714,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_905 ),
inference(avatar_component_clause,[],[f26713]) ).
fof(f42955,plain,
( spl0_1152
| ~ spl0_142
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f5515,f5007,f1537,f42953]) ).
fof(f42953,plain,
( spl0_1152
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f5007,plain,
( spl0_381
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f5515,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_142
| ~ spl0_381 ),
inference(superposition,[],[f5008,f1538]) ).
fof(f5008,plain,
( ! [X6,X7,X5] :
( c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f5007]) ).
fof(f42951,plain,
( spl0_1151
| ~ spl0_138
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f4924,f3893,f1521,f42949]) ).
fof(f42949,plain,
( spl0_1151
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1521,plain,
( spl0_138
<=> ! [X5,X1] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f3893,plain,
( spl0_367
<=> ! [X9,X7,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X9),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f4924,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) )
| ~ spl0_138
| ~ spl0_367 ),
inference(resolution,[],[f3894,f1522]) ).
fof(f1522,plain,
( ! [X1,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat)),tc_nat)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1521]) ).
fof(f3894,plain,
( ! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X9),X7,tc_nat) )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f3893]) ).
fof(f42947,plain,
( spl0_1150
| ~ spl0_137
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f4923,f3893,f1517,f42945]) ).
fof(f42945,plain,
( spl0_1150
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1517,plain,
( spl0_137
<=> ! [X9,X5] : c_HOL_Oord__class_Oless(X9,c_Suc(c_HOL_Oplus__class_Oplus(X5,X9,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f4923,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) )
| ~ spl0_137
| ~ spl0_367 ),
inference(resolution,[],[f3894,f1518]) ).
fof(f1518,plain,
( ! [X9,X5] : c_HOL_Oord__class_Oless(X9,c_Suc(c_HOL_Oplus__class_Oplus(X5,X9,tc_nat)),tc_nat)
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1517]) ).
fof(f42943,plain,
( spl0_1149
| ~ spl0_139
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f4918,f3893,f1525,f42941]) ).
fof(f42941,plain,
( spl0_1149
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f1525,plain,
( spl0_139
<=> ! [X6,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f4918,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_139
| ~ spl0_367 ),
inference(resolution,[],[f3894,f1526]) ).
fof(f1526,plain,
( ! [X6,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),c_Suc(X5),tc_nat)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1525]) ).
fof(f42939,plain,
( spl0_1148
| ~ spl0_204
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4813,f3776,f2043,f42937]) ).
fof(f42937,plain,
( spl0_1148
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2043,plain,
( spl0_204
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f3776,plain,
( spl0_354
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f4813,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2) )
| ~ spl0_204
| ~ spl0_354 ),
inference(duplicate_literal_removal,[],[f4789]) ).
fof(f4789,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_204
| ~ spl0_354 ),
inference(resolution,[],[f3777,f2044]) ).
fof(f2044,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f2043]) ).
fof(f3777,plain,
( ! [X3,X0,X1,X4] :
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_354 ),
inference(avatar_component_clause,[],[f3776]) ).
fof(f42935,plain,
( spl0_1147
| ~ spl0_221
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4812,f3776,f2119,f42933]) ).
fof(f42933,plain,
( spl0_1147
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2119,plain,
( spl0_221
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f4812,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2) )
| ~ spl0_221
| ~ spl0_354 ),
inference(duplicate_literal_removal,[],[f4793]) ).
fof(f4793,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X0,X3,X2),X2) )
| ~ spl0_221
| ~ spl0_354 ),
inference(resolution,[],[f3777,f2120]) ).
fof(f2120,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_221 ),
inference(avatar_component_clause,[],[f2119]) ).
fof(f42931,plain,
( spl0_1146
| ~ spl0_204
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4781,f3772,f2043,f42929]) ).
fof(f42929,plain,
( spl0_1146
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f3772,plain,
( spl0_353
<=> ! [X4,X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f4781,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2) )
| ~ spl0_204
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4757]) ).
fof(f4757,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_204
| ~ spl0_353 ),
inference(resolution,[],[f3773,f2044]) ).
fof(f3773,plain,
( ! [X3,X0,X1,X4] :
( c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f3772]) ).
fof(f42927,plain,
( spl0_1145
| ~ spl0_221
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4780,f3772,f2119,f42925]) ).
fof(f42925,plain,
( spl0_1145
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f4780,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2) )
| ~ spl0_221
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4761]) ).
fof(f4761,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omin(X3,X0,X2),X2) )
| ~ spl0_221
| ~ spl0_353 ),
inference(resolution,[],[f3773,f2120]) ).
fof(f42857,plain,
( ~ spl0_34
| spl0_1144
| ~ spl0_144
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4767,f3772,f1545,f42855,f1068]) ).
fof(f1068,plain,
( spl0_34
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f42855,plain,
( spl0_1144
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X0,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f1545,plain,
( spl0_144
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f4767,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(c_Orderings_Oord__class_Omin(X2,X0,tc_nat),X1,tc_nat) )
| ~ spl0_144
| ~ spl0_353 ),
inference(resolution,[],[f3773,f1546]) ).
fof(f1546,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1545]) ).
fof(f42792,plain,
( ~ spl0_34
| spl0_1143
| ~ spl0_143
| ~ spl0_351 ),
inference(avatar_split_clause,[],[f4720,f3764,f1541,f42790,f1068]) ).
fof(f42790,plain,
( spl0_1143
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f1541,plain,
( spl0_143
<=> ! [X6] :
( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f3764,plain,
( spl0_351
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f4720,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),tc_nat) )
| ~ spl0_143
| ~ spl0_351 ),
inference(resolution,[],[f3765,f1542]) ).
fof(f1542,plain,
( ! [X6] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X6,tc_nat) )
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1541]) ).
fof(f3765,plain,
( ! [X2,X21,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(X21,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f3764]) ).
fof(f42788,plain,
( spl0_1142
| ~ spl0_220
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4621,f3740,f2115,f42786]) ).
fof(f42786,plain,
( spl0_1142
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2115,plain,
( spl0_220
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f3740,plain,
( spl0_345
<=> ! [X4,X0,X1,X3] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X1,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f4621,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2) )
| ~ spl0_220
| ~ spl0_345 ),
inference(duplicate_literal_removal,[],[f4598]) ).
fof(f4598,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_345 ),
inference(resolution,[],[f3741,f2116]) ).
fof(f2116,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f2115]) ).
fof(f3741,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0)
| c_lessequals(X4,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_345 ),
inference(avatar_component_clause,[],[f3740]) ).
fof(f42784,plain,
( spl0_1141
| ~ spl0_203
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4619,f3740,f2039,f42782]) ).
fof(f42782,plain,
( spl0_1141
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f2039,plain,
( spl0_203
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f4619,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2) )
| ~ spl0_203
| ~ spl0_345 ),
inference(duplicate_literal_removal,[],[f4600]) ).
fof(f4600,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X0,X2),X2) )
| ~ spl0_203
| ~ spl0_345 ),
inference(resolution,[],[f3741,f2040]) ).
fof(f2040,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f2039]) ).
fof(f42780,plain,
( spl0_1140
| ~ spl0_220
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4590,f3736,f2115,f42778]) ).
fof(f42778,plain,
( spl0_1140
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f3736,plain,
( spl0_344
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f4590,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2) )
| ~ spl0_220
| ~ spl0_344 ),
inference(duplicate_literal_removal,[],[f4567]) ).
fof(f4567,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_344 ),
inference(resolution,[],[f3737,f2116]) ).
fof(f3737,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0)
| c_lessequals(X3,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_344 ),
inference(avatar_component_clause,[],[f3736]) ).
fof(f42776,plain,
( spl0_1139
| ~ spl0_203
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4588,f3736,f2039,f42774]) ).
fof(f42774,plain,
( spl0_1139
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f4588,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2) )
| ~ spl0_203
| ~ spl0_344 ),
inference(duplicate_literal_removal,[],[f4569]) ).
fof(f4569,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X0,X3,X2),X2) )
| ~ spl0_203
| ~ spl0_344 ),
inference(resolution,[],[f3737,f2040]) ).
fof(f42772,plain,
( spl0_1138
| ~ spl0_220
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4496,f3724,f2115,f42770]) ).
fof(f42770,plain,
( spl0_1138
<=> ! [X2,X0,X1,X3] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f3724,plain,
( spl0_341
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X4,X0)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f4496,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2) )
| ~ spl0_220
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4487]) ).
fof(f4487,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_341 ),
inference(resolution,[],[f3725,f2116]) ).
fof(f3725,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0)
| c_lessequals(X1,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f3724]) ).
fof(f42768,plain,
( spl0_1137
| ~ spl0_203
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4494,f3724,f2039,f42766]) ).
fof(f42766,plain,
( spl0_1137
<=> ! [X2,X0,X1,X3] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f4494,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2) )
| ~ spl0_203
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4489]) ).
fof(f4489,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X1,X2),X0,X2) )
| ~ spl0_203
| ~ spl0_341 ),
inference(resolution,[],[f3725,f2040]) ).
fof(f42764,plain,
( spl0_1136
| ~ spl0_220
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4468,f3720,f2115,f42762]) ).
fof(f42762,plain,
( spl0_1136
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f3720,plain,
( spl0_340
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f4468,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2) )
| ~ spl0_220
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4459]) ).
fof(f4459,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_220
| ~ spl0_340 ),
inference(resolution,[],[f3721,f2116]) ).
fof(f3721,plain,
( ! [X3,X0,X1,X4] :
( ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0)
| c_lessequals(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_340 ),
inference(avatar_component_clause,[],[f3720]) ).
fof(f42760,plain,
( spl0_1135
| ~ spl0_203
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4466,f3720,f2039,f42758]) ).
fof(f42758,plain,
( spl0_1135
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f4466,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2) )
| ~ spl0_203
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4461]) ).
fof(f4461,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X3,X2),X0,X2) )
| ~ spl0_203
| ~ spl0_340 ),
inference(resolution,[],[f3721,f2040]) ).
fof(f42712,plain,
( spl0_1134
| ~ spl0_204
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4386,f3692,f2043,f42710]) ).
fof(f42710,plain,
( spl0_1134
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f3692,plain,
( spl0_333
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f4386,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2) )
| ~ spl0_204
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f4365]) ).
fof(f4365,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_204
| ~ spl0_333 ),
inference(resolution,[],[f3693,f2044]) ).
fof(f3693,plain,
( ! [X3,X0,X1,X4] :
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f3692]) ).
fof(f42708,plain,
( spl0_1133
| ~ spl0_221
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4385,f3692,f2119,f42706]) ).
fof(f42706,plain,
( spl0_1133
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f4385,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2) )
| ~ spl0_221
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f4369]) ).
fof(f4369,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X3,X2),X0,X2) )
| ~ spl0_221
| ~ spl0_333 ),
inference(resolution,[],[f3693,f2120]) ).
fof(f42610,plain,
( ~ spl0_34
| spl0_1132
| ~ spl0_144
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4360,f3692,f1545,f42608,f1068]) ).
fof(f42608,plain,
( spl0_1132
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f4360,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat)
| c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat) )
| ~ spl0_144
| ~ spl0_333 ),
inference(resolution,[],[f3693,f1546]) ).
fof(f42606,plain,
( spl0_1131
| ~ spl0_204
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4351,f3688,f2043,f42604]) ).
fof(f42604,plain,
( spl0_1131
<=> ! [X2,X0,X1,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f3688,plain,
( spl0_332
<=> ! [X4,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f4351,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2) )
| ~ spl0_204
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f4330]) ).
fof(f4330,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_204
| ~ spl0_332 ),
inference(resolution,[],[f3689,f2044]) ).
fof(f3689,plain,
( ! [X3,X0,X1,X4] :
( c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f3688]) ).
fof(f42602,plain,
( spl0_1130
| ~ spl0_221
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4350,f3688,f2119,f42600]) ).
fof(f42600,plain,
( spl0_1130
<=> ! [X2,X0,X1,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f4350,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2) )
| ~ spl0_221
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f4334]) ).
fof(f4334,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X3,X1,X2),X0,X2) )
| ~ spl0_221
| ~ spl0_332 ),
inference(resolution,[],[f3689,f2120]) ).
fof(f42525,plain,
( ~ spl0_34
| spl0_1129
| ~ spl0_137
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f4310,f3684,f1517,f42523,f1068]) ).
fof(f42523,plain,
( spl0_1129
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_Orderings_Oord__class_Omax(X0,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3684,plain,
( spl0_331
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f4310,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_Orderings_Oord__class_Omax(X0,X2,tc_nat),tc_nat)),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_137
| ~ spl0_331 ),
inference(resolution,[],[f3685,f1518]) ).
fof(f3685,plain,
( ! [X2,X21,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f3684]) ).
fof(f42521,plain,
( spl0_1128
| ~ spl0_145
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f4238,f3655,f1549,f42519]) ).
fof(f42519,plain,
( spl0_1128
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f1549,plain,
( spl0_145
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_lessequals(X6,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f3655,plain,
( spl0_324
<=> ! [X6,X9] :
( ~ c_lessequals(X9,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f4238,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_145
| ~ spl0_324 ),
inference(resolution,[],[f3656,f1550]) ).
fof(f1550,plain,
( ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_lessequals(X6,X5,tc_nat) )
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1549]) ).
fof(f3656,plain,
( ! [X6,X9] :
( ~ c_lessequals(X9,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = X9 )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f3655]) ).
fof(f42517,plain,
( spl0_1127
| ~ spl0_177
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4191,f3643,f1706,f42515]) ).
fof(f42515,plain,
( spl0_1127
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f1706,plain,
( spl0_177
<=> ! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X6,tc_nat) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f3643,plain,
( spl0_321
<=> ! [X6,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f4191,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0
| ~ spl0_177
| ~ spl0_321 ),
inference(superposition,[],[f1707,f3644]) ).
fof(f3644,plain,
( ! [X6,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat)
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f3643]) ).
fof(f1707,plain,
( ! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X6,tc_nat) = X5
| ~ spl0_177 ),
inference(avatar_component_clause,[],[f1706]) ).
fof(f42513,plain,
( spl0_1126
| ~ spl0_59
| ~ spl0_1114 ),
inference(avatar_split_clause,[],[f42010,f42007,f1192,f42511]) ).
fof(f42511,plain,
( spl0_1126
<=> ! [X0] : c_Orderings_Oord__class_Omin(c_Suc(X0),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1192,plain,
( spl0_59
<=> ! [X6] : c_lessequals(X6,X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f42007,plain,
( spl0_1114
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omin(c_Suc(X0),X1,tc_nat) = X1
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f42010,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(c_Suc(X0),X0,tc_nat) = X0
| ~ spl0_59
| ~ spl0_1114 ),
inference(resolution,[],[f42008,f1193]) ).
fof(f1193,plain,
( ! [X6] : c_lessequals(X6,X6,tc_nat)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f1192]) ).
fof(f42008,plain,
( ! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_nat)
| c_Orderings_Oord__class_Omin(c_Suc(X0),X1,tc_nat) = X1 )
| ~ spl0_1114 ),
inference(avatar_component_clause,[],[f42007]) ).
fof(f42509,plain,
( spl0_1125
| ~ spl0_176
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4190,f3643,f1702,f42507]) ).
fof(f42507,plain,
( spl0_1125
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1702,plain,
( spl0_176
<=> ! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X6,tc_nat) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f4190,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_176
| ~ spl0_321 ),
inference(superposition,[],[f1703,f3644]) ).
fof(f1703,plain,
( ! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X6,tc_nat) = X5
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1702]) ).
fof(f42505,plain,
( spl0_1124
| ~ spl0_162
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4177,f3643,f1646,f42503]) ).
fof(f42503,plain,
( spl0_1124
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f1646,plain,
( spl0_162
<=> ! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f4177,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_162
| ~ spl0_321 ),
inference(superposition,[],[f3644,f1647]) ).
fof(f1647,plain,
( ! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X5,tc_nat)
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1646]) ).
fof(f42501,plain,
( spl0_1123
| ~ spl0_177
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4148,f3639,f1706,f42499]) ).
fof(f42499,plain,
( spl0_1123
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f3639,plain,
( spl0_320
<=> ! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X6),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f4148,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_177
| ~ spl0_320 ),
inference(superposition,[],[f1707,f3640]) ).
fof(f3640,plain,
( ! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X6),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat)
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f3639]) ).
fof(f42497,plain,
( spl0_1122
| ~ spl0_176
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4147,f3639,f1702,f42495]) ).
fof(f42495,plain,
( spl0_1122
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f4147,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
| ~ spl0_176
| ~ spl0_320 ),
inference(superposition,[],[f1703,f3640]) ).
fof(f42493,plain,
( spl0_1121
| ~ spl0_162
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4135,f3639,f1646,f42491]) ).
fof(f42491,plain,
( spl0_1121
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f4135,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_162
| ~ spl0_320 ),
inference(superposition,[],[f3640,f1647]) ).
fof(f42489,plain,
( spl0_1120
| ~ spl0_183
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3533,f3058,f1730,f42487]) ).
fof(f42487,plain,
( spl0_1120
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1730,plain,
( spl0_183
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(X5,c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f3058,plain,
( spl0_296
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X10,X7,tc_nat)
| c_lessequals(X9,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f3533,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X2),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_183
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1731]) ).
fof(f1731,plain,
( ! [X6,X5] :
( c_lessequals(X5,c_Suc(X6),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_183 ),
inference(avatar_component_clause,[],[f1730]) ).
fof(f3059,plain,
( ! [X10,X9,X7] :
( ~ c_lessequals(X10,X7,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat)
| c_lessequals(X9,X7,tc_nat) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f3058]) ).
fof(f42485,plain,
( spl0_1119
| ~ spl0_154
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3519,f3058,f1614,f42483]) ).
fof(f42483,plain,
( spl0_1119
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1614,plain,
( spl0_154
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| c_lessequals(c_Suc(X6),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f3519,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_154
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1615]) ).
fof(f1615,plain,
( ! [X6,X5] :
( c_lessequals(c_Suc(X6),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,X5,tc_nat) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1614]) ).
fof(f42481,plain,
( spl0_1118
| ~ spl0_188
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3518,f3058,f1750,f42479]) ).
fof(f42479,plain,
( spl0_1118
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1750,plain,
( spl0_188
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_Suc(X6),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f3518,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_188
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1751]) ).
fof(f1751,plain,
( ! [X6,X5] :
( c_lessequals(c_Suc(X6),X5,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1750]) ).
fof(f42336,plain,
( spl0_1117
| ~ spl0_34
| ~ spl0_154
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3379,f3017,f1614,f1068,f42334]) ).
fof(f42334,plain,
( spl0_1117
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f3017,plain,
( spl0_286
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f3379,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat) = X1
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_154
| ~ spl0_286 ),
inference(resolution,[],[f3018,f1615]) ).
fof(f3018,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2 )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f3017]) ).
fof(f42332,plain,
( spl0_1116
| ~ spl0_59
| ~ spl0_1113 ),
inference(avatar_split_clause,[],[f41801,f41798,f1192,f42330]) ).
fof(f42330,plain,
( spl0_1116
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f41798,plain,
( spl0_1113
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omin(X0,c_Suc(X1),tc_nat) = X0
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f41801,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_59
| ~ spl0_1113 ),
inference(resolution,[],[f41799,f1193]) ).
fof(f41799,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_Orderings_Oord__class_Omin(X0,c_Suc(X1),tc_nat) = X0 )
| ~ spl0_1113 ),
inference(avatar_component_clause,[],[f41798]) ).
fof(f42201,plain,
( spl0_1115
| ~ spl0_34
| ~ spl0_188
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3378,f3017,f1750,f1068,f42199]) ).
fof(f42199,plain,
( spl0_1115
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat) = X1
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f3378,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat) = X1
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_188
| ~ spl0_286 ),
inference(resolution,[],[f3018,f1751]) ).
fof(f42009,plain,
( spl0_1114
| ~ spl0_34
| ~ spl0_183
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3348,f3013,f1730,f1068,f42007]) ).
fof(f3013,plain,
( spl0_285
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f3348,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omin(c_Suc(X0),X1,tc_nat) = X1
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_183
| ~ spl0_285 ),
inference(resolution,[],[f3014,f1731]) ).
fof(f3014,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2 )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f3013]) ).
fof(f41800,plain,
( spl0_1113
| ~ spl0_34
| ~ spl0_183
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3301,f3005,f1730,f1068,f41798]) ).
fof(f3005,plain,
( spl0_283
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3301,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omin(X0,c_Suc(X1),tc_nat) = X0
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_183
| ~ spl0_283 ),
inference(resolution,[],[f3006,f1731]) ).
fof(f3006,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1 )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f3005]) ).
fof(f41796,plain,
( spl0_1112
| ~ spl0_205
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3125,f2949,f2047,f41794]) ).
fof(f41794,plain,
( spl0_1112
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f2949,plain,
( spl0_269
<=> ! [X6,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),X5,tc_nat) = c_Orderings_Oord__class_Omax(X6,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f3125,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_269 ),
inference(superposition,[],[f2048,f2950]) ).
fof(f2950,plain,
( ! [X6,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),X5,tc_nat) = c_Orderings_Oord__class_Omax(X6,X5,tc_nat)
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f2949]) ).
fof(f41792,plain,
( spl0_1111
| ~ spl0_194
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3124,f2949,f2003,f41790]) ).
fof(f41790,plain,
( spl0_1111
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_Orderings_Oord__class_Omax(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f2003,plain,
( spl0_194
<=> ! [X1,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f3124,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) != c_Orderings_Oord__class_Omax(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_194
| ~ spl0_269 ),
inference(superposition,[],[f2004,f2950]) ).
fof(f2004,plain,
( ! [X3,X1] :
( c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != X1
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f2003]) ).
fof(f41788,plain,
( spl0_1110
| ~ spl0_247
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2939,f2524,f2456,f41786]) ).
fof(f41786,plain,
( spl0_1110
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(c_Suc(X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f2456,plain,
( spl0_247
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2524,plain,
( spl0_264
<=> ! [X6,X5] : c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X5),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2939,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(c_Suc(X0),X2,tc_nat) )
| ~ spl0_247
| ~ spl0_264 ),
inference(superposition,[],[f2457,f2525]) ).
fof(f2525,plain,
( ! [X6,X5] : c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X5),X6,tc_nat)
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2524]) ).
fof(f2457,plain,
( ! [X6,X7,X5] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2456]) ).
fof(f41784,plain,
( spl0_1109
| ~ spl0_245
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2937,f2524,f2444,f41782]) ).
fof(f41782,plain,
( spl0_1109
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f2444,plain,
( spl0_245
<=> ! [X2,X21,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2937,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,c_Suc(X0),tc_nat) )
| ~ spl0_245
| ~ spl0_264 ),
inference(superposition,[],[f2445,f2525]) ).
fof(f2445,plain,
( ! [X2,X21,X1] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat)
| ~ c_lessequals(X1,X2,tc_nat) )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2444]) ).
fof(f41676,plain,
( spl0_1108
| ~ spl0_238
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2935,f2524,f2416,f41674]) ).
fof(f41674,plain,
( spl0_1108
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f2416,plain,
( spl0_238
<=> ! [X9,X7,X10] :
( c_HOL_Oord__class_Oless(X9,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f2935,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) )
| ~ spl0_238
| ~ spl0_264 ),
inference(superposition,[],[f2417,f2525]) ).
fof(f2417,plain,
( ! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(X9,X7,tc_nat) )
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f41672,plain,
( spl0_1107
| ~ spl0_237
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2934,f2524,f2412,f41670]) ).
fof(f41670,plain,
( spl0_1107
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f2412,plain,
( spl0_237
<=> ! [X2,X21,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f2934,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) )
| ~ spl0_237
| ~ spl0_264 ),
inference(superposition,[],[f2413,f2525]) ).
fof(f2413,plain,
( ! [X2,X21,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_237 ),
inference(avatar_component_clause,[],[f2412]) ).
fof(f41668,plain,
( spl0_1106
| ~ spl0_248
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2909,f2520,f2460,f41666]) ).
fof(f41666,plain,
( spl0_1106
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f2460,plain,
( spl0_248
<=> ! [X6,X5,X7] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2520,plain,
( spl0_263
<=> ! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X6),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2909,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(c_Suc(X1),X2,tc_nat) )
| ~ spl0_248
| ~ spl0_263 ),
inference(superposition,[],[f2461,f2521]) ).
fof(f2521,plain,
( ! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X6),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat))
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2520]) ).
fof(f2461,plain,
( ! [X6,X7,X5] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat)
| c_lessequals(X7,X6,tc_nat) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f2460]) ).
fof(f41664,plain,
( spl0_1105
| ~ spl0_246
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2907,f2520,f2448,f41662]) ).
fof(f41662,plain,
( spl0_1105
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f2448,plain,
( spl0_246
<=> ! [X2,X21,X1] :
( ~ c_lessequals(X1,X21,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2907,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,c_Suc(X1),tc_nat) )
| ~ spl0_246
| ~ spl0_263 ),
inference(superposition,[],[f2449,f2521]) ).
fof(f2449,plain,
( ! [X2,X21,X1] :
( c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat)
| ~ c_lessequals(X1,X21,tc_nat) )
| ~ spl0_246 ),
inference(avatar_component_clause,[],[f2448]) ).
fof(f41660,plain,
( spl0_1104
| ~ spl0_239
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2905,f2520,f2420,f41658]) ).
fof(f41658,plain,
( spl0_1104
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f2420,plain,
( spl0_239
<=> ! [X9,X5,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X5,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f2905,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) )
| ~ spl0_239
| ~ spl0_263 ),
inference(superposition,[],[f2421,f2521]) ).
fof(f2421,plain,
( ! [X10,X9,X5] :
( c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X5,X10,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat) )
| ~ spl0_239 ),
inference(avatar_component_clause,[],[f2420]) ).
fof(f41656,plain,
( spl0_1103
| ~ spl0_255
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2882,f2516,f2488,f41654]) ).
fof(f41654,plain,
( spl0_1103
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f2488,plain,
( spl0_255
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2516,plain,
( spl0_262
<=> ! [X6,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X6),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2882,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_255
| ~ spl0_262 ),
inference(superposition,[],[f2489,f2517]) ).
fof(f2517,plain,
( ! [X6,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X6),tc_nat)
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2516]) ).
fof(f2489,plain,
( ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2488]) ).
fof(f41652,plain,
( spl0_1102
| ~ spl0_101
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2878,f2512,f1361,f41650]) ).
fof(f41650,plain,
( spl0_1102
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = X0
| ~ class_OrderedGroup_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1361,plain,
( spl0_101
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f2512,plain,
( spl0_261
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2878,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = X0
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_101
| ~ spl0_261 ),
inference(resolution,[],[f2513,f1362]) ).
fof(f1362,plain,
( ! [X34] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Oab__group__add(X34) )
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1361]) ).
fof(f2513,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) = X3 )
| ~ spl0_261 ),
inference(avatar_component_clause,[],[f2512]) ).
fof(f41648,plain,
( spl0_1101
| ~ spl0_200
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2858,f2504,f2027,f41646]) ).
fof(f41646,plain,
( spl0_1101
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f2027,plain,
( spl0_200
<=> ! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2504,plain,
( spl0_259
<=> ! [X6,X7,X10] :
( ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,X6,tc_nat),X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2858,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
| ~ spl0_200
| ~ spl0_259 ),
inference(resolution,[],[f2505,f2028]) ).
fof(f2028,plain,
( ! [X6] :
( ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X6 )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f2027]) ).
fof(f2505,plain,
( ! [X10,X6,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,X6,tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2504]) ).
fof(f41644,plain,
( spl0_1100
| ~ spl0_93
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2851,f2500,f1329,f41642]) ).
fof(f41642,plain,
( spl0_1100
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1329,plain,
( spl0_93
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2500,plain,
( spl0_258
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2851,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Ocomm__monoid__add(X2) )
| ~ spl0_93
| ~ spl0_258 ),
inference(resolution,[],[f2501,f1330]) ).
fof(f1330,plain,
( ! [X34] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Ocomm__monoid__add(X34) )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f1329]) ).
fof(f2501,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2500]) ).
fof(f41640,plain,
( spl0_1099
| ~ spl0_87
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2848,f2492,f1305,f41638]) ).
fof(f41638,plain,
( spl0_1099
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1305,plain,
( spl0_87
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f2492,plain,
( spl0_256
<=> ! [X0,X8,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2848,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_87
| ~ spl0_256 ),
inference(resolution,[],[f2493,f1306]) ).
fof(f1306,plain,
( ! [X34] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X34) )
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f1305]) ).
fof(f2493,plain,
( ! [X3,X0,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X3,X0) )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2492]) ).
fof(f41579,plain,
( spl0_1098
| ~ spl0_195
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2824,f2484,f2007,f41577]) ).
fof(f41577,plain,
( spl0_1098
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f2007,plain,
( spl0_195
<=> ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f2484,plain,
( spl0_254
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2824,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_195
| ~ spl0_254 ),
inference(resolution,[],[f2485,f2008]) ).
fof(f2008,plain,
( ! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),tc_nat)
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2007]) ).
fof(f2485,plain,
( ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) )
| ~ spl0_254 ),
inference(avatar_component_clause,[],[f2484]) ).
fof(f41575,plain,
( spl0_1097
| ~ spl0_106
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2796,f2468,f1381,f41573]) ).
fof(f41573,plain,
( spl0_1097
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X1,tc_Polynomial_Opoly(X2)) = c_Orderings_Oord__class_Omin(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1381,plain,
( spl0_106
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2468,plain,
( spl0_250
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X2,X1,X0) = c_Orderings_Oord__class_Omin(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2796,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X1,tc_Polynomial_Opoly(X2)) = c_Orderings_Oord__class_Omin(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_106
| ~ spl0_250 ),
inference(resolution,[],[f2469,f1382]) ).
fof(f1382,plain,
( ! [X34] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oordered__idom(X34) )
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1381]) ).
fof(f2469,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X2,X1,X0) = c_Orderings_Oord__class_Omin(X1,X2,X0) )
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f2468]) ).
fof(f41571,plain,
( spl0_1096
| ~ spl0_106
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2794,f2464,f1381,f41569]) ).
fof(f41569,plain,
( spl0_1096
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f2464,plain,
( spl0_249
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2794,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_106
| ~ spl0_249 ),
inference(resolution,[],[f2465,f1382]) ).
fof(f2465,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) = X1 )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2464]) ).
fof(f41567,plain,
( spl0_1095
| ~ spl0_124
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2777,f2460,f1454,f41565]) ).
fof(f41565,plain,
( spl0_1095
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f2777,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_124
| ~ spl0_248 ),
inference(resolution,[],[f2461,f1455]) ).
fof(f41563,plain,
( spl0_1094
| ~ spl0_124
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2752,f2456,f1454,f41561]) ).
fof(f41561,plain,
( spl0_1094
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f2752,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_124
| ~ spl0_247 ),
inference(resolution,[],[f2457,f1455]) ).
fof(f41559,plain,
( spl0_1093
| ~ spl0_87
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2720,f2440,f1305,f41557]) ).
fof(f41557,plain,
( spl0_1093
<=> ! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f2440,plain,
( spl0_244
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2720,plain,
( ! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_87
| ~ spl0_244 ),
inference(resolution,[],[f2441,f1306]) ).
fof(f2441,plain,
( ! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2440]) ).
fof(f41555,plain,
( spl0_1092
| ~ spl0_101
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2717,f2436,f1361,f41553]) ).
fof(f41553,plain,
( spl0_1092
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = X0
| ~ class_OrderedGroup_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f2436,plain,
( spl0_243
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X4,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2717,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = X0
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_101
| ~ spl0_243 ),
inference(resolution,[],[f2437,f1362]) ).
fof(f2437,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X4,X0) = X3 )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2436]) ).
fof(f41551,plain,
( spl0_1091
| ~ spl0_106
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2709,f2428,f1381,f41549]) ).
fof(f41549,plain,
( spl0_1091
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_Polynomial_Opoly(X2)) = c_Orderings_Oord__class_Omax(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f2428,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2709,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_Polynomial_Opoly(X2)) = c_Orderings_Oord__class_Omax(X1,X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_106
| ~ spl0_241 ),
inference(resolution,[],[f2429,f1382]) ).
fof(f2429,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X2,X1,X0) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2428]) ).
fof(f41547,plain,
( spl0_1090
| ~ spl0_106
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2707,f2424,f1381,f41545]) ).
fof(f41545,plain,
( spl0_1090
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f2424,plain,
( spl0_240
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f2707,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_106
| ~ spl0_240 ),
inference(resolution,[],[f2425,f1382]) ).
fof(f2425,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) = X1 )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2424]) ).
fof(f41543,plain,
( spl0_1089
| ~ spl0_192
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2683,f2420,f1995,f41541]) ).
fof(f41541,plain,
( spl0_1089
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1995,plain,
( spl0_192
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f2683,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) = X0 )
| ~ spl0_192
| ~ spl0_239 ),
inference(resolution,[],[f2421,f1996]) ).
fof(f1996,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = X5 )
| ~ spl0_192 ),
inference(avatar_component_clause,[],[f1995]) ).
fof(f41485,plain,
( spl0_1088
| ~ spl0_192
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2645,f2412,f1995,f41483]) ).
fof(f41483,plain,
( spl0_1088
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f2645,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Divides_Odiv__class_Omod(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = X0 )
| ~ spl0_192
| ~ spl0_237 ),
inference(resolution,[],[f2413,f1996]) ).
fof(f41481,plain,
( spl0_1087
| ~ spl0_124
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2617,f2387,f1454,f41479]) ).
fof(f41479,plain,
( spl0_1087
<=> ! [X0] :
( c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f2387,plain,
( spl0_232
<=> ! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2617,plain,
( ! [X0] :
( c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = X0
| c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) )
| ~ spl0_124
| ~ spl0_232 ),
inference(resolution,[],[f2388,f1455]) ).
fof(f2388,plain,
( ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f41477,plain,
( spl0_1086
| ~ spl0_123
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2604,f2387,f1450,f41475]) ).
fof(f41475,plain,
( spl0_1086
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f2604,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) )
| ~ spl0_123
| ~ spl0_232 ),
inference(resolution,[],[f2388,f1451]) ).
fof(f41473,plain,
( spl0_1085
| ~ spl0_122
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2603,f2387,f1446,f41471]) ).
fof(f41471,plain,
( spl0_1085
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f2603,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) )
| ~ spl0_122
| ~ spl0_232 ),
inference(resolution,[],[f2388,f1447]) ).
fof(f41469,plain,
( spl0_1084
| ~ spl0_130
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2573,f2383,f1478,f41467]) ).
fof(f41467,plain,
( spl0_1084
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f2383,plain,
( spl0_231
<=> ! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f2573,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
| ~ spl0_130
| ~ spl0_231 ),
inference(resolution,[],[f2384,f1479]) ).
fof(f2384,plain,
( ! [X2,X1] :
( c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| X1 = X2 )
| ~ spl0_231 ),
inference(avatar_component_clause,[],[f2383]) ).
fof(f41465,plain,
( spl0_1083
| ~ spl0_129
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2572,f2383,f1474,f41463]) ).
fof(f41463,plain,
( spl0_1083
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f2572,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 )
| ~ spl0_129
| ~ spl0_231 ),
inference(resolution,[],[f2384,f1475]) ).
fof(f41461,plain,
( spl0_1082
| ~ spl0_161
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2559,f2383,f1642,f41459]) ).
fof(f41459,plain,
( spl0_1082
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
| c_Suc(X1) = X0
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f1642,plain,
( spl0_161
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2559,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_Suc(X1),X0,tc_nat)
| c_Suc(X1) = X0
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_161
| ~ spl0_231 ),
inference(resolution,[],[f2384,f1643]) ).
fof(f1643,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f41457,plain,
( spl0_1081
| ~ spl0_192
| ~ spl0_231 ),
inference(avatar_split_clause,[],[f2555,f2383,f1995,f41455]) ).
fof(f41455,plain,
( spl0_1081
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| X0 = X1
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f2555,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| X0 = X1
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
| ~ spl0_192
| ~ spl0_231 ),
inference(resolution,[],[f2384,f1996]) ).
fof(f41453,plain,
( spl0_1080
| ~ spl0_128
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2547,f2379,f1470,f41451]) ).
fof(f41451,plain,
( spl0_1080
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f2379,plain,
( spl0_230
<=> ! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(X6,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2547,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
| ~ spl0_128
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1471]) ).
fof(f2380,plain,
( ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| ~ c_lessequals(X5,X6,tc_nat)
| X5 = X6 )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2379]) ).
fof(f41449,plain,
( spl0_1079
| ~ spl0_127
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2546,f2379,f1466,f41447]) ).
fof(f41447,plain,
( spl0_1079
<=> ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f2546,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 )
| ~ spl0_127
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1467]) ).
fof(f41368,plain,
( spl0_1078
| ~ spl0_124
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2543,f2379,f1454,f41366]) ).
fof(f41366,plain,
( spl0_1078
<=> ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat)
| c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f2543,plain,
( ! [X0] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat)
| c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = X0 )
| ~ spl0_124
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1455]) ).
fof(f41364,plain,
( spl0_1077
| ~ spl0_154
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2538,f2379,f1614,f41362]) ).
fof(f41362,plain,
( spl0_1077
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_Suc(X1) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f2538,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Suc(X1),tc_nat)
| c_Suc(X1) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_154
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1615]) ).
fof(f41360,plain,
( spl0_1076
| ~ spl0_123
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2530,f2379,f1450,f41358]) ).
fof(f41358,plain,
( spl0_1076
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f2530,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
| ~ spl0_123
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1451]) ).
fof(f41356,plain,
( spl0_1075
| ~ spl0_122
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2529,f2379,f1446,f41354]) ).
fof(f41354,plain,
( spl0_1075
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f2529,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 )
| ~ spl0_122
| ~ spl0_230 ),
inference(resolution,[],[f2380,f1447]) ).
fof(f41352,plain,
( spl0_1074
| ~ spl0_192
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2366,f2139,f1995,f41350]) ).
fof(f41350,plain,
( spl0_1074
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Suc(X0) = c_Divides_Odiv__class_Omod(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f2139,plain,
( spl0_226
<=> ! [X6,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f2366,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Suc(X0) = c_Divides_Odiv__class_Omod(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_192
| ~ spl0_226 ),
inference(resolution,[],[f2140,f1996]) ).
fof(f2140,plain,
( ! [X1,X6] :
( c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2139]) ).
fof(f41348,plain,
( spl0_1073
| ~ spl0_77
| ~ spl0_213 ),
inference(avatar_split_clause,[],[f2244,f2082,f1265,f41346]) ).
fof(f41346,plain,
( spl0_1073
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f1265,plain,
( spl0_77
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f2082,plain,
( spl0_213
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f2244,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_77
| ~ spl0_213 ),
inference(resolution,[],[f2083,f1266]) ).
fof(f1266,plain,
( ! [X34] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oidom(X34) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f1265]) ).
fof(f2083,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_213 ),
inference(avatar_component_clause,[],[f2082]) ).
fof(f41344,plain,
( spl0_1072
| ~ spl0_77
| ~ spl0_212 ),
inference(avatar_split_clause,[],[f2242,f2078,f1265,f41342]) ).
fof(f41342,plain,
( spl0_1072
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f2078,plain,
( spl0_212
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f2242,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_77
| ~ spl0_212 ),
inference(resolution,[],[f2079,f1266]) ).
fof(f2079,plain,
( ! [X0,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f2078]) ).
fof(f41340,plain,
( spl0_1071
| ~ spl0_97
| ~ spl0_211 ),
inference(avatar_split_clause,[],[f2240,f2074,f1345,f41338]) ).
fof(f41338,plain,
( spl0_1071
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f1345,plain,
( spl0_97
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f2074,plain,
( spl0_211
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f2240,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_97
| ~ spl0_211 ),
inference(resolution,[],[f2075,f1346]) ).
fof(f1346,plain,
( ! [X34] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X34) )
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1345]) ).
fof(f2075,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f2074]) ).
fof(f41336,plain,
( spl0_1070
| ~ spl0_97
| ~ spl0_210 ),
inference(avatar_split_clause,[],[f2237,f2070,f1345,f41334]) ).
fof(f41334,plain,
( spl0_1070
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f2070,plain,
( spl0_210
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f2237,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_97
| ~ spl0_210 ),
inference(resolution,[],[f2071,f1346]) ).
fof(f2071,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_210 ),
inference(avatar_component_clause,[],[f2070]) ).
fof(f41332,plain,
( spl0_1069
| ~ spl0_87
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f2234,f2066,f1305,f41330]) ).
fof(f41330,plain,
( spl0_1069
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2066,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f2234,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_87
| ~ spl0_209 ),
inference(resolution,[],[f2067,f1306]) ).
fof(f2067,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f2066]) ).
fof(f41271,plain,
( spl0_1068
| ~ spl0_87
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2229,f2051,f1305,f41269]) ).
fof(f41269,plain,
( spl0_1068
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f2051,plain,
( spl0_206
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f2229,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_87
| ~ spl0_206 ),
inference(resolution,[],[f2052,f1306]) ).
fof(f2052,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f2051]) ).
fof(f41267,plain,
( spl0_1067
| ~ spl0_102
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2175,f2023,f1365,f41265]) ).
fof(f41265,plain,
( spl0_1067
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f1365,plain,
( spl0_102
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f2023,plain,
( spl0_199
<=> ! [X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2175,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_102
| ~ spl0_199 ),
inference(resolution,[],[f2024,f1366]) ).
fof(f1366,plain,
( ! [X34] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ofield(X34) )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1365]) ).
fof(f2024,plain,
( ! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2023]) ).
fof(f41263,plain,
( spl0_1066
| ~ spl0_155
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2165,f2007,f1618,f41261]) ).
fof(f41261,plain,
( spl0_1066
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f1618,plain,
( spl0_155
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| ~ c_lessequals(c_Suc(X6),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f2165,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),tc_nat)
| ~ spl0_155
| ~ spl0_195 ),
inference(resolution,[],[f2008,f1619]) ).
fof(f1619,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Suc(X6),X5,tc_nat)
| c_HOL_Oord__class_Oless(X6,X5,tc_nat) )
| ~ spl0_155 ),
inference(avatar_component_clause,[],[f1618]) ).
fof(f41259,plain,
( spl0_1065
| ~ spl0_182
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2164,f2007,f1726,f41257]) ).
fof(f41257,plain,
( spl0_1065
<=> ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f1726,plain,
( spl0_182
<=> ! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_Suc(X5),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2164,plain,
( ! [X0] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),tc_nat)
| ~ spl0_182
| ~ spl0_195 ),
inference(resolution,[],[f2008,f1727]) ).
fof(f1727,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Suc(X5),X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1726]) ).
fof(f41255,plain,
( spl0_1064
| ~ spl0_189
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f2163,f2007,f1754,f41253]) ).
fof(f41253,plain,
( spl0_1064
<=> ! [X0] : ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f1754,plain,
( spl0_189
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_Suc(X6),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f2163,plain,
( ! [X0] : ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X0),c_HOL_Otimes__class_Otimes(c_Suc(X0),c_Suc(X0),tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_189
| ~ spl0_195 ),
inference(resolution,[],[f2008,f1755]) ).
fof(f1755,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Suc(X6),X5,tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1754]) ).
fof(f41251,plain,
( spl0_1063
| ~ spl0_139
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2144,f1995,f1525,f41249]) ).
fof(f41249,plain,
( spl0_1063
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2144,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_139
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1526]) ).
fof(f38324,plain,
( spl0_1062
| ~ spl0_677
| ~ spl0_803 ),
inference(avatar_split_clause,[],[f23645,f21758,f13163,f38322]) ).
fof(f38322,plain,
( spl0_1062
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f13163,plain,
( spl0_677
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f21758,plain,
( spl0_803
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f23645,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_677
| ~ spl0_803 ),
inference(superposition,[],[f21759,f13164]) ).
fof(f13164,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
| ~ spl0_677 ),
inference(avatar_component_clause,[],[f13163]) ).
fof(f21759,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_803 ),
inference(avatar_component_clause,[],[f21758]) ).
fof(f37531,plain,
( spl0_1061
| ~ spl0_649
| ~ spl0_802 ),
inference(avatar_split_clause,[],[f23580,f21754,f12209,f37529]) ).
fof(f37529,plain,
( spl0_1061
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f21754,plain,
( spl0_802
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f23580,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_649
| ~ spl0_802 ),
inference(superposition,[],[f12210,f21755]) ).
fof(f21755,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f21754]) ).
fof(f36253,plain,
( spl0_1060
| ~ spl0_649
| ~ spl0_783 ),
inference(avatar_split_clause,[],[f22259,f21678,f12209,f36251]) ).
fof(f36251,plain,
( spl0_1060
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_Orderings_Oord__class_Omax(X1,X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f21678,plain,
( spl0_783
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f22259,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_Orderings_Oord__class_Omax(X1,X0,tc_nat)),tc_nat)
| ~ spl0_649
| ~ spl0_783 ),
inference(superposition,[],[f12210,f21679]) ).
fof(f21679,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat)
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f21678]) ).
fof(f35032,plain,
( spl0_1059
| ~ spl0_649
| ~ spl0_781 ),
inference(avatar_split_clause,[],[f22221,f21669,f12209,f35030]) ).
fof(f35030,plain,
( spl0_1059
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f21669,plain,
( spl0_781
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f22221,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_649
| ~ spl0_781 ),
inference(superposition,[],[f12210,f21670]) ).
fof(f21670,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f21669]) ).
fof(f32311,plain,
( spl0_1058
| ~ spl0_129
| ~ spl0_732 ),
inference(avatar_split_clause,[],[f17391,f17186,f1474,f32309]) ).
fof(f32309,plain,
( spl0_1058
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f17186,plain,
( spl0_732
<=> ! [X17,X4,X16,X8] :
( ~ c_HOL_Oord__class_Oless(X17,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X16,X8,tc_nat),tc_nat),X17,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f17391,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X1,tc_nat) )
| ~ spl0_129
| ~ spl0_732 ),
inference(resolution,[],[f17187,f1475]) ).
fof(f17187,plain,
( ! [X8,X16,X4,X17] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X16,X8,tc_nat),tc_nat),X17,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| ~ c_HOL_Oord__class_Oless(X17,X4,tc_nat) )
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f17186]) ).
fof(f32307,plain,
( spl0_1057
| ~ spl0_193
| ~ spl0_613 ),
inference(avatar_split_clause,[],[f12608,f12063,f1999,f32305]) ).
fof(f32305,plain,
( spl0_1057
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f1999,plain,
( spl0_193
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f12063,plain,
( spl0_613
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f12608,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_193
| ~ spl0_613 ),
inference(duplicate_literal_removal,[],[f12584]) ).
fof(f12584,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| c_lessequals(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_193
| ~ spl0_613 ),
inference(resolution,[],[f12064,f2000]) ).
fof(f2000,plain,
( ! [X3,X0] :
( c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X3,X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f12064,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_613 ),
inference(avatar_component_clause,[],[f12063]) ).
fof(f32303,plain,
( spl0_1056
| ~ spl0_140
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f9488,f9306,f1529,f32301]) ).
fof(f32301,plain,
( spl0_1056
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f1529,plain,
( spl0_140
<=> ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f9306,plain,
( spl0_505
<=> ! [X6,X5] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f9488,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_140
| ~ spl0_505 ),
inference(trivial_inequality_removal,[],[f9484]) ).
fof(f9484,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_140
| ~ spl0_505 ),
inference(superposition,[],[f9307,f1530]) ).
fof(f1530,plain,
( ! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1529]) ).
fof(f9307,plain,
( ! [X6,X5] :
( c_HOL_Ominus__class_Ominus(X6,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)
| X5 = X6 )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f9306]) ).
fof(f32299,plain,
( spl0_1055
| ~ spl0_163
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f7092,f6948,f1650,f32297]) ).
fof(f32297,plain,
( spl0_1055
<=> ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f1650,plain,
( spl0_163
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f6948,plain,
( spl0_445
<=> ! [X6,X5,X7] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f7092,plain,
( ! [X2,X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_163
| ~ spl0_445 ),
inference(superposition,[],[f1651,f6949]) ).
fof(f6949,plain,
( ! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat)
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f6948]) ).
fof(f1651,plain,
( ! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1650]) ).
fof(f32295,plain,
( spl0_1054
| ~ spl0_123
| ~ spl0_437 ),
inference(avatar_split_clause,[],[f6904,f5276,f1450,f32293]) ).
fof(f32293,plain,
( spl0_1054
<=> ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat),c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f5276,plain,
( spl0_437
<=> ! [X6,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f6904,plain,
( ! [X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat),c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)),tc_nat)
| ~ spl0_123
| ~ spl0_437 ),
inference(superposition,[],[f1451,f5277]) ).
fof(f5277,plain,
( ! [X6,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)),X6,tc_nat)
| ~ spl0_437 ),
inference(avatar_component_clause,[],[f5276]) ).
fof(f32291,plain,
( ~ spl0_1053
| ~ spl0_115
| spl0_1006 ),
inference(avatar_split_clause,[],[f31905,f31693,f1417,f32288]) ).
fof(f32288,plain,
( spl0_1053
<=> class_Orderings_Opreorder(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f31693,plain,
( spl0_1006
<=> c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f31905,plain,
( ~ class_Orderings_Opreorder(tc_Complex_Ocomplex)
| ~ spl0_115
| spl0_1006 ),
inference(resolution,[],[f31694,f1418]) ).
fof(f31694,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_1006 ),
inference(avatar_component_clause,[],[f31693]) ).
fof(f32218,plain,
( ~ spl0_33
| spl0_1052
| ~ spl0_111
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f6651,f5225,f1401,f32216,f1063]) ).
fof(f1063,plain,
( spl0_33
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f32216,plain,
( spl0_1052
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(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_1052])]) ).
fof(f1401,plain,
( spl0_111
<=> ! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f5225,plain,
( spl0_430
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f6651,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
| ~ spl0_111
| ~ spl0_430 ),
inference(resolution,[],[f5226,f1402]) ).
fof(f1402,plain,
( ! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat)
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1401]) ).
fof(f5226,plain,
( ! [X2,X21,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X21,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f5225]) ).
fof(f32157,plain,
( ~ spl0_33
| spl0_1051
| ~ spl0_111
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f6615,f5221,f1401,f32155,f1063]) ).
fof(f32155,plain,
( spl0_1051
<=> ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f5221,plain,
( spl0_429
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f6615,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
| ~ spl0_111
| ~ spl0_429 ),
inference(resolution,[],[f5222,f1402]) ).
fof(f5222,plain,
( ! [X2,X21,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f5221]) ).
fof(f32153,plain,
( spl0_1050
| ~ spl0_115
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f6305,f5170,f1417,f32151]) ).
fof(f32151,plain,
( spl0_1050
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f5170,plain,
( spl0_419
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f6305,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_115
| ~ spl0_419 ),
inference(resolution,[],[f5171,f1418]) ).
fof(f5171,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f5170]) ).
fof(f32149,plain,
( spl0_1049
| ~ spl0_116
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f6304,f5170,f1421,f32147]) ).
fof(f32147,plain,
( spl0_1049
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f6304,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_116
| ~ spl0_419 ),
inference(resolution,[],[f5171,f1422]) ).
fof(f32145,plain,
( spl0_1048
| ~ spl0_115
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f6268,f5166,f1417,f32143]) ).
fof(f32143,plain,
( spl0_1048
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X1,X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f5166,plain,
( spl0_418
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f6268,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_115
| ~ spl0_418 ),
inference(resolution,[],[f5167,f1418]) ).
fof(f5167,plain,
( ! [X3,X0,X4] :
( ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f5166]) ).
fof(f32141,plain,
( spl0_1047
| ~ spl0_116
| ~ spl0_418 ),
inference(avatar_split_clause,[],[f6267,f5166,f1421,f32139]) ).
fof(f32139,plain,
( spl0_1047
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X1,X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f6267,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X1,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_116
| ~ spl0_418 ),
inference(resolution,[],[f5167,f1422]) ).
fof(f32137,plain,
( spl0_1046
| ~ spl0_119
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f5945,f5107,f1434,f32135]) ).
fof(f32135,plain,
( spl0_1046
<=> ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f1434,plain,
( spl0_119
<=> ! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f5107,plain,
( spl0_406
<=> ! [X6,X29,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X29,X6,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f5945,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_119
| ~ spl0_406 ),
inference(superposition,[],[f5108,f1435]) ).
fof(f1435,plain,
( ! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1434]) ).
fof(f5108,plain,
( ! [X29,X6,X5] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X29,X6,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f5107]) ).
fof(f32133,plain,
( spl0_1045
| ~ spl0_34
| ~ spl0_402 ),
inference(avatar_split_clause,[],[f5819,f5091,f1068,f32131]) ).
fof(f32131,plain,
( spl0_1045
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f5091,plain,
( spl0_402
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f5819,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat)
| ~ spl0_34
| ~ spl0_402 ),
inference(resolution,[],[f5092,f1070]) ).
fof(f1070,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_34 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f5092,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) )
| ~ spl0_402 ),
inference(avatar_component_clause,[],[f5091]) ).
fof(f32129,plain,
( ~ spl0_1044
| ~ spl0_116
| spl0_1006 ),
inference(avatar_split_clause,[],[f31904,f31693,f1421,f32126]) ).
fof(f32126,plain,
( spl0_1044
<=> class_Orderings_Oorder(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f31904,plain,
( ~ class_Orderings_Oorder(tc_Complex_Ocomplex)
| ~ spl0_116
| spl0_1006 ),
inference(resolution,[],[f31694,f1422]) ).
fof(f32124,plain,
( spl0_1043
| ~ spl0_32
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f5793,f5075,f1058,f32122]) ).
fof(f32122,plain,
( spl0_1043
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f1058,plain,
( spl0_32
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f5075,plain,
( spl0_398
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f5793,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_32
| ~ spl0_398 ),
inference(resolution,[],[f5076,f1060]) ).
fof(f1060,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f1058]) ).
fof(f5076,plain,
( ! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X4,X0),X4,X0) )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f5075]) ).
fof(f32120,plain,
( spl0_1042
| ~ spl0_34
| ~ spl0_384 ),
inference(avatar_split_clause,[],[f5579,f5019,f1068,f32118]) ).
fof(f32118,plain,
( spl0_1042
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f5019,plain,
( spl0_384
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f5579,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_34
| ~ spl0_384 ),
inference(resolution,[],[f5020,f1070]) ).
fof(f5020,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) )
| ~ spl0_384 ),
inference(avatar_component_clause,[],[f5019]) ).
fof(f32116,plain,
( spl0_1041
| ~ spl0_143
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f5546,f5015,f1541,f32114]) ).
fof(f32114,plain,
( spl0_1041
<=> ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f5546,plain,
( ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) )
| ~ spl0_143
| ~ spl0_383 ),
inference(resolution,[],[f5016,f1542]) ).
fof(f32112,plain,
( spl0_1040
| ~ spl0_32
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f5466,f4995,f1058,f32110]) ).
fof(f32110,plain,
( spl0_1040
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f4995,plain,
( spl0_378
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f5466,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_32
| ~ spl0_378 ),
inference(resolution,[],[f4996,f1060]) ).
fof(f4996,plain,
( ! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f4995]) ).
fof(f32108,plain,
( spl0_1039
| ~ spl0_32
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f5464,f4991,f1058,f32106]) ).
fof(f32106,plain,
( spl0_1039
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f4991,plain,
( spl0_377
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f5464,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X1,X0,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_32
| ~ spl0_377 ),
inference(resolution,[],[f4992,f1060]) ).
fof(f4992,plain,
( ! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(X3,X4,X0) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f4991]) ).
fof(f32104,plain,
( spl0_1038
| ~ spl0_125
| ~ spl0_374 ),
inference(avatar_split_clause,[],[f5424,f4979,f1458,f32102]) ).
fof(f32102,plain,
( spl0_1038
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1458,plain,
( spl0_125
<=> ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f4979,plain,
( spl0_374
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f5424,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_125
| ~ spl0_374 ),
inference(superposition,[],[f4980,f1459]) ).
fof(f1459,plain,
( ! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f4980,plain,
( ! [X6,X7,X5] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f4979]) ).
fof(f32100,plain,
( spl0_1037
| ~ spl0_126
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f5353,f4971,f1462,f32098]) ).
fof(f32098,plain,
( spl0_1037
<=> ! [X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f1462,plain,
( spl0_126
<=> ! [X6] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f4971,plain,
( spl0_372
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f5353,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_126
| ~ spl0_372 ),
inference(superposition,[],[f4972,f1463]) ).
fof(f1463,plain,
( ! [X6] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f4972,plain,
( ! [X10,X9,X7] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f4971]) ).
fof(f32096,plain,
( spl0_1036
| ~ spl0_179
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4705,f3756,f1714,f32094]) ).
fof(f32094,plain,
( spl0_1036
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3756,plain,
( spl0_349
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f4705,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_179
| ~ spl0_349 ),
inference(resolution,[],[f3757,f1715]) ).
fof(f3757,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) )
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f3756]) ).
fof(f32092,plain,
( spl0_1035
| ~ spl0_179
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4691,f3752,f1714,f32090]) ).
fof(f32090,plain,
( spl0_1035
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3752,plain,
( spl0_348
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f4691,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
| ~ spl0_179
| ~ spl0_348 ),
inference(resolution,[],[f3753,f1715]) ).
fof(f3753,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat) )
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f3752]) ).
fof(f32088,plain,
( spl0_1034
| ~ spl0_156
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4618,f3740,f1622,f32086]) ).
fof(f32086,plain,
( spl0_1034
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X0,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1622,plain,
( spl0_156
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f4618,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X0,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_156
| ~ spl0_345 ),
inference(duplicate_literal_removal,[],[f4611]) ).
fof(f4611,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X0,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_156
| ~ spl0_345 ),
inference(resolution,[],[f3741,f1623]) ).
fof(f1623,plain,
( ! [X2,X0,X1] :
( c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1622]) ).
fof(f32084,plain,
( ~ spl0_1033
| ~ spl0_229
| spl0_1006 ),
inference(avatar_split_clause,[],[f31903,f31693,f2341,f32081]) ).
fof(f32081,plain,
( spl0_1033
<=> class_Orderings_Olinorder(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2341,plain,
( spl0_229
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f31903,plain,
( ~ class_Orderings_Olinorder(tc_Complex_Ocomplex)
| ~ spl0_229
| spl0_1006 ),
inference(resolution,[],[f31694,f2342]) ).
fof(f2342,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f2341]) ).
fof(f32079,plain,
( spl0_1032
| ~ spl0_157
| ~ spl0_345 ),
inference(avatar_split_clause,[],[f4617,f3740,f1626,f32077]) ).
fof(f32077,plain,
( spl0_1032
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X0,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1626,plain,
( spl0_157
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f4617,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X0,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_157
| ~ spl0_345 ),
inference(duplicate_literal_removal,[],[f4612]) ).
fof(f4612,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X0,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_157
| ~ spl0_345 ),
inference(resolution,[],[f3741,f1627]) ).
fof(f1627,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X1,X2,X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1626]) ).
fof(f32075,plain,
( spl0_1031
| ~ spl0_156
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4587,f3736,f1622,f32073]) ).
fof(f32073,plain,
( spl0_1031
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X0,X1,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f4587,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X0,X1,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_156
| ~ spl0_344 ),
inference(duplicate_literal_removal,[],[f4580]) ).
fof(f4580,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X0,X1,X2),X3,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_156
| ~ spl0_344 ),
inference(resolution,[],[f3737,f1623]) ).
fof(f32071,plain,
( spl0_1030
| ~ spl0_157
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4586,f3736,f1626,f32069]) ).
fof(f32069,plain,
( spl0_1030
<=> ! [X0,X3,X2,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X0,X2,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f4586,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X0,X2,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_157
| ~ spl0_344 ),
inference(duplicate_literal_removal,[],[f4581]) ).
fof(f4581,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X0,X2,X3),X3),X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_157
| ~ spl0_344 ),
inference(resolution,[],[f3737,f1627]) ).
fof(f31993,plain,
( ~ spl0_34
| spl0_1029
| ~ spl0_127
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f4573,f3736,f1466,f31991,f1068]) ).
fof(f31991,plain,
( spl0_1029
<=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_Orderings_Oord__class_Omax(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f4573,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_Orderings_Oord__class_Omax(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_127
| ~ spl0_344 ),
inference(resolution,[],[f3737,f1467]) ).
fof(f31989,plain,
( spl0_1028
| ~ spl0_159
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4498,f3724,f1634,f31987]) ).
fof(f31987,plain,
( spl0_1028
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1634,plain,
( spl0_159
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f4498,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_159
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4480]) ).
fof(f4480,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_159
| ~ spl0_341 ),
inference(resolution,[],[f3725,f1635]) ).
fof(f1635,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1634]) ).
fof(f31985,plain,
( spl0_1027
| ~ spl0_158
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4497,f3724,f1630,f31983]) ).
fof(f31983,plain,
( spl0_1027
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1630,plain,
( spl0_158
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f4497,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_158
| ~ spl0_341 ),
inference(duplicate_literal_removal,[],[f4486]) ).
fof(f4486,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X2,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_158
| ~ spl0_341 ),
inference(resolution,[],[f3725,f1631]) ).
fof(f1631,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1630]) ).
fof(f31981,plain,
( spl0_1026
| ~ spl0_159
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4470,f3720,f1634,f31979]) ).
fof(f31979,plain,
( spl0_1026
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f4470,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_159
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4452]) ).
fof(f4452,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X0,X1,X2),X3,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_159
| ~ spl0_340 ),
inference(resolution,[],[f3721,f1635]) ).
fof(f31977,plain,
( spl0_1025
| ~ spl0_158
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4469,f3720,f1630,f31975]) ).
fof(f31975,plain,
( spl0_1025
<=> ! [X0,X3,X2,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f4469,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_158
| ~ spl0_340 ),
inference(duplicate_literal_removal,[],[f4458]) ).
fof(f4458,plain,
( ! [X2,X3,X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omin(X1,X2,X3),X3),X1,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ class_Orderings_Olinorder(X3) )
| ~ spl0_158
| ~ spl0_340 ),
inference(resolution,[],[f3721,f1631]) ).
fof(f31902,plain,
( ~ spl0_34
| spl0_1024
| ~ spl0_123
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4447,f3720,f1450,f31900,f1068]) ).
fof(f31900,plain,
( spl0_1024
<=> ! [X2,X0,X1] : c_lessequals(c_Divides_Odiv__class_Omod(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f4447,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_Divides_Odiv__class_Omod(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_123
| ~ spl0_340 ),
inference(resolution,[],[f3721,f1451]) ).
fof(f31824,plain,
( ~ spl0_34
| spl0_1023
| ~ spl0_122
| ~ spl0_340 ),
inference(avatar_split_clause,[],[f4446,f3720,f1446,f31822,f1068]) ).
fof(f31822,plain,
( spl0_1023
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f4446,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X2,tc_nat),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_122
| ~ spl0_340 ),
inference(resolution,[],[f3721,f1447]) ).
fof(f31760,plain,
( ~ spl0_34
| spl0_1022
| ~ spl0_129
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4371,f3692,f1474,f31758,f1068]) ).
fof(f31758,plain,
( spl0_1022
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f4371,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_129
| ~ spl0_333 ),
inference(resolution,[],[f3693,f1475]) ).
fof(f31756,plain,
( spl0_1021
| ~ spl0_247
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4201,f3643,f2456,f31754]) ).
fof(f31754,plain,
( spl0_1021
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f4201,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_247
| ~ spl0_321 ),
inference(superposition,[],[f2457,f3644]) ).
fof(f31752,plain,
( spl0_1020
| ~ spl0_245
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4199,f3643,f2444,f31750]) ).
fof(f31750,plain,
( spl0_1020
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f4199,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) )
| ~ spl0_245
| ~ spl0_321 ),
inference(superposition,[],[f2445,f3644]) ).
fof(f31748,plain,
( spl0_1019
| ~ spl0_238
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4197,f3643,f2416,f31746]) ).
fof(f31746,plain,
( spl0_1019
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f4197,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_238
| ~ spl0_321 ),
inference(superposition,[],[f2417,f3644]) ).
fof(f31744,plain,
( spl0_1018
| ~ spl0_237
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4196,f3643,f2412,f31742]) ).
fof(f31742,plain,
( spl0_1018
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f4196,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_237
| ~ spl0_321 ),
inference(superposition,[],[f2413,f3644]) ).
fof(f31740,plain,
( spl0_1017
| ~ spl0_234
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4194,f3643,f2395,f31738]) ).
fof(f31738,plain,
( spl0_1017
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f2395,plain,
( spl0_234
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f4194,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_234
| ~ spl0_321 ),
inference(superposition,[],[f2396,f3644]) ).
fof(f2396,plain,
( ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X5 )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2395]) ).
fof(f31736,plain,
( spl0_1016
| ~ spl0_137
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4188,f3643,f1517,f31734]) ).
fof(f31734,plain,
( spl0_1016
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f4188,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_321 ),
inference(superposition,[],[f1518,f3644]) ).
fof(f31732,plain,
( spl0_1015
| ~ spl0_247
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4158,f3639,f2456,f31730]) ).
fof(f31730,plain,
( spl0_1015
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f4158,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_247
| ~ spl0_320 ),
inference(superposition,[],[f2457,f3640]) ).
fof(f31728,plain,
( spl0_1014
| ~ spl0_245
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4156,f3639,f2444,f31726]) ).
fof(f31726,plain,
( spl0_1014
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f4156,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) )
| ~ spl0_245
| ~ spl0_320 ),
inference(superposition,[],[f2445,f3640]) ).
fof(f31724,plain,
( spl0_1013
| ~ spl0_238
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4154,f3639,f2416,f31722]) ).
fof(f31722,plain,
( spl0_1013
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f4154,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_238
| ~ spl0_320 ),
inference(superposition,[],[f2417,f3640]) ).
fof(f31720,plain,
( spl0_1012
| ~ spl0_237
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4153,f3639,f2412,f31718]) ).
fof(f31718,plain,
( spl0_1012
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f4153,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_237
| ~ spl0_320 ),
inference(superposition,[],[f2413,f3640]) ).
fof(f31716,plain,
( spl0_1011
| ~ spl0_234
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4151,f3639,f2395,f31714]) ).
fof(f31714,plain,
( spl0_1011
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f4151,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_234
| ~ spl0_320 ),
inference(superposition,[],[f2396,f3640]) ).
fof(f31712,plain,
( spl0_1010
| ~ spl0_137
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4145,f3639,f1517,f31710]) ).
fof(f31710,plain,
( spl0_1010
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f4145,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_320 ),
inference(superposition,[],[f1518,f3640]) ).
fof(f31708,plain,
( spl0_1009
| ~ spl0_225
| ~ spl0_305
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f3875,f3843,f3094,f2135,f31706]) ).
fof(f31706,plain,
( spl0_1009
<=> ! [X0,X1] :
( c_Suc(X0) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat))
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f2135,plain,
( spl0_225
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f3094,plain,
( spl0_305
<=> ! [X6,X5] : c_Orderings_Oord__class_Omax(c_Suc(X5),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X5,X6,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3843,plain,
( spl0_362
<=> ! [X6,X5] :
( c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f3875,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat))
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_225
| ~ spl0_305
| ~ spl0_362 ),
inference(forward_demodulation,[],[f3872,f3095]) ).
fof(f3095,plain,
( ! [X6,X5] : c_Orderings_Oord__class_Omax(c_Suc(X5),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X5,X6,tc_nat))
| ~ spl0_305 ),
inference(avatar_component_clause,[],[f3094]) ).
fof(f3872,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_225
| ~ spl0_362 ),
inference(resolution,[],[f3844,f2136]) ).
fof(f2136,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X6),tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f2135]) ).
fof(f3844,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5 )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f3843]) ).
fof(f31704,plain,
( spl0_1008
| ~ spl0_186
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f3870,f3843,f1742,f31702]) ).
fof(f31702,plain,
( spl0_1008
<=> ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1742,plain,
( spl0_186
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f3870,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_186
| ~ spl0_362 ),
inference(resolution,[],[f3844,f1743]) ).
fof(f1743,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X5),X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f1742]) ).
fof(f31700,plain,
( spl0_1007
| ~ spl0_200
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f3854,f3843,f2027,f31698]) ).
fof(f31698,plain,
( spl0_1007
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f3854,plain,
( ! [X0] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_200
| ~ spl0_362 ),
inference(resolution,[],[f3844,f2028]) ).
fof(f31696,plain,
( ~ spl0_1005
| spl0_1006
| ~ spl0_288
| ~ spl0_605
| ~ spl0_619 ),
inference(avatar_split_clause,[],[f18103,f12087,f12031,f3025,f31693,f31689]) ).
fof(f31689,plain,
( spl0_1005
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f3025,plain,
( spl0_288
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f12031,plain,
( spl0_605
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f12087,plain,
( spl0_619
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f18103,plain,
( c_lessequals(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex)
| ~ spl0_288
| ~ spl0_605
| ~ spl0_619 ),
inference(forward_demodulation,[],[f17977,f3026]) ).
fof(f3026,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f3025]) ).
fof(f17977,plain,
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex)
| ~ spl0_605
| ~ spl0_619 ),
inference(superposition,[],[f12088,f12032]) ).
fof(f12032,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f12031]) ).
fof(f12088,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_619 ),
inference(avatar_component_clause,[],[f12087]) ).
fof(f31687,plain,
( spl0_1004
| ~ spl0_192
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f3847,f3843,f1995,f31685]) ).
fof(f31685,plain,
( spl0_1004
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = X0
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f3847,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = X0
| c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = X0 )
| ~ spl0_192
| ~ spl0_362 ),
inference(resolution,[],[f3844,f1996]) ).
fof(f31683,plain,
( spl0_1003
| ~ spl0_224
| ~ spl0_305
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3836,f3801,f3094,f2131,f31681]) ).
fof(f31681,plain,
( spl0_1003
<=> ! [X0,X1] :
( c_Suc(X0) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat))
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f2131,plain,
( spl0_224
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f3801,plain,
( spl0_360
<=> ! [X6,X5] :
( c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5
| ~ c_lessequals(X6,X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f3836,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat))
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_224
| ~ spl0_305
| ~ spl0_360 ),
inference(forward_demodulation,[],[f3833,f3095]) ).
fof(f3833,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),c_Suc(X1),tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_224
| ~ spl0_360 ),
inference(resolution,[],[f3802,f2132]) ).
fof(f2132,plain,
( ! [X6,X5] :
( c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat)
| ~ c_lessequals(X6,X5,tc_nat) )
| ~ spl0_224 ),
inference(avatar_component_clause,[],[f2131]) ).
fof(f3802,plain,
( ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5 )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f3801]) ).
fof(f31679,plain,
( spl0_1002
| ~ spl0_183
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3831,f3801,f1730,f31677]) ).
fof(f31677,plain,
( spl0_1002
<=> ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f3831,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_183
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1731]) ).
fof(f31675,plain,
( spl0_1001
| ~ spl0_128
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3829,f3801,f1470,f31673]) ).
fof(f31673,plain,
( spl0_1001
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f3829,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_128
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1471]) ).
fof(f31671,plain,
( spl0_1000
| ~ spl0_124
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3823,f3801,f1454,f31669]) ).
fof(f3823,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,X0,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat)
| ~ spl0_124
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1455]) ).
fof(f31667,plain,
( spl0_999
| ~ spl0_145
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3516,f3058,f1549,f31665]) ).
fof(f31665,plain,
( spl0_999
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f3516,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,X2,tc_nat)
| c_lessequals(X2,X1,tc_nat) )
| ~ spl0_145
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1550]) ).
fof(f31663,plain,
( spl0_998
| ~ spl0_220
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3449,f3029,f2115,f31661]) ).
fof(f31661,plain,
( spl0_998
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f3029,plain,
( spl0_289
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f3449,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| c_lessequals(X1,X2,X0) )
| ~ spl0_220
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3429]) ).
fof(f3429,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220
| ~ spl0_289 ),
inference(resolution,[],[f3030,f2116]) ).
fof(f3030,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1 )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f3029]) ).
fof(f31659,plain,
( spl0_997
| ~ spl0_203
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3447,f3029,f2039,f31657]) ).
fof(f31657,plain,
( spl0_997
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f3447,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_203
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3431]) ).
fof(f3431,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_203
| ~ spl0_289 ),
inference(resolution,[],[f3030,f2040]) ).
fof(f31655,plain,
( spl0_996
| ~ spl0_220
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3402,f3017,f2115,f31653]) ).
fof(f31653,plain,
( spl0_996
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f3402,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| c_lessequals(X2,X1,X0) )
| ~ spl0_220
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f3382]) ).
fof(f3382,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220
| ~ spl0_286 ),
inference(resolution,[],[f3018,f2116]) ).
fof(f31651,plain,
( spl0_995
| ~ spl0_203
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3400,f3017,f2039,f31649]) ).
fof(f31649,plain,
( spl0_995
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f3400,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_203
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f3384]) ).
fof(f3384,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_203
| ~ spl0_286 ),
inference(resolution,[],[f3018,f2040]) ).
fof(f31647,plain,
( spl0_994
| ~ spl0_269
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f16912,f9867,f2949,f31645]) ).
fof(f31645,plain,
( spl0_994
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f9867,plain,
( spl0_550
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f16912,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_269
| ~ spl0_550 ),
inference(superposition,[],[f9868,f2950]) ).
fof(f9868,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f9867]) ).
fof(f31643,plain,
( spl0_993
| ~ spl0_220
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3357,f3013,f2115,f31641]) ).
fof(f31641,plain,
( spl0_993
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f3357,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0) )
| ~ spl0_220
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f3337]) ).
fof(f3337,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_lessequals(X1,X2,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220
| ~ spl0_285 ),
inference(resolution,[],[f3014,f2116]) ).
fof(f31639,plain,
( spl0_992
| ~ spl0_203
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3355,f3013,f2039,f31637]) ).
fof(f31637,plain,
( spl0_992
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f3355,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_203
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f3339]) ).
fof(f3339,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_203
| ~ spl0_285 ),
inference(resolution,[],[f3014,f2040]) ).
fof(f31635,plain,
( spl0_991
| ~ spl0_220
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3310,f3005,f2115,f31633]) ).
fof(f31633,plain,
( spl0_991
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f3310,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0) )
| ~ spl0_220
| ~ spl0_283 ),
inference(duplicate_literal_removal,[],[f3290]) ).
fof(f3290,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_lessequals(X2,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_220
| ~ spl0_283 ),
inference(resolution,[],[f3006,f2116]) ).
fof(f31631,plain,
( spl0_990
| ~ spl0_203
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3308,f3005,f2039,f31629]) ).
fof(f31629,plain,
( spl0_990
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f3308,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_203
| ~ spl0_283 ),
inference(duplicate_literal_removal,[],[f3292]) ).
fof(f3292,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) )
| ~ spl0_203
| ~ spl0_283 ),
inference(resolution,[],[f3006,f2040]) ).
fof(f31627,plain,
( spl0_989
| ~ spl0_167
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3227,f2993,f1666,f31625]) ).
fof(f31625,plain,
( spl0_989
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f2993,plain,
( spl0_280
<=> ! [X6,X5,X7] :
( X5 = X6
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f3227,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
| X0 = X2 )
| ~ spl0_167
| ~ spl0_280 ),
inference(superposition,[],[f2994,f1667]) ).
fof(f2994,plain,
( ! [X6,X7,X5] :
( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X6,X7,tc_nat)
| X5 = X6 )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2993]) ).
fof(f31623,plain,
( spl0_988
| ~ spl0_177
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f3158,f2953,f1706,f31621]) ).
fof(f31621,plain,
( spl0_988
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f2953,plain,
( spl0_270
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f3158,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_177
| ~ spl0_270 ),
inference(superposition,[],[f2954,f1707]) ).
fof(f2954,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_270 ),
inference(avatar_component_clause,[],[f2953]) ).
fof(f31619,plain,
( spl0_987
| ~ spl0_176
| ~ spl0_270 ),
inference(avatar_split_clause,[],[f3157,f2953,f1702,f31617]) ).
fof(f31617,plain,
( spl0_987
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f3157,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_176
| ~ spl0_270 ),
inference(superposition,[],[f2954,f1703]) ).
fof(f31615,plain,
( spl0_986
| ~ spl0_126
| ~ spl0_205
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3138,f2949,f2047,f1462,f31613]) ).
fof(f31613,plain,
( spl0_986
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f3138,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_126
| ~ spl0_205
| ~ spl0_269 ),
inference(forward_demodulation,[],[f3104,f1463]) ).
fof(f3104,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_269 ),
inference(superposition,[],[f2950,f2048]) ).
fof(f31611,plain,
( spl0_985
| ~ spl0_177
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3123,f2949,f1706,f31609]) ).
fof(f31609,plain,
( spl0_985
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f3123,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_177
| ~ spl0_269 ),
inference(superposition,[],[f1707,f2950]) ).
fof(f31607,plain,
( spl0_984
| ~ spl0_176
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3122,f2949,f1702,f31605]) ).
fof(f31605,plain,
( spl0_984
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f3122,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X1
| ~ spl0_176
| ~ spl0_269 ),
inference(superposition,[],[f1703,f2950]) ).
fof(f31603,plain,
( spl0_983
| ~ spl0_139
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f16438,f9502,f1525,f31601]) ).
fof(f31601,plain,
( spl0_983
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f9502,plain,
( spl0_548
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f16438,plain,
( ! [X0,X1] : ~ c_lessequals(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_139
| ~ spl0_548 ),
inference(resolution,[],[f9503,f1526]) ).
fof(f9503,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_548 ),
inference(avatar_component_clause,[],[f9502]) ).
fof(f31599,plain,
( spl0_982
| ~ spl0_167
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3110,f2949,f1666,f31597]) ).
fof(f31597,plain,
( spl0_982
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f3110,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_167
| ~ spl0_269 ),
inference(superposition,[],[f2950,f1667]) ).
fof(f31595,plain,
( spl0_981
| ~ spl0_177
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3106,f2949,f1706,f31593]) ).
fof(f31593,plain,
( spl0_981
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f3106,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_177
| ~ spl0_269 ),
inference(superposition,[],[f2950,f1707]) ).
fof(f31591,plain,
( spl0_980
| ~ spl0_176
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3105,f2949,f1702,f31589]) ).
fof(f31589,plain,
( spl0_980
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f3105,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_176
| ~ spl0_269 ),
inference(superposition,[],[f2950,f1703]) ).
fof(f31587,plain,
( spl0_979
| ~ spl0_248
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2940,f2524,f2460,f31585]) ).
fof(f31585,plain,
( spl0_979
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f2940,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) )
| ~ spl0_248
| ~ spl0_264 ),
inference(superposition,[],[f2461,f2525]) ).
fof(f31583,plain,
( spl0_978
| ~ spl0_246
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2938,f2524,f2448,f31581]) ).
fof(f31581,plain,
( spl0_978
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f2938,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) )
| ~ spl0_246
| ~ spl0_264 ),
inference(superposition,[],[f2449,f2525]) ).
fof(f31579,plain,
( spl0_977
| ~ spl0_239
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2936,f2524,f2420,f31577]) ).
fof(f31577,plain,
( spl0_977
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f2936,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_239
| ~ spl0_264 ),
inference(superposition,[],[f2421,f2525]) ).
fof(f31575,plain,
( spl0_976
| ~ spl0_205
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2931,f2524,f2047,f31573]) ).
fof(f31573,plain,
( spl0_976
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2931,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_205
| ~ spl0_264 ),
inference(superposition,[],[f2048,f2525]) ).
fof(f31571,plain,
( spl0_975
| ~ spl0_194
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2930,f2524,f2003,f31569]) ).
fof(f31569,plain,
( spl0_975
<=> ! [X0,X1] :
( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2930,plain,
( ! [X0,X1] :
( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_194
| ~ spl0_264 ),
inference(superposition,[],[f2004,f2525]) ).
fof(f31567,plain,
( spl0_974
| ~ spl0_247
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2908,f2520,f2456,f31565]) ).
fof(f31565,plain,
( spl0_974
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2908,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_lessequals(X0,X2,tc_nat) )
| ~ spl0_247
| ~ spl0_263 ),
inference(superposition,[],[f2457,f2521]) ).
fof(f31563,plain,
( spl0_973
| ~ spl0_245
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2906,f2520,f2444,f31561]) ).
fof(f31561,plain,
( spl0_973
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2906,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_lessequals(X2,X0,tc_nat) )
| ~ spl0_245
| ~ spl0_263 ),
inference(superposition,[],[f2445,f2521]) ).
fof(f31559,plain,
( spl0_972
| ~ spl0_143
| ~ spl0_548 ),
inference(avatar_split_clause,[],[f16411,f9502,f1541,f31557]) ).
fof(f31557,plain,
( spl0_972
<=> ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f16411,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X0,tc_nat) )
| ~ spl0_143
| ~ spl0_548 ),
inference(resolution,[],[f9503,f1542]) ).
fof(f31555,plain,
( spl0_971
| ~ spl0_238
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2904,f2520,f2416,f31553]) ).
fof(f31553,plain,
( spl0_971
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2904,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_238
| ~ spl0_263 ),
inference(superposition,[],[f2417,f2521]) ).
fof(f31551,plain,
( spl0_970
| ~ spl0_237
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2903,f2520,f2412,f31549]) ).
fof(f31549,plain,
( spl0_970
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2903,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_237
| ~ spl0_263 ),
inference(superposition,[],[f2413,f2521]) ).
fof(f31547,plain,
( spl0_969
| ~ spl0_194
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2899,f2520,f2003,f31545]) ).
fof(f31545,plain,
( spl0_969
<=> ! [X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2899,plain,
( ! [X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) )
| ~ spl0_194
| ~ spl0_263 ),
inference(superposition,[],[f2004,f2521]) ).
fof(f31543,plain,
( spl0_968
| ~ spl0_215
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2883,f2516,f2090,f31541]) ).
fof(f31541,plain,
( spl0_968
<=> ! [X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f2090,plain,
( spl0_215
<=> ! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f2883,plain,
( ! [X0,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_215
| ~ spl0_262 ),
inference(superposition,[],[f2091,f2517]) ).
fof(f2091,plain,
( ! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f2090]) ).
fof(f31539,plain,
( spl0_967
| ~ spl0_259
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2881,f2516,f2504,f31537]) ).
fof(f31537,plain,
( spl0_967
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f2881,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) )
| ~ spl0_259
| ~ spl0_262 ),
inference(superposition,[],[f2505,f2517]) ).
fof(f31535,plain,
( spl0_966
| ~ spl0_161
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2857,f2504,f1642,f31533]) ).
fof(f31533,plain,
( spl0_966
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2857,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_161
| ~ spl0_259 ),
inference(resolution,[],[f2505,f1643]) ).
fof(f31531,plain,
( spl0_965
| ~ spl0_185
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2856,f2504,f1738,f31529]) ).
fof(f31529,plain,
( spl0_965
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f1738,plain,
( spl0_185
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f2856,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_185
| ~ spl0_259 ),
inference(resolution,[],[f2505,f1739]) ).
fof(f1739,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_185 ),
inference(avatar_component_clause,[],[f1738]) ).
fof(f31527,plain,
( spl0_964
| ~ spl0_183
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2831,f2484,f1730,f31525]) ).
fof(f31525,plain,
( spl0_964
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2831,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_183
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1731]) ).
fof(f31523,plain,
( spl0_963
| ~ spl0_154
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2818,f2484,f1614,f31521]) ).
fof(f31521,plain,
( spl0_963
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2818,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_154
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1615]) ).
fof(f31519,plain,
( spl0_962
| ~ spl0_188
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2817,f2484,f1750,f31517]) ).
fof(f31517,plain,
( spl0_962
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2817,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_188
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1751]) ).
fof(f31515,plain,
( spl0_961
| ~ spl0_269
| ~ spl0_519 ),
inference(avatar_split_clause,[],[f15117,f9362,f2949,f31513]) ).
fof(f31513,plain,
( spl0_961
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f9362,plain,
( spl0_519
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f15117,plain,
( ! [X0,X1] : ~ c_lessequals(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_269
| ~ spl0_519 ),
inference(superposition,[],[f9363,f2950]) ).
fof(f9363,plain,
( ! [X0,X1] : ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_519 ),
inference(avatar_component_clause,[],[f9362]) ).
fof(f31511,plain,
( spl0_960
| ~ spl0_183
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2784,f2460,f1730,f31509]) ).
fof(f31509,plain,
( spl0_960
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2784,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X1,tc_nat) )
| ~ spl0_183
| ~ spl0_248 ),
inference(resolution,[],[f2461,f1731]) ).
fof(f31507,plain,
( spl0_959
| ~ spl0_183
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2759,f2456,f1730,f31505]) ).
fof(f31505,plain,
( spl0_959
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2759,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_183
| ~ spl0_247 ),
inference(resolution,[],[f2457,f1731]) ).
fof(f31503,plain,
( spl0_958
| ~ spl0_155
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2735,f2448,f1618,f31501]) ).
fof(f31501,plain,
( spl0_958
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2735,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_155
| ~ spl0_246 ),
inference(resolution,[],[f2449,f1619]) ).
fof(f31499,plain,
( spl0_957
| ~ spl0_182
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2734,f2448,f1726,f31497]) ).
fof(f31497,plain,
( spl0_957
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2734,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_182
| ~ spl0_246 ),
inference(resolution,[],[f2449,f1727]) ).
fof(f31495,plain,
( spl0_956
| ~ spl0_189
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2733,f2448,f1754,f31493]) ).
fof(f31493,plain,
( spl0_956
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2733,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat) )
| ~ spl0_189
| ~ spl0_246 ),
inference(resolution,[],[f2449,f1755]) ).
fof(f31491,plain,
( spl0_955
| ~ spl0_155
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2724,f2444,f1618,f31489]) ).
fof(f31489,plain,
( spl0_955
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2724,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_155
| ~ spl0_245 ),
inference(resolution,[],[f2445,f1619]) ).
fof(f31487,plain,
( spl0_954
| ~ spl0_182
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2723,f2444,f1726,f31485]) ).
fof(f31485,plain,
( spl0_954
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2723,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_182
| ~ spl0_245 ),
inference(resolution,[],[f2445,f1727]) ).
fof(f31483,plain,
( spl0_953
| ~ spl0_189
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2722,f2444,f1754,f31481]) ).
fof(f31481,plain,
( spl0_953
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2722,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),X0,tc_nat) )
| ~ spl0_189
| ~ spl0_245 ),
inference(resolution,[],[f2445,f1755]) ).
fof(f31479,plain,
( spl0_952
| ~ spl0_186
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2698,f2420,f1742,f31477]) ).
fof(f31477,plain,
( spl0_952
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2698,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_186
| ~ spl0_239 ),
inference(resolution,[],[f2421,f1743]) ).
fof(f31475,plain,
( spl0_951
| ~ spl0_160
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2673,f2416,f1638,f31473]) ).
fof(f31473,plain,
( spl0_951
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1638,plain,
( spl0_160
<=> ! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2673,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_160
| ~ spl0_238 ),
inference(resolution,[],[f2417,f1639]) ).
fof(f1639,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1638]) ).
fof(f31471,plain,
( spl0_950
| ~ spl0_269
| ~ spl0_503 ),
inference(avatar_split_clause,[],[f14341,f8627,f2949,f31469]) ).
fof(f31469,plain,
( spl0_950
<=> ! [X0,X1] : c_lessequals(X1,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f8627,plain,
( spl0_503
<=> ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f14341,plain,
( ! [X0,X1] : c_lessequals(X1,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat)
| ~ spl0_269
| ~ spl0_503 ),
inference(superposition,[],[f8628,f2950]) ).
fof(f8628,plain,
( ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat)
| ~ spl0_503 ),
inference(avatar_component_clause,[],[f8627]) ).
fof(f31467,plain,
( spl0_949
| ~ spl0_184
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2672,f2416,f1734,f31465]) ).
fof(f31465,plain,
( spl0_949
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1734,plain,
( spl0_184
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f2672,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_184
| ~ spl0_238 ),
inference(resolution,[],[f2417,f1735]) ).
fof(f1735,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1734]) ).
fof(f31463,plain,
( spl0_948
| ~ spl0_187
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2671,f2416,f1746,f31461]) ).
fof(f31461,plain,
( spl0_948
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1746,plain,
( spl0_187
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f2671,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_187
| ~ spl0_238 ),
inference(resolution,[],[f2417,f1747]) ).
fof(f1747,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f1746]) ).
fof(f31459,plain,
( spl0_947
| ~ spl0_186
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2659,f2412,f1742,f31457]) ).
fof(f31457,plain,
( spl0_947
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2659,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_186
| ~ spl0_237 ),
inference(resolution,[],[f2413,f1743]) ).
fof(f31455,plain,
( spl0_946
| ~ spl0_110
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2248,f2086,f1397,f31453]) ).
fof(f31453,plain,
( spl0_946
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1397,plain,
( spl0_110
<=> ! [X34] :
( ~ class_HOL_Ozero(X34)
| class_HOL_Ozero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2086,plain,
( spl0_214
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f2248,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) )
| ~ spl0_110
| ~ spl0_214 ),
inference(resolution,[],[f2087,f1398]) ).
fof(f1398,plain,
( ! [X34] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X34))
| ~ class_HOL_Ozero(X34) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1397]) ).
fof(f2087,plain,
( ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f2086]) ).
fof(f31451,plain,
( spl0_945
| ~ spl0_110
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2173,f2019,f1397,f31449]) ).
fof(f31449,plain,
( spl0_945
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2019,plain,
( spl0_198
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2173,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) )
| ~ spl0_110
| ~ spl0_198 ),
inference(resolution,[],[f2020,f1398]) ).
fof(f2020,plain,
( ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2019]) ).
fof(f31447,plain,
( spl0_944
| ~ spl0_81
| ~ spl0_181 ),
inference(avatar_split_clause,[],[f1912,f1722,f1281,f31445]) ).
fof(f31445,plain,
( spl0_944
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1281,plain,
( spl0_81
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1722,plain,
( spl0_181
<=> ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1912,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_81
| ~ spl0_181 ),
inference(resolution,[],[f1723,f1282]) ).
fof(f1282,plain,
( ! [X34] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oordered__idom(X34) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f1281]) ).
fof(f1723,plain,
( ! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_181 ),
inference(avatar_component_clause,[],[f1722]) ).
fof(f31111,plain,
( spl0_943
| ~ spl0_155
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f6756,f6388,f1618,f31109]) ).
fof(f31109,plain,
( spl0_943
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f6388,plain,
( spl0_442
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f6756,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),tc_nat)
| ~ spl0_155
| ~ spl0_442 ),
inference(resolution,[],[f6389,f1619]) ).
fof(f6389,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f6388]) ).
fof(f30402,plain,
( spl0_942
| ~ spl0_182
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f6755,f6388,f1726,f30400]) ).
fof(f30400,plain,
( spl0_942
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f6755,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),tc_nat)
| ~ spl0_182
| ~ spl0_442 ),
inference(resolution,[],[f6389,f1727]) ).
fof(f29941,plain,
( spl0_941
| ~ spl0_189
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f6754,f6388,f1754,f29939]) ).
fof(f29939,plain,
( spl0_941
<=> ! [X0,X1] : ~ c_lessequals(c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f6754,plain,
( ! [X0,X1] : ~ c_lessequals(c_Orderings_Oord__class_Omax(c_Suc(X0),X1,tc_nat),X0,tc_nat)
| ~ spl0_189
| ~ spl0_442 ),
inference(resolution,[],[f6389,f1755]) ).
fof(f29299,plain,
( spl0_940
| ~ spl0_153
| ~ spl0_167
| ~ spl0_263
| ~ spl0_269
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6075,f5123,f2949,f2520,f1666,f1610,f29297]) ).
fof(f29297,plain,
( spl0_940
<=> ! [X0,X1] : c_lessequals(X0,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1610,plain,
( spl0_153
<=> ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f6075,plain,
( ! [X0,X1] : c_lessequals(X0,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat)
| ~ spl0_153
| ~ spl0_167
| ~ spl0_263
| ~ spl0_269
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6074,f3110]) ).
fof(f6074,plain,
( ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)),tc_nat)
| ~ spl0_153
| ~ spl0_167
| ~ spl0_263
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6073,f2521]) ).
fof(f6073,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat),tc_nat)
| ~ spl0_153
| ~ spl0_167
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6041,f1667]) ).
fof(f6041,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),X1,tc_nat),tc_nat)
| ~ spl0_153
| ~ spl0_410 ),
inference(resolution,[],[f5124,f1611]) ).
fof(f1611,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1610]) ).
fof(f28871,plain,
( spl0_939
| ~ spl0_187
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f5670,f5083,f1746,f28869]) ).
fof(f28869,plain,
( spl0_939
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f5083,plain,
( spl0_400
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f5670,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat),X1,tc_nat)
| ~ spl0_187
| ~ spl0_400 ),
inference(resolution,[],[f5084,f1747]) ).
fof(f5084,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f5083]) ).
fof(f27805,plain,
( spl0_938
| ~ spl0_155
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5472,f5039,f1618,f27803]) ).
fof(f27803,plain,
( spl0_938
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omax(X1,c_Suc(X0),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f5039,plain,
( spl0_389
<=> ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f5472,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omax(X1,c_Suc(X0),tc_nat),tc_nat)
| ~ spl0_155
| ~ spl0_389 ),
inference(resolution,[],[f5040,f1619]) ).
fof(f5040,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_389 ),
inference(avatar_component_clause,[],[f5039]) ).
fof(f26901,plain,
( spl0_937
| ~ spl0_182
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5471,f5039,f1726,f26899]) ).
fof(f26899,plain,
( spl0_937
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Suc(X0),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f5471,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,c_Suc(X0),tc_nat),tc_nat)
| ~ spl0_182
| ~ spl0_389 ),
inference(resolution,[],[f5040,f1727]) ).
fof(f26877,plain,
( spl0_936
| ~ spl0_59
| ~ spl0_167
| ~ spl0_269
| ~ spl0_558 ),
inference(avatar_split_clause,[],[f10643,f10151,f2949,f1666,f1192,f26875]) ).
fof(f26875,plain,
( spl0_936
<=> ! [X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f10151,plain,
( spl0_558
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| ~ c_lessequals(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f10643,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_59
| ~ spl0_167
| ~ spl0_269
| ~ spl0_558 ),
inference(forward_demodulation,[],[f10642,f3110]) ).
fof(f10642,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat),X1,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_59
| ~ spl0_167
| ~ spl0_558 ),
inference(forward_demodulation,[],[f10607,f1667]) ).
fof(f10607,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),X0,tc_nat),X1,tc_nat) )
| ~ spl0_59
| ~ spl0_558 ),
inference(resolution,[],[f10152,f1193]) ).
fof(f10152,plain,
( ! [X10,X9,X7] :
( ~ c_lessequals(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat)
| ~ c_lessequals(X7,X10,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) )
| ~ spl0_558 ),
inference(avatar_component_clause,[],[f10151]) ).
fof(f26873,plain,
( spl0_935
| ~ spl0_189
| ~ spl0_389 ),
inference(avatar_split_clause,[],[f5470,f5039,f1754,f26871]) ).
fof(f26871,plain,
( spl0_935
<=> ! [X0,X1] : ~ c_lessequals(c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f5470,plain,
( ! [X0,X1] : ~ c_lessequals(c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat),X1,tc_nat)
| ~ spl0_189
| ~ spl0_389 ),
inference(resolution,[],[f5040,f1755]) ).
fof(f26869,plain,
( spl0_934
| ~ spl0_137
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f7521,f7029,f1517,f26867]) ).
fof(f26867,plain,
( spl0_934
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f7521,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_462 ),
inference(superposition,[],[f1518,f7030]) ).
fof(f26865,plain,
( spl0_933
| ~ spl0_139
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7373,f6992,f1525,f26863]) ).
fof(f26863,plain,
( spl0_933
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f6992,plain,
( spl0_456
<=> ! [X6,X5,X7] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f7373,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_139
| ~ spl0_456 ),
inference(superposition,[],[f1526,f6993]) ).
fof(f6993,plain,
( ! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ spl0_456 ),
inference(avatar_component_clause,[],[f6992]) ).
fof(f26861,plain,
( spl0_932
| ~ spl0_139
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f7317,f6988,f1525,f26859]) ).
fof(f26859,plain,
( spl0_932
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f6988,plain,
( spl0_455
<=> ! [X6,X5,X7] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f7317,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_139
| ~ spl0_455 ),
inference(superposition,[],[f1526,f6989]) ).
fof(f6989,plain,
( ! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat)
| ~ spl0_455 ),
inference(avatar_component_clause,[],[f6988]) ).
fof(f26857,plain,
( spl0_931
| ~ spl0_238
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f6550,f5217,f2416,f26855]) ).
fof(f26855,plain,
( spl0_931
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f5217,plain,
( spl0_428
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f6550,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_238
| ~ spl0_428 ),
inference(resolution,[],[f5218,f2417]) ).
fof(f5218,plain,
( ! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f5217]) ).
fof(f26853,plain,
( spl0_930
| ~ spl0_167
| ~ spl0_269
| ~ spl0_405
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6072,f5123,f5103,f2949,f1666,f26851]) ).
fof(f26851,plain,
( spl0_930
<=> ! [X2,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f5103,plain,
( spl0_405
<=> ! [X6,X29,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X29,tc_nat),c_HOL_Ominus__class_Ominus(X6,X29,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f6072,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_Orderings_Oord__class_Omax(X1,X2,tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_167
| ~ spl0_269
| ~ spl0_405
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6071,f3110]) ).
fof(f6071,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_167
| ~ spl0_405
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6039,f1667]) ).
fof(f6039,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X2,tc_nat),tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_405
| ~ spl0_410 ),
inference(resolution,[],[f5124,f5104]) ).
fof(f5104,plain,
( ! [X29,X6,X5] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X5,X29,tc_nat),c_HOL_Ominus__class_Ominus(X6,X29,tc_nat),tc_nat)
| ~ c_lessequals(X5,X6,tc_nat) )
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f5103]) ).
fof(f26849,plain,
( spl0_929
| ~ spl0_245
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5980,f5119,f2444,f26847]) ).
fof(f26847,plain,
( spl0_929
<=> ! [X2,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f5980,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X2,tc_nat) )
| ~ spl0_245
| ~ spl0_409 ),
inference(resolution,[],[f5120,f2445]) ).
fof(f26845,plain,
( spl0_928
| ~ spl0_246
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f5979,f5119,f2448,f26843]) ).
fof(f26843,plain,
( spl0_928
<=> ! [X2,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f5979,plain,
( ! [X2,X0,X1] :
( c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_246
| ~ spl0_409 ),
inference(resolution,[],[f5120,f2449]) ).
fof(f26841,plain,
( spl0_927
| ~ spl0_245
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f5364,f4975,f2444,f26839]) ).
fof(f26839,plain,
( spl0_927
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f4975,plain,
( spl0_373
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f5364,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),X2,tc_nat) )
| ~ spl0_245
| ~ spl0_373 ),
inference(resolution,[],[f4976,f2445]) ).
fof(f4976,plain,
( ! [X6,X7,X5] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat)
| c_lessequals(X5,X6,tc_nat) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f4975]) ).
fof(f26837,plain,
( spl0_926
| ~ spl0_52
| ~ spl0_358 ),
inference(avatar_split_clause,[],[f4821,f3792,f1158,f26835]) ).
fof(f26835,plain,
( spl0_926
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1158,plain,
( spl0_52
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f3792,plain,
( spl0_358
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f4821,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| ~ spl0_52
| ~ spl0_358 ),
inference(resolution,[],[f3793,f1160]) ).
fof(f1160,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f3793,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = X4 )
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f3792]) ).
fof(f26833,plain,
( spl0_925
| ~ spl0_48
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f4819,f3788,f1138,f26831]) ).
fof(f26831,plain,
( spl0_925
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f3788,plain,
( spl0_357
<=> ! [X2,X0,X21] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f4819,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| ~ spl0_48
| ~ spl0_357 ),
inference(resolution,[],[f3789,f1140]) ).
fof(f3789,plain,
( ! [X2,X21,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = X2 )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f3788]) ).
fof(f26829,plain,
( spl0_924
| ~ spl0_262
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f5248,f3485,f2516,f26827]) ).
fof(f26827,plain,
( spl0_924
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f3485,plain,
( spl0_309
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f5248,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_262
| ~ spl0_309 ),
inference(superposition,[],[f3486,f2517]) ).
fof(f3486,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f26825,plain,
( spl0_923
| ~ spl0_48
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f4817,f3784,f1138,f26823]) ).
fof(f26823,plain,
( spl0_923
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f26821,plain,
( spl0_922
| ~ spl0_52
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f4815,f3780,f1158,f26819]) ).
fof(f26819,plain,
( spl0_922
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f3780,plain,
( spl0_355
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f4815,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_52
| ~ spl0_355 ),
inference(resolution,[],[f3781,f1160]) ).
fof(f3781,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f3780]) ).
fof(f26817,plain,
( spl0_921
| ~ spl0_143
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4706,f3756,f1541,f26815]) ).
fof(f26815,plain,
( spl0_921
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f4706,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) )
| ~ spl0_143
| ~ spl0_349 ),
inference(resolution,[],[f3757,f1542]) ).
fof(f26813,plain,
( spl0_920
| ~ spl0_143
| ~ spl0_348 ),
inference(avatar_split_clause,[],[f4692,f3752,f1541,f26811]) ).
fof(f26811,plain,
( spl0_920
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f4692,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) )
| ~ spl0_143
| ~ spl0_348 ),
inference(resolution,[],[f3753,f1542]) ).
fof(f26809,plain,
( spl0_919
| ~ spl0_56
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4442,f3712,f1178,f26807]) ).
fof(f26807,plain,
( spl0_919
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f3712,plain,
( spl0_338
<=> ! [X0,X3] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f4442,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_56
| ~ spl0_338 ),
inference(resolution,[],[f3713,f1180]) ).
fof(f3713,plain,
( ! [X3,X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) )
| ~ spl0_338 ),
inference(avatar_component_clause,[],[f3712]) ).
fof(f26805,plain,
( spl0_918
| ~ spl0_36
| ~ spl0_338 ),
inference(avatar_split_clause,[],[f4441,f3712,f1078,f26803]) ).
fof(f26803,plain,
( spl0_918
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f4441,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),tc_nat)
| ~ spl0_36
| ~ spl0_338 ),
inference(resolution,[],[f3713,f1080]) ).
fof(f26801,plain,
( spl0_917
| ~ spl0_56
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4277,f3671,f1178,f26798]) ).
fof(f26798,plain,
( spl0_917
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f3671,plain,
( spl0_328
<=> ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f4277,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_56
| ~ spl0_328 ),
inference(resolution,[],[f3672,f1180]) ).
fof(f3672,plain,
( ! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_328 ),
inference(avatar_component_clause,[],[f3671]) ).
fof(f26796,plain,
( spl0_916
| ~ spl0_36
| ~ spl0_328 ),
inference(avatar_split_clause,[],[f4276,f3671,f1078,f26793]) ).
fof(f26793,plain,
( spl0_916
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f4276,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_36
| ~ spl0_328 ),
inference(resolution,[],[f3672,f1080]) ).
fof(f26791,plain,
( spl0_915
| ~ spl0_55
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f4270,f3659,f1173,f26789]) ).
fof(f26789,plain,
( spl0_915
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1173,plain,
( spl0_55
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f3659,plain,
( spl0_325
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f4270,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_55
| ~ spl0_325 ),
inference(resolution,[],[f3660,f1175]) ).
fof(f1175,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f3660,plain,
( ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f3659]) ).
fof(f26787,plain,
( spl0_914
| ~ spl0_205
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4193,f3643,f2047,f26785]) ).
fof(f26785,plain,
( spl0_914
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f4193,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_321 ),
inference(superposition,[],[f2048,f3644]) ).
fof(f26747,plain,
( spl0_913
| ~ spl0_129
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4186,f3643,f1474,f26745]) ).
fof(f26745,plain,
( spl0_913
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f4186,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_321 ),
inference(superposition,[],[f1475,f3644]) ).
fof(f26743,plain,
( spl0_912
| ~ spl0_127
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4184,f3643,f1466,f26741]) ).
fof(f26741,plain,
( spl0_912
<=> ! [X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f4184,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_321 ),
inference(superposition,[],[f1467,f3644]) ).
fof(f26739,plain,
( spl0_911
| ~ spl0_205
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4150,f3639,f2047,f26737]) ).
fof(f26737,plain,
( spl0_911
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f4150,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_205
| ~ spl0_320 ),
inference(superposition,[],[f2048,f3640]) ).
fof(f26735,plain,
( spl0_910
| ~ spl0_129
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4143,f3639,f1474,f26733]) ).
fof(f26733,plain,
( spl0_910
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f4143,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_129
| ~ spl0_320 ),
inference(superposition,[],[f1475,f3640]) ).
fof(f26731,plain,
( spl0_909
| ~ spl0_127
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4141,f3639,f1466,f26729]) ).
fof(f26729,plain,
( spl0_909
<=> ! [X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f4141,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_320 ),
inference(superposition,[],[f1467,f3640]) ).
fof(f26727,plain,
( spl0_908
| ~ spl0_52
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f4063,f3627,f1158,f26725]) ).
fof(f26725,plain,
( spl0_908
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f3627,plain,
( spl0_317
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f4063,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| ~ spl0_52
| ~ spl0_317 ),
inference(resolution,[],[f3628,f1160]) ).
fof(f3628,plain,
( ! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0),X0) = X4 )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f26723,plain,
( spl0_907
| ~ spl0_154
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3817,f3801,f1614,f26721]) ).
fof(f26721,plain,
( spl0_907
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f3817,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_154
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1615]) ).
fof(f26719,plain,
( spl0_906
| ~ spl0_188
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3816,f3801,f1750,f26717]) ).
fof(f26717,plain,
( spl0_906
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat) = X0
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f3816,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,c_Suc(X1),tc_nat) = X0
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_188
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1751]) ).
fof(f26715,plain,
( spl0_905
| ~ spl0_124
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3525,f3058,f1454,f26713]) ).
fof(f3525,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Otimes__class_Otimes(X1,X1,tc_nat),tc_nat) )
| ~ spl0_124
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1455]) ).
fof(f26711,plain,
( spl0_904
| ~ spl0_123
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3511,f3058,f1450,f26709]) ).
fof(f26709,plain,
( spl0_904
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f3511,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_123
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1451]) ).
fof(f26707,plain,
( spl0_903
| ~ spl0_855
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f26598,f26581,f25766,f26705]) ).
fof(f26705,plain,
( spl0_903
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f25766,plain,
( spl0_855
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f26581,plain,
( spl0_893
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f26598,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),X0,tc_nat)
| ~ spl0_855
| ~ spl0_893 ),
inference(superposition,[],[f25767,f26582]) ).
fof(f26582,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) = X0
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f26581]) ).
fof(f25767,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,tc_nat),tc_nat)
| ~ spl0_855 ),
inference(avatar_component_clause,[],[f25766]) ).
fof(f26703,plain,
( spl0_902
| ~ spl0_122
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f3510,f3058,f1446,f26701]) ).
fof(f26701,plain,
( spl0_902
<=> ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f3510,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_122
| ~ spl0_296 ),
inference(resolution,[],[f3059,f1447]) ).
fof(f26699,plain,
( spl0_901
| ~ spl0_158
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f3450,f3029,f1630,f26697]) ).
fof(f26697,plain,
( spl0_901
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f3450,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0) = X1 )
| ~ spl0_158
| ~ spl0_289 ),
inference(duplicate_literal_removal,[],[f3428]) ).
fof(f3428,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X1,X0),X0) = X1
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_158
| ~ spl0_289 ),
inference(resolution,[],[f3030,f1631]) ).
fof(f26695,plain,
( spl0_900
| ~ spl0_159
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3404,f3017,f1634,f26693]) ).
fof(f26693,plain,
( spl0_900
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f3404,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0) = X1 )
| ~ spl0_159
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f3375]) ).
fof(f3375,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0) = X1
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_159
| ~ spl0_286 ),
inference(resolution,[],[f3018,f1635]) ).
fof(f26691,plain,
( spl0_899
| ~ spl0_158
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f3403,f3017,f1630,f26689]) ).
fof(f26689,plain,
( spl0_899
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f3403,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0) = X2 )
| ~ spl0_158
| ~ spl0_286 ),
inference(duplicate_literal_removal,[],[f3381]) ).
fof(f3381,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0) = X2
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_158
| ~ spl0_286 ),
inference(resolution,[],[f3018,f1631]) ).
fof(f26687,plain,
( spl0_898
| ~ spl0_156
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3354,f3013,f1622,f26685]) ).
fof(f26685,plain,
( spl0_898
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f3354,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X1,X0) = X1 )
| ~ spl0_156
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f3351]) ).
fof(f3351,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X1,X0) = X1
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_156
| ~ spl0_285 ),
inference(resolution,[],[f3014,f1623]) ).
fof(f26683,plain,
( spl0_897
| ~ spl0_157
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f3353,f3013,f1626,f26681]) ).
fof(f26681,plain,
( spl0_897
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X2,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f3353,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X2,X0) = X2 )
| ~ spl0_157
| ~ spl0_285 ),
inference(duplicate_literal_removal,[],[f3352]) ).
fof(f3352,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),X2,X0) = X2
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_157
| ~ spl0_285 ),
inference(resolution,[],[f3014,f1627]) ).
fof(f26679,plain,
( spl0_896
| ~ spl0_157
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3306,f3005,f1626,f26677]) ).
fof(f26677,plain,
( spl0_896
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f3306,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X1,X0),X0) = X1 )
| ~ spl0_157
| ~ spl0_283 ),
inference(duplicate_literal_removal,[],[f3305]) ).
fof(f3305,plain,
( ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X1,X0),X0) = X1
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_157
| ~ spl0_283 ),
inference(resolution,[],[f3006,f1627]) ).
fof(f26628,plain,
( spl0_895
| ~ spl0_34
| ~ spl0_127
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3296,f3005,f1466,f1068,f26626]) ).
fof(f26626,plain,
( spl0_895
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f3296,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omin(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) = X0 )
| ~ spl0_127
| ~ spl0_283 ),
inference(resolution,[],[f3006,f1467]) ).
fof(f26587,plain,
( spl0_894
| ~ spl0_153
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3830,f3801,f1610,f26585]) ).
fof(f26585,plain,
( spl0_894
<=> ! [X0] : c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f3830,plain,
( ! [X0] : c_Suc(X0) = c_Orderings_Oord__class_Omax(c_Suc(X0),X0,tc_nat)
| ~ spl0_153
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1611]) ).
fof(f26583,plain,
( spl0_893
| ~ spl0_34
| ~ spl0_124
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f3293,f3005,f1454,f1068,f26581]) ).
fof(f3293,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(tc_nat)
| c_Orderings_Oord__class_Omin(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) = X0 )
| ~ spl0_124
| ~ spl0_283 ),
inference(resolution,[],[f3006,f1455]) ).
fof(f26579,plain,
( spl0_892
| ~ spl0_179
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3166,f2957,f1714,f26577]) ).
fof(f26577,plain,
( spl0_892
<=> ! [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_892])]) ).
fof(f2957,plain,
( spl0_271
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f3166,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_179
| ~ spl0_271 ),
inference(resolution,[],[f2958,f1715]) ).
fof(f2958,plain,
( ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2957]) ).
fof(f26575,plain,
( spl0_891
| ~ spl0_248
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3134,f2949,f2460,f26573]) ).
fof(f26573,plain,
( spl0_891
<=> ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f3134,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X2,tc_nat)
| c_lessequals(X1,X2,tc_nat) )
| ~ spl0_248
| ~ spl0_269 ),
inference(superposition,[],[f2461,f2950]) ).
fof(f26571,plain,
( spl0_890
| ~ spl0_246
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3132,f2949,f2448,f26569]) ).
fof(f26569,plain,
( spl0_890
<=> ! [X2,X0,X1] :
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f3132,plain,
( ! [X2,X0,X1] :
( c_lessequals(X2,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ c_lessequals(X2,X1,tc_nat) )
| ~ spl0_246
| ~ spl0_269 ),
inference(superposition,[],[f2449,f2950]) ).
fof(f26567,plain,
( spl0_889
| ~ spl0_239
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3130,f2949,f2420,f26565]) ).
fof(f26565,plain,
( spl0_889
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f3130,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_239
| ~ spl0_269 ),
inference(superposition,[],[f2421,f2950]) ).
fof(f26563,plain,
( spl0_888
| ~ spl0_235
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3127,f2949,f2399,f26561]) ).
fof(f26561,plain,
( spl0_888
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Orderings_Oord__class_Omax(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2399,plain,
( spl0_235
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f3127,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Orderings_Oord__class_Omax(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_235
| ~ spl0_269 ),
inference(superposition,[],[f2400,f2950]) ).
fof(f2400,plain,
( ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X6 )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2399]) ).
fof(f26559,plain,
( spl0_887
| ~ spl0_138
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3119,f2949,f1521,f26557]) ).
fof(f26557,plain,
( spl0_887
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f3119,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat)
| ~ spl0_138
| ~ spl0_269 ),
inference(superposition,[],[f1522,f2950]) ).
fof(f26555,plain,
( spl0_886
| ~ spl0_177
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2929,f2524,f1706,f26553]) ).
fof(f26553,plain,
( spl0_886
<=> ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2929,plain,
( ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_177
| ~ spl0_264 ),
inference(superposition,[],[f1707,f2525]) ).
fof(f26551,plain,
( spl0_885
| ~ spl0_176
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2928,f2524,f1702,f26549]) ).
fof(f26549,plain,
( spl0_885
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2928,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1
| ~ spl0_176
| ~ spl0_264 ),
inference(superposition,[],[f1703,f2525]) ).
fof(f26547,plain,
( spl0_884
| ~ spl0_167
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2916,f2524,f1666,f26545]) ).
fof(f26545,plain,
( spl0_884
<=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2916,plain,
( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)
| ~ spl0_167
| ~ spl0_264 ),
inference(superposition,[],[f2525,f1667]) ).
fof(f26543,plain,
( spl0_883
| ~ spl0_153
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2830,f2484,f1610,f26541]) ).
fof(f26541,plain,
( spl0_883
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2830,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat)
| ~ spl0_153
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1611]) ).
fof(f26539,plain,
( spl0_882
| ~ spl0_205
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2900,f2520,f2047,f26537]) ).
fof(f26537,plain,
( spl0_882
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2900,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_205
| ~ spl0_263 ),
inference(superposition,[],[f2048,f2521]) ).
fof(f26535,plain,
( spl0_881
| ~ spl0_177
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2898,f2520,f1706,f26533]) ).
fof(f26533,plain,
( spl0_881
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2898,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0
| ~ spl0_177
| ~ spl0_263 ),
inference(superposition,[],[f1707,f2521]) ).
fof(f26531,plain,
( spl0_880
| ~ spl0_176
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2897,f2520,f1702,f26529]) ).
fof(f26529,plain,
( spl0_880
<=> ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2897,plain,
( ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
| ~ spl0_176
| ~ spl0_263 ),
inference(superposition,[],[f1703,f2521]) ).
fof(f26527,plain,
( spl0_879
| ~ spl0_167
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2886,f2520,f1666,f26525]) ).
fof(f26525,plain,
( spl0_879
<=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2886,plain,
( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat)
| ~ spl0_167
| ~ spl0_263 ),
inference(superposition,[],[f2521,f1667]) ).
fof(f26523,plain,
( spl0_878
| ~ spl0_144
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2854,f2504,f1545,f26521]) ).
fof(f26521,plain,
( spl0_878
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2854,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_144
| ~ spl0_259 ),
inference(resolution,[],[f2505,f1546]) ).
fof(f26519,plain,
( spl0_877
| ~ spl0_177
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2842,f2488,f1706,f26517]) ).
fof(f26517,plain,
( spl0_877
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2842,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X1,tc_nat) )
| ~ spl0_177
| ~ spl0_255 ),
inference(superposition,[],[f2489,f1707]) ).
fof(f26515,plain,
( spl0_876
| ~ spl0_176
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2841,f2488,f1702,f26513]) ).
fof(f26513,plain,
( spl0_876
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X1
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2841,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X1
| c_lessequals(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X0,tc_nat) )
| ~ spl0_176
| ~ spl0_255 ),
inference(superposition,[],[f2489,f1703]) ).
fof(f26511,plain,
( spl0_875
| ~ spl0_145
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2815,f2484,f1549,f26509]) ).
fof(f26509,plain,
( spl0_875
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2815,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_145
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1550]) ).
fof(f26507,plain,
( spl0_874
| ~ spl0_145
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2772,f2460,f1549,f26505]) ).
fof(f26505,plain,
( spl0_874
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2772,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat) )
| ~ spl0_145
| ~ spl0_248 ),
inference(resolution,[],[f2461,f1550]) ).
fof(f26503,plain,
( spl0_873
| ~ spl0_145
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2747,f2456,f1549,f26501]) ).
fof(f26501,plain,
( spl0_873
<=> ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2747,plain,
( ! [X2,X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_145
| ~ spl0_247 ),
inference(resolution,[],[f2457,f1550]) ).
fof(f26450,plain,
( spl0_872
| ~ spl0_144
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2684,f2420,f1545,f26448]) ).
fof(f26448,plain,
( spl0_872
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2684,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_144
| ~ spl0_239 ),
inference(resolution,[],[f2421,f1546]) ).
fof(f26446,plain,
( spl0_871
| ~ spl0_167
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2678,f2416,f1666,f26444]) ).
fof(f26444,plain,
( spl0_871
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2678,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_167
| ~ spl0_238 ),
inference(superposition,[],[f2417,f1667]) ).
fof(f26442,plain,
( spl0_870
| ~ spl0_137
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2674,f2416,f1517,f26440]) ).
fof(f26440,plain,
( spl0_870
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2674,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_238 ),
inference(resolution,[],[f2417,f1518]) ).
fof(f26438,plain,
( spl0_869
| ~ spl0_144
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2646,f2412,f1545,f26436]) ).
fof(f26436,plain,
( spl0_869
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2646,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_144
| ~ spl0_237 ),
inference(resolution,[],[f2413,f1546]) ).
fof(f26434,plain,
( spl0_868
| ~ spl0_160
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2147,f1995,f1638,f26432]) ).
fof(f26432,plain,
( spl0_868
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| ~ c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2147,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| ~ c_lessequals(X0,X1,tc_nat) )
| ~ spl0_160
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1639]) ).
fof(f26430,plain,
( spl0_867
| ~ spl0_184
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2146,f1995,f1734,f26428]) ).
fof(f26428,plain,
( spl0_867
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2146,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_184
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1735]) ).
fof(f26426,plain,
( spl0_866
| ~ spl0_187
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2145,f1995,f1746,f26424]) ).
fof(f26424,plain,
( spl0_866
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2145,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_Suc(X1),tc_nat) = X0
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_187
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1747]) ).
fof(f26422,plain,
( spl0_865
| ~ spl0_101
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1902,f1710,f1361,f26420]) ).
fof(f26420,plain,
( spl0_865
<=> ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1710,plain,
( spl0_178
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1902,plain,
( ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_101
| ~ spl0_178 ),
inference(resolution,[],[f1711,f1362]) ).
fof(f1711,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = X3 )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f1710]) ).
fof(f26418,plain,
( spl0_864
| ~ spl0_87
| ~ spl0_175 ),
inference(avatar_split_clause,[],[f1884,f1698,f1305,f26416]) ).
fof(f26416,plain,
( spl0_864
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1698,plain,
( spl0_175
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1884,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_87
| ~ spl0_175 ),
inference(resolution,[],[f1699,f1306]) ).
fof(f1699,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f26414,plain,
( spl0_863
| ~ spl0_87
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f1879,f1690,f1305,f26412]) ).
fof(f26412,plain,
( spl0_863
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1690,plain,
( spl0_173
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1879,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_87
| ~ spl0_173 ),
inference(resolution,[],[f1691,f1306]) ).
fof(f1691,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 )
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f1690]) ).
fof(f26385,plain,
( spl0_862
| ~ spl0_100
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1870,f1678,f1357,f26383]) ).
fof(f26383,plain,
( spl0_862
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1357,plain,
( spl0_100
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1678,plain,
( spl0_170
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1870,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) )
| ~ spl0_100
| ~ spl0_170 ),
inference(resolution,[],[f1679,f1358]) ).
fof(f1358,plain,
( ! [X34] :
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Ocomm__monoid__add(X34) )
| ~ spl0_100 ),
inference(avatar_component_clause,[],[f1357]) ).
fof(f1679,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 )
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f26381,plain,
( spl0_861
| ~ spl0_100
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1867,f1674,f1357,f26379]) ).
fof(f26379,plain,
( spl0_861
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1674,plain,
( spl0_169
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1867,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) )
| ~ spl0_100
| ~ spl0_169 ),
inference(resolution,[],[f1675,f1358]) ).
fof(f1675,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 )
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f1674]) ).
fof(f26377,plain,
( spl0_860
| ~ spl0_102
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1843,f1662,f1365,f26375]) ).
fof(f26375,plain,
( spl0_860
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1662,plain,
( spl0_166
<=> ! [X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1843,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_102
| ~ spl0_166 ),
inference(resolution,[],[f1663,f1366]) ).
fof(f1663,plain,
( ! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X3,X3,X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1662]) ).
fof(f26373,plain,
( spl0_859
| ~ spl0_102
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1841,f1658,f1365,f26371]) ).
fof(f26371,plain,
( spl0_859
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ofield(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1658,plain,
( spl0_165
<=> ! [X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1841,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ofield(X1) )
| ~ spl0_102
| ~ spl0_165 ),
inference(resolution,[],[f1659,f1366]) ).
fof(f1659,plain,
( ! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1658]) ).
fof(f26369,plain,
( spl0_858
| ~ spl0_101
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1769,f1602,f1361,f26367]) ).
fof(f26367,plain,
( spl0_858
<=> ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1602,plain,
( spl0_151
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1769,plain,
( ! [X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_101
| ~ spl0_151 ),
inference(resolution,[],[f1603,f1362]) ).
fof(f1603,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 )
| ~ spl0_151 ),
inference(avatar_component_clause,[],[f1602]) ).
fof(f26365,plain,
( spl0_857
| ~ spl0_96
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1767,f1598,f1341,f26363]) ).
fof(f26363,plain,
( spl0_857
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1341,plain,
( spl0_96
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1598,plain,
( spl0_150
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1767,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_96
| ~ spl0_150 ),
inference(resolution,[],[f1599,f1342]) ).
fof(f1342,plain,
( ! [X34] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Oab__group__add(X34) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1599,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f26070,plain,
( spl0_856
| ~ spl0_789
| ~ spl0_811 ),
inference(avatar_split_clause,[],[f24132,f23788,f21702,f26068]) ).
fof(f26068,plain,
( spl0_856
<=> ! [X0,X1] : c_lessequals(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f21702,plain,
( spl0_789
<=> ! [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_789])]) ).
fof(f23788,plain,
( spl0_811
<=> ! [X0,X1] : c_lessequals(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f24132,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat)
| ~ spl0_789
| ~ spl0_811 ),
inference(superposition,[],[f23789,f21703]) ).
fof(f21703,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat)
| ~ spl0_789 ),
inference(avatar_component_clause,[],[f21702]) ).
fof(f23789,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_811 ),
inference(avatar_component_clause,[],[f23788]) ).
fof(f25768,plain,
( spl0_855
| ~ spl0_789
| ~ spl0_810 ),
inference(avatar_split_clause,[],[f23973,f23368,f21702,f25766]) ).
fof(f23368,plain,
( spl0_810
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f23973,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,tc_nat),tc_nat)
| ~ spl0_789
| ~ spl0_810 ),
inference(superposition,[],[f23369,f21703]) ).
fof(f23369,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat)
| ~ spl0_810 ),
inference(avatar_component_clause,[],[f23368]) ).
fof(f24157,plain,
( spl0_854
| ~ spl0_118
| ~ spl0_136
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f10317,f10130,f1513,f1430,f24155]) ).
fof(f24155,plain,
( spl0_854
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1430,plain,
( spl0_118
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X5,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f10317,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat)
| ~ spl0_118
| ~ spl0_136
| ~ spl0_553 ),
inference(forward_demodulation,[],[f10283,f1514]) ).
fof(f10283,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X0,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_118
| ~ spl0_553 ),
inference(superposition,[],[f10131,f1431]) ).
fof(f1431,plain,
( ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X5,tc_nat)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1430]) ).
fof(f24153,plain,
( spl0_853
| ~ spl0_118
| ~ spl0_135
| ~ spl0_553 ),
inference(avatar_split_clause,[],[f10312,f10130,f1509,f1430,f24151]) ).
fof(f24151,plain,
( spl0_853
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f10312,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_118
| ~ spl0_135
| ~ spl0_553 ),
inference(forward_demodulation,[],[f10271,f1510]) ).
fof(f10271,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat)
| ~ spl0_118
| ~ spl0_553 ),
inference(superposition,[],[f10131,f1431]) ).
fof(f24149,plain,
( spl0_852
| ~ spl0_495
| ~ spl0_497 ),
inference(avatar_split_clause,[],[f9140,f8137,f8129,f24147]) ).
fof(f24147,plain,
( spl0_852
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f8129,plain,
( spl0_495
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f8137,plain,
( spl0_497
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f9140,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_495
| ~ spl0_497 ),
inference(duplicate_literal_removal,[],[f9099]) ).
fof(f9099,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_495
| ~ spl0_497 ),
inference(resolution,[],[f8138,f8130]) ).
fof(f8130,plain,
( ! [X3,X0,X8,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_495 ),
inference(avatar_component_clause,[],[f8129]) ).
fof(f8138,plain,
( ! [X3,X0,X8,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_497 ),
inference(avatar_component_clause,[],[f8137]) ).
fof(f24145,plain,
( spl0_851
| ~ spl0_476
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f8317,f8041,f8037,f24143]) ).
fof(f24143,plain,
( spl0_851
<=> ! [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_851])]) ).
fof(f8037,plain,
( spl0_476
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f8041,plain,
( spl0_477
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f8317,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X2,X2,X1) )
| ~ spl0_476
| ~ spl0_477 ),
inference(duplicate_literal_removal,[],[f8267]) ).
fof(f8267,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_476
| ~ spl0_477 ),
inference(resolution,[],[f8042,f8038]) ).
fof(f8038,plain,
( ! [X3,X0,X8,X4] :
( ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0)
| c_lessequals(X3,X4,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_476 ),
inference(avatar_component_clause,[],[f8037]) ).
fof(f8042,plain,
( ! [X3,X0,X8,X4] :
( c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0)
| ~ c_lessequals(X3,X4,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_477 ),
inference(avatar_component_clause,[],[f8041]) ).
fof(f24092,plain,
( spl0_850
| ~ spl0_122
| ~ spl0_456 ),
inference(avatar_split_clause,[],[f7372,f6992,f1446,f24090]) ).
fof(f24090,plain,
( spl0_850
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f7372,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_456 ),
inference(superposition,[],[f1447,f6993]) ).
fof(f24088,plain,
( spl0_849
| ~ spl0_122
| ~ spl0_455 ),
inference(avatar_split_clause,[],[f7316,f6988,f1446,f24086]) ).
fof(f24086,plain,
( spl0_849
<=> ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f7316,plain,
( ! [X2,X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_122
| ~ spl0_455 ),
inference(superposition,[],[f1447,f6989]) ).
fof(f24053,plain,
( ~ spl0_34
| spl0_848
| ~ spl0_63
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f4633,f3744,f1208,f24051,f1068]) ).
fof(f24051,plain,
( spl0_848
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f3744,plain,
( spl0_346
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X21,X1,X0)
| c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f4633,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),X0,tc_nat)
| ~ class_Orderings_Olinorder(tc_nat) )
| ~ spl0_63
| ~ spl0_346 ),
inference(resolution,[],[f3745,f1209]) ).
fof(f3745,plain,
( ! [X2,X21,X0,X1] :
( c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0)
| ~ c_lessequals(X21,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f3744]) ).
fof(f24049,plain,
( spl0_847
| ~ spl0_145
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3814,f3801,f1549,f24047]) ).
fof(f24047,plain,
( spl0_847
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = X0
| c_lessequals(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f3814,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = X0
| c_lessequals(X0,X1,tc_nat) )
| ~ spl0_145
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1550]) ).
fof(f24045,plain,
( spl0_846
| ~ spl0_42
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3594,f3090,f1108,f24043]) ).
fof(f24043,plain,
( spl0_846
<=> ! [X0,X1] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1108,plain,
( spl0_42
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f3090,plain,
( spl0_304
<=> ! [X0,X28,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X15,X28,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f3594,plain,
( ! [X0,X1] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_42
| ~ spl0_304 ),
inference(resolution,[],[f3091,f1110]) ).
fof(f1110,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f1108]) ).
fof(f3091,plain,
( ! [X28,X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X15,X28,X0),X0) )
| ~ spl0_304 ),
inference(avatar_component_clause,[],[f3090]) ).
fof(f24041,plain,
( spl0_845
| ~ spl0_22
| ~ spl0_304 ),
inference(avatar_split_clause,[],[f3593,f3090,f1008,f24039]) ).
fof(f24039,plain,
( spl0_845
<=> ! [X0,X1] : c_Polynomial_Odegree(X0,tc_nat) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1008,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f3593,plain,
( ! [X0,X1] : c_Polynomial_Odegree(X0,tc_nat) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_304 ),
inference(resolution,[],[f3091,f1010]) ).
fof(f1010,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f24037,plain,
( spl0_844
| ~ spl0_48
| ~ spl0_303 ),
inference(avatar_split_clause,[],[f3583,f3086,f1138,f24035]) ).
fof(f24035,plain,
( spl0_844
<=> ! [X0] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f3086,plain,
( spl0_303
<=> ! [X0,X15] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X15,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f3583,plain,
( ! [X0] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_303 ),
inference(resolution,[],[f3087,f1140]) ).
fof(f3087,plain,
( ! [X0,X15] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X15,tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f3086]) ).
fof(f24033,plain,
( spl0_843
| ~ spl0_48
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f3506,f3054,f1138,f24030]) ).
fof(f24030,plain,
( spl0_843
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f3054,plain,
( spl0_295
<=> ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f3506,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
| ~ spl0_48
| ~ spl0_295 ),
inference(resolution,[],[f3055,f1140]) ).
fof(f3055,plain,
( ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f24028,plain,
( spl0_842
| ~ spl0_126
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f3245,f2997,f1462,f24026]) ).
fof(f24026,plain,
( spl0_842
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2997,plain,
( spl0_281
<=> ! [X6,X5,X7] :
( X5 = X6
| c_HOL_Oplus__class_Oplus(X7,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f3245,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 )
| ~ spl0_126
| ~ spl0_281 ),
inference(superposition,[],[f2998,f1463]) ).
fof(f2998,plain,
( ! [X6,X7,X5] :
( c_HOL_Oplus__class_Oplus(X7,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat)
| X5 = X6 )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2997]) ).
fof(f24024,plain,
( spl0_841
| ~ spl0_400
| ~ spl0_802 ),
inference(avatar_split_clause,[],[f23578,f21754,f5083,f24022]) ).
fof(f24022,plain,
( spl0_841
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f23578,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat)
| ~ spl0_400
| ~ spl0_802 ),
inference(superposition,[],[f5084,f21755]) ).
fof(f24020,plain,
( spl0_840
| ~ spl0_125
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f3226,f2993,f1458,f24018]) ).
fof(f24018,plain,
( spl0_840
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f3226,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 )
| ~ spl0_125
| ~ spl0_280 ),
inference(superposition,[],[f2994,f1459]) ).
fof(f24016,plain,
( spl0_839
| ~ spl0_42
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3184,f2969,f1108,f24014]) ).
fof(f24014,plain,
( spl0_839
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f2969,plain,
( spl0_274
<=> ! [X0,X28] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f3184,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex)
| ~ spl0_42
| ~ spl0_274 ),
inference(resolution,[],[f2970,f1110]) ).
fof(f2970,plain,
( ! [X28,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) )
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2969]) ).
fof(f24012,plain,
( spl0_838
| ~ spl0_22
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f3183,f2969,f1008,f24010]) ).
fof(f24010,plain,
( spl0_838
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f3183,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat)
| ~ spl0_22
| ~ spl0_274 ),
inference(resolution,[],[f2970,f1010]) ).
fof(f24008,plain,
( spl0_837
| ~ spl0_143
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f3167,f2957,f1541,f24006]) ).
fof(f24006,plain,
( spl0_837
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f3167,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X0,tc_nat),tc_nat) )
| ~ spl0_143
| ~ spl0_271 ),
inference(resolution,[],[f2958,f1542]) ).
fof(f24004,plain,
( spl0_836
| ~ spl0_130
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3117,f2949,f1478,f24002]) ).
fof(f24002,plain,
( spl0_836
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f3117,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_130
| ~ spl0_269 ),
inference(superposition,[],[f1479,f2950]) ).
fof(f24000,plain,
( spl0_835
| ~ spl0_128
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3115,f2949,f1470,f23998]) ).
fof(f23998,plain,
( spl0_835
<=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f3115,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_269 ),
inference(superposition,[],[f1471,f2950]) ).
fof(f23996,plain,
( spl0_834
| ~ spl0_138
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2925,f2524,f1521,f23994]) ).
fof(f23994,plain,
( spl0_834
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2925,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_138
| ~ spl0_264 ),
inference(superposition,[],[f1522,f2525]) ).
fof(f23992,plain,
( spl0_833
| ~ spl0_137
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2893,f2520,f1517,f23990]) ).
fof(f23990,plain,
( spl0_833
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2893,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_137
| ~ spl0_263 ),
inference(superposition,[],[f1518,f2521]) ).
fof(f23988,plain,
( spl0_832
| ~ spl0_124
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2823,f2484,f1454,f23986]) ).
fof(f23986,plain,
( spl0_832
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2823,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,X0,tc_nat),tc_nat)
| ~ spl0_124
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1455]) ).
fof(f23984,plain,
( spl0_831
| ~ spl0_123
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2810,f2484,f1450,f23982]) ).
fof(f23982,plain,
( spl0_831
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2810,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_123
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1451]) ).
fof(f23955,plain,
( spl0_830
| ~ spl0_122
| ~ spl0_254 ),
inference(avatar_split_clause,[],[f2809,f2484,f1446,f23953]) ).
fof(f23953,plain,
( spl0_830
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2809,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_122
| ~ spl0_254 ),
inference(resolution,[],[f2485,f1447]) ).
fof(f23951,plain,
( spl0_829
| ~ spl0_127
| ~ spl0_248 ),
inference(avatar_split_clause,[],[f2779,f2460,f1466,f23949]) ).
fof(f23949,plain,
( spl0_829
<=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2779,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_248 ),
inference(resolution,[],[f2461,f1467]) ).
fof(f23947,plain,
( spl0_828
| ~ spl0_127
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2754,f2456,f1466,f23945]) ).
fof(f23945,plain,
( spl0_828
<=> ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2754,plain,
( ! [X2,X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_247 ),
inference(resolution,[],[f2457,f1467]) ).
fof(f23943,plain,
( spl0_827
| ~ spl0_129
| ~ spl0_239 ),
inference(avatar_split_clause,[],[f2695,f2420,f1474,f23941]) ).
fof(f23941,plain,
( spl0_827
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2695,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_129
| ~ spl0_239 ),
inference(resolution,[],[f2421,f1475]) ).
fof(f23939,plain,
( spl0_826
| ~ spl0_129
| ~ spl0_237 ),
inference(avatar_split_clause,[],[f2657,f2412,f1474,f23937]) ).
fof(f23937,plain,
( spl0_826
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2657,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_129
| ~ spl0_237 ),
inference(resolution,[],[f2413,f1475]) ).
fof(f23935,plain,
( spl0_825
| ~ spl0_144
| ~ spl0_226 ),
inference(avatar_split_clause,[],[f2367,f2139,f1545,f23933]) ).
fof(f23933,plain,
( spl0_825
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2367,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_144
| ~ spl0_226 ),
inference(resolution,[],[f2140,f1546]) ).
fof(f23931,plain,
( spl0_824
| ~ spl0_145
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2335,f2127,f1549,f23929]) ).
fof(f23929,plain,
( spl0_824
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2127,plain,
( spl0_223
<=> ! [X6,X5] :
( c_lessequals(X6,X5,tc_nat)
| ~ c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2335,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(c_Suc(X1),c_Suc(X0),tc_nat) )
| ~ spl0_145
| ~ spl0_223 ),
inference(resolution,[],[f2128,f1550]) ).
fof(f2128,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat)
| c_lessequals(X6,X5,tc_nat) )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f2127]) ).
fof(f23927,plain,
( spl0_823
| ~ spl0_162
| ~ spl0_218 ),
inference(avatar_split_clause,[],[f2278,f2107,f1646,f23925]) ).
fof(f23925,plain,
( spl0_823
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2278,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat)
| ~ spl0_162
| ~ spl0_218 ),
inference(superposition,[],[f2108,f1647]) ).
fof(f23923,plain,
( spl0_822
| ~ spl0_167
| ~ spl0_205 ),
inference(avatar_split_clause,[],[f2222,f2047,f1666,f23921]) ).
fof(f23921,plain,
( spl0_822
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2222,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| ~ spl0_167
| ~ spl0_205 ),
inference(superposition,[],[f2048,f1667]) ).
fof(f23919,plain,
( spl0_821
| ~ spl0_162
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2186,f2031,f1646,f23917]) ).
fof(f23917,plain,
( spl0_821
<=> ! [X0] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2031,plain,
( spl0_201
<=> ! [X22] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f2186,plain,
( ! [X0] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)),tc_nat)
| ~ spl0_162
| ~ spl0_201 ),
inference(superposition,[],[f2032,f1647]) ).
fof(f2032,plain,
( ! [X22] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat)),tc_nat)
| ~ spl0_201 ),
inference(avatar_component_clause,[],[f2031]) ).
fof(f23915,plain,
( spl0_820
| ~ spl0_400
| ~ spl0_783 ),
inference(avatar_split_clause,[],[f22261,f21678,f5083,f23913]) ).
fof(f23913,plain,
( spl0_820
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f22261,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X0,tc_nat),X1,tc_nat)
| ~ spl0_400
| ~ spl0_783 ),
inference(superposition,[],[f5084,f21679]) ).
fof(f23911,plain,
( spl0_819
| ~ spl0_167
| ~ spl0_194 ),
inference(avatar_split_clause,[],[f2160,f2003,f1666,f23909]) ).
fof(f23909,plain,
( spl0_819
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2160,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_167
| ~ spl0_194 ),
inference(superposition,[],[f2004,f1667]) ).
fof(f23907,plain,
( spl0_818
| ~ spl0_138
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2149,f1995,f1521,f23905]) ).
fof(f23905,plain,
( spl0_818
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2149,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) = X0
| ~ spl0_138
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1522]) ).
fof(f23903,plain,
( spl0_817
| ~ spl0_137
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2148,f1995,f1517,f23901]) ).
fof(f23901,plain,
( spl0_817
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2148,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat) = X0
| ~ spl0_137
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1518]) ).
fof(f23899,plain,
( spl0_816
| ~ spl0_183
| ~ spl0_189 ),
inference(avatar_split_clause,[],[f1989,f1754,f1730,f23897]) ).
fof(f23897,plain,
( spl0_816
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f1989,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| ~ c_lessequals(c_Suc(X1),X0,tc_nat) )
| ~ spl0_183
| ~ spl0_189 ),
inference(resolution,[],[f1755,f1731]) ).
fof(f23895,plain,
( spl0_815
| ~ spl0_186
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1971,f1746,f1742,f23893]) ).
fof(f23893,plain,
( spl0_815
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f1971,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
| ~ spl0_186
| ~ spl0_187 ),
inference(resolution,[],[f1747,f1743]) ).
fof(f23891,plain,
( spl0_814
| ~ spl0_184
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1955,f1742,f1734,f23889]) ).
fof(f23889,plain,
( spl0_814
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f1955,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
| ~ spl0_184
| ~ spl0_186 ),
inference(resolution,[],[f1743,f1735]) ).
fof(f23887,plain,
( spl0_813
| ~ spl0_155
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1929,f1730,f1618,f23885]) ).
fof(f23885,plain,
( spl0_813
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f1929,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
| ~ spl0_155
| ~ spl0_183 ),
inference(resolution,[],[f1731,f1619]) ).
fof(f23883,plain,
( spl0_812
| ~ spl0_182
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1928,f1730,f1726,f23881]) ).
fof(f23881,plain,
( spl0_812
<=> ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f1928,plain,
( ! [X0,X1] :
( ~ c_lessequals(c_Suc(X0),X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) )
| ~ spl0_182
| ~ spl0_183 ),
inference(resolution,[],[f1731,f1727]) ).
fof(f23790,plain,
( spl0_811
| ~ spl0_389
| ~ spl0_781 ),
inference(avatar_split_clause,[],[f22224,f21669,f5039,f23788]) ).
fof(f22224,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Oord__class_Omin(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_389
| ~ spl0_781 ),
inference(superposition,[],[f5040,f21670]) ).
fof(f23370,plain,
( spl0_810
| ~ spl0_400
| ~ spl0_781 ),
inference(avatar_split_clause,[],[f22223,f21669,f5083,f23368]) ).
fof(f22223,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat)
| ~ spl0_400
| ~ spl0_781 ),
inference(superposition,[],[f5084,f21670]) ).
fof(f21854,plain,
( spl0_809
| ~ spl0_59
| ~ spl0_118
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f7262,f6976,f1430,f1192,f21852]) ).
fof(f21852,plain,
( spl0_809
<=> ! [X0] : c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f6976,plain,
( spl0_452
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f7262,plain,
( ! [X0] : c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat)
| ~ spl0_59
| ~ spl0_118
| ~ spl0_452 ),
inference(forward_demodulation,[],[f7212,f1431]) ).
fof(f7212,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(c_Suc(X0),X0,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X0,X0,tc_nat))
| ~ spl0_59
| ~ spl0_452 ),
inference(resolution,[],[f6977,f1193]) ).
fof(f6977,plain,
( ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f6976]) ).
fof(f21850,plain,
( spl0_808
| ~ spl0_112
| ~ spl0_354 ),
inference(avatar_split_clause,[],[f4814,f3776,f1405,f21848]) ).
fof(f21848,plain,
( spl0_808
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f1405,plain,
( spl0_112
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f4814,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_354 ),
inference(duplicate_literal_removal,[],[f4787]) ).
fof(f4787,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X0,X1,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_354 ),
inference(resolution,[],[f3777,f1406]) ).
fof(f1406,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X1,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1405]) ).
fof(f21846,plain,
( spl0_807
| ~ spl0_112
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f4782,f3772,f1405,f21844]) ).
fof(f21844,plain,
( spl0_807
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f4782,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_353 ),
inference(duplicate_literal_removal,[],[f4755]) ).
fof(f4755,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Orderings_Oord__class_Omin(X1,X0,X2),X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_353 ),
inference(resolution,[],[f3773,f1406]) ).
fof(f21842,plain,
( spl0_806
| ~ spl0_112
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f4387,f3692,f1405,f21840]) ).
fof(f21840,plain,
( spl0_806
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f4387,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_333 ),
inference(duplicate_literal_removal,[],[f4363]) ).
fof(f4363,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X0,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_333 ),
inference(resolution,[],[f3693,f1406]) ).
fof(f21838,plain,
( spl0_805
| ~ spl0_112
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f4352,f3688,f1405,f21836]) ).
fof(f21836,plain,
( spl0_805
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f4352,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_332 ),
inference(duplicate_literal_removal,[],[f4328]) ).
fof(f4328,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,X2),X1,X2)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_112
| ~ spl0_332 ),
inference(resolution,[],[f3689,f1406]) ).
fof(f21834,plain,
( spl0_804
| ~ spl0_138
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4189,f3643,f1521,f21832]) ).
fof(f21832,plain,
( spl0_804
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f4189,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
| ~ spl0_138
| ~ spl0_321 ),
inference(superposition,[],[f1522,f3644]) ).
fof(f21760,plain,
( spl0_803
| ~ spl0_138
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4146,f3639,f1521,f21758]) ).
fof(f4146,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_138
| ~ spl0_320 ),
inference(superposition,[],[f1522,f3640]) ).
fof(f21756,plain,
( spl0_802
| ~ spl0_123
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3809,f3801,f1450,f21754]) ).
fof(f3809,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_123
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1451]) ).
fof(f21752,plain,
( spl0_801
| ~ spl0_122
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f3808,f3801,f1446,f21750]) ).
fof(f21750,plain,
( spl0_801
<=> ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f3808,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_122
| ~ spl0_360 ),
inference(resolution,[],[f3802,f1447]) ).
fof(f21748,plain,
( spl0_800
| ~ spl0_130
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2923,f2524,f1478,f21746]) ).
fof(f21746,plain,
( spl0_800
<=> ! [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_800])]) ).
fof(f2923,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_130
| ~ spl0_264 ),
inference(superposition,[],[f1479,f2525]) ).
fof(f21744,plain,
( spl0_799
| ~ spl0_128
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2921,f2524,f1470,f21742]) ).
fof(f21742,plain,
( spl0_799
<=> ! [X0,X1] : c_lessequals(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f2921,plain,
( ! [X0,X1] : c_lessequals(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_128
| ~ spl0_264 ),
inference(superposition,[],[f1471,f2525]) ).
fof(f21740,plain,
( spl0_798
| ~ spl0_129
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2891,f2520,f1474,f21738]) ).
fof(f21738,plain,
( spl0_798
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2891,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat)
| ~ spl0_129
| ~ spl0_263 ),
inference(superposition,[],[f1475,f2521]) ).
fof(f21736,plain,
( spl0_797
| ~ spl0_127
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2889,f2520,f1466,f21734]) ).
fof(f21734,plain,
( spl0_797
<=> ! [X0,X1] : c_lessequals(c_Suc(X1),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2889,plain,
( ! [X0,X1] : c_lessequals(c_Suc(X1),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_127
| ~ spl0_263 ),
inference(superposition,[],[f1467,f2521]) ).
fof(f21732,plain,
( spl0_796
| ~ spl0_139
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2884,f2516,f1525,f21730]) ).
fof(f21730,plain,
( spl0_796
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2884,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_139
| ~ spl0_262 ),
inference(superposition,[],[f1526,f2517]) ).
fof(f21728,plain,
( spl0_795
| ~ spl0_52
| ~ spl0_261 ),
inference(avatar_split_clause,[],[f2877,f2512,f1158,f21726]) ).
fof(f21726,plain,
( spl0_795
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2877,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
| ~ spl0_52
| ~ spl0_261 ),
inference(resolution,[],[f2513,f1160]) ).
fof(f21724,plain,
( spl0_794
| ~ spl0_41
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2847,f2492,f1103,f21722]) ).
fof(f21722,plain,
( spl0_794
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1103,plain,
( spl0_41
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2847,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_41
| ~ spl0_256 ),
inference(resolution,[],[f2493,f1105]) ).
fof(f1105,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f21720,plain,
( spl0_793
| ~ spl0_674
| ~ spl0_676 ),
inference(avatar_split_clause,[],[f21315,f12904,f12401,f21718]) ).
fof(f21718,plain,
( spl0_793
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f12401,plain,
( spl0_674
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f12904,plain,
( spl0_676
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f21315,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_674
| ~ spl0_676 ),
inference(superposition,[],[f12905,f12402]) ).
fof(f12402,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f12401]) ).
fof(f12905,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_676 ),
inference(avatar_component_clause,[],[f12904]) ).
fof(f21716,plain,
( spl0_792
| ~ spl0_119
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2838,f2488,f1434,f21714]) ).
fof(f21714,plain,
( spl0_792
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2838,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != X0
| c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_119
| ~ spl0_255 ),
inference(superposition,[],[f2489,f1435]) ).
fof(f21712,plain,
( spl0_791
| ~ spl0_52
| ~ spl0_252 ),
inference(avatar_split_clause,[],[f2799,f2476,f1158,f21710]) ).
fof(f21710,plain,
( spl0_791
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2476,plain,
( spl0_252
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2799,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_52
| ~ spl0_252 ),
inference(resolution,[],[f2477,f1160]) ).
fof(f2477,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) )
| ~ spl0_252 ),
inference(avatar_component_clause,[],[f2476]) ).
fof(f21708,plain,
( spl0_790
| ~ spl0_48
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2797,f2472,f1138,f21706]) ).
fof(f21706,plain,
( spl0_790
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2472,plain,
( spl0_251
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2797,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_251 ),
inference(resolution,[],[f2473,f1140]) ).
fof(f2473,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2472]) ).
fof(f21704,plain,
( spl0_789
| ~ spl0_34
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2795,f2468,f1068,f21702]) ).
fof(f2795,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,X1,tc_nat) = c_Orderings_Oord__class_Omin(X1,X0,tc_nat)
| ~ spl0_34
| ~ spl0_250 ),
inference(resolution,[],[f2469,f1070]) ).
fof(f21700,plain,
( spl0_788
| ~ spl0_34
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f2793,f2464,f1068,f21698]) ).
fof(f21698,plain,
( spl0_788
<=> ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2793,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omin(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_34
| ~ spl0_249 ),
inference(resolution,[],[f2465,f1070]) ).
fof(f21696,plain,
( spl0_787
| ~ spl0_126
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2731,f2444,f1462,f21694]) ).
fof(f21694,plain,
( spl0_787
<=> ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f2731,plain,
( ! [X0,X1] :
( c_lessequals(X1,X0,tc_nat)
| ~ c_lessequals(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) )
| ~ spl0_126
| ~ spl0_245 ),
inference(superposition,[],[f2445,f1463]) ).
fof(f21692,plain,
( spl0_786
| ~ spl0_41
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2719,f2440,f1103,f21690]) ).
fof(f21690,plain,
( spl0_786
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f2719,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_41
| ~ spl0_244 ),
inference(resolution,[],[f2441,f1105]) ).
fof(f21688,plain,
( spl0_785
| ~ spl0_52
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2716,f2436,f1158,f21686]) ).
fof(f21686,plain,
( spl0_785
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f2716,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
| ~ spl0_52
| ~ spl0_243 ),
inference(resolution,[],[f2437,f1160]) ).
fof(f21684,plain,
( spl0_784
| ~ spl0_52
| ~ spl0_242 ),
inference(avatar_split_clause,[],[f2710,f2432,f1158,f21682]) ).
fof(f21682,plain,
( spl0_784
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f2432,plain,
( spl0_242
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2710,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_52
| ~ spl0_242 ),
inference(resolution,[],[f2433,f1160]) ).
fof(f2433,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X3,X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2432]) ).
fof(f21680,plain,
( spl0_783
| ~ spl0_34
| ~ spl0_241 ),
inference(avatar_split_clause,[],[f2708,f2428,f1068,f21678]) ).
fof(f2708,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,X1,tc_nat) = c_Orderings_Oord__class_Omax(X1,X0,tc_nat)
| ~ spl0_34
| ~ spl0_241 ),
inference(resolution,[],[f2429,f1070]) ).
fof(f21676,plain,
( ~ spl0_782
| ~ spl0_201
| ~ spl0_674 ),
inference(avatar_split_clause,[],[f20941,f12401,f2031,f21673]) ).
fof(f21673,plain,
( spl0_782
<=> c_Parity_Oeven__odd__class_Oeven(c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f20941,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))),tc_nat)
| ~ spl0_201
| ~ spl0_674 ),
inference(superposition,[],[f2032,f12402]) ).
fof(f21671,plain,
( spl0_781
| ~ spl0_34
| ~ spl0_240 ),
inference(avatar_split_clause,[],[f2706,f2424,f1068,f21669]) ).
fof(f2706,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Omax(X0,c_Orderings_Oord__class_Omin(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_34
| ~ spl0_240 ),
inference(resolution,[],[f2425,f1070]) ).
fof(f21667,plain,
( spl0_780
| ~ spl0_126
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f2680,f2416,f1462,f21665]) ).
fof(f21665,plain,
( spl0_780
<=> ! [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_780])]) ).
fof(f2680,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_126
| ~ spl0_238 ),
inference(superposition,[],[f2417,f1463]) ).
fof(f21663,plain,
( spl0_779
| ~ spl0_144
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1965,f1746,f1545,f21661]) ).
fof(f21661,plain,
( spl0_779
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f1965,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X0,c_Suc(X1),tc_nat) )
| ~ spl0_144
| ~ spl0_187 ),
inference(resolution,[],[f1747,f1546]) ).
fof(f21659,plain,
( spl0_778
| ~ spl0_138
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1961,f1742,f1521,f21657]) ).
fof(f21657,plain,
( spl0_778
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f1961,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_138
| ~ spl0_186 ),
inference(forward_demodulation,[],[f1958,f754]) ).
fof(f754,axiom,
! [X6,X5] : c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X5),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f1958,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)),tc_nat)
| ~ spl0_138
| ~ spl0_186 ),
inference(resolution,[],[f1743,f1522]) ).
fof(f21655,plain,
( spl0_777
| ~ spl0_137
| ~ spl0_186 ),
inference(avatar_split_clause,[],[f1960,f1742,f1517,f21653]) ).
fof(f21653,plain,
( spl0_777
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f1960,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat)
| ~ spl0_137
| ~ spl0_186 ),
inference(forward_demodulation,[],[f1957,f753]) ).
fof(f753,axiom,
! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,c_Suc(X6),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f1957,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_186 ),
inference(resolution,[],[f1743,f1518]) ).
fof(f21651,plain,
( spl0_776
| ~ spl0_145
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f1917,f1726,f1549,f21649]) ).
fof(f21649,plain,
( spl0_776
<=> ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f1917,plain,
( ! [X0,X1] :
( c_lessequals(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) )
| ~ spl0_145
| ~ spl0_182 ),
inference(resolution,[],[f1727,f1550]) ).
fof(f21647,plain,
( spl0_775
| ~ spl0_149
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f1824,f1646,f1594,f21645]) ).
fof(f21645,plain,
( spl0_775
<=> ! [X0] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f1594,plain,
( spl0_149
<=> ! [X22] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1824,plain,
( ! [X0] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X0,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)
| ~ spl0_149
| ~ spl0_162 ),
inference(superposition,[],[f1595,f1647]) ).
fof(f1595,plain,
( ! [X22] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat),tc_nat)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1594]) ).
fof(f21643,plain,
( spl0_774
| ~ spl0_145
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1778,f1618,f1549,f21641]) ).
fof(f21641,plain,
( spl0_774
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f1778,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,c_Suc(X0),tc_nat) )
| ~ spl0_145
| ~ spl0_155 ),
inference(resolution,[],[f1619,f1550]) ).
fof(f21639,plain,
( spl0_773
| ~ spl0_106
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1559,f1505,f1381,f21637]) ).
fof(f21637,plain,
( spl0_773
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1505,plain,
( spl0_134
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1559,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omin(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_106
| ~ spl0_134 ),
inference(resolution,[],[f1506,f1382]) ).
fof(f1506,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X1,X0) = X1 )
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f1505]) ).
fof(f21635,plain,
( spl0_772
| ~ spl0_106
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1557,f1501,f1381,f21633]) ).
fof(f21633,plain,
( spl0_772
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1501,plain,
( spl0_133
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1557,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Omax(X0,X0,tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_106
| ~ spl0_133 ),
inference(resolution,[],[f1502,f1382]) ).
fof(f1502,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X1,X0) = X1 )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1501]) ).
fof(f21631,plain,
( spl0_771
| ~ spl0_458
| ~ spl0_660 ),
inference(avatar_split_clause,[],[f20762,f12253,f7013,f21629]) ).
fof(f21629,plain,
( spl0_771
<=> ! [X0] : c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f7013,plain,
( spl0_458
<=> ! [X6,X5] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f12253,plain,
( spl0_660
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f20762,plain,
( ! [X0] : c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0),tc_nat)
| ~ spl0_458
| ~ spl0_660 ),
inference(resolution,[],[f12254,f7014]) ).
fof(f7014,plain,
( ! [X6,X5] :
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat) )
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f7013]) ).
fof(f12254,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_660 ),
inference(avatar_component_clause,[],[f12253]) ).
fof(f20733,plain,
spl0_770,
inference(avatar_split_clause,[],[f420,f20731]) ).
fof(f20731,plain,
( spl0_770
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ominus__class_Ominus(X2,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),X4,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ominus__class_Ominus(X2,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f420,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),c_HOL_Ominus__class_Ominus(X2,X4,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X3,X0),X4,X0),X0),c_HOL_Otimes__class_Otimes(X3,c_HOL_Ominus__class_Ominus(X2,X4,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f20532,plain,
spl0_769,
inference(avatar_split_clause,[],[f645,f20530]) ).
fof(f20530,plain,
( spl0_769
<=> ! [X23,X0,X8,X3,X4,X25] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X25,X23,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f645,axiom,
! [X3,X0,X8,X4,X25,X23] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X25,X23,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
fof(f20528,plain,
spl0_768,
inference(avatar_split_clause,[],[f514,f20526]) ).
fof(f20526,plain,
( spl0_768
<=> ! [X23,X0,X8,X3,X4,X25] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X25,X23,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f514,axiom,
! [X3,X0,X8,X4,X25,X23] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X25,X23,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
fof(f20524,plain,
spl0_767,
inference(avatar_split_clause,[],[f486,f20522]) ).
fof(f20522,plain,
( spl0_767
<=> ! [X23,X0,X8,X3,X4,X25] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X25,X23,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f486,axiom,
! [X3,X0,X8,X4,X25,X23] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X8,X0) != c_Divides_Odiv__class_Omod(X25,X8,X0)
| c_Divides_Odiv__class_Omod(X4,X8,X0) != c_Divides_Odiv__class_Omod(X23,X8,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X25,X23,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
fof(f20044,plain,
spl0_766,
inference(avatar_split_clause,[],[f333,f20042]) ).
fof(f20042,plain,
( spl0_766
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f333,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).
fof(f20040,plain,
spl0_765,
inference(avatar_split_clause,[],[f332,f20038]) ).
fof(f20038,plain,
( spl0_765
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f332,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).
fof(f19321,plain,
spl0_764,
inference(avatar_split_clause,[],[f507,f19319]) ).
fof(f19319,plain,
( spl0_764
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f507,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).
fof(f19317,plain,
spl0_763,
inference(avatar_split_clause,[],[f506,f19315]) ).
fof(f19315,plain,
( spl0_763
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f506,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_lessequals(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).
fof(f19313,plain,
spl0_762,
inference(avatar_split_clause,[],[f505,f19311]) ).
fof(f19311,plain,
( spl0_762
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X10,X9,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f505,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X10,X9,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).
fof(f19309,plain,
spl0_761,
inference(avatar_split_clause,[],[f504,f19307]) ).
fof(f19307,plain,
( spl0_761
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f504,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).
fof(f19303,plain,
spl0_760,
inference(avatar_split_clause,[],[f227,f19301]) ).
fof(f19301,plain,
( spl0_760
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f227,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X10,X9,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).
fof(f19299,plain,
spl0_759,
inference(avatar_split_clause,[],[f226,f19297]) ).
fof(f19297,plain,
( spl0_759
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X10,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f226,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X10,X9,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X26,tc_nat),X5,tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).
fof(f19295,plain,
spl0_758,
inference(avatar_split_clause,[],[f225,f19293]) ).
fof(f19293,plain,
( spl0_758
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f225,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).
fof(f19291,plain,
spl0_757,
inference(avatar_split_clause,[],[f224,f19289]) ).
fof(f19289,plain,
( spl0_757
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f224,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).
fof(f18171,plain,
spl0_756,
inference(avatar_split_clause,[],[f513,f18169]) ).
fof(f18169,plain,
( spl0_756
<=> ! [X2,X0,X21,X30,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X30
| X2 = X21
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X2,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X21,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f513,axiom,
! [X2,X21,X0,X1,X30] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X30
| X2 = X21
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X2,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X21,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
fof(f18167,plain,
spl0_755,
inference(avatar_split_clause,[],[f483,f18165]) ).
fof(f18165,plain,
( spl0_755
<=> ! [X18,X4,X0,X8,X27,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f483,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f18163,plain,
spl0_754,
inference(avatar_split_clause,[],[f482,f18161]) ).
fof(f18161,plain,
( spl0_754
<=> ! [X18,X4,X0,X8,X27,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f482,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f18159,plain,
spl0_753,
inference(avatar_split_clause,[],[f481,f18157]) ).
fof(f18157,plain,
( spl0_753
<=> ! [X18,X4,X3,X0,X27,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f481,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f18155,plain,
spl0_752,
inference(avatar_split_clause,[],[f480,f18153]) ).
fof(f18153,plain,
( spl0_752
<=> ! [X18,X4,X3,X0,X27,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f480,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f18151,plain,
spl0_751,
inference(avatar_split_clause,[],[f200,f18149]) ).
fof(f18149,plain,
( spl0_751
<=> ! [X18,X4,X3,X0,X27,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f200,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).
fof(f17976,plain,
spl0_750,
inference(avatar_split_clause,[],[f199,f17974]) ).
fof(f17974,plain,
( spl0_750
<=> ! [X18,X4,X3,X0,X27,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f199,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0),X18,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).
fof(f17972,plain,
spl0_749,
inference(avatar_split_clause,[],[f198,f17970]) ).
fof(f17970,plain,
( spl0_749
<=> ! [X18,X4,X0,X8,X27,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f198,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).
fof(f17968,plain,
spl0_748,
inference(avatar_split_clause,[],[f197,f17966]) ).
fof(f17966,plain,
( spl0_748
<=> ! [X18,X4,X0,X8,X27,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f197,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X8,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).
fof(f17964,plain,
spl0_747,
inference(avatar_split_clause,[],[f164,f17962]) ).
fof(f17962,plain,
( spl0_747
<=> ! [X5,X9,X10,X6,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat) = X5
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f164,axiom,
! [X10,X6,X9,X26,X5] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat) = X5
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),X5,tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).
fof(f17654,plain,
spl0_746,
inference(avatar_split_clause,[],[f666,f17652]) ).
fof(f17652,plain,
( spl0_746
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f666,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).
fof(f17650,plain,
spl0_745,
inference(avatar_split_clause,[],[f665,f17648]) ).
fof(f17648,plain,
( spl0_745
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f665,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).
fof(f17646,plain,
spl0_744,
inference(avatar_split_clause,[],[f244,f17644]) ).
fof(f17644,plain,
( spl0_744
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f244,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).
fof(f17642,plain,
spl0_743,
inference(avatar_split_clause,[],[f243,f17640]) ).
fof(f17640,plain,
( spl0_743
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f243,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).
fof(f17638,plain,
spl0_742,
inference(avatar_split_clause,[],[f231,f17636]) ).
fof(f17636,plain,
( spl0_742
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f231,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).
fof(f17634,plain,
spl0_741,
inference(avatar_split_clause,[],[f71,f17632]) ).
fof(f17632,plain,
( spl0_741
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f71,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).
fof(f17569,plain,
spl0_740,
inference(avatar_split_clause,[],[f451,f17567]) ).
fof(f17567,plain,
( spl0_740
<=> ! [X18,X4,X3,X0,X27,X8] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0) = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f451,axiom,
! [X3,X0,X18,X8,X27,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X27,X0),X8,X0) = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),X8,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
fof(f17514,plain,
spl0_739,
inference(avatar_split_clause,[],[f511,f17512]) ).
fof(f17512,plain,
( spl0_739
<=> ! [X21,X30,X2,X1] :
( X1 = X30
| X2 = X21
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X21,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X21,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f511,axiom,
! [X2,X21,X1,X30] :
( X1 = X30
| X2 = X21
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X21,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X30,X21,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).
fof(f17469,plain,
spl0_738,
inference(avatar_split_clause,[],[f432,f17467]) ).
fof(f17467,plain,
( spl0_738
<=> ! [X3,X4,X0,X27,X8] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X27,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f432,axiom,
! [X3,X0,X8,X27,X4] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X27,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f17465,plain,
spl0_737,
inference(avatar_split_clause,[],[f228,f17463]) ).
fof(f17463,plain,
( spl0_737
<=> ! [X18,X4,X0,X27,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f228,axiom,
! [X3,X0,X18,X27,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,X27,X0),X18,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X27,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X4,X3,X0),X27,X0),X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).
fof(f17461,plain,
spl0_736,
inference(avatar_split_clause,[],[f66,f17459]) ).
fof(f17459,plain,
( spl0_736
<=> ! [X18,X0,X17,X8,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X8 = X18
| c_HOL_Ozero__class_Ozero(X0) = X17
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f66,axiom,
! [X0,X18,X8,X1,X17] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X8 = X18
| c_HOL_Ozero__class_Ozero(X0) = X17
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X8,X0),X0) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f17247,plain,
( spl0_735
| ~ spl0_167
| ~ spl0_269
| ~ spl0_734 ),
inference(avatar_split_clause,[],[f17197,f17194,f2949,f1666,f17245]) ).
fof(f17245,plain,
( spl0_735
<=> ! [X9,X10,X6,X26] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Orderings_Oord__class_Omax(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f17194,plain,
( spl0_734
<=> ! [X9,X10,X6,X26] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X9,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat),X26,tc_nat),X6,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f17197,plain,
( ! [X10,X6,X26,X9] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Orderings_Oord__class_Omax(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) )
| ~ spl0_167
| ~ spl0_269
| ~ spl0_734 ),
inference(forward_demodulation,[],[f17195,f3110]) ).
fof(f17195,plain,
( ! [X10,X6,X26,X9] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X9,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat),X26,tc_nat),X6,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) )
| ~ spl0_734 ),
inference(avatar_component_clause,[],[f17194]) ).
fof(f17196,plain,
spl0_734,
inference(avatar_split_clause,[],[f900,f17194]) ).
fof(f900,plain,
! [X10,X6,X26,X9] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X9,c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),tc_nat),X26,tc_nat),X6,tc_nat)
| ~ c_lessequals(X9,X10,tc_nat) ),
inference(forward_demodulation,[],[f485,f433]) ).
fof(f433,axiom,
! [X10,X9,X26,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X26,tc_nat),X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
fof(f485,axiom,
! [X10,X6,X9,X26] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X6,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X10,X9,tc_nat),X26,tc_nat),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).
fof(f17192,plain,
spl0_733,
inference(avatar_split_clause,[],[f347,f17190]) ).
fof(f17190,plain,
( spl0_733
<=> ! [X18,X0,X8,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X1,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f347,axiom,
! [X0,X1,X8,X18] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X1,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X18,X0),c_HOL_Otimes__class_Otimes(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).
fof(f17188,plain,
spl0_732,
inference(avatar_split_clause,[],[f58,f17186]) ).
fof(f58,axiom,
! [X8,X16,X4,X17] :
( ~ c_HOL_Oord__class_Oless(X17,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X8,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X4,c_Divides_Odiv__class_Omod(X16,X8,tc_nat),tc_nat),X17,tc_nat),c_HOL_Otimes__class_Otimes(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).
fof(f16932,plain,
spl0_731,
inference(avatar_split_clause,[],[f664,f16930]) ).
fof(f16930,plain,
( spl0_731
<=> ! [X31,X22,X6,X2,X1] :
( c_Divides_Odiv__class_Omod(X1,X6,tc_nat) = c_Divides_Odiv__class_Omod(X2,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X6,X22,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X6,X31,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f664,axiom,
! [X2,X31,X1,X6,X22] :
( c_Divides_Odiv__class_Omod(X1,X6,tc_nat) = c_Divides_Odiv__class_Omod(X2,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X6,X22,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X6,X31,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).
fof(f16928,plain,
spl0_730,
inference(avatar_split_clause,[],[f466,f16926]) ).
fof(f16926,plain,
( spl0_730
<=> ! [X4,X0,X3,X25] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) != c_Divides_Odiv__class_Omod(X25,X4,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X25,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f466,axiom,
! [X3,X0,X4,X25] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) != c_Divides_Odiv__class_Omod(X25,X4,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X25,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
fof(f16924,plain,
spl0_729,
inference(avatar_split_clause,[],[f433,f16922]) ).
fof(f16922,plain,
( spl0_729
<=> ! [X10,X9,X26,X7] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X9,X26,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X10,X26,tc_nat),X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X26,tc_nat),X7,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f16708,plain,
( spl0_728
| ~ spl0_167
| ~ spl0_269
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f16704,f16701,f2949,f1666,f16706]) ).
fof(f16706,plain,
( spl0_728
<=> ! [X6,X5,X7] :
( c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Oord__class_Omax(X6,X7,tc_nat),tc_nat)
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f16701,plain,
( spl0_727
<=> ! [X6,X5,X7] :
( c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(X7,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f16704,plain,
( ! [X6,X7,X5] :
( c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_Orderings_Oord__class_Omax(X6,X7,tc_nat),tc_nat)
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) )
| ~ spl0_167
| ~ spl0_269
| ~ spl0_727 ),
inference(forward_demodulation,[],[f16702,f3110]) ).
fof(f16702,plain,
( ! [X6,X7,X5] :
( c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(X7,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) )
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f16701]) ).
fof(f16703,plain,
spl0_727,
inference(avatar_split_clause,[],[f902,f16701]) ).
fof(f902,plain,
! [X6,X7,X5] :
( c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(X7,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat) ),
inference(forward_demodulation,[],[f561,f400]) ).
fof(f400,axiom,
! [X10,X9,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f561,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).
fof(f16616,plain,
spl0_726,
inference(avatar_split_clause,[],[f553,f16614]) ).
fof(f16614,plain,
( spl0_726
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ominus__class_Ominus(X8,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f553,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ominus__class_Ominus(X8,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f16612,plain,
spl0_725,
inference(avatar_split_clause,[],[f467,f16610]) ).
fof(f16610,plain,
( spl0_725
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f467,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
fof(f16608,plain,
spl0_724,
inference(avatar_split_clause,[],[f361,f16606]) ).
fof(f16606,plain,
( spl0_724
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f361,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f16604,plain,
spl0_723,
inference(avatar_split_clause,[],[f278,f16602]) ).
fof(f16602,plain,
( spl0_723
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f278,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X8,X0),c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
fof(f16600,plain,
spl0_722,
inference(avatar_split_clause,[],[f273,f16598]) ).
fof(f16598,plain,
( spl0_722
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Oplus__class_Oplus(X8,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f273,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Oplus__class_Oplus(X8,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f16596,plain,
spl0_721,
inference(avatar_split_clause,[],[f169,f16594]) ).
fof(f16594,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f169,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).
fof(f16592,plain,
spl0_720,
inference(avatar_split_clause,[],[f168,f16590]) ).
fof(f16590,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f168,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).
fof(f16588,plain,
spl0_719,
inference(avatar_split_clause,[],[f139,f16586]) ).
fof(f16586,plain,
( spl0_719
<=> ! [X11,X13,X0,X14,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X12,X0),c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),c_HOL_Otimes__class_Otimes(X12,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f139,axiom,
! [X0,X11,X14,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X12,X0),c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),c_HOL_Otimes__class_Otimes(X12,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f16298,plain,
spl0_718,
inference(avatar_split_clause,[],[f676,f16296]) ).
fof(f16296,plain,
( spl0_718
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f676,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).
fof(f16294,plain,
spl0_717,
inference(avatar_split_clause,[],[f395,f16292]) ).
fof(f16292,plain,
( spl0_717
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f395,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X5,X7,tc_nat),c_HOL_Ominus__class_Ominus(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).
fof(f16290,plain,
spl0_716,
inference(avatar_split_clause,[],[f261,f16288]) ).
fof(f16288,plain,
( spl0_716
<=> ! [X4,X0,X8,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f261,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f16286,plain,
spl0_715,
inference(avatar_split_clause,[],[f259,f16284]) ).
fof(f16284,plain,
( spl0_715
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f259,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f16282,plain,
spl0_714,
inference(avatar_split_clause,[],[f65,f16280]) ).
fof(f16280,plain,
( spl0_714
<=> ! [X18,X17,X8,X1] :
( X8 = X18
| c_HOL_Ozero__class_Ozero(tc_nat) = X17
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f65,axiom,
! [X18,X8,X1,X17] :
( X8 = X18
| c_HOL_Ozero__class_Ozero(tc_nat) = X17
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X17,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(f14499,plain,
spl0_713,
inference(avatar_split_clause,[],[f722,f14497]) ).
fof(f14497,plain,
( spl0_713
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),c_Orderings_Oord__class_Omax(X1,X21,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f722,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),c_Orderings_Oord__class_Omax(X1,X21,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
fof(f14495,plain,
spl0_712,
inference(avatar_split_clause,[],[f720,f14493]) ).
fof(f14493,plain,
( spl0_712
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f720,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f14491,plain,
spl0_711,
inference(avatar_split_clause,[],[f719,f14489]) ).
fof(f14489,plain,
( spl0_711
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f719,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f14487,plain,
spl0_710,
inference(avatar_split_clause,[],[f718,f14485]) ).
fof(f14485,plain,
( spl0_710
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f718,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f14483,plain,
spl0_709,
inference(avatar_split_clause,[],[f717,f14481]) ).
fof(f14481,plain,
( spl0_709
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f717,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f14479,plain,
spl0_708,
inference(avatar_split_clause,[],[f694,f14477]) ).
fof(f14477,plain,
( spl0_708
<=> ! [X6,X5] :
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f694,axiom,
! [X6,X5] :
( ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).
fof(f14475,plain,
spl0_707,
inference(avatar_split_clause,[],[f596,f14473]) ).
fof(f14473,plain,
( spl0_707
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f596,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f14471,plain,
spl0_706,
inference(avatar_split_clause,[],[f594,f14469]) ).
fof(f14469,plain,
( spl0_706
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f594,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f14400,plain,
spl0_705,
inference(avatar_split_clause,[],[f591,f14398]) ).
fof(f14398,plain,
( spl0_705
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f591,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f14396,plain,
spl0_704,
inference(avatar_split_clause,[],[f590,f14394]) ).
fof(f14394,plain,
( spl0_704
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f590,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f14392,plain,
spl0_703,
inference(avatar_split_clause,[],[f589,f14390]) ).
fof(f14390,plain,
( spl0_703
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f589,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).
fof(f14388,plain,
spl0_702,
inference(avatar_split_clause,[],[f588,f14386]) ).
fof(f14386,plain,
( spl0_702
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f588,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).
fof(f14384,plain,
spl0_701,
inference(avatar_split_clause,[],[f587,f14382]) ).
fof(f14382,plain,
( spl0_701
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f587,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f14380,plain,
spl0_700,
inference(avatar_split_clause,[],[f586,f14378]) ).
fof(f14378,plain,
( spl0_700
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f586,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f14376,plain,
spl0_699,
inference(avatar_split_clause,[],[f584,f14374]) ).
fof(f14374,plain,
( spl0_699
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f584,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f14372,plain,
spl0_698,
inference(avatar_split_clause,[],[f413,f14370]) ).
fof(f14370,plain,
( spl0_698
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f413,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).
fof(f14368,plain,
spl0_697,
inference(avatar_split_clause,[],[f412,f14366]) ).
fof(f14366,plain,
( spl0_697
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f412,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).
fof(f14364,plain,
spl0_696,
inference(avatar_split_clause,[],[f411,f14362]) ).
fof(f14362,plain,
( spl0_696
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f411,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).
fof(f14295,plain,
spl0_695,
inference(avatar_split_clause,[],[f410,f14293]) ).
fof(f14293,plain,
( spl0_695
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f410,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).
fof(f14291,plain,
spl0_694,
inference(avatar_split_clause,[],[f409,f14289]) ).
fof(f14289,plain,
( spl0_694
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f409,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).
fof(f14287,plain,
spl0_693,
inference(avatar_split_clause,[],[f408,f14285]) ).
fof(f14285,plain,
( spl0_693
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f408,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).
fof(f14283,plain,
spl0_692,
inference(avatar_split_clause,[],[f340,f14281]) ).
fof(f14281,plain,
( spl0_692
<=> ! [X5,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat)),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X10),c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f340,axiom,
! [X10,X7,X5] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat)),X5,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X10),c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).
fof(f14279,plain,
spl0_691,
inference(avatar_split_clause,[],[f300,f14277]) ).
fof(f14277,plain,
( spl0_691
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f300,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
fof(f14275,plain,
spl0_690,
inference(avatar_split_clause,[],[f267,f14273]) ).
fof(f14273,plain,
( spl0_690
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),c_Orderings_Oord__class_Omin(X1,X21,X0),X0),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f267,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),c_Orderings_Oord__class_Omin(X1,X21,X0),X0),c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
fof(f14271,plain,
spl0_689,
inference(avatar_split_clause,[],[f187,f14269]) ).
fof(f14269,plain,
( spl0_689
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f187,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).
fof(f14267,plain,
spl0_688,
inference(avatar_split_clause,[],[f186,f14265]) ).
fof(f14265,plain,
( spl0_688
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f186,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).
fof(f14263,plain,
spl0_687,
inference(avatar_split_clause,[],[f185,f14261]) ).
fof(f14261,plain,
( spl0_687
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f185,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).
fof(f14259,plain,
spl0_686,
inference(avatar_split_clause,[],[f184,f14257]) ).
fof(f14257,plain,
( spl0_686
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f184,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).
fof(f14202,plain,
spl0_685,
inference(avatar_split_clause,[],[f63,f14200]) ).
fof(f14200,plain,
( spl0_685
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f63,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).
fof(f14198,plain,
spl0_684,
inference(avatar_split_clause,[],[f62,f14196]) ).
fof(f14196,plain,
( spl0_684
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f62,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(X8,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).
fof(f14194,plain,
spl0_683,
inference(avatar_split_clause,[],[f61,f14192]) ).
fof(f14192,plain,
( spl0_683
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f61,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).
fof(f14190,plain,
spl0_682,
inference(avatar_split_clause,[],[f60,f14188]) ).
fof(f14188,plain,
( spl0_682
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f60,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).
fof(f14186,plain,
spl0_681,
inference(avatar_split_clause,[],[f59,f14184]) ).
fof(f14184,plain,
( spl0_681
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f59,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Omult__mono1(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).
fof(f14182,plain,
spl0_680,
inference(avatar_split_clause,[],[f17,f14180]) ).
fof(f14180,plain,
( spl0_680
<=> ! [X5,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),c_Suc(X10),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f17,axiom,
! [X10,X7,X5] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X5,c_Suc(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat)),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),c_Suc(X10),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).
fof(f13466,plain,
( ~ spl0_678
| spl0_311
| ~ spl0_679
| ~ spl0_140
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f6169,f5150,f1529,f13463,f3590,f13459]) ).
fof(f13459,plain,
( spl0_678
<=> class_Int_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f3590,plain,
( spl0_311
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f13463,plain,
( spl0_679
<=> class_Ring__and__Field_Oidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f5150,plain,
( spl0_414
<=> ! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f6169,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Int_Onumber__ring(tc_nat) )
| ~ spl0_140
| ~ spl0_414 ),
inference(trivial_inequality_removal,[],[f6165]) ).
fof(f6165,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| ~ class_Ring__and__Field_Oidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_Int_Onumber__ring(tc_nat) )
| ~ spl0_140
| ~ spl0_414 ),
inference(superposition,[],[f5151,f1530]) ).
fof(f5151,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| ~ class_Int_Onumber__ring(X0) )
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f5150]) ).
fof(f13165,plain,
( spl0_677
| ~ spl0_125
| ~ spl0_142
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4214,f3643,f1537,f1458,f13163]) ).
fof(f4214,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
| ~ spl0_125
| ~ spl0_142
| ~ spl0_321 ),
inference(forward_demodulation,[],[f4179,f1459]) ).
fof(f4179,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
| ~ spl0_142
| ~ spl0_321 ),
inference(superposition,[],[f3644,f1538]) ).
fof(f12906,plain,
( spl0_676
| ~ spl0_130
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4187,f3643,f1478,f12904]) ).
fof(f4187,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_130
| ~ spl0_321 ),
inference(superposition,[],[f1479,f3644]) ).
fof(f12583,plain,
( spl0_675
| ~ spl0_128
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f4185,f3643,f1470,f12581]) ).
fof(f12581,plain,
( spl0_675
<=> ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f4185,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_321 ),
inference(superposition,[],[f1471,f3644]) ).
fof(f12403,plain,
( spl0_674
| ~ spl0_125
| ~ spl0_141
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4170,f3639,f1533,f1458,f12401]) ).
fof(f4170,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| ~ spl0_125
| ~ spl0_141
| ~ spl0_320 ),
inference(forward_demodulation,[],[f4134,f1459]) ).
fof(f4134,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_141
| ~ spl0_320 ),
inference(superposition,[],[f3640,f1534]) ).
fof(f12307,plain,
spl0_673,
inference(avatar_split_clause,[],[f728,f12305]) ).
fof(f12305,plain,
( spl0_673
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f728,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
fof(f12303,plain,
spl0_672,
inference(avatar_split_clause,[],[f727,f12301]) ).
fof(f12301,plain,
( spl0_672
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f727,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X8,c_Divides_Odiv__class_Omod(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
fof(f12299,plain,
( spl0_671
| ~ spl0_130
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4144,f3639,f1478,f12297]) ).
fof(f12297,plain,
( spl0_671
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f4144,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
| ~ spl0_130
| ~ spl0_320 ),
inference(superposition,[],[f1479,f3640]) ).
fof(f12295,plain,
spl0_670,
inference(avatar_split_clause,[],[f704,f12293]) ).
fof(f12293,plain,
( spl0_670
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f704,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).
fof(f12291,plain,
spl0_669,
inference(avatar_split_clause,[],[f702,f12289]) ).
fof(f12289,plain,
( spl0_669
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f702,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0)
| c_lessequals(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).
fof(f12287,plain,
spl0_668,
inference(avatar_split_clause,[],[f649,f12285]) ).
fof(f12285,plain,
( spl0_668
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f649,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f12283,plain,
spl0_667,
inference(avatar_split_clause,[],[f640,f12281]) ).
fof(f12281,plain,
( spl0_667
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f640,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f12279,plain,
spl0_666,
inference(avatar_split_clause,[],[f630,f12277]) ).
fof(f12277,plain,
( spl0_666
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f630,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X8,X18,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).
fof(f12275,plain,
spl0_665,
inference(avatar_split_clause,[],[f629,f12273]) ).
fof(f629,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_lessequals(X8,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).
fof(f12271,plain,
spl0_664,
inference(avatar_split_clause,[],[f577,f12269]) ).
fof(f12269,plain,
( spl0_664
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f577,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f12267,plain,
spl0_663,
inference(avatar_split_clause,[],[f576,f12265]) ).
fof(f12265,plain,
( spl0_663
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f576,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f12263,plain,
spl0_662,
inference(avatar_split_clause,[],[f571,f12261]) ).
fof(f12261,plain,
( spl0_662
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f571,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).
fof(f12259,plain,
spl0_661,
inference(avatar_split_clause,[],[f570,f12257]) ).
fof(f12257,plain,
( spl0_661
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f570,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
fof(f12255,plain,
( spl0_660
| ~ spl0_128
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f4142,f3639,f1470,f12253]) ).
fof(f4142,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_128
| ~ spl0_320 ),
inference(superposition,[],[f1471,f3640]) ).
fof(f12251,plain,
spl0_659,
inference(avatar_split_clause,[],[f552,f12249]) ).
fof(f12249,plain,
( spl0_659
<=> ! [X24,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X24,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X24,X0),c_HOL_Otimes__class_Otimes(X2,X24,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f552,axiom,
! [X2,X0,X1,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X24,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X24,X0),c_HOL_Otimes__class_Otimes(X2,X24,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f12247,plain,
spl0_658,
inference(avatar_split_clause,[],[f547,f12245]) ).
fof(f12245,plain,
( spl0_658
<=> ! [X2,X0,X22,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X22,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X22,X1,X0),c_HOL_Otimes__class_Otimes(X22,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f547,axiom,
! [X2,X0,X1,X22] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X22,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X22,X1,X0),c_HOL_Otimes__class_Otimes(X22,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).
fof(f12243,plain,
spl0_657,
inference(avatar_split_clause,[],[f546,f12241]) ).
fof(f12241,plain,
( spl0_657
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f546,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).
fof(f12239,plain,
spl0_656,
inference(avatar_split_clause,[],[f545,f12237]) ).
fof(f12237,plain,
( spl0_656
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f545,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).
fof(f12235,plain,
spl0_655,
inference(avatar_split_clause,[],[f541,f12233]) ).
fof(f12233,plain,
( spl0_655
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f541,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f12231,plain,
spl0_654,
inference(avatar_split_clause,[],[f401,f12229]) ).
fof(f12229,plain,
( spl0_654
<=> ! [X6,X5,X7] :
( X5 = X6
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X7,tc_nat) != c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f401,axiom,
! [X6,X7,X5] :
( X5 = X6
| ~ c_lessequals(X7,X5,tc_nat)
| ~ c_lessequals(X7,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X5,X7,tc_nat) != c_HOL_Ominus__class_Ominus(X6,X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).
fof(f12227,plain,
spl0_653,
inference(avatar_split_clause,[],[f394,f12225]) ).
fof(f12225,plain,
( spl0_653
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f394,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).
fof(f12223,plain,
spl0_652,
inference(avatar_split_clause,[],[f393,f12221]) ).
fof(f12221,plain,
( spl0_652
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f393,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).
fof(f12219,plain,
spl0_651,
inference(avatar_split_clause,[],[f392,f12217]) ).
fof(f12217,plain,
( spl0_651
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f392,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
fof(f12215,plain,
spl0_650,
inference(avatar_split_clause,[],[f338,f12213]) ).
fof(f12213,plain,
( spl0_650
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X21,X0),c_HOL_Ominus__class_Ominus(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f338,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X1,X21,X0),c_HOL_Ominus__class_Ominus(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
fof(f12211,plain,
( spl0_649
| ~ spl0_137
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3118,f2949,f1517,f12209]) ).
fof(f3118,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X1,c_Suc(c_Orderings_Oord__class_Omax(X0,X1,tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_269 ),
inference(superposition,[],[f1518,f2950]) ).
fof(f12207,plain,
spl0_648,
inference(avatar_split_clause,[],[f337,f12205]) ).
fof(f12205,plain,
( spl0_648
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f337,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).
fof(f12203,plain,
spl0_647,
inference(avatar_split_clause,[],[f331,f12201]) ).
fof(f12201,plain,
( spl0_647
<=> ! [X18,X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f331,axiom,
! [X3,X0,X18,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(X8,X18,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).
fof(f12199,plain,
spl0_646,
inference(avatar_split_clause,[],[f325,f12197]) ).
fof(f12197,plain,
( spl0_646
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f325,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).
fof(f12195,plain,
spl0_645,
inference(avatar_split_clause,[],[f316,f12193]) ).
fof(f12193,plain,
( spl0_645
<=> ! [X26,X2,X0,X21,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X21,X0) = X26
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f316,axiom,
! [X2,X21,X0,X1,X26] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X21,X0) = X26
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X26,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f12191,plain,
spl0_644,
inference(avatar_split_clause,[],[f315,f12189]) ).
fof(f12189,plain,
( spl0_644
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f315,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,c_Divides_Odiv__class_Omod(X4,X8,X0),X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
fof(f12187,plain,
spl0_643,
inference(avatar_split_clause,[],[f314,f12185]) ).
fof(f12185,plain,
( spl0_643
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f314,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X3,X8,X0),X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
fof(f12183,plain,
spl0_642,
inference(avatar_split_clause,[],[f310,f12181]) ).
fof(f12181,plain,
( spl0_642
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X21,X0),c_HOL_Ominus__class_Ominus(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f310,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(X1,X21,X0),c_HOL_Ominus__class_Ominus(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
fof(f12179,plain,
spl0_641,
inference(avatar_split_clause,[],[f296,f12177]) ).
fof(f12177,plain,
( spl0_641
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f296,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).
fof(f12175,plain,
spl0_640,
inference(avatar_split_clause,[],[f295,f12173]) ).
fof(f12173,plain,
( spl0_640
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f295,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).
fof(f12171,plain,
spl0_639,
inference(avatar_split_clause,[],[f294,f12169]) ).
fof(f12169,plain,
( spl0_639
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f294,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).
fof(f12167,plain,
( spl0_638
| ~ spl0_56
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2247,f2086,f1178,f12164]) ).
fof(f12164,plain,
( spl0_638
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2247,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_56
| ~ spl0_214 ),
inference(resolution,[],[f2087,f1180]) ).
fof(f12162,plain,
spl0_637,
inference(avatar_split_clause,[],[f290,f12160]) ).
fof(f12160,plain,
( spl0_637
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f290,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).
fof(f12158,plain,
spl0_636,
inference(avatar_split_clause,[],[f289,f12156]) ).
fof(f12156,plain,
( spl0_636
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f289,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).
fof(f12154,plain,
spl0_635,
inference(avatar_split_clause,[],[f288,f12152]) ).
fof(f12152,plain,
( spl0_635
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f288,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).
fof(f12150,plain,
spl0_634,
inference(avatar_split_clause,[],[f279,f12148]) ).
fof(f12148,plain,
( spl0_634
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f279,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(X1,X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__add__distrib__left_0) ).
fof(f12146,plain,
spl0_633,
inference(avatar_split_clause,[],[f262,f12144]) ).
fof(f12144,plain,
( spl0_633
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f262,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f12142,plain,
spl0_632,
inference(avatar_split_clause,[],[f260,f12140]) ).
fof(f12140,plain,
( spl0_632
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f260,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X3,X0),c_HOL_Otimes__class_Otimes(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f12138,plain,
spl0_631,
inference(avatar_split_clause,[],[f245,f12136]) ).
fof(f12136,plain,
( spl0_631
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f245,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(X1,X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__add__distrib__left_0) ).
fof(f12134,plain,
spl0_630,
inference(avatar_split_clause,[],[f213,f12132]) ).
fof(f12132,plain,
( spl0_630
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),c_Orderings_Oord__class_Omin(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f213,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X1,X2,X0),c_Orderings_Oord__class_Omin(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
fof(f12130,plain,
spl0_629,
inference(avatar_split_clause,[],[f212,f12128]) ).
fof(f12128,plain,
( spl0_629
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X21,X0),X1,X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X1,X0),c_Orderings_Oord__class_Omin(X21,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f212,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X21,X0),X1,X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X1,X0),c_Orderings_Oord__class_Omin(X21,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
fof(f12126,plain,
spl0_628,
inference(avatar_split_clause,[],[f211,f12124]) ).
fof(f12124,plain,
( spl0_628
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f211,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X8,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).
fof(f12122,plain,
( spl0_627
| ~ spl0_36
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f2246,f2086,f1078,f12119]) ).
fof(f12119,plain,
( spl0_627
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2246,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_36
| ~ spl0_214 ),
inference(resolution,[],[f2087,f1080]) ).
fof(f12117,plain,
spl0_626,
inference(avatar_split_clause,[],[f210,f12115]) ).
fof(f12115,plain,
( spl0_626
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f210,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_lessequals(X4,X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_lessequals(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).
fof(f12113,plain,
spl0_625,
inference(avatar_split_clause,[],[f154,f12111]) ).
fof(f12111,plain,
( spl0_625
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f154,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f12109,plain,
spl0_624,
inference(avatar_split_clause,[],[f153,f12107]) ).
fof(f12107,plain,
( spl0_624
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f153,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f12105,plain,
spl0_623,
inference(avatar_split_clause,[],[f152,f12103]) ).
fof(f12103,plain,
( spl0_623
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f152,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f12101,plain,
spl0_622,
inference(avatar_split_clause,[],[f151,f12099]) ).
fof(f12099,plain,
( spl0_622
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f151,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X4,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f12097,plain,
spl0_621,
inference(avatar_split_clause,[],[f145,f12095]) ).
fof(f12095,plain,
( spl0_621
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f145,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).
fof(f12093,plain,
spl0_620,
inference(avatar_split_clause,[],[f144,f12091]) ).
fof(f12091,plain,
( spl0_620
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f144,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).
fof(f12089,plain,
spl0_619,
inference(avatar_split_clause,[],[f143,f12087]) ).
fof(f143,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).
fof(f12085,plain,
spl0_618,
inference(avatar_split_clause,[],[f133,f12083]) ).
fof(f12083,plain,
( spl0_618
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f133,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).
fof(f12081,plain,
spl0_617,
inference(avatar_split_clause,[],[f130,f12079]) ).
fof(f12079,plain,
( spl0_617
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f130,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).
fof(f12077,plain,
( spl0_616
| ~ spl0_43
| ~ spl0_207 ),
inference(avatar_split_clause,[],[f2230,f2055,f1113,f12075]) ).
fof(f12075,plain,
( spl0_616
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1113,plain,
( spl0_43
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f2055,plain,
( spl0_207
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f2230,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_43
| ~ spl0_207 ),
inference(resolution,[],[f2056,f1115]) ).
fof(f1115,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f1113]) ).
fof(f2056,plain,
( ! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f2055]) ).
fof(f12073,plain,
spl0_615,
inference(avatar_split_clause,[],[f129,f12071]) ).
fof(f12071,plain,
( spl0_615
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f129,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).
fof(f12069,plain,
spl0_614,
inference(avatar_split_clause,[],[f128,f12067]) ).
fof(f12067,plain,
( spl0_614
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f128,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).
fof(f12065,plain,
spl0_613,
inference(avatar_split_clause,[],[f127,f12063]) ).
fof(f127,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).
fof(f12061,plain,
spl0_612,
inference(avatar_split_clause,[],[f122,f12059]) ).
fof(f12059,plain,
( spl0_612
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f122,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f12057,plain,
spl0_611,
inference(avatar_split_clause,[],[f121,f12055]) ).
fof(f12055,plain,
( spl0_611
<=> ! [X0,X21,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f121,axiom,
! [X2,X21,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f12053,plain,
spl0_610,
inference(avatar_split_clause,[],[f118,f12051]) ).
fof(f12051,plain,
( spl0_610
<=> ! [X4,X0,X3,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X25,X0),X4,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f118,axiom,
! [X3,X0,X4,X25] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X25,X0),X4,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X25,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).
fof(f12049,plain,
spl0_609,
inference(avatar_split_clause,[],[f115,f12047]) ).
fof(f12047,plain,
( spl0_609
<=> ! [X2,X0,X22,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X22,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X1,X0),c_HOL_Otimes__class_Otimes(X22,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f115,axiom,
! [X2,X0,X1,X22] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X22,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X22,X1,X0),c_HOL_Otimes__class_Otimes(X22,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).
fof(f12045,plain,
spl0_608,
inference(avatar_split_clause,[],[f114,f12043]) ).
fof(f12043,plain,
( spl0_608
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f114,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X8,X0),c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f12041,plain,
spl0_607,
inference(avatar_split_clause,[],[f106,f12039]) ).
fof(f12039,plain,
( spl0_607
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f106,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).
fof(f12037,plain,
spl0_606,
inference(avatar_split_clause,[],[f105,f12035]) ).
fof(f12035,plain,
( spl0_606
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f105,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).
fof(f12033,plain,
( spl0_605
| ~ spl0_41
| ~ spl0_206 ),
inference(avatar_split_clause,[],[f2228,f2051,f1103,f12031]) ).
fof(f2228,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_41
| ~ spl0_206 ),
inference(resolution,[],[f2052,f1105]) ).
fof(f12029,plain,
spl0_604,
inference(avatar_split_clause,[],[f104,f12027]) ).
fof(f12027,plain,
( spl0_604
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f104,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).
fof(f12025,plain,
spl0_603,
inference(avatar_split_clause,[],[f101,f12023]) ).
fof(f12023,plain,
( spl0_603
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f101,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).
fof(f12021,plain,
spl0_602,
inference(avatar_split_clause,[],[f100,f12019]) ).
fof(f12019,plain,
( spl0_602
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f100,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).
fof(f12017,plain,
spl0_601,
inference(avatar_split_clause,[],[f88,f12015]) ).
fof(f12015,plain,
( spl0_601
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X21,X0),X1,X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X1,X0),c_Orderings_Oord__class_Omax(X21,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f88,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(X2,X21,X0),X1,X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X2,X1,X0),c_Orderings_Oord__class_Omax(X21,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
fof(f12013,plain,
spl0_600,
inference(avatar_split_clause,[],[f87,f12011]) ).
fof(f12011,plain,
( spl0_600
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),c_Orderings_Oord__class_Omax(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f87,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(X1,X2,X0),c_Orderings_Oord__class_Omax(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
fof(f12009,plain,
spl0_599,
inference(avatar_split_clause,[],[f51,f12007]) ).
fof(f12007,plain,
( spl0_599
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f51,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X4,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).
fof(f12005,plain,
spl0_598,
inference(avatar_split_clause,[],[f50,f12003]) ).
fof(f12003,plain,
( spl0_598
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f50,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f12001,plain,
spl0_597,
inference(avatar_split_clause,[],[f48,f11999]) ).
fof(f11999,plain,
( spl0_597
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f48,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).
fof(f11997,plain,
spl0_596,
inference(avatar_split_clause,[],[f47,f11995]) ).
fof(f11995,plain,
( spl0_596
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f47,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X4,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).
fof(f11993,plain,
spl0_595,
inference(avatar_split_clause,[],[f46,f11991]) ).
fof(f11991,plain,
( spl0_595
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f46,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).
fof(f11970,plain,
spl0_594,
inference(avatar_split_clause,[],[f45,f11968]) ).
fof(f11968,plain,
( spl0_594
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f45,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).
fof(f11447,plain,
( spl0_593
| ~ spl0_574
| ~ spl0_579 ),
inference(avatar_split_clause,[],[f11289,f11246,f10216,f11445]) ).
fof(f11445,plain,
( spl0_593
<=> ! [X2,X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat),X2,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X2,tc_nat)) = X2
| c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f10216,plain,
( spl0_574
<=> ! [X6,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) = X6
| c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f11246,plain,
( spl0_579
<=> ! [X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f11289,plain,
( ! [X2,X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat),X2,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X2,tc_nat)) = X2
| c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1 )
| ~ spl0_574
| ~ spl0_579 ),
inference(superposition,[],[f11247,f10217]) ).
fof(f10217,plain,
( ! [X6,X5] :
( c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat))
| c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) = X6 )
| ~ spl0_574 ),
inference(avatar_component_clause,[],[f10216]) ).
fof(f11247,plain,
( ! [X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1 )
| ~ spl0_579 ),
inference(avatar_component_clause,[],[f11246]) ).
fof(f11309,plain,
spl0_592,
inference(avatar_split_clause,[],[f716,f11307]) ).
fof(f11307,plain,
( spl0_592
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f716,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).
fof(f11305,plain,
spl0_591,
inference(avatar_split_clause,[],[f671,f11303]) ).
fof(f11303,plain,
( spl0_591
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f671,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
fof(f11301,plain,
spl0_590,
inference(avatar_split_clause,[],[f670,f11299]) ).
fof(f11299,plain,
( spl0_590
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X6,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f670,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_HOL_Otimes__class_Otimes(X6,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
fof(f11288,plain,
spl0_589,
inference(avatar_split_clause,[],[f663,f11286]) ).
fof(f11286,plain,
( spl0_589
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f663,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).
fof(f11284,plain,
spl0_588,
inference(avatar_split_clause,[],[f662,f11282]) ).
fof(f11282,plain,
( spl0_588
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f662,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).
fof(f11280,plain,
spl0_587,
inference(avatar_split_clause,[],[f602,f11278]) ).
fof(f11278,plain,
( spl0_587
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f602,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
fof(f11276,plain,
spl0_586,
inference(avatar_split_clause,[],[f601,f11274]) ).
fof(f11274,plain,
( spl0_586
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f601,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
fof(f11272,plain,
spl0_585,
inference(avatar_split_clause,[],[f529,f11270]) ).
fof(f11270,plain,
( spl0_585
<=> ! [X9,X7,X10] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f529,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X7,X10,tc_nat)
| c_HOL_Ominus__class_Ominus(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).
fof(f11268,plain,
spl0_584,
inference(avatar_split_clause,[],[f417,f11266]) ).
fof(f11266,plain,
( spl0_584
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f417,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).
fof(f11264,plain,
spl0_583,
inference(avatar_split_clause,[],[f416,f11262]) ).
fof(f11262,plain,
( spl0_583
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f416,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).
fof(f11260,plain,
spl0_582,
inference(avatar_split_clause,[],[f191,f11258]) ).
fof(f11258,plain,
( spl0_582
<=> ! [X0,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X3,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X15,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f191,axiom,
! [X3,X0,X15] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X3,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X15,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pCons_0) ).
fof(f11256,plain,
spl0_581,
inference(avatar_split_clause,[],[f183,f11254]) ).
fof(f11254,plain,
( spl0_581
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,X0) != c_HOL_Otimes__class_Otimes(X4,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f183,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Otimes__class_Otimes(X3,X3,X0) != c_HOL_Otimes__class_Otimes(X4,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f11252,plain,
spl0_580,
inference(avatar_split_clause,[],[f82,f11250]) ).
fof(f11250,plain,
( spl0_580
<=> ! [X19,X0,X20,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f82,axiom,
! [X2,X0,X1,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X2,X1,X0)
| c_lessequals(X20,X19,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
fof(f11248,plain,
( spl0_579
| ~ spl0_2
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f11167,f10216,f909,f11246]) ).
fof(f11167,plain,
( ! [X0,X1] :
( c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) != c_Divides_Odiv__class_Omod(c_Suc(X0),X1,tc_nat)
| c_Suc(c_Divides_Odiv__class_Omod(X0,X1,tc_nat)) = X1 )
| ~ spl0_2
| ~ spl0_574 ),
inference(superposition,[],[f910,f10217]) ).
fof(f11244,plain,
spl0_578,
inference(avatar_split_clause,[],[f80,f11242]) ).
fof(f11242,plain,
( spl0_578
<=> ! [X19,X20,X0,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f80,axiom,
! [X2,X0,X1,X19,X20] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X19,X20,X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) != c_HOL_Ominus__class_Ominus(X19,X20,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
fof(f11240,plain,
spl0_577,
inference(avatar_split_clause,[],[f68,f11238]) ).
fof(f11238,plain,
( spl0_577
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f68,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f11236,plain,
spl0_576,
inference(avatar_split_clause,[],[f67,f11234]) ).
fof(f11234,plain,
( spl0_576
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f67,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f10579,plain,
( ~ spl0_33
| spl0_575
| ~ spl0_111
| ~ spl0_202 ),
inference(avatar_split_clause,[],[f2189,f2035,f1401,f10577,f1063]) ).
fof(f10577,plain,
( spl0_575
<=> ! [X0] : ~ c_lessequals(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2035,plain,
( spl0_202
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f2189,plain,
( ! [X0] :
( ~ c_lessequals(c_Suc(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat) )
| ~ spl0_111
| ~ spl0_202 ),
inference(resolution,[],[f2036,f1402]) ).
fof(f2036,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f2035]) ).
fof(f10218,plain,
spl0_574,
inference(avatar_split_clause,[],[f779,f10216]) ).
fof(f779,axiom,
! [X6,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) = X6
| c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).
fof(f10214,plain,
spl0_573,
inference(avatar_split_clause,[],[f776,f10212]) ).
fof(f10212,plain,
( spl0_573
<=> ! [X0,X3,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X15,X0),X0) = c_Suc(c_Polynomial_Odegree(X15,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f776,axiom,
! [X3,X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X15,X0),X0) = c_Suc(c_Polynomial_Odegree(X15,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__eq_0) ).
fof(f10210,plain,
spl0_572,
inference(avatar_split_clause,[],[f648,f10208]) ).
fof(f10208,plain,
( spl0_572
<=> ! [X10,X9,X7,X29] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X29,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X29,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f648,axiom,
! [X10,X29,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X7,X29,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X29,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f10206,plain,
spl0_571,
inference(avatar_split_clause,[],[f583,f10204]) ).
fof(f583,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_Divides_Odiv__class_Omod(X5,X6,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).
fof(f10202,plain,
spl0_570,
inference(avatar_split_clause,[],[f582,f10200]) ).
fof(f582,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X7,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).
fof(f10198,plain,
spl0_569,
inference(avatar_split_clause,[],[f563,f10196]) ).
fof(f10196,plain,
( spl0_569
<=> ! [X4,X8,X3] :
( ~ c_lessequals(X8,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f563,axiom,
! [X3,X8,X4] :
( ~ c_lessequals(X8,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X8,tc_nat),c_HOL_Ominus__class_Ominus(X4,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).
fof(f10194,plain,
( spl0_568
| ~ spl0_56
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2172,f2019,f1178,f10191]) ).
fof(f10191,plain,
( spl0_568
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2172,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_56
| ~ spl0_198 ),
inference(resolution,[],[f2020,f1180]) ).
fof(f10189,plain,
spl0_567,
inference(avatar_split_clause,[],[f550,f10187]) ).
fof(f550,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
fof(f10185,plain,
spl0_566,
inference(avatar_split_clause,[],[f549,f10183]) ).
fof(f549,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
fof(f10181,plain,
spl0_565,
inference(avatar_split_clause,[],[f489,f10179]) ).
fof(f10179,plain,
( spl0_565
<=> ! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f489,axiom,
! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f10177,plain,
spl0_564,
inference(avatar_split_clause,[],[f463,f10175]) ).
fof(f10175,plain,
( spl0_564
<=> ! [X6,X29,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X29,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X29,X6,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f463,axiom,
! [X29,X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X29,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X29,X6,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f10173,plain,
spl0_563,
inference(avatar_split_clause,[],[f375,f10171]) ).
fof(f10171,plain,
( spl0_563
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f375,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f10169,plain,
spl0_562,
inference(avatar_split_clause,[],[f330,f10167]) ).
fof(f10167,plain,
( spl0_562
<=> ! [X10,X9,X7,X29] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X7,X29,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X29,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f330,axiom,
! [X10,X29,X9,X7] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X7,X29,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X29,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).
fof(f10165,plain,
spl0_561,
inference(avatar_split_clause,[],[f272,f10163]) ).
fof(f10163,plain,
( spl0_561
<=> ! [X0,X28,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X28,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f272,axiom,
! [X3,X28,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X28,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).
fof(f10161,plain,
spl0_560,
inference(avatar_split_clause,[],[f263,f10159]) ).
fof(f10159,plain,
( spl0_560
<=> ! [X4,X0,X3] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X3,X4,X0),X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f263,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X3,X4,X0),X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
fof(f10157,plain,
spl0_559,
inference(avatar_split_clause,[],[f241,f10155]) ).
fof(f10155,plain,
( spl0_559
<=> ! [X10,X9,X7,X29] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X7,X29,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X7,tc_nat),c_HOL_Otimes__class_Otimes(X10,X29,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f241,axiom,
! [X10,X29,X9,X7] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X7,X29,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X9,X7,tc_nat),c_HOL_Otimes__class_Otimes(X10,X29,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).
fof(f10153,plain,
spl0_558,
inference(avatar_split_clause,[],[f219,f10151]) ).
fof(f219,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X7,X10,tc_nat)
| ~ c_lessequals(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).
fof(f10149,plain,
( spl0_557
| ~ spl0_36
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2171,f2019,f1078,f10146]) ).
fof(f10146,plain,
( spl0_557
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2171,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_36
| ~ spl0_198 ),
inference(resolution,[],[f2020,f1080]) ).
fof(f10144,plain,
spl0_556,
inference(avatar_split_clause,[],[f155,f10142]) ).
fof(f10142,plain,
( spl0_556
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f155,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
fof(f10140,plain,
spl0_555,
inference(avatar_split_clause,[],[f120,f10138]) ).
fof(f120,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
fof(f10136,plain,
spl0_554,
inference(avatar_split_clause,[],[f119,f10134]) ).
fof(f119,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(X7,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
fof(f10132,plain,
spl0_553,
inference(avatar_split_clause,[],[f69,f10130]) ).
fof(f69,axiom,
! [X6,X9,X5] : c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(X5,X9,tc_nat),c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(X5,X6,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff_0) ).
fof(f10128,plain,
spl0_552,
inference(avatar_split_clause,[],[f55,f10126]) ).
fof(f10126,plain,
( spl0_552
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f55,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X4,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f10008,plain,
( spl0_551
| ~ spl0_130
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1973,f1746,f1478,f10006]) ).
fof(f10006,plain,
( spl0_551
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f1973,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
| ~ spl0_130
| ~ spl0_187 ),
inference(forward_demodulation,[],[f1970,f754]) ).
fof(f1970,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),X0,tc_nat)
| ~ spl0_130
| ~ spl0_187 ),
inference(resolution,[],[f1747,f1479]) ).
fof(f9869,plain,
( spl0_550
| ~ spl0_129
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1972,f1746,f1474,f9867]) ).
fof(f1972,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_129
| ~ spl0_187 ),
inference(forward_demodulation,[],[f1969,f753]) ).
fof(f1969,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),X1,tc_nat)
| ~ spl0_129
| ~ spl0_187 ),
inference(resolution,[],[f1747,f1475]) ).
fof(f9713,plain,
( spl0_549
| ~ spl0_185
| ~ spl0_187 ),
inference(avatar_split_clause,[],[f1962,f1746,f1738,f9711]) ).
fof(f9711,plain,
( spl0_549
<=> ! [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_549])]) ).
fof(f1962,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_185
| ~ spl0_187 ),
inference(resolution,[],[f1747,f1739]) ).
fof(f9504,plain,
( spl0_548
| ~ spl0_160
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1948,f1738,f1638,f9502]) ).
fof(f1948,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_lessequals(X1,X0,tc_nat) )
| ~ spl0_160
| ~ spl0_185 ),
inference(resolution,[],[f1739,f1639]) ).
fof(f9476,plain,
spl0_547,
inference(avatar_split_clause,[],[f897,f9474]) ).
fof(f9474,plain,
( spl0_547
<=> ! [X6,X5,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat),c_Suc(X7),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f897,plain,
! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat),c_Suc(X7),tc_nat) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat),
inference(forward_demodulation,[],[f757,f400]) ).
fof(f757,axiom,
! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat),c_Suc(X7),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X7,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f9472,plain,
spl0_546,
inference(avatar_split_clause,[],[f892,f9470]) ).
fof(f892,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,[],[f355]) ).
fof(f355,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/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).
fof(f9468,plain,
spl0_545,
inference(avatar_split_clause,[],[f732,f9466]) ).
fof(f9466,plain,
( spl0_545
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f732,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f9464,plain,
spl0_544,
inference(avatar_split_clause,[],[f731,f9462]) ).
fof(f9462,plain,
( spl0_544
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f731,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f9460,plain,
spl0_543,
inference(avatar_split_clause,[],[f721,f9458]) ).
fof(f9458,plain,
( spl0_543
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X5,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f721,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f9456,plain,
spl0_542,
inference(avatar_split_clause,[],[f681,f9454]) ).
fof(f681,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f9452,plain,
( spl0_541
| ~ spl0_161
| ~ spl0_184 ),
inference(avatar_split_clause,[],[f1930,f1734,f1642,f9450]) ).
fof(f9450,plain,
( spl0_541
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f1930,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_lessequals(X1,X0,tc_nat) )
| ~ spl0_161
| ~ spl0_184 ),
inference(resolution,[],[f1735,f1643]) ).
fof(f9448,plain,
spl0_540,
inference(avatar_split_clause,[],[f607,f9446]) ).
fof(f9446,plain,
( spl0_540
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X8,X4,X0),X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f607,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X8,X4,X0),X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
fof(f9444,plain,
spl0_539,
inference(avatar_split_clause,[],[f606,f9442]) ).
fof(f9442,plain,
( spl0_539
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f606,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
fof(f9440,plain,
spl0_538,
inference(avatar_split_clause,[],[f604,f9438]) ).
fof(f9438,plain,
( spl0_538
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f604,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
fof(f9436,plain,
spl0_537,
inference(avatar_split_clause,[],[f603,f9434]) ).
fof(f9434,plain,
( spl0_537
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f603,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X2,X21,X0),X0) = c_Orderings_Oord__class_Omax(X2,c_Orderings_Oord__class_Omax(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
fof(f9432,plain,
spl0_536,
inference(avatar_split_clause,[],[f573,f9430]) ).
fof(f9430,plain,
( spl0_536
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f573,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
fof(f9428,plain,
spl0_535,
inference(avatar_split_clause,[],[f572,f9426]) ).
fof(f9426,plain,
( spl0_535
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f572,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
fof(f9424,plain,
spl0_534,
inference(avatar_split_clause,[],[f509,f9422]) ).
fof(f9422,plain,
( spl0_534
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0)
| c_HOL_Oord__class_Oless(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f509,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0)
| c_HOL_Oord__class_Oless(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
fof(f9420,plain,
spl0_533,
inference(avatar_split_clause,[],[f508,f9418]) ).
fof(f9418,plain,
( spl0_533
<=> ! [X6,X5,X7] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X5,tc_nat)),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f508,axiom,
! [X6,X7,X5] : c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X5,tc_nat)),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).
fof(f9416,plain,
spl0_532,
inference(avatar_split_clause,[],[f500,f9414]) ).
fof(f9414,plain,
( spl0_532
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X1,X0)
| c_HOL_Oord__class_Oless(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f500,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X1,X0)
| c_HOL_Oord__class_Oless(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
fof(f9412,plain,
spl0_531,
inference(avatar_split_clause,[],[f484,f9410]) ).
fof(f9410,plain,
( spl0_531
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X21,X0)
| c_lessequals(X2,X21,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f484,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X21,X0)
| c_lessequals(X2,X21,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
fof(f9408,plain,
( spl0_530
| ~ spl0_130
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1810,f1638,f1478,f9406]) ).
fof(f9406,plain,
( spl0_530
<=> ! [X0,X1] : ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f1810,plain,
( ! [X0,X1] : ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
| ~ spl0_130
| ~ spl0_160 ),
inference(forward_demodulation,[],[f1808,f754]) ).
fof(f1808,plain,
( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),X0,tc_nat)
| ~ spl0_130
| ~ spl0_160 ),
inference(resolution,[],[f1639,f1479]) ).
fof(f9404,plain,
spl0_529,
inference(avatar_split_clause,[],[f468,f9402]) ).
fof(f9402,plain,
( spl0_529
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X21,X1,X0)
| c_lessequals(X21,X2,X0)
| ~ c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f468,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X21,X1,X0)
| c_lessequals(X21,X2,X0)
| ~ c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
fof(f9400,plain,
spl0_528,
inference(avatar_split_clause,[],[f459,f9398]) ).
fof(f9398,plain,
( spl0_528
<=> ! [X5,X6,X7,X29] :
( ~ c_HOL_Oord__class_Oless(X7,X29,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X29,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f459,axiom,
! [X29,X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X7,X29,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X29,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f9396,plain,
spl0_527,
inference(avatar_split_clause,[],[f405,f9394]) ).
fof(f9394,plain,
( spl0_527
<=> ! [X6,X5,X7] :
( X5 = X6
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Otimes__class_Otimes(X7,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f405,axiom,
! [X6,X7,X5] :
( X5 = X6
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_HOL_Otimes__class_Otimes(X7,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
fof(f9392,plain,
spl0_526,
inference(avatar_split_clause,[],[f374,f9390]) ).
fof(f9390,plain,
( spl0_526
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f374,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f9388,plain,
spl0_525,
inference(avatar_split_clause,[],[f373,f9386]) ).
fof(f9386,plain,
( spl0_525
<=> ! [X18,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X8,X18,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f373,axiom,
! [X3,X0,X18,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X8,X18,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f9384,plain,
spl0_524,
inference(avatar_split_clause,[],[f372,f9382]) ).
fof(f9382,plain,
( spl0_524
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X8,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f372,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X8,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f9380,plain,
spl0_523,
inference(avatar_split_clause,[],[f370,f9378]) ).
fof(f9378,plain,
( spl0_523
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f370,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f9376,plain,
spl0_522,
inference(avatar_split_clause,[],[f369,f9374]) ).
fof(f9374,plain,
( spl0_522
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f369,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f9372,plain,
spl0_521,
inference(avatar_split_clause,[],[f365,f9370]) ).
fof(f9370,plain,
( spl0_521
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f365,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f9368,plain,
spl0_520,
inference(avatar_split_clause,[],[f364,f9366]) ).
fof(f9366,plain,
( spl0_520
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f364,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f9364,plain,
( spl0_519
| ~ spl0_129
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f1809,f1638,f1474,f9362]) ).
fof(f1809,plain,
( ! [X0,X1] : ~ c_lessequals(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_129
| ~ spl0_160 ),
inference(forward_demodulation,[],[f1807,f753]) ).
fof(f1807,plain,
( ! [X0,X1] : ~ c_lessequals(c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),X1,tc_nat)
| ~ spl0_129
| ~ spl0_160 ),
inference(resolution,[],[f1639,f1475]) ).
fof(f9360,plain,
spl0_518,
inference(avatar_split_clause,[],[f345,f9358]) ).
fof(f9358,plain,
( spl0_518
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f345,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X21,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
fof(f9356,plain,
spl0_517,
inference(avatar_split_clause,[],[f339,f9354]) ).
fof(f9354,plain,
( spl0_517
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X21,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f339,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X21,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
fof(f9352,plain,
spl0_516,
inference(avatar_split_clause,[],[f305,f9350]) ).
fof(f9350,plain,
( spl0_516
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f305,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) = c_Orderings_Oord__class_Omin(X2,c_Orderings_Oord__class_Omin(X1,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
fof(f9348,plain,
spl0_515,
inference(avatar_split_clause,[],[f304,f9346]) ).
fof(f9346,plain,
( spl0_515
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f304,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
fof(f9344,plain,
spl0_514,
inference(avatar_split_clause,[],[f234,f9342]) ).
fof(f9342,plain,
( spl0_514
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X21,X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f234,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X1,X21,X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omin(X2,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
fof(f9340,plain,
spl0_513,
inference(avatar_split_clause,[],[f215,f9338]) ).
fof(f9338,plain,
( spl0_513
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X21,X1,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X2,X21,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f215,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X21,X1,X0)
| c_lessequals(c_Orderings_Oord__class_Omax(X2,X21,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
fof(f9336,plain,
spl0_512,
inference(avatar_split_clause,[],[f161,f9334]) ).
fof(f9334,plain,
( spl0_512
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f161,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f9332,plain,
spl0_511,
inference(avatar_split_clause,[],[f160,f9330]) ).
fof(f9330,plain,
( spl0_511
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f160,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Otimes__class_Otimes(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f9328,plain,
spl0_510,
inference(avatar_split_clause,[],[f111,f9326]) ).
fof(f9326,plain,
( spl0_510
<=> ! [X11,X13,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X11,X14,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f111,axiom,
! [X0,X11,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(X13,c_HOL_Otimes__class_Otimes(X11,X14,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f9324,plain,
spl0_509,
inference(avatar_split_clause,[],[f110,f9322]) ).
fof(f9322,plain,
( spl0_509
<=> ! [X11,X13,X0,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),X14,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f110,axiom,
! [X0,X11,X14,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X11,c_HOL_Otimes__class_Otimes(X13,X14,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),X14,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f9320,plain,
( spl0_508
| ~ spl0_123
| ~ spl0_148 ),
inference(avatar_split_clause,[],[f1760,f1590,f1450,f9318]) ).
fof(f9318,plain,
( spl0_508
<=> ! [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_508])]) ).
fof(f1590,plain,
( spl0_148
<=> ! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1760,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_123
| ~ spl0_148 ),
inference(resolution,[],[f1591,f1451]) ).
fof(f1591,plain,
( ! [X6] :
( ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X6 )
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1590]) ).
fof(f9316,plain,
spl0_507,
inference(avatar_split_clause,[],[f108,f9314]) ).
fof(f9314,plain,
( spl0_507
<=> ! [X11,X13,X0,X12] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X12,X0),X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f108,axiom,
! [X0,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X12,X0),X13,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X11,X13,X0),X12,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f9312,plain,
spl0_506,
inference(avatar_split_clause,[],[f107,f9310]) ).
fof(f9310,plain,
( spl0_506
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f107,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f9308,plain,
spl0_505,
inference(avatar_split_clause,[],[f26,f9306]) ).
fof(f26,axiom,
! [X6,X5] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,X5,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f8976,plain,
( spl0_504
| ~ spl0_138
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1583,f1545,f1521,f8974]) ).
fof(f8974,plain,
( spl0_504
<=> ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f1583,plain,
( ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_138
| ~ spl0_144 ),
inference(resolution,[],[f1546,f1522]) ).
fof(f8629,plain,
( spl0_503
| ~ spl0_137
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1582,f1545,f1517,f8627]) ).
fof(f1582,plain,
( ! [X0,X1] : c_lessequals(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)),tc_nat)
| ~ spl0_137
| ~ spl0_144 ),
inference(resolution,[],[f1546,f1518]) ).
fof(f8159,plain,
spl0_502,
inference(avatar_split_clause,[],[f715,f8157]) ).
fof(f8157,plain,
( spl0_502
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f715,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_0) ).
fof(f8155,plain,
( spl0_501
| ~ spl0_139
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1581,f1545,f1525,f8153]) ).
fof(f8153,plain,
( spl0_501
<=> ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f1581,plain,
( ! [X0,X1] : c_lessequals(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(X0),tc_nat)
| ~ spl0_139
| ~ spl0_144 ),
inference(resolution,[],[f1546,f1526]) ).
fof(f8151,plain,
spl0_500,
inference(avatar_split_clause,[],[f714,f8149]) ).
fof(f8149,plain,
( spl0_500
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f714,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_1) ).
fof(f8147,plain,
spl0_499,
inference(avatar_split_clause,[],[f693,f8145]) ).
fof(f8145,plain,
( spl0_499
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f693,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f8143,plain,
spl0_498,
inference(avatar_split_clause,[],[f692,f8141]) ).
fof(f8141,plain,
( spl0_498
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f692,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f8139,plain,
spl0_497,
inference(avatar_split_clause,[],[f691,f8137]) ).
fof(f691,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f8135,plain,
spl0_496,
inference(avatar_split_clause,[],[f690,f8133]) ).
fof(f8133,plain,
( spl0_496
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f690,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f8131,plain,
spl0_495,
inference(avatar_split_clause,[],[f689,f8129]) ).
fof(f689,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f8127,plain,
spl0_494,
inference(avatar_split_clause,[],[f688,f8125]) ).
fof(f8125,plain,
( spl0_494
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f688,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f8123,plain,
spl0_493,
inference(avatar_split_clause,[],[f579,f8121]) ).
fof(f8121,plain,
( spl0_493
<=> ! [X0,X21,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X21,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f579,axiom,
! [X2,X21,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X21,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f8119,plain,
spl0_492,
inference(avatar_split_clause,[],[f574,f8117]) ).
fof(f8117,plain,
( spl0_492
<=> ! [X6,X5,X7] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f574,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).
fof(f8115,plain,
spl0_491,
inference(avatar_split_clause,[],[f565,f8113]) ).
fof(f8113,plain,
( spl0_491
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f565,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
fof(f8095,plain,
spl0_490,
inference(avatar_split_clause,[],[f471,f8093]) ).
fof(f8093,plain,
( spl0_490
<=> ! [X6,X5,X7] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Otimes__class_Otimes(X7,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f471,axiom,
! [X6,X7,X5] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Otimes__class_Otimes(X7,X5,tc_nat) != c_HOL_Otimes__class_Otimes(X7,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).
fof(f8091,plain,
spl0_489,
inference(avatar_split_clause,[],[f469,f8089]) ).
fof(f8089,plain,
( spl0_489
<=> ! [X6,X5,X7] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Otimes__class_Otimes(X5,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X6,X7,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f469,axiom,
! [X6,X7,X5] :
( X5 = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X7
| c_HOL_Otimes__class_Otimes(X5,X7,tc_nat) != c_HOL_Otimes__class_Otimes(X6,X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
fof(f8087,plain,
spl0_488,
inference(avatar_split_clause,[],[f418,f8085]) ).
fof(f8085,plain,
( spl0_488
<=> ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f418,axiom,
! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X1
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X1
| ~ c_HOL_Oord__class_Oless(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).
fof(f8083,plain,
spl0_487,
inference(avatar_split_clause,[],[f283,f8081]) ).
fof(f8081,plain,
( spl0_487
<=> ! [X0,X21,X2,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X21
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f283,axiom,
! [X2,X21,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X2 = X21
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f8079,plain,
spl0_486,
inference(avatar_split_clause,[],[f195,f8077]) ).
fof(f8077,plain,
( spl0_486
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f195,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).
fof(f8075,plain,
spl0_485,
inference(avatar_split_clause,[],[f167,f8073]) ).
fof(f167,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).
fof(f8071,plain,
spl0_484,
inference(avatar_split_clause,[],[f148,f8069]) ).
fof(f8069,plain,
( spl0_484
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f148,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f8067,plain,
spl0_483,
inference(avatar_split_clause,[],[f85,f8065]) ).
fof(f8065,plain,
( spl0_483
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f85,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f8063,plain,
spl0_482,
inference(avatar_split_clause,[],[f64,f8061]) ).
fof(f8061,plain,
( spl0_482
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f64,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).
fof(f8059,plain,
spl0_481,
inference(avatar_split_clause,[],[f13,f8057]) ).
fof(f8057,plain,
( spl0_481
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f13,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).
fof(f8055,plain,
( spl0_480
| ~ spl0_187
| ~ spl0_257 ),
inference(avatar_split_clause,[],[f2629,f2496,f1746,f8053]) ).
fof(f8053,plain,
( spl0_480
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2496,plain,
( spl0_257
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2629,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_187
| ~ spl0_257 ),
inference(resolution,[],[f2497,f1747]) ).
fof(f2497,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_257 ),
inference(avatar_component_clause,[],[f2496]) ).
fof(f8051,plain,
spl0_479,
inference(avatar_split_clause,[],[f12,f8049]) ).
fof(f8049,plain,
( spl0_479
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f12,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).
fof(f8047,plain,
spl0_478,
inference(avatar_split_clause,[],[f11,f8045]) ).
fof(f8045,plain,
( spl0_478
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f11,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).
fof(f8043,plain,
spl0_477,
inference(avatar_split_clause,[],[f10,f8041]) ).
fof(f10,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X8,X3,X0),c_HOL_Oplus__class_Oplus(X8,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).
fof(f8039,plain,
spl0_476,
inference(avatar_split_clause,[],[f9,f8037]) ).
fof(f9,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).
fof(f8035,plain,
spl0_475,
inference(avatar_split_clause,[],[f8,f8033]) ).
fof(f8033,plain,
( spl0_475
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f8,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Oplus__class_Oplus(X3,X8,X0),c_HOL_Oplus__class_Oplus(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).
fof(f7407,plain,
( spl0_474
| ~ spl0_182
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2453,f2154,f1726,f7405]) ).
fof(f7405,plain,
( spl0_474
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2154,plain,
( spl0_227
<=> ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2453,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_182
| ~ spl0_227 ),
inference(resolution,[],[f2155,f1727]) ).
fof(f2155,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f7075,plain,
spl0_473,
inference(avatar_split_clause,[],[f896,f7073]) ).
fof(f896,plain,
! [X10,X9,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(X9,c_HOL_Oplus__class_Oplus(X7,X10,tc_nat),tc_nat),
inference(forward_demodulation,[],[f560,f400]) ).
fof(f560,axiom,
! [X10,X9,X7] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X10,tc_nat),X7,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X9,X7,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f7071,plain,
spl0_472,
inference(avatar_split_clause,[],[f768,f7069]) ).
fof(f768,axiom,
! [X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X15,X0) = c_Suc(c_Polynomial_Odegree(X15,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def_1) ).
fof(f7067,plain,
spl0_471,
inference(avatar_split_clause,[],[f668,f7065]) ).
fof(f7065,plain,
( spl0_471
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f668,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f7063,plain,
spl0_470,
inference(avatar_split_clause,[],[f608,f7061]) ).
fof(f608,axiom,
! [X6,X7,X5] : c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),X5,tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).
fof(f7059,plain,
spl0_469,
inference(avatar_split_clause,[],[f569,f7057]) ).
fof(f7057,plain,
( spl0_469
<=> ! [X6,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) != X6
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f569,axiom,
! [X6,X5] :
( c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)) != X6
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).
fof(f7055,plain,
spl0_468,
inference(avatar_split_clause,[],[f464,f7053]) ).
fof(f7053,plain,
( spl0_468
<=> ! [X0,X3,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_OpCons(X3,X15,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f464,axiom,
! [X3,X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_Polynomial_OpCons(X3,X15,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
fof(f7051,plain,
( spl0_467
| ~ spl0_186
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1959,f1833,f1742,f7049]) ).
fof(f7049,plain,
( spl0_467
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f1833,plain,
( spl0_190
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1959,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_186
| ~ spl0_190 ),
inference(resolution,[],[f1743,f1834]) ).
fof(f1834,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f1833]) ).
fof(f7047,plain,
spl0_466,
inference(avatar_split_clause,[],[f407,f7045]) ).
fof(f7045,plain,
( spl0_466
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f407,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
fof(f7043,plain,
spl0_465,
inference(avatar_split_clause,[],[f406,f7041]) ).
fof(f7041,plain,
( spl0_465
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f406,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
fof(f7039,plain,
spl0_464,
inference(avatar_split_clause,[],[f400,f7037]) ).
fof(f7035,plain,
spl0_463,
inference(avatar_split_clause,[],[f368,f7033]) ).
fof(f368,axiom,
! [X2,X21,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f7031,plain,
spl0_462,
inference(avatar_split_clause,[],[f367,f7029]) ).
fof(f367,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f7027,plain,
spl0_461,
inference(avatar_split_clause,[],[f354,f7025]) ).
fof(f354,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).
fof(f7023,plain,
spl0_460,
inference(avatar_split_clause,[],[f353,f7021]) ).
fof(f353,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X7,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).
fof(f7019,plain,
spl0_459,
inference(avatar_split_clause,[],[f318,f7017]) ).
fof(f7017,plain,
( spl0_459
<=> ! [X6,X5] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f318,axiom,
! [X6,X5] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X5,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).
fof(f7015,plain,
spl0_458,
inference(avatar_split_clause,[],[f317,f7013]) ).
fof(f317,axiom,
! [X6,X5] :
( c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X6,tc_nat)
| ~ c_lessequals(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).
fof(f7011,plain,
spl0_457,
inference(avatar_split_clause,[],[f306,f7009]) ).
fof(f7009,plain,
( spl0_457
<=> ! [X0,X28,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X15,X28,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f306,axiom,
! [X28,X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X15,X28,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).
fof(f6994,plain,
spl0_456,
inference(avatar_split_clause,[],[f299,f6992]) ).
fof(f299,axiom,
! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f6990,plain,
spl0_455,
inference(avatar_split_clause,[],[f298,f6988]) ).
fof(f298,axiom,
! [X6,X7,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f6986,plain,
spl0_454,
inference(avatar_split_clause,[],[f240,f6984]) ).
fof(f240,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f6982,plain,
spl0_453,
inference(avatar_split_clause,[],[f239,f6980]) ).
fof(f6980,plain,
( spl0_453
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(X4,X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f239,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(X4,X4,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f6978,plain,
spl0_452,
inference(avatar_split_clause,[],[f196,f6976]) ).
fof(f196,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Ominus__class_Ominus(c_Suc(X5),X6,tc_nat) = c_Suc(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).
fof(f6974,plain,
spl0_451,
inference(avatar_split_clause,[],[f163,f6972]) ).
fof(f6972,plain,
( spl0_451
<=> ! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f163,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
fof(f6970,plain,
spl0_450,
inference(avatar_split_clause,[],[f159,f6968]) ).
fof(f6968,plain,
( spl0_450
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f159,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f6966,plain,
spl0_449,
inference(avatar_split_clause,[],[f158,f6964]) ).
fof(f6964,plain,
( spl0_449
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f158,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f6962,plain,
spl0_448,
inference(avatar_split_clause,[],[f137,f6960]) ).
fof(f6960,plain,
( spl0_448
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f137,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f6958,plain,
spl0_447,
inference(avatar_split_clause,[],[f135,f6956]) ).
fof(f6956,plain,
( spl0_447
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f135,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f6954,plain,
( spl0_446
| ~ spl0_183
| ~ spl0_191 ),
inference(avatar_split_clause,[],[f2105,f1941,f1730,f6952]) ).
fof(f6952,plain,
( spl0_446
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1941,plain,
( spl0_191
<=> ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f2105,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_183
| ~ spl0_191 ),
inference(resolution,[],[f1942,f1731]) ).
fof(f1942,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1941]) ).
fof(f6950,plain,
spl0_445,
inference(avatar_split_clause,[],[f112,f6948]) ).
fof(f112,axiom,
! [X6,X7,X5] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),X7,tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f6946,plain,
spl0_444,
inference(avatar_split_clause,[],[f7,f6944]) ).
fof(f7,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f6942,plain,
spl0_443,
inference(avatar_split_clause,[],[f6,f6940]) ).
fof(f6,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f6390,plain,
( spl0_442
| ~ spl0_59
| ~ spl0_167
| ~ spl0_269
| ~ spl0_410 ),
inference(avatar_split_clause,[],[f6057,f5123,f2949,f1666,f1192,f6388]) ).
fof(f6057,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_59
| ~ spl0_167
| ~ spl0_269
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6056,f3110]) ).
fof(f6056,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_59
| ~ spl0_167
| ~ spl0_410 ),
inference(forward_demodulation,[],[f6023,f1667]) ).
fof(f6023,plain,
( ! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X1,tc_nat),tc_nat)
| ~ spl0_59
| ~ spl0_410 ),
inference(resolution,[],[f5124,f1193]) ).
fof(f5828,plain,
( ~ spl0_440
| spl0_441
| ~ spl0_62
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f5766,f5067,f1204,f5826,f5822]) ).
fof(f5822,plain,
( spl0_440
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f5826,plain,
( spl0_441
<=> ! [X0] : c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f1204,plain,
( spl0_62
<=> ! [X6] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f5067,plain,
( spl0_396
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f5766,plain,
( ! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_62
| ~ spl0_396 ),
inference(resolution,[],[f5068,f1205]) ).
fof(f1205,plain,
( ! [X6] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f5068,plain,
( ! [X3,X0] :
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_396 ),
inference(avatar_component_clause,[],[f5067]) ).
fof(f5286,plain,
spl0_439,
inference(avatar_split_clause,[],[f762,f5284]) ).
fof(f5284,plain,
( spl0_439
<=> ! [X6,X5,X7] :
( X5 = X6
| c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f762,axiom,
! [X6,X7,X5] :
( X5 = X6
| c_HOL_Otimes__class_Otimes(c_Suc(X7),X5,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X7),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f5282,plain,
spl0_438,
inference(avatar_split_clause,[],[f755,f5280]) ).
fof(f5280,plain,
( spl0_438
<=> ! [X0,X3,X15] :
( ~ class_HOL_Ozero(X0)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X15,X0),X0),c_Suc(c_Polynomial_Odegree(X15,X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f755,axiom,
! [X3,X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(X3,X15,X0),X0),c_Suc(c_Polynomial_Odegree(X15,X0)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__le_0) ).
fof(f5278,plain,
spl0_437,
inference(avatar_split_clause,[],[f741,f5276]) ).
fof(f741,axiom,
! [X6,X5] : c_Divides_Odiv__class_Omod(c_Suc(X5),X6,tc_nat) = c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(X5,X6,tc_nat)),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).
fof(f5274,plain,
spl0_436,
inference(avatar_split_clause,[],[f724,f5272]) ).
fof(f5272,plain,
( spl0_436
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f724,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f5270,plain,
spl0_435,
inference(avatar_split_clause,[],[f723,f5268]) ).
fof(f5268,plain,
( spl0_435
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f723,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f5266,plain,
spl0_434,
inference(avatar_split_clause,[],[f707,f5264]) ).
fof(f5264,plain,
( spl0_434
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X21,X2,X0)
| c_lessequals(X21,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f707,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_lessequals(X21,X2,X0)
| c_lessequals(X21,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
fof(f5262,plain,
spl0_433,
inference(avatar_split_clause,[],[f706,f5260]) ).
fof(f5260,plain,
( spl0_433
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f706,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
fof(f5258,plain,
spl0_432,
inference(avatar_split_clause,[],[f705,f5256]) ).
fof(f5256,plain,
( spl0_432
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f705,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
fof(f5254,plain,
spl0_431,
inference(avatar_split_clause,[],[f703,f5252]) ).
fof(f5252,plain,
( spl0_431
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X21,X0)
| c_lessequals(X1,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f703,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X21,X0)
| c_lessequals(X1,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
fof(f5227,plain,
spl0_430,
inference(avatar_split_clause,[],[f701,f5225]) ).
fof(f701,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
fof(f5223,plain,
spl0_429,
inference(avatar_split_clause,[],[f700,f5221]) ).
fof(f700,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
fof(f5219,plain,
spl0_428,
inference(avatar_split_clause,[],[f687,f5217]) ).
fof(f687,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f5215,plain,
spl0_427,
inference(avatar_split_clause,[],[f686,f5213]) ).
fof(f5213,plain,
( spl0_427
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f686,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f5211,plain,
spl0_426,
inference(avatar_split_clause,[],[f685,f5209]) ).
fof(f5209,plain,
( spl0_426
<=> ! [X9,X7,X10] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f685,axiom,
! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f5207,plain,
spl0_425,
inference(avatar_split_clause,[],[f684,f5205]) ).
fof(f5205,plain,
( spl0_425
<=> ! [X9,X7,X10] :
( ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f684,axiom,
! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f5203,plain,
spl0_424,
inference(avatar_split_clause,[],[f683,f5201]) ).
fof(f5201,plain,
( spl0_424
<=> ! [X9,X7,X10] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f683,axiom,
! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f5199,plain,
spl0_423,
inference(avatar_split_clause,[],[f657,f5197]) ).
fof(f5197,plain,
( spl0_423
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f657,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f5195,plain,
spl0_422,
inference(avatar_split_clause,[],[f656,f5193]) ).
fof(f5193,plain,
( spl0_422
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f656,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f5191,plain,
spl0_421,
inference(avatar_split_clause,[],[f647,f5189]) ).
fof(f5189,plain,
( spl0_421
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f647,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).
fof(f5176,plain,
spl0_420,
inference(avatar_split_clause,[],[f646,f5174]) ).
fof(f5174,plain,
( spl0_420
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f646,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Ominus__class_Ominus(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).
fof(f5172,plain,
spl0_419,
inference(avatar_split_clause,[],[f638,f5170]) ).
fof(f638,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| c_lessequals(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
fof(f5168,plain,
spl0_418,
inference(avatar_split_clause,[],[f635,f5166]) ).
fof(f635,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
fof(f5164,plain,
spl0_417,
inference(avatar_split_clause,[],[f634,f5162]) ).
fof(f5162,plain,
( spl0_417
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f634,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| c_HOL_Oord__class_Oless(X4,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f5160,plain,
spl0_416,
inference(avatar_split_clause,[],[f632,f5158]) ).
fof(f5158,plain,
( spl0_416
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f632,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
fof(f5156,plain,
spl0_415,
inference(avatar_split_clause,[],[f568,f5154]) ).
fof(f5154,plain,
( spl0_415
<=> ! [X6,X5,X7] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(X5,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f568,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X7,X6,tc_nat)
| c_lessequals(X5,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).
fof(f5152,plain,
spl0_414,
inference(avatar_split_clause,[],[f544,f5150]) ).
fof(f544,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f5148,plain,
spl0_413,
inference(avatar_split_clause,[],[f538,f5146]) ).
fof(f5146,plain,
( spl0_413
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f538,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
fof(f5144,plain,
spl0_412,
inference(avatar_split_clause,[],[f503,f5142]) ).
fof(f5142,plain,
( spl0_412
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f503,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X4,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f5140,plain,
spl0_411,
inference(avatar_split_clause,[],[f502,f5138]) ).
fof(f5138,plain,
( spl0_411
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f502,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f5125,plain,
spl0_410,
inference(avatar_split_clause,[],[f499,f5123]) ).
fof(f499,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat)
| c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).
fof(f5121,plain,
spl0_409,
inference(avatar_split_clause,[],[f498,f5119]) ).
fof(f498,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X10,c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X10,X7,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).
fof(f5117,plain,
spl0_408,
inference(avatar_split_clause,[],[f465,f5115]) ).
fof(f5115,plain,
( spl0_408
<=> ! [X0,X3,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Polynomial_OpCons(X3,X15,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f465,axiom,
! [X3,X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_Polynomial_OpCons(X3,X15,X0) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
fof(f5113,plain,
spl0_407,
inference(avatar_split_clause,[],[f402,f5111]) ).
fof(f5111,plain,
( spl0_407
<=> ! [X19,X20,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f402,axiom,
! [X0,X1,X19,X20] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X19 = X20
| c_HOL_Ominus__class_Ominus(X19,X20,X0) != c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f5109,plain,
spl0_406,
inference(avatar_split_clause,[],[f398,f5107]) ).
fof(f398,axiom,
! [X29,X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X29,X6,tc_nat),c_HOL_Ominus__class_Ominus(X29,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).
fof(f5105,plain,
spl0_405,
inference(avatar_split_clause,[],[f397,f5103]) ).
fof(f397,axiom,
! [X29,X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Ominus__class_Ominus(X5,X29,tc_nat),c_HOL_Ominus__class_Ominus(X6,X29,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).
fof(f5101,plain,
spl0_404,
inference(avatar_split_clause,[],[f363,f5099]) ).
fof(f5099,plain,
( spl0_404
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f363,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X21,X0)
| c_HOL_Oord__class_Oless(X1,X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f5097,plain,
spl0_403,
inference(avatar_split_clause,[],[f362,f5095]) ).
fof(f5095,plain,
( spl0_403
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f362,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,X2,X0)
| c_HOL_Oord__class_Oless(X21,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f5093,plain,
spl0_402,
inference(avatar_split_clause,[],[f351,f5091]) ).
fof(f351,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
fof(f5089,plain,
spl0_401,
inference(avatar_split_clause,[],[f343,f5087]) ).
fof(f5087,plain,
( spl0_401
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f343,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f5085,plain,
( spl0_400
| ~ spl0_129
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3116,f2949,f1474,f5083]) ).
fof(f3116,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_129
| ~ spl0_269 ),
inference(superposition,[],[f1475,f2950]) ).
fof(f5081,plain,
spl0_399,
inference(avatar_split_clause,[],[f342,f5079]) ).
fof(f5079,plain,
( spl0_399
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f342,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f5077,plain,
spl0_398,
inference(avatar_split_clause,[],[f336,f5075]) ).
fof(f336,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f5073,plain,
spl0_397,
inference(avatar_split_clause,[],[f308,f5071]) ).
fof(f5071,plain,
( spl0_397
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f308,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).
fof(f5069,plain,
spl0_396,
inference(avatar_split_clause,[],[f307,f5067]) ).
fof(f307,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).
fof(f5065,plain,
spl0_395,
inference(avatar_split_clause,[],[f286,f5063]) ).
fof(f5063,plain,
( spl0_395
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X8,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f286,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X8,X3,X0) != c_HOL_Oplus__class_Oplus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f5061,plain,
spl0_394,
inference(avatar_split_clause,[],[f285,f5059]) ).
fof(f5059,plain,
( spl0_394
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f285,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f5057,plain,
spl0_393,
inference(avatar_split_clause,[],[f284,f5055]) ).
fof(f5055,plain,
( spl0_393
<=> ! [X4,X0,X3,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f284,axiom,
! [X3,X0,X8,X4] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X4 = X8
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f5053,plain,
spl0_392,
inference(avatar_split_clause,[],[f270,f5051]) ).
fof(f5051,plain,
( spl0_392
<=> ! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f270,axiom,
! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_0) ).
fof(f5049,plain,
spl0_391,
inference(avatar_split_clause,[],[f269,f5047]) ).
fof(f5047,plain,
( spl0_391
<=> ! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f269,axiom,
! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def_1) ).
fof(f5045,plain,
spl0_390,
inference(avatar_split_clause,[],[f230,f5043]) ).
fof(f5043,plain,
( spl0_390
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f230,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X4,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
fof(f5041,plain,
( spl0_389
| ~ spl0_127
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f3114,f2949,f1466,f5039]) ).
fof(f3114,plain,
( ! [X0,X1] : c_lessequals(X1,c_Orderings_Oord__class_Omax(X0,X1,tc_nat),tc_nat)
| ~ spl0_127
| ~ spl0_269 ),
inference(superposition,[],[f1467,f2950]) ).
fof(f5037,plain,
spl0_388,
inference(avatar_split_clause,[],[f229,f5035]) ).
fof(f5035,plain,
( spl0_388
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f229,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
fof(f5033,plain,
spl0_387,
inference(avatar_split_clause,[],[f188,f5031]) ).
fof(f5031,plain,
( spl0_387
<=> ! [X0,X1,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f188,axiom,
! [X3,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f5029,plain,
spl0_386,
inference(avatar_split_clause,[],[f147,f5027]) ).
fof(f5027,plain,
( spl0_386
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f147,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f5025,plain,
spl0_385,
inference(avatar_split_clause,[],[f146,f5023]) ).
fof(f5023,plain,
( spl0_385
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f146,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X4,X0),c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f5021,plain,
spl0_384,
inference(avatar_split_clause,[],[f131,f5019]) ).
fof(f131,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
fof(f5017,plain,
spl0_383,
inference(avatar_split_clause,[],[f78,f5015]) ).
fof(f78,axiom,
! [X6] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f5013,plain,
spl0_382,
inference(avatar_split_clause,[],[f73,f5011]) ).
fof(f73,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).
fof(f5009,plain,
spl0_381,
inference(avatar_split_clause,[],[f72,f5007]) ).
fof(f72,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).
fof(f5005,plain,
spl0_380,
inference(avatar_split_clause,[],[f54,f5003]) ).
fof(f5003,plain,
( spl0_380
<=> ! [X15,X4,X0,X16,X3] :
( ~ class_HOL_Ozero(X0)
| X3 = X4
| c_Polynomial_OpCons(X3,X15,X0) != c_Polynomial_OpCons(X4,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f54,axiom,
! [X3,X0,X16,X4,X15] :
( ~ class_HOL_Ozero(X0)
| X3 = X4
| c_Polynomial_OpCons(X3,X15,X0) != c_Polynomial_OpCons(X4,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
fof(f5001,plain,
spl0_379,
inference(avatar_split_clause,[],[f53,f4999]) ).
fof(f4999,plain,
( spl0_379
<=> ! [X3,X4,X0,X16,X15] :
( ~ class_HOL_Ozero(X0)
| X15 = X16
| c_Polynomial_OpCons(X3,X15,X0) != c_Polynomial_OpCons(X4,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f53,axiom,
! [X3,X0,X16,X4,X15] :
( ~ class_HOL_Ozero(X0)
| X15 = X16
| c_Polynomial_OpCons(X3,X15,X0) != c_Polynomial_OpCons(X4,X16,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
fof(f4997,plain,
spl0_378,
inference(avatar_split_clause,[],[f44,f4995]) ).
fof(f44,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,X4,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f4993,plain,
spl0_377,
inference(avatar_split_clause,[],[f43,f4991]) ).
fof(f43,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X4,X3,X0),X4,X0) = c_Divides_Odiv__class_Omod(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f4989,plain,
spl0_376,
inference(avatar_split_clause,[],[f40,f4987]) ).
fof(f4987,plain,
( spl0_376
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f40,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).
fof(f4985,plain,
spl0_375,
inference(avatar_split_clause,[],[f39,f4983]) ).
fof(f4983,plain,
( spl0_375
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f39,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).
fof(f4981,plain,
spl0_374,
inference(avatar_split_clause,[],[f16,f4979]) ).
fof(f16,axiom,
! [X6,X7,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).
fof(f4977,plain,
spl0_373,
inference(avatar_split_clause,[],[f15,f4975]) ).
fof(f15,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X7,X5,tc_nat),c_HOL_Oplus__class_Oplus(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).
fof(f4973,plain,
spl0_372,
inference(avatar_split_clause,[],[f14,f4971]) ).
fof(f14,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X9,X10,tc_nat)
| c_lessequals(c_HOL_Oplus__class_Oplus(X9,X7,tc_nat),c_HOL_Oplus__class_Oplus(X10,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).
fof(f4969,plain,
spl0_371,
inference(avatar_split_clause,[],[f5,f4967]) ).
fof(f4967,plain,
( spl0_371
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f5,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X5,X7,tc_nat),c_HOL_Otimes__class_Otimes(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f4965,plain,
spl0_370,
inference(avatar_split_clause,[],[f4,f4963]) ).
fof(f4963,plain,
( spl0_370
<=> ! [X6,X5,X7] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f4,axiom,
! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X7,X5,tc_nat),c_HOL_Otimes__class_Otimes(X7,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f4532,plain,
( spl0_369
| ~ spl0_277
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f4357,f3619,f2981,f4529]) ).
fof(f4529,plain,
( spl0_369
<=> c_Parity_Oeven__odd__class_Oeven(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2981,plain,
( spl0_277
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f3619,plain,
( spl0_315
<=> ! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f4357,plain,
( c_Parity_Oeven__odd__class_Oeven(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| ~ spl0_277
| ~ spl0_315 ),
inference(trivial_inequality_removal,[],[f4356]) ).
fof(f4356,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| ~ spl0_277
| ~ spl0_315 ),
inference(superposition,[],[f3620,f2982]) ).
fof(f2982,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2981]) ).
fof(f3620,plain,
( ! [X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat) )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f3899,plain,
spl0_368,
inference(avatar_split_clause,[],[f780,f3897]) ).
fof(f3897,plain,
( spl0_368
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Suc(X5) = X6
| c_HOL_Oord__class_Oless(c_Suc(X5),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f780,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Suc(X5) = X6
| c_HOL_Oord__class_Oless(c_Suc(X5),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f3895,plain,
spl0_367,
inference(avatar_split_clause,[],[f771,f3893]) ).
fof(f771,axiom,
! [X10,X9,X7] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X9),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f3891,plain,
spl0_366,
inference(avatar_split_clause,[],[f758,f3889]) ).
fof(f3889,plain,
( spl0_366
<=> ! [X6,X5] :
( c_Suc(X6) = X5
| c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(X5,c_Suc(X6),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f758,axiom,
! [X6,X5] :
( c_Suc(X6) = X5
| c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(X5,c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
fof(f3887,plain,
spl0_365,
inference(avatar_split_clause,[],[f730,f3885]) ).
fof(f3885,plain,
( spl0_365
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f730,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3883,plain,
spl0_364,
inference(avatar_split_clause,[],[f729,f3881]) ).
fof(f3881,plain,
( spl0_364
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f729,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3879,plain,
spl0_363,
inference(avatar_split_clause,[],[f726,f3877]) ).
fof(f3877,plain,
( spl0_363
<=> ! [X6,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Suc(X9),tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f726,axiom,
! [X6,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X6,c_Suc(X9),tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f3845,plain,
( spl0_362
| ~ spl0_167
| ~ spl0_269
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f3841,f3838,f2949,f1666,f3843]) ).
fof(f3838,plain,
( spl0_361
<=> ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f3841,plain,
( ! [X6,X5] :
( c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_167
| ~ spl0_269
| ~ spl0_361 ),
inference(forward_demodulation,[],[f3839,f3110]) ).
fof(f3839,plain,
( ! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f3838]) ).
fof(f3840,plain,
spl0_361,
inference(avatar_split_clause,[],[f725,f3838]) ).
fof(f725,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f3803,plain,
( spl0_360
| ~ spl0_167
| ~ spl0_269
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f3799,f3796,f2949,f1666,f3801]) ).
fof(f3796,plain,
( spl0_359
<=> ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f3799,plain,
( ! [X6,X5] :
( c_Orderings_Oord__class_Omax(X5,X6,tc_nat) = X5
| ~ c_lessequals(X6,X5,tc_nat) )
| ~ spl0_167
| ~ spl0_269
| ~ spl0_359 ),
inference(forward_demodulation,[],[f3797,f3110]) ).
fof(f3797,plain,
( ! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f3796]) ).
fof(f3798,plain,
spl0_359,
inference(avatar_split_clause,[],[f659,f3796]) ).
fof(f659,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_HOL_Oplus__class_Oplus(X6,c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),tc_nat) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).
fof(f3794,plain,
spl0_358,
inference(avatar_split_clause,[],[f655,f3792]) ).
fof(f655,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3790,plain,
spl0_357,
inference(avatar_split_clause,[],[f654,f3788]) ).
fof(f654,axiom,
! [X2,X21,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X21,X0),c_HOL_Oplus__class_Oplus(X2,X21,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3786,plain,
spl0_356,
inference(avatar_split_clause,[],[f628,f3784]) ).
fof(f628,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X4,X3,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3782,plain,
spl0_355,
inference(avatar_split_clause,[],[f605,f3780]) ).
fof(f605,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3778,plain,
spl0_354,
inference(avatar_split_clause,[],[f559,f3776]) ).
fof(f559,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
fof(f3774,plain,
spl0_353,
inference(avatar_split_clause,[],[f558,f3772]) ).
fof(f558,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X1,X0)
| c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
fof(f3770,plain,
spl0_352,
inference(avatar_split_clause,[],[f557,f3768]) ).
fof(f3768,plain,
( spl0_352
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f557,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X1,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
fof(f3766,plain,
spl0_351,
inference(avatar_split_clause,[],[f556,f3764]) ).
fof(f556,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X21,X2,X0)
| ~ c_HOL_Oord__class_Oless(X21,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
fof(f3762,plain,
( spl0_350
| ~ spl0_64
| ~ spl0_192 ),
inference(avatar_split_clause,[],[f2142,f1995,f1212,f3760]) ).
fof(f3760,plain,
( spl0_350
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f1212,plain,
( spl0_64
<=> ! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f2142,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_64
| ~ spl0_192 ),
inference(resolution,[],[f1996,f1213]) ).
fof(f1213,plain,
( ! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1212]) ).
fof(f3758,plain,
spl0_349,
inference(avatar_split_clause,[],[f540,f3756]) ).
fof(f540,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f3754,plain,
spl0_348,
inference(avatar_split_clause,[],[f539,f3752]) ).
fof(f539,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f3750,plain,
spl0_347,
inference(avatar_split_clause,[],[f495,f3748]) ).
fof(f3748,plain,
( spl0_347
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X21,X2,X0)
| c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f495,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X21,X2,X0)
| c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
fof(f3746,plain,
spl0_346,
inference(avatar_split_clause,[],[f494,f3744]) ).
fof(f494,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X21,X1,X0)
| c_lessequals(X21,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
fof(f3742,plain,
spl0_345,
inference(avatar_split_clause,[],[f491,f3740]) ).
fof(f491,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X4,X1,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
fof(f3738,plain,
spl0_344,
inference(avatar_split_clause,[],[f490,f3736]) ).
fof(f490,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_Orderings_Oord__class_Omax(X3,X4,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
fof(f3734,plain,
spl0_343,
inference(avatar_split_clause,[],[f477,f3732]) ).
fof(f3732,plain,
( spl0_343
<=> ! [X2,X0,X21,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X21,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f477,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X21,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
fof(f3730,plain,
spl0_342,
inference(avatar_split_clause,[],[f476,f3728]) ).
fof(f3728,plain,
( spl0_342
<=> ! [X0,X21,X2,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X21,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f476,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X21,X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
fof(f3726,plain,
spl0_341,
inference(avatar_split_clause,[],[f473,f3724]) ).
fof(f473,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X4,X0)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
fof(f3722,plain,
spl0_340,
inference(avatar_split_clause,[],[f472,f3720]) ).
fof(f472,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X3,X0)
| ~ c_lessequals(X1,c_Orderings_Oord__class_Omin(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
fof(f3718,plain,
spl0_339,
inference(avatar_split_clause,[],[f455,f3716]) ).
fof(f3716,plain,
( spl0_339
<=> ! [X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f455,axiom,
! [X0,X15] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X15
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X15,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__eq__0__iff_0) ).
fof(f3714,plain,
spl0_338,
inference(avatar_split_clause,[],[f450,f3712]) ).
fof(f450,axiom,
! [X3,X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X3,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).
fof(f3710,plain,
spl0_337,
inference(avatar_split_clause,[],[f448,f3708]) ).
fof(f3708,plain,
( spl0_337
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f448,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).
fof(f3706,plain,
spl0_336,
inference(avatar_split_clause,[],[f447,f3704]) ).
fof(f3704,plain,
( spl0_336
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f447,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).
fof(f3702,plain,
spl0_335,
inference(avatar_split_clause,[],[f446,f3700]) ).
fof(f3700,plain,
( spl0_335
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f446,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).
fof(f3698,plain,
spl0_334,
inference(avatar_split_clause,[],[f445,f3696]) ).
fof(f3696,plain,
( spl0_334
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f445,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_lessequals(X3,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_lessequals(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).
fof(f3694,plain,
spl0_333,
inference(avatar_split_clause,[],[f430,f3692]) ).
fof(f430,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
fof(f3690,plain,
spl0_332,
inference(avatar_split_clause,[],[f429,f3688]) ).
fof(f429,axiom,
! [X3,X0,X1,X4] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X4,X0)
| c_HOL_Oord__class_Oless(X1,c_Orderings_Oord__class_Omax(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
fof(f3686,plain,
spl0_331,
inference(avatar_split_clause,[],[f426,f3684]) ).
fof(f426,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
fof(f3682,plain,
spl0_330,
inference(avatar_split_clause,[],[f425,f3680]) ).
fof(f3680,plain,
( spl0_330
<=> ! [X2,X0,X21,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f425,axiom,
! [X2,X21,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X2,X21,X0)
| ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(X1,X2,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
fof(f3678,plain,
( ~ spl0_329
| spl0_311
| ~ spl0_140
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f3504,f3050,f1529,f3590,f3675]) ).
fof(f3675,plain,
( spl0_329
<=> class_OrderedGroup_Ogroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f3050,plain,
( spl0_294
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f3504,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_140
| ~ spl0_294 ),
inference(trivial_inequality_removal,[],[f3502]) ).
fof(f3502,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Ogroup__add(tc_nat) )
| ~ spl0_140
| ~ spl0_294 ),
inference(superposition,[],[f3051,f1530]) ).
fof(f3051,plain,
( ! [X3,X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0)
| X3 = X4
| ~ class_OrderedGroup_Ogroup__add(X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f3050]) ).
fof(f3673,plain,
spl0_328,
inference(avatar_split_clause,[],[f297,f3671]) ).
fof(f297,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__0__0_0) ).
fof(f3669,plain,
spl0_327,
inference(avatar_split_clause,[],[f277,f3667]) ).
fof(f3667,plain,
( spl0_327
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f277,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).
fof(f3665,plain,
spl0_326,
inference(avatar_split_clause,[],[f276,f3663]) ).
fof(f3663,plain,
( spl0_326
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f276,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).
fof(f3661,plain,
spl0_325,
inference(avatar_split_clause,[],[f275,f3659]) ).
fof(f275,axiom,
! [X2,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).
fof(f3657,plain,
spl0_324,
inference(avatar_split_clause,[],[f258,f3655]) ).
fof(f258,axiom,
! [X6,X9] :
( ~ c_lessequals(X9,X6,tc_nat)
| c_HOL_Ominus__class_Ominus(X6,c_HOL_Ominus__class_Ominus(X6,X9,tc_nat),tc_nat) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).
fof(f3653,plain,
spl0_323,
inference(avatar_split_clause,[],[f194,f3651]) ).
fof(f3651,plain,
( spl0_323
<=> ! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f194,axiom,
! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X6
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f3649,plain,
spl0_322,
inference(avatar_split_clause,[],[f193,f3647]) ).
fof(f3647,plain,
( spl0_322
<=> ! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f193,axiom,
! [X6,X5] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X5
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f3645,plain,
spl0_321,
inference(avatar_split_clause,[],[f150,f3643]) ).
fof(f150,axiom,
! [X6,X5] : c_HOL_Otimes__class_Otimes(c_Suc(X5),X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
fof(f3641,plain,
spl0_320,
inference(avatar_split_clause,[],[f149,f3639]) ).
fof(f149,axiom,
! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,c_Suc(X6),tc_nat) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X5,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
fof(f3637,plain,
spl0_319,
inference(avatar_split_clause,[],[f98,f3635]) ).
fof(f3635,plain,
( spl0_319
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f98,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| X3 = X4
| ~ c_lessequals(X4,X3,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
fof(f3633,plain,
spl0_318,
inference(avatar_split_clause,[],[f96,f3631]) ).
fof(f3631,plain,
( spl0_318
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f96,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
fof(f3629,plain,
spl0_317,
inference(avatar_split_clause,[],[f52,f3627]) ).
fof(f52,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3625,plain,
spl0_316,
inference(avatar_split_clause,[],[f42,f3623]) ).
fof(f3623,plain,
( spl0_316
<=> ! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f42,axiom,
! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_0) ).
fof(f3621,plain,
spl0_315,
inference(avatar_split_clause,[],[f41,f3619]) ).
fof(f41,axiom,
! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Divides_Odiv__class_Omod(X1,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def_1) ).
fof(f3617,plain,
spl0_314,
inference(avatar_split_clause,[],[f28,f3615]) ).
fof(f3615,plain,
( spl0_314
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f28,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| X1 = X2
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
fof(f3613,plain,
spl0_313,
inference(avatar_split_clause,[],[f20,f3611]) ).
fof(f3611,plain,
( spl0_313
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f20,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f3609,plain,
spl0_312,
inference(avatar_split_clause,[],[f19,f3607]) ).
fof(f3607,plain,
( spl0_312
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f19,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3592,plain,
( ~ spl0_310
| spl0_311
| ~ spl0_140
| ~ spl0_293 ),
inference(avatar_split_clause,[],[f3495,f3046,f1529,f3590,f3586]) ).
fof(f3586,plain,
( spl0_310
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f3046,plain,
( spl0_293
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f3495,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_140
| ~ spl0_293 ),
inference(trivial_inequality_removal,[],[f3493]) ).
fof(f3493,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_140
| ~ spl0_293 ),
inference(superposition,[],[f3047,f1530]) ).
fof(f3047,plain,
( ! [X3,X0,X4] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0)
| X3 = X4
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_293 ),
inference(avatar_component_clause,[],[f3046]) ).
fof(f3487,plain,
( spl0_309
| ~ spl0_139
| ~ spl0_185 ),
inference(avatar_split_clause,[],[f1946,f1738,f1525,f3485]) ).
fof(f1946,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_139
| ~ spl0_185 ),
inference(resolution,[],[f1739,f1526]) ).
fof(f3260,plain,
( spl0_308
| ~ spl0_52
| ~ spl0_180 ),
inference(avatar_split_clause,[],[f1910,f1718,f1158,f3257]) ).
fof(f3257,plain,
( spl0_308
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f1718,plain,
( spl0_180
<=> ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1910,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_52
| ~ spl0_180 ),
inference(resolution,[],[f1719,f1160]) ).
fof(f1719,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_180 ),
inference(avatar_component_clause,[],[f1718]) ).
fof(f3164,plain,
( spl0_307
| ~ spl0_52
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f1901,f1710,f1158,f3162]) ).
fof(f3162,plain,
( spl0_307
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1901,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_52
| ~ spl0_178 ),
inference(resolution,[],[f1711,f1160]) ).
fof(f3100,plain,
spl0_306,
inference(avatar_split_clause,[],[f786,f3098]) ).
fof(f3098,plain,
( spl0_306
<=> ! [X6,X5] : c_Orderings_Oord__class_Omin(c_Suc(X5),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X5,X6,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f786,axiom,
! [X6,X5] : c_Orderings_Oord__class_Omin(c_Suc(X5),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omin(X5,X6,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__Suc__Suc_0) ).
fof(f3096,plain,
spl0_305,
inference(avatar_split_clause,[],[f778,f3094]) ).
fof(f778,axiom,
! [X6,X5] : c_Orderings_Oord__class_Omax(c_Suc(X5),c_Suc(X6),tc_nat) = c_Suc(c_Orderings_Oord__class_Omax(X5,X6,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__Suc__Suc_0) ).
fof(f3092,plain,
spl0_304,
inference(avatar_split_clause,[],[f777,f3090]) ).
fof(f777,axiom,
! [X28,X0,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X15,X28,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).
fof(f3088,plain,
spl0_303,
inference(avatar_split_clause,[],[f767,f3086]) ).
fof(f767,axiom,
! [X0,X15] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_Polynomial_Odegree(X15,X0) = c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X15,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__minus_0) ).
fof(f3084,plain,
spl0_302,
inference(avatar_split_clause,[],[f749,f3082]) ).
fof(f3082,plain,
( spl0_302
<=> ! [X6,X5] :
( X5 = X6
| c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f749,axiom,
! [X6,X5] :
( X5 = X6
| c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f3080,plain,
spl0_301,
inference(avatar_split_clause,[],[f713,f3078]) ).
fof(f3078,plain,
( spl0_301
<=> ! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f713,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
fof(f3076,plain,
spl0_300,
inference(avatar_split_clause,[],[f712,f3074]) ).
fof(f3074,plain,
( spl0_300
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f712,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X3,X4,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f3072,plain,
( spl0_299
| ~ spl0_51
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f1869,f1678,f1153,f3070]) ).
fof(f3070,plain,
( spl0_299
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f1153,plain,
( spl0_51
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1869,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_51
| ~ spl0_170 ),
inference(resolution,[],[f1679,f1155]) ).
fof(f1155,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f1153]) ).
fof(f3068,plain,
spl0_298,
inference(avatar_split_clause,[],[f711,f3066]) ).
fof(f3066,plain,
( spl0_298
<=> ! [X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f711,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X4,X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f3064,plain,
spl0_297,
inference(avatar_split_clause,[],[f708,f3062]) ).
fof(f3062,plain,
( spl0_297
<=> ! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f708,axiom,
! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_0) ).
fof(f3060,plain,
spl0_296,
inference(avatar_split_clause,[],[f698,f3058]) ).
fof(f698,axiom,
! [X10,X9,X7] :
( ~ c_lessequals(X9,X10,tc_nat)
| ~ c_lessequals(X10,X7,tc_nat)
| c_lessequals(X9,X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
fof(f3056,plain,
spl0_295,
inference(avatar_split_clause,[],[f674,f3054]) ).
fof(f674,axiom,
! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).
fof(f3052,plain,
spl0_294,
inference(avatar_split_clause,[],[f543,f3050]) ).
fof(f543,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).
fof(f3048,plain,
spl0_293,
inference(avatar_split_clause,[],[f542,f3046]) ).
fof(f542,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X3 = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).
fof(f3044,plain,
spl0_292,
inference(avatar_split_clause,[],[f515,f3041]) ).
fof(f3041,plain,
( spl0_292
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f515,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f3039,plain,
spl0_291,
inference(avatar_split_clause,[],[f422,f3037]) ).
fof(f3037,plain,
( spl0_291
<=> ! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f422,axiom,
! [X2,X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_4) ).
fof(f3035,plain,
spl0_290,
inference(avatar_split_clause,[],[f421,f3033]) ).
fof(f3033,plain,
( spl0_290
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f421,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_3) ).
fof(f3031,plain,
spl0_289,
inference(avatar_split_clause,[],[f323,f3029]) ).
fof(f323,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
fof(f3027,plain,
( spl0_288
| ~ spl0_51
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f1866,f1674,f1153,f3025]) ).
fof(f1866,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_51
| ~ spl0_169 ),
inference(resolution,[],[f1675,f1155]) ).
fof(f3023,plain,
spl0_287,
inference(avatar_split_clause,[],[f322,f3021]) ).
fof(f3021,plain,
( spl0_287
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f322,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
fof(f3019,plain,
spl0_286,
inference(avatar_split_clause,[],[f321,f3017]) ).
fof(f321,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
fof(f3015,plain,
spl0_285,
inference(avatar_split_clause,[],[f313,f3013]) ).
fof(f313,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
fof(f3011,plain,
spl0_284,
inference(avatar_split_clause,[],[f312,f3009]) ).
fof(f3009,plain,
( spl0_284
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f312,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
fof(f3007,plain,
spl0_283,
inference(avatar_split_clause,[],[f311,f3005]) ).
fof(f311,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X1,X2,X0)
| c_Orderings_Oord__class_Omin(X1,X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
fof(f3003,plain,
spl0_282,
inference(avatar_split_clause,[],[f309,f3001]) ).
fof(f3001,plain,
( spl0_282
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f309,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).
fof(f2999,plain,
spl0_281,
inference(avatar_split_clause,[],[f281,f2997]) ).
fof(f281,axiom,
! [X6,X7,X5] :
( X5 = X6
| c_HOL_Oplus__class_Oplus(X7,X5,tc_nat) != c_HOL_Oplus__class_Oplus(X7,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).
fof(f2995,plain,
spl0_280,
inference(avatar_split_clause,[],[f280,f2993]) ).
fof(f280,axiom,
! [X6,X7,X5] :
( X5 = X6
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X6,X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f2991,plain,
spl0_279,
inference(avatar_split_clause,[],[f256,f2989]) ).
fof(f2989,plain,
( spl0_279
<=> ! [X6,X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f256,axiom,
! [X6,X5] :
( c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__add_1) ).
fof(f2987,plain,
spl0_278,
inference(avatar_split_clause,[],[f252,f2985]) ).
fof(f2985,plain,
( spl0_278
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f252,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_1) ).
fof(f2983,plain,
( spl0_277
| ~ spl0_32
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f1842,f1662,f1058,f2981]) ).
fof(f1842,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_32
| ~ spl0_166 ),
inference(resolution,[],[f1663,f1060]) ).
fof(f2979,plain,
spl0_276,
inference(avatar_split_clause,[],[f250,f2977]) ).
fof(f2977,plain,
( spl0_276
<=> ! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f250,axiom,
! [X6,X5] :
( ~ c_Parity_Oeven__odd__class_Oeven(X5,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__add_3) ).
fof(f2975,plain,
spl0_275,
inference(avatar_split_clause,[],[f248,f2973]) ).
fof(f2973,plain,
( spl0_275
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f248,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__sum__nat_1) ).
fof(f2971,plain,
spl0_274,
inference(avatar_split_clause,[],[f238,f2969]) ).
fof(f238,axiom,
! [X28,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).
fof(f2967,plain,
spl0_273,
inference(avatar_split_clause,[],[f192,f2965]) ).
fof(f2965,plain,
( spl0_273
<=> ! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f192,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat)
| c_lessequals(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).
fof(f2963,plain,
spl0_272,
inference(avatar_split_clause,[],[f140,f2961]) ).
fof(f2961,plain,
( spl0_272
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f140,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).
fof(f2959,plain,
spl0_271,
inference(avatar_split_clause,[],[f77,f2957]) ).
fof(f77,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f2955,plain,
spl0_270,
inference(avatar_split_clause,[],[f76,f2953]) ).
fof(f76,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f2951,plain,
spl0_269,
inference(avatar_split_clause,[],[f33,f2949]) ).
fof(f33,axiom,
! [X6,X5] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X6,X5,tc_nat),X5,tc_nat) = c_Orderings_Oord__class_Omax(X6,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__minus__add__max_0) ).
fof(f2947,plain,
spl0_268,
inference(avatar_split_clause,[],[f32,f2945]) ).
fof(f2945,plain,
( spl0_268
<=> ! [X4,X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f32,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X3 = X4
| c_HOL_Ouminus__class_Ouminus(X4,X0) != c_HOL_Ouminus__class_Ouminus(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2914,plain,
( spl0_267
| ~ spl0_32
| ~ spl0_165 ),
inference(avatar_split_clause,[],[f1840,f1658,f1058,f2912]) ).
fof(f2912,plain,
( spl0_267
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1840,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_32
| ~ spl0_165 ),
inference(resolution,[],[f1659,f1060]) ).
fof(f2804,plain,
( spl0_266
| ~ spl0_52
| ~ spl0_151 ),
inference(avatar_split_clause,[],[f1768,f1602,f1158,f2802]) ).
fof(f2802,plain,
( spl0_266
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1768,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_52
| ~ spl0_151 ),
inference(resolution,[],[f1603,f1160]) ).
fof(f2715,plain,
( spl0_265
| ~ spl0_48
| ~ spl0_150 ),
inference(avatar_split_clause,[],[f1766,f1598,f1138,f2713]) ).
fof(f2713,plain,
( spl0_265
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1766,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_48
| ~ spl0_150 ),
inference(resolution,[],[f1599,f1140]) ).
fof(f2526,plain,
spl0_264,
inference(avatar_split_clause,[],[f754,f2524]) ).
fof(f2522,plain,
spl0_263,
inference(avatar_split_clause,[],[f753,f2520]) ).
fof(f2518,plain,
spl0_262,
inference(avatar_split_clause,[],[f750,f2516]) ).
fof(f750,axiom,
! [X6,X5] : c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X5),c_Suc(X6),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f2514,plain,
spl0_261,
inference(avatar_split_clause,[],[f620,f2512]) ).
fof(f620,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,X0),X4,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2510,plain,
spl0_260,
inference(avatar_split_clause,[],[f612,f2508]) ).
fof(f2508,plain,
( spl0_260
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f612,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2506,plain,
spl0_259,
inference(avatar_split_clause,[],[f531,f2504]) ).
fof(f531,axiom,
! [X10,X6,X7] :
( ~ c_HOL_Oord__class_Oless(X10,X7,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X10,X6,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f2502,plain,
spl0_258,
inference(avatar_split_clause,[],[f462,f2500]) ).
fof(f462,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2498,plain,
( spl0_257
| ~ spl0_187
| ~ spl0_197 ),
inference(avatar_split_clause,[],[f2058,f2015,f1746,f2496]) ).
fof(f2015,plain,
( spl0_197
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f2058,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_187
| ~ spl0_197 ),
inference(resolution,[],[f2016,f1747]) ).
fof(f2016,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f2015]) ).
fof(f2494,plain,
spl0_256,
inference(avatar_split_clause,[],[f458,f2492]) ).
fof(f458,axiom,
! [X3,X0,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,X8,X0) = c_HOL_Oplus__class_Oplus(X8,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2490,plain,
spl0_255,
inference(avatar_split_clause,[],[f440,f2488]) ).
fof(f440,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).
fof(f2486,plain,
spl0_254,
inference(avatar_split_clause,[],[f439,f2484]) ).
fof(f439,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).
fof(f2482,plain,
spl0_253,
inference(avatar_split_clause,[],[f438,f2480]) ).
fof(f2480,plain,
( spl0_253
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f438,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2478,plain,
spl0_252,
inference(avatar_split_clause,[],[f437,f2476]) ).
fof(f437,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2474,plain,
spl0_251,
inference(avatar_split_clause,[],[f436,f2472]) ).
fof(f436,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2470,plain,
spl0_250,
inference(avatar_split_clause,[],[f431,f2468]) ).
fof(f431,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X2,X1,X0) = c_Orderings_Oord__class_Omin(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
fof(f2466,plain,
spl0_249,
inference(avatar_split_clause,[],[f404,f2464]) ).
fof(f404,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
fof(f2462,plain,
spl0_248,
inference(avatar_split_clause,[],[f380,f2460]) ).
fof(f380,axiom,
! [X6,X7,X5] :
( c_lessequals(X7,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).
fof(f2458,plain,
spl0_247,
inference(avatar_split_clause,[],[f379,f2456]) ).
fof(f379,axiom,
! [X6,X7,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).
fof(f2450,plain,
spl0_246,
inference(avatar_split_clause,[],[f378,f2448]) ).
fof(f378,axiom,
! [X2,X21,X1] :
( ~ c_lessequals(X1,X21,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).
fof(f2446,plain,
spl0_245,
inference(avatar_split_clause,[],[f377,f2444]) ).
fof(f377,axiom,
! [X2,X21,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_lessequals(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).
fof(f2442,plain,
spl0_244,
inference(avatar_split_clause,[],[f360,f2440]) ).
fof(f360,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,X4,X0) = c_HOL_Otimes__class_Otimes(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2438,plain,
spl0_243,
inference(avatar_split_clause,[],[f352,f2436]) ).
fof(f352,axiom,
! [X3,X0,X4] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,X4,X0),X4,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2434,plain,
spl0_242,
inference(avatar_split_clause,[],[f271,f2432]) ).
fof(f271,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2430,plain,
spl0_241,
inference(avatar_split_clause,[],[f268,f2428]) ).
fof(f268,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X2,X0) = c_Orderings_Oord__class_Omax(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
fof(f2426,plain,
spl0_240,
inference(avatar_split_clause,[],[f264,f2424]) ).
fof(f264,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,c_Orderings_Oord__class_Omin(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
fof(f2422,plain,
spl0_239,
inference(avatar_split_clause,[],[f205,f2420]) ).
fof(f205,axiom,
! [X10,X9,X5] :
( ~ c_HOL_Oord__class_Oless(X9,X10,tc_nat)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(X5,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f2418,plain,
spl0_238,
inference(avatar_split_clause,[],[f203,f2416]) ).
fof(f203,axiom,
! [X10,X9,X7] :
( c_HOL_Oord__class_Oless(X9,X7,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X7,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f2414,plain,
spl0_237,
inference(avatar_split_clause,[],[f201,f2412]) ).
fof(f201,axiom,
! [X2,X21,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X2,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f2405,plain,
spl0_236,
inference(avatar_split_clause,[],[f180,f2403]) ).
fof(f2403,plain,
( spl0_236
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f180,axiom,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2401,plain,
spl0_235,
inference(avatar_split_clause,[],[f171,f2399]) ).
fof(f171,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f2397,plain,
spl0_234,
inference(avatar_split_clause,[],[f170,f2395]) ).
fof(f170,axiom,
! [X6,X5] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X5
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f2393,plain,
spl0_233,
inference(avatar_split_clause,[],[f132,f2391]) ).
fof(f2391,plain,
( spl0_233
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f132,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ouminus__class_Ouminus(X3,X0) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2389,plain,
spl0_232,
inference(avatar_split_clause,[],[f92,f2387]) ).
fof(f92,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
fof(f2385,plain,
spl0_231,
inference(avatar_split_clause,[],[f27,f2383]) ).
fof(f27,axiom,
! [X2,X1] :
( X1 = X2
| c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
fof(f2381,plain,
spl0_230,
inference(avatar_split_clause,[],[f24,f2379]) ).
fof(f24,axiom,
! [X6,X5] :
( X5 = X6
| ~ c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(X6,X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
fof(f2343,plain,
( spl0_229
| ~ spl0_220 ),
inference(avatar_split_clause,[],[f2305,f2115,f2341]) ).
fof(f2305,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_220 ),
inference(factoring,[],[f2116]) ).
fof(f2209,plain,
( ~ spl0_228
| ~ spl0_141
| ~ spl0_201 ),
inference(avatar_split_clause,[],[f2185,f2031,f1533,f2206]) ).
fof(f2206,plain,
( spl0_228
<=> c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2185,plain,
( ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_141
| ~ spl0_201 ),
inference(superposition,[],[f2032,f1534]) ).
fof(f2156,plain,
( spl0_227
| ~ spl0_144
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1881,f1833,f1545,f2154]) ).
fof(f1881,plain,
( ! [X0] : c_lessequals(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_144
| ~ spl0_190 ),
inference(resolution,[],[f1834,f1546]) ).
fof(f2141,plain,
spl0_226,
inference(avatar_split_clause,[],[f790,f2139]) ).
fof(f790,axiom,
! [X1,X6] :
( ~ c_HOL_Oord__class_Oless(X1,X6,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
fof(f2137,plain,
spl0_225,
inference(avatar_split_clause,[],[f789,f2135]) ).
fof(f789,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f2133,plain,
spl0_224,
inference(avatar_split_clause,[],[f740,f2131]) ).
fof(f740,axiom,
! [X6,X5] :
( ~ c_lessequals(X6,X5,tc_nat)
| c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
fof(f2129,plain,
spl0_223,
inference(avatar_split_clause,[],[f739,f2127]) ).
fof(f739,axiom,
! [X6,X5] :
( c_lessequals(X6,X5,tc_nat)
| ~ c_lessequals(c_Suc(X6),c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
fof(f2125,plain,
spl0_222,
inference(avatar_split_clause,[],[f738,f2123]) ).
fof(f2123,plain,
( spl0_222
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f738,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f2121,plain,
spl0_221,
inference(avatar_split_clause,[],[f737,f2119]) ).
fof(f737,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f2117,plain,
spl0_220,
inference(avatar_split_clause,[],[f735,f2115]) ).
fof(f735,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,X2,X0)
| c_lessequals(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
fof(f2113,plain,
spl0_219,
inference(avatar_split_clause,[],[f734,f2111]) ).
fof(f2111,plain,
( spl0_219
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f734,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2109,plain,
spl0_218,
inference(avatar_split_clause,[],[f710,f2107]) ).
fof(f710,axiom,
! [X18,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X18,X1,tc_nat),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).
fof(f2100,plain,
spl0_217,
inference(avatar_split_clause,[],[f652,f2098]) ).
fof(f2098,plain,
( spl0_217
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f652,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
fof(f2096,plain,
spl0_216,
inference(avatar_split_clause,[],[f650,f2094]) ).
fof(f2094,plain,
( spl0_216
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f650,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
fof(f2092,plain,
spl0_215,
inference(avatar_split_clause,[],[f581,f2090]) ).
fof(f581,axiom,
! [X2,X1] :
( ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__difference__nat_2) ).
fof(f2088,plain,
spl0_214,
inference(avatar_split_clause,[],[f578,f2086]) ).
fof(f578,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).
fof(f2084,plain,
spl0_213,
inference(avatar_split_clause,[],[f528,f2082]) ).
fof(f528,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2080,plain,
spl0_212,
inference(avatar_split_clause,[],[f527,f2078]) ).
fof(f527,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2076,plain,
spl0_211,
inference(avatar_split_clause,[],[f526,f2074]) ).
fof(f526,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2072,plain,
spl0_210,
inference(avatar_split_clause,[],[f525,f2070]) ).
fof(f525,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f2068,plain,
spl0_209,
inference(avatar_split_clause,[],[f524,f2066]) ).
fof(f524,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f2064,plain,
spl0_208,
inference(avatar_split_clause,[],[f522,f2062]) ).
fof(f2062,plain,
( spl0_208
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f522,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).
fof(f2057,plain,
spl0_207,
inference(avatar_split_clause,[],[f519,f2055]) ).
fof(f519,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).
fof(f2053,plain,
spl0_206,
inference(avatar_split_clause,[],[f517,f2051]) ).
fof(f517,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2049,plain,
spl0_205,
inference(avatar_split_clause,[],[f399,f2047]) ).
fof(f399,axiom,
! [X6,X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f2045,plain,
spl0_204,
inference(avatar_split_clause,[],[f388,f2043]) ).
fof(f388,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
fof(f2041,plain,
spl0_203,
inference(avatar_split_clause,[],[f385,f2039]) ).
fof(f385,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,X1,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
fof(f2037,plain,
spl0_202,
inference(avatar_split_clause,[],[f384,f2035]) ).
fof(f384,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_lessequals(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
fof(f2033,plain,
spl0_201,
inference(avatar_split_clause,[],[f383,f2031]) ).
fof(f383,axiom,
! [X22] : ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__nat__equiv__def2_1) ).
fof(f2029,plain,
spl0_200,
inference(avatar_split_clause,[],[f350,f2027]) ).
fof(f350,axiom,
! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f2025,plain,
spl0_199,
inference(avatar_split_clause,[],[f344,f2023]) ).
fof(f344,axiom,
! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f2021,plain,
spl0_198,
inference(avatar_split_clause,[],[f324,f2019]) ).
fof(f324,axiom,
! [X0] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psize__def_0) ).
fof(f2017,plain,
( spl0_197
| ~ spl0_185
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f1951,f1833,f1738,f2015]) ).
fof(f1951,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_185
| ~ spl0_190 ),
inference(resolution,[],[f1739,f1834]) ).
fof(f2013,plain,
spl0_196,
inference(avatar_split_clause,[],[f287,f2011]) ).
fof(f2011,plain,
( spl0_196
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f287,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2009,plain,
spl0_195,
inference(avatar_split_clause,[],[f242,f2007]) ).
fof(f242,axiom,
! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).
fof(f2005,plain,
spl0_194,
inference(avatar_split_clause,[],[f189,f2003]) ).
fof(f189,axiom,
! [X3,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Oplus__class_Oplus(X1,X3,tc_nat) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f2001,plain,
spl0_193,
inference(avatar_split_clause,[],[f103,f1999]) ).
fof(f103,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_lessequals(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X3,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).
fof(f1997,plain,
spl0_192,
inference(avatar_split_clause,[],[f36,f1995]) ).
fof(f36,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_Divides_Odiv__class_Omod(X5,X6,tc_nat) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).
fof(f1943,plain,
( spl0_191
| ~ spl0_63
| ~ spl0_183 ),
inference(avatar_split_clause,[],[f1927,f1730,f1208,f1941]) ).
fof(f1927,plain,
( ! [X0] : ~ c_lessequals(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_63
| ~ spl0_183 ),
inference(resolution,[],[f1731,f1209]) ).
fof(f1835,plain,
( spl0_190
| ~ spl0_153
| ~ spl0_155 ),
inference(avatar_split_clause,[],[f1783,f1618,f1610,f1833]) ).
fof(f1783,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_153
| ~ spl0_155 ),
inference(resolution,[],[f1619,f1611]) ).
fof(f1756,plain,
spl0_189,
inference(avatar_split_clause,[],[f782,f1754]) ).
fof(f782,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_Suc(X6),X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
fof(f1752,plain,
spl0_188,
inference(avatar_split_clause,[],[f781,f1750]) ).
fof(f781,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_lessequals(c_Suc(X6),X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
fof(f1748,plain,
spl0_187,
inference(avatar_split_clause,[],[f764,f1746]) ).
fof(f764,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f1744,plain,
spl0_186,
inference(avatar_split_clause,[],[f763,f1742]) ).
fof(f763,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X5),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f1740,plain,
spl0_185,
inference(avatar_split_clause,[],[f760,f1738]) ).
fof(f760,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1736,plain,
spl0_184,
inference(avatar_split_clause,[],[f759,f1734]) ).
fof(f759,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X6,c_Suc(X5),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1732,plain,
spl0_183,
inference(avatar_split_clause,[],[f744,f1730]) ).
fof(f744,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_lessequals(X5,c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
fof(f1728,plain,
spl0_182,
inference(avatar_split_clause,[],[f743,f1726]) ).
fof(f743,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_lessequals(c_Suc(X5),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
fof(f1724,plain,
spl0_181,
inference(avatar_split_clause,[],[f673,f1722]) ).
fof(f673,axiom,
! [X0] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).
fof(f1720,plain,
spl0_180,
inference(avatar_split_clause,[],[f672,f1718]) ).
fof(f672,axiom,
! [X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).
fof(f1716,plain,
spl0_179,
inference(avatar_split_clause,[],[f667,f1714]) ).
fof(f667,axiom,
! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f1712,plain,
spl0_178,
inference(avatar_split_clause,[],[f627,f1710]) ).
fof(f627,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).
fof(f1708,plain,
spl0_177,
inference(avatar_split_clause,[],[f622,f1706]) ).
fof(f622,axiom,
! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),X6,tc_nat) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f1704,plain,
spl0_176,
inference(avatar_split_clause,[],[f621,f1702]) ).
fof(f621,axiom,
! [X6,X5] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),X6,tc_nat) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f1700,plain,
spl0_175,
inference(avatar_split_clause,[],[f619,f1698]) ).
fof(f619,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f1696,plain,
( spl0_174
| ~ spl0_34
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f1558,f1505,f1068,f1694]) ).
fof(f1694,plain,
( spl0_174
<=> ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1558,plain,
( ! [X0] : c_Orderings_Oord__class_Omin(X0,X0,tc_nat) = X0
| ~ spl0_34
| ~ spl0_134 ),
inference(resolution,[],[f1506,f1070]) ).
fof(f1692,plain,
spl0_173,
inference(avatar_split_clause,[],[f618,f1690]) ).
fof(f618,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f1688,plain,
spl0_172,
inference(avatar_split_clause,[],[f614,f1686]) ).
fof(f1686,plain,
( spl0_172
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f614,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f1684,plain,
spl0_171,
inference(avatar_split_clause,[],[f611,f1682]) ).
fof(f1682,plain,
( spl0_171
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f611,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f1680,plain,
spl0_170,
inference(avatar_split_clause,[],[f610,f1678]) ).
fof(f610,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f1676,plain,
spl0_169,
inference(avatar_split_clause,[],[f609,f1674]) ).
fof(f609,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f1672,plain,
spl0_168,
inference(avatar_split_clause,[],[f530,f1670]) ).
fof(f1670,plain,
( spl0_168
<=> ! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f530,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X5,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).
fof(f1668,plain,
spl0_167,
inference(avatar_split_clause,[],[f460,f1666]) ).
fof(f460,axiom,
! [X6,X5] : c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) = c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f1664,plain,
spl0_166,
inference(avatar_split_clause,[],[f457,f1662]) ).
fof(f457,axiom,
! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f1660,plain,
spl0_165,
inference(avatar_split_clause,[],[f456,f1658]) ).
fof(f456,axiom,
! [X3,X0] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f1656,plain,
spl0_164,
inference(avatar_split_clause,[],[f454,f1654]) ).
fof(f1654,plain,
( spl0_164
<=> ! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f454,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_1) ).
fof(f1652,plain,
spl0_163,
inference(avatar_split_clause,[],[f453,f1650]) ).
fof(f453,axiom,
! [X2,X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X2,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__product__nat_2) ).
fof(f1648,plain,
spl0_162,
inference(avatar_split_clause,[],[f359,f1646]) ).
fof(f359,axiom,
! [X6,X5] : c_HOL_Otimes__class_Otimes(X5,X6,tc_nat) = c_HOL_Otimes__class_Otimes(X6,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1644,plain,
spl0_161,
inference(avatar_split_clause,[],[f328,f1642]) ).
fof(f328,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
fof(f1640,plain,
spl0_160,
inference(avatar_split_clause,[],[f327,f1638]) ).
fof(f327,axiom,
! [X6,X5] :
( ~ c_lessequals(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_Suc(X6),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
fof(f1636,plain,
spl0_159,
inference(avatar_split_clause,[],[f237,f1634]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
fof(f1632,plain,
spl0_158,
inference(avatar_split_clause,[],[f236,f1630]) ).
fof(f236,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(c_Orderings_Oord__class_Omin(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
fof(f1628,plain,
spl0_157,
inference(avatar_split_clause,[],[f218,f1626]) ).
fof(f218,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X2,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
fof(f1624,plain,
spl0_156,
inference(avatar_split_clause,[],[f217,f1622]) ).
fof(f217,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X1,c_Orderings_Oord__class_Omax(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
fof(f1620,plain,
spl0_155,
inference(avatar_split_clause,[],[f209,f1618]) ).
fof(f209,axiom,
! [X6,X5] :
( c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| ~ c_lessequals(c_Suc(X6),X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
fof(f1616,plain,
spl0_154,
inference(avatar_split_clause,[],[f208,f1614]) ).
fof(f208,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X5,tc_nat)
| c_lessequals(c_Suc(X6),X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
fof(f1612,plain,
( spl0_153
| ~ spl0_64
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1579,f1545,f1212,f1610]) ).
fof(f1579,plain,
( ! [X0] : c_lessequals(X0,c_Suc(X0),tc_nat)
| ~ spl0_64
| ~ spl0_144 ),
inference(resolution,[],[f1546,f1213]) ).
fof(f1608,plain,
spl0_152,
inference(avatar_split_clause,[],[f179,f1606]) ).
fof(f1606,plain,
( spl0_152
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f179,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).
fof(f1604,plain,
spl0_151,
inference(avatar_split_clause,[],[f178,f1602]) ).
fof(f178,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f1600,plain,
spl0_150,
inference(avatar_split_clause,[],[f176,f1598]) ).
fof(f176,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f1596,plain,
spl0_149,
inference(avatar_split_clause,[],[f166,f1594]) ).
fof(f166,axiom,
! [X22] : c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),X22,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__nat__equiv__def2_1) ).
fof(f1592,plain,
spl0_148,
inference(avatar_split_clause,[],[f34,f1590]) ).
fof(f34,axiom,
! [X6] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| ~ c_lessequals(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
fof(f1572,plain,
( spl0_147
| ~ spl0_34
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1556,f1501,f1068,f1570]) ).
fof(f1570,plain,
( spl0_147
<=> ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1556,plain,
( ! [X0] : c_Orderings_Oord__class_Omax(X0,X0,tc_nat) = X0
| ~ spl0_34
| ~ spl0_133 ),
inference(resolution,[],[f1502,f1070]) ).
fof(f1555,plain,
spl0_146,
inference(avatar_split_clause,[],[f751,f1553]) ).
fof(f1553,plain,
( spl0_146
<=> ! [X2,X1] :
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f751,axiom,
! [X2,X1] :
( X1 = X2
| c_Suc(X1) != c_Suc(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f1551,plain,
spl0_145,
inference(avatar_split_clause,[],[f736,f1549]) ).
fof(f736,axiom,
! [X6,X5] :
( c_lessequals(X5,X6,tc_nat)
| c_lessequals(X6,X5,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
fof(f1547,plain,
spl0_144,
inference(avatar_split_clause,[],[f651,f1545]) ).
fof(f651,axiom,
! [X6,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_lessequals(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
fof(f1543,plain,
spl0_143,
inference(avatar_split_clause,[],[f566,f1541]) ).
fof(f566,axiom,
! [X6] :
( c_Parity_Oeven__odd__class_Oeven(X6,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_odd__pos_0) ).
fof(f1539,plain,
spl0_142,
inference(avatar_split_clause,[],[f521,f1537]) ).
fof(f521,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f1535,plain,
spl0_141,
inference(avatar_split_clause,[],[f520,f1533]) ).
fof(f520,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f1531,plain,
spl0_140,
inference(avatar_split_clause,[],[f419,f1529]) ).
fof(f419,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f1527,plain,
spl0_139,
inference(avatar_split_clause,[],[f326,f1525]) ).
fof(f326,axiom,
! [X6,X5] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1523,plain,
spl0_138,
inference(avatar_split_clause,[],[f223,f1521]) ).
fof(f223,axiom,
! [X1,X5] : c_HOL_Oord__class_Oless(X5,c_Suc(c_HOL_Oplus__class_Oplus(X5,X1,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1519,plain,
spl0_137,
inference(avatar_split_clause,[],[f222,f1517]) ).
fof(f222,axiom,
! [X9,X5] : c_HOL_Oord__class_Oless(X9,c_Suc(c_HOL_Oplus__class_Oplus(X5,X9,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1515,plain,
spl0_136,
inference(avatar_split_clause,[],[f174,f1513]) ).
fof(f174,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0R_0) ).
fof(f1511,plain,
spl0_135,
inference(avatar_split_clause,[],[f173,f1509]) ).
fof(f173,axiom,
! [X6] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Orderings_Oord__class_Omin(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__0L_0) ).
fof(f1507,plain,
spl0_134,
inference(avatar_split_clause,[],[f35,f1505]) ).
fof(f35,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omin(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
fof(f1503,plain,
spl0_133,
inference(avatar_split_clause,[],[f18,f1501]) ).
fof(f18,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_Orderings_Oord__class_Omax(X1,X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
fof(f1488,plain,
spl0_132,
inference(avatar_split_clause,[],[f785,f1486]) ).
fof(f1486,plain,
( spl0_132
<=> ! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f785,axiom,
! [X1] :
( c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_1) ).
fof(f1484,plain,
spl0_131,
inference(avatar_split_clause,[],[f784,f1482]) ).
fof(f1482,plain,
( spl0_131
<=> ! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f784,axiom,
! [X1] :
( ~ c_Parity_Oeven__odd__class_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven__odd__class_Oeven(c_Suc(X1),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__Suc_0) ).
fof(f1480,plain,
spl0_130,
inference(avatar_split_clause,[],[f680,f1478]) ).
fof(f680,axiom,
! [X10,X9] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X10,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f1476,plain,
spl0_129,
inference(avatar_split_clause,[],[f679,f1474]) ).
fof(f679,axiom,
! [X10,X9] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X10,X9,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f1472,plain,
spl0_128,
inference(avatar_split_clause,[],[f644,f1470]) ).
fof(f644,axiom,
! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X6,X5,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f1468,plain,
spl0_127,
inference(avatar_split_clause,[],[f643,f1466]) ).
fof(f643,axiom,
! [X6,X5] : c_lessequals(X6,c_HOL_Oplus__class_Oplus(X5,X6,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).
fof(f1464,plain,
spl0_126,
inference(avatar_split_clause,[],[f617,f1462]) ).
fof(f617,axiom,
! [X6] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f1460,plain,
spl0_125,
inference(avatar_split_clause,[],[f616,f1458]) ).
fof(f616,axiom,
! [X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f1456,plain,
spl0_124,
inference(avatar_split_clause,[],[f580,f1454]) ).
fof(f580,axiom,
! [X5] : c_lessequals(X5,c_HOL_Otimes__class_Otimes(X5,X5,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).
fof(f1452,plain,
spl0_123,
inference(avatar_split_clause,[],[f567,f1450]) ).
fof(f567,axiom,
! [X6,X5] : c_lessequals(c_Divides_Odiv__class_Omod(X5,X6,tc_nat),X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).
fof(f1448,plain,
spl0_122,
inference(avatar_split_clause,[],[f434,f1446]) ).
fof(f434,axiom,
! [X6,X5] : c_lessequals(c_HOL_Ominus__class_Ominus(X5,X6,tc_nat),X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).
fof(f1444,plain,
spl0_121,
inference(avatar_split_clause,[],[f266,f1442]) ).
fof(f1442,plain,
( spl0_121
<=> ! [X6] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f266,axiom,
! [X6] : c_Orderings_Oord__class_Omax(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0L_0) ).
fof(f1440,plain,
spl0_120,
inference(avatar_split_clause,[],[f265,f1438]) ).
fof(f1438,plain,
( spl0_120
<=> ! [X6] : c_Orderings_Oord__class_Omax(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f265,axiom,
! [X6] : c_Orderings_Oord__class_Omax(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__0R_0) ).
fof(f1436,plain,
spl0_119,
inference(avatar_split_clause,[],[f182,f1434]) ).
fof(f182,axiom,
! [X5] : c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f1432,plain,
spl0_118,
inference(avatar_split_clause,[],[f181,f1430]) ).
fof(f181,axiom,
! [X5] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X5,X5,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f1428,plain,
~ spl0_117,
inference(avatar_split_clause,[],[f787,f1425]) ).
fof(f787,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dp_0) ).
fof(f1423,plain,
spl0_116,
inference(avatar_split_clause,[],[f696,f1421]) ).
fof(f696,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
fof(f1419,plain,
spl0_115,
inference(avatar_split_clause,[],[f695,f1417]) ).
fof(f695,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| c_lessequals(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
fof(f1415,plain,
spl0_114,
inference(avatar_split_clause,[],[f537,f1413]) ).
fof(f1413,plain,
( spl0_114
<=> ! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f537,axiom,
! [X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1411,plain,
spl0_113,
inference(avatar_split_clause,[],[f534,f1409]) ).
fof(f1409,plain,
( spl0_113
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f534,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1407,plain,
spl0_112,
inference(avatar_split_clause,[],[f533,f1405]) ).
fof(f533,axiom,
! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1403,plain,
spl0_111,
inference(avatar_split_clause,[],[f424,f1401]) ).
fof(f424,axiom,
! [X6] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X6),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f1399,plain,
spl0_110,
inference(avatar_split_clause,[],[f891,f1397]) ).
fof(f891,axiom,
! [X34] :
( ~ class_HOL_Ozero(X34)
| class_HOL_Ozero(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).
fof(f1395,plain,
spl0_109,
inference(avatar_split_clause,[],[f890,f1393]) ).
fof(f1393,plain,
( spl0_109
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f890,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f1391,plain,
spl0_108,
inference(avatar_split_clause,[],[f889,f1389]) ).
fof(f1389,plain,
( spl0_108
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f889,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f1387,plain,
spl0_107,
inference(avatar_split_clause,[],[f888,f1385]) ).
fof(f1385,plain,
( spl0_107
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f888,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Oring__div) ).
fof(f1383,plain,
spl0_106,
inference(avatar_split_clause,[],[f887,f1381]) ).
fof(f887,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f1379,plain,
spl0_105,
inference(avatar_split_clause,[],[f886,f1377]) ).
fof(f1377,plain,
( spl0_105
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f886,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f1375,plain,
spl0_104,
inference(avatar_split_clause,[],[f885,f1373]) ).
fof(f1373,plain,
( spl0_104
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f885,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).
fof(f1371,plain,
spl0_103,
inference(avatar_split_clause,[],[f884,f1369]) ).
fof(f1369,plain,
( spl0_103
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f884,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).
fof(f1367,plain,
spl0_102,
inference(avatar_split_clause,[],[f883,f1365]) ).
fof(f883,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f1363,plain,
spl0_101,
inference(avatar_split_clause,[],[f882,f1361]) ).
fof(f882,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).
fof(f1359,plain,
spl0_100,
inference(avatar_split_clause,[],[f881,f1357]) ).
fof(f881,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).
fof(f1355,plain,
spl0_99,
inference(avatar_split_clause,[],[f880,f1353]) ).
fof(f1353,plain,
( spl0_99
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f880,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).
fof(f1351,plain,
spl0_98,
inference(avatar_split_clause,[],[f879,f1349]) ).
fof(f1349,plain,
( spl0_98
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f879,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).
fof(f1347,plain,
spl0_97,
inference(avatar_split_clause,[],[f878,f1345]) ).
fof(f878,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).
fof(f1343,plain,
spl0_96,
inference(avatar_split_clause,[],[f877,f1341]) ).
fof(f877,axiom,
! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).
fof(f1339,plain,
spl0_95,
inference(avatar_split_clause,[],[f876,f1337]) ).
fof(f1337,plain,
( spl0_95
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f876,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).
fof(f1335,plain,
spl0_94,
inference(avatar_split_clause,[],[f875,f1333]) ).
fof(f1333,plain,
( spl0_94
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f875,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).
fof(f1331,plain,
spl0_93,
inference(avatar_split_clause,[],[f874,f1329]) ).
fof(f874,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).
fof(f1327,plain,
spl0_92,
inference(avatar_split_clause,[],[f873,f1325]) ).
fof(f1325,plain,
( spl0_92
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f873,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).
fof(f1323,plain,
spl0_91,
inference(avatar_split_clause,[],[f872,f1321]) ).
fof(f1321,plain,
( spl0_91
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f872,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).
fof(f1319,plain,
spl0_90,
inference(avatar_split_clause,[],[f871,f1317]) ).
fof(f1317,plain,
( spl0_90
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f871,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).
fof(f1315,plain,
spl0_89,
inference(avatar_split_clause,[],[f870,f1313]) ).
fof(f1313,plain,
( spl0_89
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f870,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).
fof(f1311,plain,
spl0_88,
inference(avatar_split_clause,[],[f869,f1309]) ).
fof(f1309,plain,
( spl0_88
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f869,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1307,plain,
spl0_87,
inference(avatar_split_clause,[],[f868,f1305]) ).
fof(f868,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1303,plain,
spl0_86,
inference(avatar_split_clause,[],[f867,f1301]) ).
fof(f1301,plain,
( spl0_86
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f867,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).
fof(f1299,plain,
spl0_85,
inference(avatar_split_clause,[],[f866,f1297]) ).
fof(f1297,plain,
( spl0_85
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f866,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).
fof(f1295,plain,
spl0_84,
inference(avatar_split_clause,[],[f865,f1293]) ).
fof(f1293,plain,
( spl0_84
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f865,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).
fof(f1291,plain,
spl0_83,
inference(avatar_split_clause,[],[f864,f1289]) ).
fof(f1289,plain,
( spl0_83
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f864,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).
fof(f1287,plain,
spl0_82,
inference(avatar_split_clause,[],[f863,f1285]) ).
fof(f1285,plain,
( spl0_82
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f863,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1283,plain,
spl0_81,
inference(avatar_split_clause,[],[f862,f1281]) ).
fof(f862,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).
fof(f1279,plain,
spl0_80,
inference(avatar_split_clause,[],[f861,f1277]) ).
fof(f1277,plain,
( spl0_80
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f861,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).
fof(f1275,plain,
spl0_79,
inference(avatar_split_clause,[],[f860,f1273]) ).
fof(f1273,plain,
( spl0_79
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f860,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).
fof(f1271,plain,
spl0_78,
inference(avatar_split_clause,[],[f859,f1269]) ).
fof(f1269,plain,
( spl0_78
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f859,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1267,plain,
spl0_77,
inference(avatar_split_clause,[],[f858,f1265]) ).
fof(f858,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1263,plain,
spl0_76,
inference(avatar_split_clause,[],[f857,f1261]) ).
fof(f1261,plain,
( spl0_76
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f857,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1259,plain,
spl0_75,
inference(avatar_split_clause,[],[f856,f1257]) ).
fof(f1257,plain,
( spl0_75
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f856,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f1255,plain,
spl0_74,
inference(avatar_split_clause,[],[f855,f1253]) ).
fof(f1253,plain,
( spl0_74
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f855,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1251,plain,
spl0_73,
inference(avatar_split_clause,[],[f854,f1249]) ).
fof(f1249,plain,
( spl0_73
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f854,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f1247,plain,
spl0_72,
inference(avatar_split_clause,[],[f853,f1245]) ).
fof(f1245,plain,
( spl0_72
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f853,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1243,plain,
spl0_71,
inference(avatar_split_clause,[],[f852,f1241]) ).
fof(f1241,plain,
( spl0_71
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f852,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1239,plain,
spl0_70,
inference(avatar_split_clause,[],[f851,f1237]) ).
fof(f1237,plain,
( spl0_70
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f851,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1235,plain,
spl0_69,
inference(avatar_split_clause,[],[f796,f1233]) ).
fof(f1233,plain,
( spl0_69
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f796,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).
fof(f1231,plain,
spl0_68,
inference(avatar_split_clause,[],[f795,f1229]) ).
fof(f1229,plain,
( spl0_68
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f795,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).
fof(f1227,plain,
spl0_67,
inference(avatar_split_clause,[],[f794,f1225]) ).
fof(f1225,plain,
( spl0_67
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f794,axiom,
! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f1223,plain,
spl0_66,
inference(avatar_split_clause,[],[f774,f1221]) ).
fof(f1221,plain,
( spl0_66
<=> ! [X32] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f774,axiom,
! [X32] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
fof(f1219,plain,
~ spl0_65,
inference(avatar_split_clause,[],[f772,f1216]) ).
fof(f1216,plain,
( spl0_65
<=> v_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f772,axiom,
v_p != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pe_0) ).
fof(f1214,plain,
spl0_64,
inference(avatar_split_clause,[],[f769,f1212]) ).
fof(f769,axiom,
! [X6] : c_HOL_Oord__class_Oless(X6,c_Suc(X6),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
fof(f1210,plain,
spl0_63,
inference(avatar_split_clause,[],[f742,f1208]) ).
fof(f742,axiom,
! [X6] : ~ c_lessequals(c_Suc(X6),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
fof(f1206,plain,
spl0_62,
inference(avatar_split_clause,[],[f562,f1204]) ).
fof(f562,axiom,
! [X6] : c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
fof(f1202,plain,
spl0_61,
inference(avatar_split_clause,[],[f320,f1200]) ).
fof(f1200,plain,
( spl0_61
<=> ! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f320,axiom,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f1198,plain,
spl0_60,
inference(avatar_split_clause,[],[f765,f1196]) ).
fof(f1196,plain,
( spl0_60
<=> ! [X6] : c_Suc(X6) != X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f765,axiom,
! [X6] : c_Suc(X6) != X6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1194,plain,
spl0_59,
inference(avatar_split_clause,[],[f699,f1192]) ).
fof(f699,axiom,
! [X6] : c_lessequals(X6,X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
fof(f1190,plain,
spl0_58,
inference(avatar_split_clause,[],[f535,f1188]) ).
fof(f1188,plain,
( spl0_58
<=> ! [X6] : ~ c_HOL_Oord__class_Oless(X6,X6,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f535,axiom,
! [X6] : ~ c_HOL_Oord__class_Oless(X6,X6,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f1186,plain,
spl0_57,
inference(avatar_split_clause,[],[f501,f1183]) ).
fof(f1183,plain,
( spl0_57
<=> c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f501,axiom,
c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__zero__nat_0) ).
fof(f1181,plain,
spl0_56,
inference(avatar_split_clause,[],[f850,f1178]) ).
fof(f850,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1176,plain,
spl0_55,
inference(avatar_split_clause,[],[f849,f1173]) ).
fof(f849,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1171,plain,
spl0_54,
inference(avatar_split_clause,[],[f848,f1168]) ).
fof(f1168,plain,
( spl0_54
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f848,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1166,plain,
spl0_53,
inference(avatar_split_clause,[],[f847,f1163]) ).
fof(f847,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1161,plain,
spl0_52,
inference(avatar_split_clause,[],[f846,f1158]) ).
fof(f846,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1156,plain,
spl0_51,
inference(avatar_split_clause,[],[f845,f1153]) ).
fof(f845,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1151,plain,
spl0_50,
inference(avatar_split_clause,[],[f844,f1148]) ).
fof(f1148,plain,
( spl0_50
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f844,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1146,plain,
spl0_49,
inference(avatar_split_clause,[],[f843,f1143]) ).
fof(f1143,plain,
( spl0_49
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f843,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).
fof(f1141,plain,
spl0_48,
inference(avatar_split_clause,[],[f842,f1138]) ).
fof(f842,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1136,plain,
spl0_47,
inference(avatar_split_clause,[],[f841,f1133]) ).
fof(f1133,plain,
( spl0_47
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f841,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1131,plain,
spl0_46,
inference(avatar_split_clause,[],[f840,f1128]) ).
fof(f1128,plain,
( spl0_46
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f840,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).
fof(f1126,plain,
spl0_45,
inference(avatar_split_clause,[],[f839,f1123]) ).
fof(f1123,plain,
( spl0_45
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f839,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1121,plain,
spl0_44,
inference(avatar_split_clause,[],[f838,f1118]) ).
fof(f1118,plain,
( spl0_44
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f838,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1116,plain,
spl0_43,
inference(avatar_split_clause,[],[f837,f1113]) ).
fof(f837,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1111,plain,
spl0_42,
inference(avatar_split_clause,[],[f836,f1108]) ).
fof(f836,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1106,plain,
spl0_41,
inference(avatar_split_clause,[],[f835,f1103]) ).
fof(f835,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1101,plain,
spl0_40,
inference(avatar_split_clause,[],[f834,f1098]) ).
fof(f1098,plain,
( spl0_40
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f834,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).
fof(f1096,plain,
spl0_39,
inference(avatar_split_clause,[],[f833,f1093]) ).
fof(f1093,plain,
( spl0_39
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f833,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1091,plain,
spl0_38,
inference(avatar_split_clause,[],[f832,f1088]) ).
fof(f1088,plain,
( spl0_38
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f832,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1086,plain,
spl0_37,
inference(avatar_split_clause,[],[f831,f1083]) ).
fof(f1083,plain,
( spl0_37
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f831,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1081,plain,
spl0_36,
inference(avatar_split_clause,[],[f830,f1078]) ).
fof(f830,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
fof(f1076,plain,
spl0_35,
inference(avatar_split_clause,[],[f829,f1073]) ).
fof(f1073,plain,
( spl0_35
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f829,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1071,plain,
spl0_34,
inference(avatar_split_clause,[],[f828,f1068]) ).
fof(f828,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1066,plain,
spl0_33,
inference(avatar_split_clause,[],[f827,f1063]) ).
fof(f827,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1061,plain,
spl0_32,
inference(avatar_split_clause,[],[f826,f1058]) ).
fof(f826,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1056,plain,
spl0_31,
inference(avatar_split_clause,[],[f825,f1053]) ).
fof(f1053,plain,
( spl0_31
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f825,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1051,plain,
spl0_30,
inference(avatar_split_clause,[],[f824,f1048]) ).
fof(f1048,plain,
( spl0_30
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f824,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1046,plain,
spl0_29,
inference(avatar_split_clause,[],[f823,f1043]) ).
fof(f1043,plain,
( spl0_29
<=> class_Ring__and__Field_Omult__mono(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f823,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).
fof(f1041,plain,
spl0_28,
inference(avatar_split_clause,[],[f822,f1038]) ).
fof(f1038,plain,
( spl0_28
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f822,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1036,plain,
spl0_27,
inference(avatar_split_clause,[],[f821,f1033]) ).
fof(f1033,plain,
( spl0_27
<=> class_Ring__and__Field_Omult__mono1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f821,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).
fof(f1031,plain,
spl0_26,
inference(avatar_split_clause,[],[f820,f1028]) ).
fof(f1028,plain,
( spl0_26
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f820,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1026,plain,
spl0_25,
inference(avatar_split_clause,[],[f819,f1023]) ).
fof(f1023,plain,
( spl0_25
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f819,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1021,plain,
spl0_24,
inference(avatar_split_clause,[],[f818,f1018]) ).
fof(f1018,plain,
( spl0_24
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f818,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1016,plain,
spl0_23,
inference(avatar_split_clause,[],[f817,f1013]) ).
fof(f1013,plain,
( spl0_23
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f817,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1011,plain,
spl0_22,
inference(avatar_split_clause,[],[f816,f1008]) ).
fof(f816,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1006,plain,
spl0_21,
inference(avatar_split_clause,[],[f815,f1003]) ).
fof(f1003,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f815,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1001,plain,
spl0_20,
inference(avatar_split_clause,[],[f814,f998]) ).
fof(f998,plain,
( spl0_20
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f814,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f996,plain,
spl0_19,
inference(avatar_split_clause,[],[f813,f993]) ).
fof(f993,plain,
( spl0_19
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f813,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f991,plain,
spl0_18,
inference(avatar_split_clause,[],[f812,f988]) ).
fof(f988,plain,
( spl0_18
<=> class_Ring__and__Field_Oordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f812,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).
fof(f986,plain,
spl0_17,
inference(avatar_split_clause,[],[f811,f983]) ).
fof(f983,plain,
( spl0_17
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f811,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).
fof(f981,plain,
spl0_16,
inference(avatar_split_clause,[],[f810,f978]) ).
fof(f978,plain,
( spl0_16
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f810,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f976,plain,
spl0_15,
inference(avatar_split_clause,[],[f809,f973]) ).
fof(f973,plain,
( spl0_15
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f809,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f971,plain,
spl0_14,
inference(avatar_split_clause,[],[f808,f968]) ).
fof(f968,plain,
( spl0_14
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f808,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f966,plain,
spl0_13,
inference(avatar_split_clause,[],[f807,f963]) ).
fof(f963,plain,
( spl0_13
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f807,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).
fof(f961,plain,
spl0_12,
inference(avatar_split_clause,[],[f806,f958]) ).
fof(f958,plain,
( spl0_12
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f806,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f956,plain,
spl0_11,
inference(avatar_split_clause,[],[f805,f953]) ).
fof(f953,plain,
( spl0_11
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f805,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).
fof(f951,plain,
spl0_10,
inference(avatar_split_clause,[],[f804,f948]) ).
fof(f948,plain,
( spl0_10
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f804,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f946,plain,
spl0_9,
inference(avatar_split_clause,[],[f803,f943]) ).
fof(f943,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f803,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f941,plain,
spl0_8,
inference(avatar_split_clause,[],[f802,f938]) ).
fof(f802,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f936,plain,
spl0_7,
inference(avatar_split_clause,[],[f801,f933]) ).
fof(f933,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f801,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f931,plain,
spl0_6,
inference(avatar_split_clause,[],[f800,f928]) ).
fof(f928,plain,
( spl0_6
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f800,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).
fof(f926,plain,
spl0_5,
inference(avatar_split_clause,[],[f799,f923]) ).
fof(f923,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f799,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).
fof(f921,plain,
spl0_4,
inference(avatar_split_clause,[],[f798,f918]) ).
fof(f918,plain,
( spl0_4
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f798,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f916,plain,
spl0_3,
inference(avatar_split_clause,[],[f797,f913]) ).
fof(f913,plain,
( spl0_3
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f797,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f911,plain,
( spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f793,f904,f909]) ).
fof(f904,plain,
( spl0_1
<=> v_thesis____ ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f793,axiom,
! [X1] :
( v_thesis____
| c_Suc(X1) != c_Polynomial_Odegree(v_p,tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f907,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f792,f904]) ).
fof(f792,axiom,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ALG428-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n008.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Fri May 3 19:56:38 EDT 2024
% 0.14/0.38 % CPUTime :
% 0.21/0.38 % (20046)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.44 % (20049)WARNING: value z3 for option sas not known
% 0.21/0.45 % (20049)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.45 % (20050)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.45 % (20048)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.45 % (20051)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.45 % (20052)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.45 % (20053)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.45 % (20047)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.52 TRYING [1]
% 0.83/0.54 TRYING [2]
% 1.89/0.72 TRYING [1]
% 2.34/0.75 TRYING [2]
% 2.45/0.77 TRYING [3]
% 8.09/1.61 TRYING [3]
% 8.09/1.62 TRYING [1]
% 8.09/1.63 TRYING [2]
% 9.83/1.84 TRYING [3]
% 14.53/2.53 TRYING [4]
% 22.96/3.75 % (20051)First to succeed.
% 23.49/3.81 % (20051)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20046"
% 23.49/3.81 % (20051)Refutation found. Thanks to Tanya!
% 23.49/3.81 % SZS status Unsatisfiable for theBenchmark
% 23.49/3.81 % SZS output start Proof for theBenchmark
% See solution above
% 23.49/3.84 % (20051)------------------------------
% 23.49/3.84 % (20051)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 23.49/3.84 % (20051)Termination reason: Refutation
% 23.49/3.84
% 23.49/3.84 % (20051)Memory used [KB]: 24519
% 23.49/3.84 % (20051)Time elapsed: 3.361 s
% 23.49/3.84 % (20051)Instructions burned: 6182 (million)
% 23.49/3.84 % (20046)Success in time 3.414 s
%------------------------------------------------------------------------------