TSTP Solution File: ALG432-1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG432-1 : 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 : n018.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 04:30:28 EDT 2024
% Result : Unsatisfiable 14.48s 2.47s
% Output : Refutation 14.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2436
% Syntax : Number of formulae : 5346 ( 999 unt; 0 def)
% Number of atoms : 15533 (2643 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 18671 (8484 ~;8588 |; 0 &)
% (1599 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 11 ( 1 avg)
% Number of predicates : 1678 (1676 usr;1600 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 7 con; 0-3 aty)
% Number of variables : 8371 (8371 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f58760,plain,
$false,
inference(avatar_sat_refutation,[],[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,f1191,f1196,f1201,f1206,f1211,f1216,f1221,f1226,f1231,f1236,f1241,f1246,f1251,f1256,f1261,f1266,f1271,f1276,f1281,f1286,f1291,f1296,f1301,f1306,f1311,f1316,f1321,f1326,f1331,f1336,f1341,f1346,f1351,f1356,f1361,f1366,f1371,f1376,f1381,f1386,f1391,f1396,f1401,f1406,f1411,f1416,f1421,f1426,f1431,f1436,f1441,f1446,f1451,f1456,f1461,f1466,f1471,f1476,f1481,f1486,f1491,f1496,f1501,f1506,f1511,f1516,f1521,f1526,f1531,f1536,f1541,f1546,f1551,f1556,f1561,f1566,f1571,f1576,f1581,f1586,f1591,f1596,f1601,f1606,f1611,f1616,f1621,f1626,f1631,f1636,f1641,f1646,f1651,f1656,f1661,f1666,f1671,f1676,f1681,f1686,f1691,f1696,f1701,f1705,f1710,f1715,f1719,f1723,f1727,f1731,f1735,f1739,f1743,f1747,f1751,f1755,f1759,f1763,f1767,f1771,f1775,f1779,f1783,f1787,f1791,f1795,f1799,f1803,f1807,f1811,f1815,f1819,f1823,f1827,f1831,f1835,f1839,f1843,f1847,f1851,f1855,f1859,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1899,f1903,f1907,f1911,f1915,f1919,f1923,f1927,f1931,f1935,f1940,f1944,f1948,f1952,f1956,f1960,f1965,f1971,f1975,f1979,f1983,f1987,f1991,f1995,f1999,f2003,f2007,f2011,f2018,f2031,f2035,f2039,f2043,f2047,f2051,f2055,f2059,f2063,f2067,f2071,f2075,f2079,f2083,f2087,f2091,f2095,f2099,f2103,f2107,f2111,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2143,f2147,f2151,f2155,f2159,f2163,f2167,f2171,f2175,f2179,f2183,f2187,f2191,f2195,f2199,f2203,f2288,f2311,f2315,f2319,f2323,f2327,f2331,f2335,f2339,f2343,f2347,f2351,f2355,f2359,f2363,f2367,f2371,f2375,f2379,f2383,f2387,f2391,f2395,f2399,f2403,f2407,f2411,f2415,f2419,f2423,f2443,f2477,f2495,f2499,f2503,f2507,f2511,f2515,f2519,f2523,f2527,f2531,f2535,f2539,f2543,f2547,f2551,f2555,f2559,f2563,f2567,f2571,f2575,f2579,f2583,f2587,f2591,f2595,f2599,f2603,f2607,f2611,f2615,f2619,f2623,f2627,f2631,f2635,f2639,f2648,f2652,f2656,f2660,f2664,f2673,f2703,f2737,f2773,f2787,f2791,f2795,f2799,f2803,f2807,f2811,f2815,f2819,f2823,f2827,f2831,f2835,f2839,f2843,f2847,f2851,f2855,f2859,f2863,f2867,f2871,f2875,f2879,f2883,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2934,f2969,f3004,f3036,f3040,f3044,f3048,f3052,f3056,f3060,f3064,f3068,f3072,f3077,f3081,f3085,f3089,f3093,f3097,f3101,f3105,f3109,f3113,f3117,f3122,f3126,f3130,f3134,f3138,f3142,f3146,f3150,f3154,f3158,f3162,f3166,f3170,f3174,f3178,f3182,f3186,f3190,f3194,f3198,f3202,f3206,f3210,f3214,f3285,f3382,f3419,f3459,f3467,f3471,f3475,f3479,f3483,f3487,f3491,f3495,f3499,f3513,f3517,f3521,f3525,f3529,f3533,f3537,f3541,f3545,f3549,f3553,f3557,f3561,f3565,f3569,f3573,f3577,f3581,f3585,f3589,f3593,f3597,f3601,f3605,f3609,f3613,f3617,f3621,f3625,f3629,f3633,f3637,f3641,f3645,f3649,f3653,f3657,f3661,f3665,f3669,f3673,f3677,f3681,f3685,f3689,f3731,f3789,f3864,f3922,f3973,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4507,f4511,f4516,f4625,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4777,f4781,f4785,f4789,f4793,f4797,f4801,f4805,f4809,f4813,f4817,f4821,f4825,f4829,f4833,f4837,f4841,f4845,f4849,f4853,f4857,f4873,f4877,f4881,f4885,f4889,f4893,f4897,f4901,f4905,f4909,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5485,f5489,f5493,f5497,f5501,f5505,f5509,f5513,f5528,f5532,f5536,f5540,f5544,f5548,f5552,f5556,f5564,f5777,f5781,f5785,f5789,f5801,f5805,f5809,f5813,f5817,f5821,f5825,f5829,f5833,f5837,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5889,f5893,f5897,f6168,f6172,f6176,f6180,f6184,f6188,f6192,f6196,f6200,f6204,f6223,f6227,f6231,f6235,f6239,f6243,f6247,f6251,f6255,f6259,f6276,f6280,f6284,f6288,f6292,f6296,f6300,f6304,f6308,f6312,f6331,f6335,f6339,f6343,f6347,f6351,f6355,f6359,f6363,f6367,f6386,f6390,f6394,f6398,f6402,f6406,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6446,f6450,f6454,f6458,f6462,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f7320,f7350,f7354,f7358,f7362,f7366,f7370,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7441,f7445,f7449,f7453,f7457,f7461,f7465,f7469,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7783,f8024,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8344,f8486,f8490,f8494,f8498,f8502,f8506,f8510,f8514,f8518,f8522,f8526,f8530,f8534,f8538,f8621,f8634,f8638,f8642,f8646,f8650,f8654,f8658,f8662,f8666,f8670,f8766,f8776,f8780,f8784,f8788,f8792,f8796,f8814,f8864,f8868,f8872,f8876,f8880,f8884,f8888,f8892,f8896,f8900,f8904,f8908,f9040,f9104,f9108,f9112,f9116,f9120,f9124,f9128,f9132,f9136,f9140,f9144,f9148,f9152,f9156,f9160,f9164,f9503,f9611,f9615,f9619,f9713,f9717,f9721,f9725,f9729,f9884,f9888,f9892,f9896,f9900,f9904,f9908,f10177,f10181,f10185,f10189,f10201,f10205,f10209,f10213,f10217,f10274,f10278,f10286,f10292,f10296,f10300,f11654,f11744,f11748,f11752,f11756,f11760,f11764,f11789,f11793,f11797,f11801,f11805,f11809,f11813,f11817,f11821,f11825,f11855,f11885,f11889,f11893,f11898,f11904,f11909,f11913,f11917,f11921,f11925,f11929,f11933,f11937,f11941,f11945,f11949,f11953,f11978,f11982,f11986,f11990,f11994,f11998,f12002,f12006,f12010,f12014,f12018,f12022,f12026,f12030,f12034,f12038,f12042,f12305,f13444,f13996,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14275,f14279,f14283,f14340,f14397,f14401,f14405,f14409,f14413,f14417,f14421,f14425,f14429,f14816,f14906,f14910,f14914,f14918,f14922,f14926,f14930,f14934,f14938,f14942,f14946,f14950,f14954,f14958,f14962,f14966,f14970,f14981,f14985,f14989,f14993,f14997,f15001,f15005,f15009,f15013,f15017,f15022,f15026,f15030,f15034,f15038,f15042,f15046,f15050,f15054,f15058,f15062,f15076,f15095,f15114,f15133,f15137,f15141,f15145,f15154,f15158,f15162,f15166,f15170,f15174,f15178,f15182,f15186,f15190,f15194,f15198,f15203,f15208,f15213,f15217,f15221,f15276,f16111,f17356,f17400,f17404,f17408,f17412,f17416,f17420,f17424,f17433,f17437,f17441,f17445,f17449,f17453,f17457,f17461,f17465,f17469,f17473,f17477,f17481,f17485,f17489,f17493,f17497,f17501,f17505,f17509,f17513,f17523,f17639,f18265,f18292,f18296,f18300,f18304,f18308,f18312,f18316,f18320,f18324,f18328,f18355,f18359,f18363,f18367,f18371,f18375,f18379,f18383,f18387,f18391,f18395,f18399,f18403,f18407,f18411,f18415,f18419,f18423,f18427,f18472,f18476,f18518,f18559,f18600,f18604,f18608,f18612,f18616,f18644,f18648,f18652,f18656,f18660,f18665,f18670,f18674,f18678,f18682,f18686,f18690,f18694,f18698,f18702,f18706,f18710,f18714,f18718,f18722,f18726,f18755,f18759,f18763,f18802,f18806,f18810,f18844,f18878,f18882,f18886,f18890,f18894,f18898,f18902,f19011,f20503,f20603,f20607,f23043,f23620,f23624,f23628,f23632,f23636,f23640,f23644,f23648,f23652,f23656,f23660,f23664,f23668,f23672,f23676,f23680,f23684,f23688,f23692,f23696,f23735,f23739,f23743,f23747,f23751,f23755,f23759,f23763,f23767,f23771,f23776,f23780,f23784,f23788,f23792,f23796,f23827,f23857,f23903,f23907,f23911,f23915,f23919,f23923,f23927,f23931,f23935,f23939,f23943,f23947,f23951,f23955,f23959,f23976,f24028,f25886,f25953,f25957,f25961,f25965,f25969,f25973,f25977,f25983,f25987,f25991,f25995,f25999,f26003,f26007,f26011,f26015,f26019,f26042,f26046,f26050,f26054,f26058,f26062,f26066,f26070,f26074,f26078,f26086,f26090,f26094,f26098,f26102,f26106,f26110,f26114,f26118,f26122,f26168,f26210,f26214,f26218,f26222,f26226,f26230,f26234,f26238,f26242,f26246,f26250,f26254,f26258,f26262,f26266,f26270,f26274,f26278,f26282,f26286,f26290,f26294,f26298,f26302,f26306,f26310,f26314,f26318,f26322,f26326,f26372,f26376,f26380,f26384,f26388,f26392,f26396,f26400,f26404,f26408,f26454,f26458,f26462,f26466,f26470,f26474,f26478,f26662,f26833,f26837,f26841,f26846,f26850,f26854,f26858,f26862,f26866,f26870,f26874,f26879,f26883,f26887,f26891,f26895,f26899,f26903,f26907,f26911,f26915,f26980,f27044,f27048,f27184,f27633,f30670,f31460,f35606,f36259,f36263,f36267,f36271,f36275,f36279,f36283,f36287,f36291,f36295,f36299,f36303,f36307,f36311,f36315,f36319,f36323,f36327,f36331,f36346,f36350,f36354,f36358,f36362,f36366,f36370,f36374,f36378,f36382,f36386,f36390,f36394,f36398,f36402,f36406,f36410,f36414,f36418,f36422,f36426,f36446,f36450,f36454,f36458,f36462,f36466,f36470,f36474,f36478,f36482,f36486,f36490,f36494,f36498,f36502,f36506,f36510,f36514,f36518,f36522,f37340,f37856,f39006,f40782,f40786,f40790,f40794,f40844,f40848,f40852,f40856,f40860,f40864,f40868,f40872,f40876,f40880,f40884,f40888,f40892,f40896,f40900,f40904,f40908,f40912,f40916,f40920,f40924,f40984,f40988,f40992,f40996,f41000,f41004,f41008,f41012,f41016,f41020,f41024,f41028,f41032,f41036,f41040,f41044,f41048,f41052,f41056,f41060,f41064,f41109,f41113,f41117,f41121,f41125,f41129,f41133,f41137,f41141,f41145,f41149,f41153,f41157,f41161,f41209,f41257,f41326,f41535,f41676,f41681,f41686,f41690,f41694,f41698,f41702,f41706,f41710,f43581,f44035,f46401,f46981,f46985,f46989,f46993,f46997,f47001,f47005,f47009,f47081,f47085,f47089,f47093,f47097,f47101,f47105,f47109,f47113,f47117,f47121,f47125,f47129,f47133,f47137,f47141,f47145,f47149,f47153,f47157,f47161,f47219,f47223,f47227,f47231,f47235,f47239,f47243,f47247,f47251,f47255,f47259,f47263,f47267,f47271,f47275,f47279,f47283,f47287,f47291,f47295,f47299,f47356,f47360,f47364,f47368,f47372,f47376,f47380,f47384,f47388,f47392,f47396,f47400,f47404,f47408,f47412,f47416,f47420,f47424,f47428,f47432,f47436,f47521,f47525,f47529,f47533,f47537,f47541,f47545,f47549,f47553,f47557,f47561,f47565,f47569,f47573,f47577,f47581,f47585,f47589,f47593,f47597,f47601,f47605,f47609,f47613,f47617,f47621,f47625,f47629,f47633,f47637,f47641,f49664,f51722,f52947,f56604,f58694,f58698,f58702,f58706,f58710,f58714,f58718,f58722,f58726,f58730,f58734,f58738,f58742,f58746,f58750,f58759]) ).
fof(f58759,plain,
( spl0_152
| ~ spl0_1589 ),
inference(avatar_contradiction_clause,[],[f58758]) ).
fof(f58758,plain,
( $false
| spl0_152
| ~ spl0_1589 ),
inference(trivial_inequality_removal,[],[f58753]) ).
fof(f58753,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| spl0_152
| ~ spl0_1589 ),
inference(superposition,[],[f1700,f58709]) ).
fof(f58709,plain,
( ! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = X0
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f58708]) ).
fof(f58708,plain,
( spl0_1589
<=> ! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f1700,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| spl0_152 ),
inference(avatar_component_clause,[],[f1698]) ).
fof(f1698,plain,
( spl0_152
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f58750,plain,
( spl0_1599
| ~ spl0_406
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3825,f3575,f3091,f58748]) ).
fof(f58748,plain,
( spl0_1599
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f3091,plain,
( spl0_406
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f3575,plain,
( spl0_466
<=> ! [X18,X4,X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X18,X4,X0)
| c_HOL_Oord__class_Oless(X18,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f3825,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X3,X1,X2)
| c_HOL_Oord__class_Oless(X0,X3,X2)
| X0 = X3
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_406
| ~ spl0_466 ),
inference(resolution,[],[f3576,f3092]) ).
fof(f3092,plain,
( ! [X3,X0,X4] :
( c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| X3 = X4
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_406 ),
inference(avatar_component_clause,[],[f3091]) ).
fof(f3576,plain,
( ! [X3,X0,X18,X4] :
( ~ c_HOL_Oord__class_Oless(X18,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X18,X3,X0) )
| ~ spl0_466 ),
inference(avatar_component_clause,[],[f3575]) ).
fof(f58746,plain,
( spl0_1598
| ~ spl0_394
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3824,f3575,f3042,f58744]) ).
fof(f58744,plain,
( spl0_1598
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X4,X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f3042,plain,
( spl0_394
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f3824,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X4,X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_394
| ~ spl0_466 ),
inference(resolution,[],[f3576,f3043]) ).
fof(f3043,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_394 ),
inference(avatar_component_clause,[],[f3042]) ).
fof(f58742,plain,
( spl0_1597
| ~ spl0_395
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3823,f3575,f3046,f58740]) ).
fof(f58740,plain,
( spl0_1597
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X4,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f3046,plain,
( spl0_395
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f3823,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X3,X2)
| ~ class_Orderings_Oorder(X2)
| c_HOL_Oord__class_Oless(X4,X3,X2)
| ~ c_HOL_Oord__class_Oless(X4,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2) )
| ~ spl0_395
| ~ spl0_466 ),
inference(resolution,[],[f3576,f3047]) ).
fof(f3047,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_395 ),
inference(avatar_component_clause,[],[f3046]) ).
fof(f58738,plain,
( spl0_1596
| ~ spl0_427
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3822,f3575,f3176,f58736]) ).
fof(f58736,plain,
( spl0_1596
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f3176,plain,
( spl0_427
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f3822,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_427
| ~ spl0_466 ),
inference(resolution,[],[f3576,f3177]) ).
fof(f3177,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_427 ),
inference(avatar_component_clause,[],[f3176]) ).
fof(f58734,plain,
( spl0_1595
| ~ spl0_427
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f3757,f3519,f3176,f58732]) ).
fof(f58732,plain,
( spl0_1595
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f3519,plain,
( spl0_452
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f3757,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_427
| ~ spl0_452 ),
inference(duplicate_literal_removal,[],[f3748]) ).
fof(f3748,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X1,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_427
| ~ spl0_452 ),
inference(resolution,[],[f3520,f3177]) ).
fof(f3520,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_452 ),
inference(avatar_component_clause,[],[f3519]) ).
fof(f58730,plain,
( spl0_1594
| ~ spl0_405
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f3756,f3519,f3087,f58728]) ).
fof(f58728,plain,
( spl0_1594
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f3087,plain,
( spl0_405
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f3756,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X2 )
| ~ spl0_405
| ~ spl0_452 ),
inference(duplicate_literal_removal,[],[f3753]) ).
fof(f3753,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X2
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_405
| ~ spl0_452 ),
inference(resolution,[],[f3520,f3088]) ).
fof(f3088,plain,
( ! [X3,X0,X4] :
( c_HOL_Oord__class_Oless(X4,X3,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| X3 = X4
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_405 ),
inference(avatar_component_clause,[],[f3087]) ).
fof(f58726,plain,
( spl0_1593
| ~ spl0_394
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f3750,f3519,f3042,f58724]) ).
fof(f58724,plain,
( spl0_1593
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f3750,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_394
| ~ spl0_452 ),
inference(resolution,[],[f3520,f3043]) ).
fof(f58722,plain,
( spl0_1592
| ~ spl0_395
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f3749,f3519,f3046,f58720]) ).
fof(f58720,plain,
( spl0_1592
<=> ! [X0,X3,X2,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f3749,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X3,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_395
| ~ spl0_452 ),
inference(resolution,[],[f3520,f3047]) ).
fof(f58718,plain,
( spl0_1591
| ~ spl0_411
| ~ spl0_448 ),
inference(avatar_split_clause,[],[f3704,f3493,f3111,f58716]) ).
fof(f58716,plain,
( spl0_1591
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f3111,plain,
( spl0_411
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f3493,plain,
( spl0_448
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f3704,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) )
| ~ spl0_411
| ~ spl0_448 ),
inference(resolution,[],[f3494,f3112]) ).
fof(f3112,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) )
| ~ spl0_411 ),
inference(avatar_component_clause,[],[f3111]) ).
fof(f3494,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_448 ),
inference(avatar_component_clause,[],[f3493]) ).
fof(f58714,plain,
( spl0_1590
| ~ spl0_411
| ~ spl0_447 ),
inference(avatar_split_clause,[],[f3701,f3489,f3111,f58712]) ).
fof(f58712,plain,
( spl0_1590
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f3489,plain,
( spl0_447
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f3701,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) )
| ~ spl0_411
| ~ spl0_447 ),
inference(resolution,[],[f3490,f3112]) ).
fof(f3490,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_447 ),
inference(avatar_component_clause,[],[f3489]) ).
fof(f58710,plain,
( spl0_1589
| ~ spl0_498
| ~ spl0_1339
| ~ spl0_1575 ),
inference(avatar_split_clause,[],[f58144,f47619,f35604,f3920,f58708]) ).
fof(f3920,plain,
( spl0_498
<=> ! [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_498])]) ).
fof(f35604,plain,
( spl0_1339
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f47619,plain,
( spl0_1575
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f58144,plain,
( ! [X0] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) = X0
| ~ spl0_498
| ~ spl0_1339
| ~ spl0_1575 ),
inference(forward_demodulation,[],[f58005,f3921]) ).
fof(f3921,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_498 ),
inference(avatar_component_clause,[],[f3920]) ).
fof(f58005,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1339
| ~ spl0_1575 ),
inference(superposition,[],[f47620,f35605]) ).
fof(f35605,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1339 ),
inference(avatar_component_clause,[],[f35604]) ).
fof(f47620,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1575 ),
inference(avatar_component_clause,[],[f47619]) ).
fof(f58706,plain,
( spl0_1588
| ~ spl0_278
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f3335,f3091,f2321,f58704]) ).
fof(f58704,plain,
( spl0_1588
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f2321,plain,
( spl0_278
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3335,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_278
| ~ spl0_406 ),
inference(resolution,[],[f3092,f2322]) ).
fof(f2322,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_278 ),
inference(avatar_component_clause,[],[f2321]) ).
fof(f58702,plain,
( spl0_1587
| ~ spl0_278
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3308,f3087,f2321,f58700]) ).
fof(f58700,plain,
( spl0_1587
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f3308,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| c_HOL_Ozero__class_Ozero(X1) = c_HOL_Otimes__class_Otimes(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_278
| ~ spl0_405 ),
inference(resolution,[],[f3088,f2322]) ).
fof(f58698,plain,
( spl0_1586
| ~ spl0_277
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f2994,f2861,f2317,f58696]) ).
fof(f58696,plain,
( spl0_1586
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f2317,plain,
( spl0_277
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2861,plain,
( spl0_372
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2994,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_372 ),
inference(resolution,[],[f2862,f2318]) ).
fof(f2318,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277 ),
inference(avatar_component_clause,[],[f2317]) ).
fof(f2862,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 )
| ~ spl0_372 ),
inference(avatar_component_clause,[],[f2861]) ).
fof(f58694,plain,
( spl0_1585
| ~ spl0_356
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f2993,f2861,f2797,f58692]) ).
fof(f58692,plain,
( spl0_1585
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f2797,plain,
( spl0_356
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2993,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_356
| ~ spl0_372 ),
inference(resolution,[],[f2862,f2798]) ).
fof(f2798,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_356 ),
inference(avatar_component_clause,[],[f2797]) ).
fof(f56604,plain,
( spl0_1584
| ~ spl0_1309
| ~ spl0_1571 ),
inference(avatar_split_clause,[],[f48847,f47603,f26476,f56602]) ).
fof(f56602,plain,
( spl0_1584
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f26476,plain,
( spl0_1309
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f47603,plain,
( spl0_1571
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f48847,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
| ~ spl0_1309
| ~ spl0_1571 ),
inference(superposition,[],[f47604,f26477]) ).
fof(f26477,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
| ~ spl0_1309 ),
inference(avatar_component_clause,[],[f26476]) ).
fof(f47604,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1571 ),
inference(avatar_component_clause,[],[f47603]) ).
fof(f52947,plain,
( spl0_1583
| ~ spl0_970
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f47504,f47394,f14240,f52945]) ).
fof(f52945,plain,
( spl0_1583
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f14240,plain,
( spl0_970
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f47394,plain,
( spl0_1539
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f47504,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_970
| ~ spl0_1539 ),
inference(superposition,[],[f47395,f14241]) ).
fof(f14241,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_970 ),
inference(avatar_component_clause,[],[f14240]) ).
fof(f47395,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1539 ),
inference(avatar_component_clause,[],[f47394]) ).
fof(f51722,plain,
( spl0_1582
| ~ spl0_1145
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f47477,f47394,f18712,f51720]) ).
fof(f51720,plain,
( spl0_1582
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f18712,plain,
( spl0_1145
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f47477,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1145
| ~ spl0_1539 ),
inference(superposition,[],[f47395,f18713]) ).
fof(f18713,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f18712]) ).
fof(f49664,plain,
( spl0_1581
| ~ spl0_1048
| ~ spl0_1571 ),
inference(avatar_split_clause,[],[f48839,f47603,f15188,f49662]) ).
fof(f49662,plain,
( spl0_1581
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f15188,plain,
( spl0_1048
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f48839,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1048
| ~ spl0_1571 ),
inference(superposition,[],[f47604,f15189]) ).
fof(f15189,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1048 ),
inference(avatar_component_clause,[],[f15188]) ).
fof(f47641,plain,
( spl0_1580
| ~ spl0_661
| ~ spl0_821 ),
inference(avatar_split_clause,[],[f8557,f8488,f5550,f47639]) ).
fof(f47639,plain,
( spl0_1580
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f5550,plain,
( spl0_661
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f8488,plain,
( spl0_821
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f8557,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_661
| ~ spl0_821 ),
inference(duplicate_literal_removal,[],[f8547]) ).
fof(f8547,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) )
| ~ spl0_661
| ~ spl0_821 ),
inference(resolution,[],[f8489,f5551]) ).
fof(f5551,plain,
( ! [X2,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) )
| ~ spl0_661 ),
inference(avatar_component_clause,[],[f5550]) ).
fof(f8489,plain,
( ! [X2,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0) )
| ~ spl0_821 ),
inference(avatar_component_clause,[],[f8488]) ).
fof(f47637,plain,
( spl0_1579
| ~ spl0_63
| ~ spl0_758 ),
inference(avatar_split_clause,[],[f7346,f6501,f1253,f47635]) ).
fof(f47635,plain,
( spl0_1579
<=> ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osynthetic__div(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f1253,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f6501,plain,
( spl0_758
<=> ! [X23,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(c_Polynomial_Opoly(X23,X9,X0),c_Polynomial_Osynthetic__div(X23,X9,X0),X0) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X23,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f7346,plain,
( ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osynthetic__div(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_758 ),
inference(resolution,[],[f6502,f1255]) ).
fof(f1255,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f1253]) ).
fof(f6502,plain,
( ! [X0,X1,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(c_Polynomial_Opoly(X23,X9,X0),c_Polynomial_Osynthetic__div(X23,X9,X0),X0) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X23,X0),X9,X0) )
| ~ spl0_758 ),
inference(avatar_component_clause,[],[f6501]) ).
fof(f47633,plain,
( spl0_1578
| ~ spl0_118
| ~ spl0_758 ),
inference(avatar_split_clause,[],[f7345,f6501,f1528,f47631]) ).
fof(f47631,plain,
( spl0_1578
<=> ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f1528,plain,
( spl0_118
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f7345,plain,
( ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osynthetic__div(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_758 ),
inference(resolution,[],[f6502,f1530]) ).
fof(f1530,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1528]) ).
fof(f47629,plain,
( spl0_1577
| ~ spl0_15
| ~ spl0_758 ),
inference(avatar_split_clause,[],[f7343,f6501,f1013,f47627]) ).
fof(f47627,plain,
( spl0_1577
<=> ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_nat),c_Polynomial_Osynthetic__div(X0,X1,tc_nat),tc_nat) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f1013,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f7343,plain,
( ! [X2,X0,X1] : c_Polynomial_OpCons(c_Polynomial_Opoly(X0,X1,tc_nat),c_Polynomial_Osynthetic__div(X0,X1,tc_nat),tc_nat) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X2,X0,tc_nat),X1,tc_nat)
| ~ spl0_15
| ~ spl0_758 ),
inference(resolution,[],[f6502,f1015]) ).
fof(f1015,plain,
( class_Ring__and__Field_Ocomm__semiring__0(tc_nat)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f1013]) ).
fof(f47625,plain,
( spl0_1576
| ~ spl0_63
| ~ spl0_632
| ~ spl0_757 ),
inference(avatar_split_clause,[],[f7342,f6497,f5004,f1253,f47623]) ).
fof(f47623,plain,
( spl0_1576
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f5004,plain,
( spl0_632
<=> ! [X3,X0,X23,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X23,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X23,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f6497,plain,
( spl0_757
<=> ! [X3,X0,X23,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X23,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X23,X3,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f7342,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_632
| ~ spl0_757 ),
inference(forward_demodulation,[],[f7339,f5377]) ).
fof(f5377,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_632 ),
inference(resolution,[],[f5005,f1255]) ).
fof(f5005,plain,
( ! [X3,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X23,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X23,X3,X0),X0) )
| ~ spl0_632 ),
inference(avatar_component_clause,[],[f5004]) ).
fof(f7339,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_757 ),
inference(resolution,[],[f6498,f1255]) ).
fof(f6498,plain,
( ! [X3,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X23,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X23,X3,X0),X0),X0) )
| ~ spl0_757 ),
inference(avatar_component_clause,[],[f6497]) ).
fof(f47621,plain,
( spl0_1575
| ~ spl0_118
| ~ spl0_632
| ~ spl0_757 ),
inference(avatar_split_clause,[],[f7341,f6497,f5004,f1528,f47619]) ).
fof(f7341,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_632
| ~ spl0_757 ),
inference(forward_demodulation,[],[f7338,f5376]) ).
fof(f5376,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_632 ),
inference(resolution,[],[f5005,f1530]) ).
fof(f7338,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_757 ),
inference(resolution,[],[f6498,f1530]) ).
fof(f47617,plain,
( spl0_1574
| ~ spl0_15
| ~ spl0_632
| ~ spl0_757 ),
inference(avatar_split_clause,[],[f7340,f6497,f5004,f1013,f47615]) ).
fof(f47615,plain,
( spl0_1574
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_nat),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f7340,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_nat),X2,tc_nat),tc_nat)
| ~ spl0_15
| ~ spl0_632
| ~ spl0_757 ),
inference(forward_demodulation,[],[f7336,f5374]) ).
fof(f5374,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_nat),tc_nat)
| ~ spl0_15
| ~ spl0_632 ),
inference(resolution,[],[f5005,f1015]) ).
fof(f7336,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,c_Polynomial_Opoly(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_15
| ~ spl0_757 ),
inference(resolution,[],[f6498,f1015]) ).
fof(f47613,plain,
( spl0_1573
| ~ spl0_31
| ~ spl0_754 ),
inference(avatar_split_clause,[],[f7315,f6485,f1093,f47611]) ).
fof(f47611,plain,
( spl0_1573
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f1093,plain,
( spl0_31
<=> class_Divides_Osemiring__div(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f6485,plain,
( spl0_754
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f7315,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_754 ),
inference(resolution,[],[f6486,f1095]) ).
fof(f1095,plain,
( class_Divides_Osemiring__div(tc_nat)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f1093]) ).
fof(f6486,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) )
| ~ spl0_754 ),
inference(avatar_component_clause,[],[f6485]) ).
fof(f47609,plain,
( spl0_1572
| ~ spl0_31
| ~ spl0_753 ),
inference(avatar_split_clause,[],[f7313,f6481,f1093,f47607]) ).
fof(f47607,plain,
( spl0_1572
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f6481,plain,
( spl0_753
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f7313,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ spl0_31
| ~ spl0_753 ),
inference(resolution,[],[f6482,f1095]) ).
fof(f6482,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X1,X2,X0),X0) )
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f6481]) ).
fof(f47605,plain,
( spl0_1571
| ~ spl0_933
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f47482,f47394,f11891,f47603]) ).
fof(f11891,plain,
( spl0_933
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f47482,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_933
| ~ spl0_1539 ),
inference(superposition,[],[f47395,f11892]) ).
fof(f11892,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal)
| ~ spl0_933 ),
inference(avatar_component_clause,[],[f11891]) ).
fof(f47601,plain,
( spl0_1570
| ~ spl0_143
| ~ spl0_745 ),
inference(avatar_split_clause,[],[f7205,f6436,f1653,f47599]) ).
fof(f47599,plain,
( spl0_1570
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f1653,plain,
( spl0_143
<=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f6436,plain,
( spl0_745
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f7205,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_745 ),
inference(resolution,[],[f6437,f1655]) ).
fof(f1655,plain,
( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ spl0_143 ),
inference(avatar_component_clause,[],[f1653]) ).
fof(f6437,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) )
| ~ spl0_745 ),
inference(avatar_component_clause,[],[f6436]) ).
fof(f47597,plain,
( spl0_1569
| ~ spl0_96
| ~ spl0_745 ),
inference(avatar_split_clause,[],[f7204,f6436,f1418,f47595]) ).
fof(f47595,plain,
( spl0_1569
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f1418,plain,
( spl0_96
<=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f7204,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_745 ),
inference(resolution,[],[f6437,f1420]) ).
fof(f1420,plain,
( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f1418]) ).
fof(f47593,plain,
( spl0_1568
| ~ spl0_139
| ~ spl0_741 ),
inference(avatar_split_clause,[],[f7077,f6420,f1633,f47591]) ).
fof(f47591,plain,
( spl0_1568
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f1633,plain,
( spl0_139
<=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f6420,plain,
( spl0_741
<=> ! [X4,X0,X3,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f7077,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_139
| ~ spl0_741 ),
inference(resolution,[],[f6421,f1635]) ).
fof(f1635,plain,
( class_RealVector_Oreal__vector(tc_Complex_Ocomplex)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1633]) ).
fof(f6421,plain,
( ! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) )
| ~ spl0_741 ),
inference(avatar_component_clause,[],[f6420]) ).
fof(f47589,plain,
( spl0_1567
| ~ spl0_90
| ~ spl0_741 ),
inference(avatar_split_clause,[],[f7076,f6420,f1388,f47587]) ).
fof(f47587,plain,
( spl0_1567
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f1388,plain,
( spl0_90
<=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f7076,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_90
| ~ spl0_741 ),
inference(resolution,[],[f6421,f1390]) ).
fof(f1390,plain,
( class_RealVector_Oreal__vector(tc_RealDef_Oreal)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f1388]) ).
fof(f47585,plain,
( spl0_1566
| ~ spl0_31
| ~ spl0_738 ),
inference(avatar_split_clause,[],[f7016,f6408,f1093,f47583]) ).
fof(f47583,plain,
( spl0_1566
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f6408,plain,
( spl0_738
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f7016,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_31
| ~ spl0_738 ),
inference(resolution,[],[f6409,f1095]) ).
fof(f6409,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) )
| ~ spl0_738 ),
inference(avatar_component_clause,[],[f6408]) ).
fof(f47581,plain,
( spl0_1565
| ~ spl0_119
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f7015,f6404,f1533,f47579]) ).
fof(f47579,plain,
( spl0_1565
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f1533,plain,
( spl0_119
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f6404,plain,
( spl0_737
<=> ! [X4,X0,X3,X21] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X21,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X21,X0),c_HOL_Otimes__class_Otimes(X4,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f7015,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_737 ),
inference(resolution,[],[f6405,f1535]) ).
fof(f1535,plain,
( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1533]) ).
fof(f6405,plain,
( ! [X21,X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X21,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X21,X0),c_HOL_Otimes__class_Otimes(X4,X21,X0),X0) )
| ~ spl0_737 ),
inference(avatar_component_clause,[],[f6404]) ).
fof(f47577,plain,
( spl0_1564
| ~ spl0_64
| ~ spl0_737 ),
inference(avatar_split_clause,[],[f7014,f6404,f1258,f47575]) ).
fof(f47575,plain,
( spl0_1564
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f1258,plain,
( spl0_64
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f7014,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_64
| ~ spl0_737 ),
inference(resolution,[],[f6405,f1260]) ).
fof(f1260,plain,
( class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f1258]) ).
fof(f47573,plain,
( spl0_1563
| ~ spl0_119
| ~ spl0_736 ),
inference(avatar_split_clause,[],[f7013,f6400,f1533,f47571]) ).
fof(f47571,plain,
( spl0_1563
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f6400,plain,
( spl0_736
<=> ! [X2,X20,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f7013,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_736 ),
inference(resolution,[],[f6401,f1535]) ).
fof(f6401,plain,
( ! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) )
| ~ spl0_736 ),
inference(avatar_component_clause,[],[f6400]) ).
fof(f47569,plain,
( spl0_1562
| ~ spl0_64
| ~ spl0_736 ),
inference(avatar_split_clause,[],[f7012,f6400,f1258,f47567]) ).
fof(f47567,plain,
( spl0_1562
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f7012,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_64
| ~ spl0_736 ),
inference(resolution,[],[f6401,f1260]) ).
fof(f47565,plain,
( spl0_1561
| ~ spl0_31
| ~ spl0_731 ),
inference(avatar_split_clause,[],[f6921,f6365,f1093,f47563]) ).
fof(f47563,plain,
( spl0_1561
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f6365,plain,
( spl0_731
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f6921,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_Divides_Odiv__class_Omod(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_31
| ~ spl0_731 ),
inference(resolution,[],[f6366,f1095]) ).
fof(f6366,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) )
| ~ spl0_731 ),
inference(avatar_component_clause,[],[f6365]) ).
fof(f47561,plain,
( spl0_1560
| ~ spl0_1208
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f47478,f47394,f23909,f47559]) ).
fof(f47559,plain,
( spl0_1560
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f23909,plain,
( spl0_1208
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f47478,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1208
| ~ spl0_1539 ),
inference(superposition,[],[f47395,f23910]) ).
fof(f23910,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_1208 ),
inference(avatar_component_clause,[],[f23909]) ).
fof(f47557,plain,
( spl0_1559
| ~ spl0_44
| ~ spl0_728 ),
inference(avatar_split_clause,[],[f6918,f6353,f1158,f47555]) ).
fof(f47555,plain,
( spl0_1559
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f1158,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f6353,plain,
( spl0_728
<=> ! [X2,X0,X9,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X9,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f6918,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_44
| ~ spl0_728 ),
inference(resolution,[],[f6354,f1160]) ).
fof(f1160,plain,
( class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f1158]) ).
fof(f6354,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X9,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) )
| ~ spl0_728 ),
inference(avatar_component_clause,[],[f6353]) ).
fof(f47553,plain,
( spl0_1558
| ~ spl0_44
| ~ spl0_727 ),
inference(avatar_split_clause,[],[f6917,f6349,f1158,f47551]) ).
fof(f47551,plain,
( spl0_1558
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f6349,plain,
( spl0_727
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f6917,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_44
| ~ spl0_727 ),
inference(resolution,[],[f6350,f1160]) ).
fof(f6350,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) )
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f6349]) ).
fof(f47549,plain,
( spl0_1557
| ~ spl0_86
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f6916,f6345,f1368,f47547]) ).
fof(f47547,plain,
( spl0_1557
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f1368,plain,
( spl0_86
<=> class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f6345,plain,
( spl0_726
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f6916,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_726 ),
inference(resolution,[],[f6346,f1370]) ).
fof(f1370,plain,
( class_Lattices_Odistrib__lattice(tc_RealDef_Oreal)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f1368]) ).
fof(f6346,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) )
| ~ spl0_726 ),
inference(avatar_component_clause,[],[f6345]) ).
fof(f47545,plain,
( spl0_1556
| ~ spl0_28
| ~ spl0_726 ),
inference(avatar_split_clause,[],[f6915,f6345,f1078,f47543]) ).
fof(f47543,plain,
( spl0_1556
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f1078,plain,
( spl0_28
<=> class_Lattices_Odistrib__lattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f6915,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat)
| ~ spl0_28
| ~ spl0_726 ),
inference(resolution,[],[f6346,f1080]) ).
fof(f1080,plain,
( class_Lattices_Odistrib__lattice(tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f1078]) ).
fof(f47541,plain,
( spl0_1555
| ~ spl0_86
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f6914,f6341,f1368,f47539]) ).
fof(f47539,plain,
( spl0_1555
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f6341,plain,
( spl0_725
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X18,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f6914,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_725 ),
inference(resolution,[],[f6342,f1370]) ).
fof(f6342,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X18,X3,X0),X0) )
| ~ spl0_725 ),
inference(avatar_component_clause,[],[f6341]) ).
fof(f47537,plain,
( spl0_1554
| ~ spl0_28
| ~ spl0_725 ),
inference(avatar_split_clause,[],[f6913,f6341,f1078,f47535]) ).
fof(f47535,plain,
( spl0_1554
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f6913,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat)
| ~ spl0_28
| ~ spl0_725 ),
inference(resolution,[],[f6342,f1080]) ).
fof(f47533,plain,
( spl0_1553
| ~ spl0_31
| ~ spl0_724 ),
inference(avatar_split_clause,[],[f6864,f6337,f1093,f47531]) ).
fof(f47531,plain,
( spl0_1553
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f6337,plain,
( spl0_724
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f6864,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X2,tc_nat),X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_724 ),
inference(resolution,[],[f6338,f1095]) ).
fof(f6338,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) )
| ~ spl0_724 ),
inference(avatar_component_clause,[],[f6337]) ).
fof(f47529,plain,
( spl0_1552
| ~ spl0_143
| ~ spl0_722 ),
inference(avatar_split_clause,[],[f6861,f6329,f1653,f47527]) ).
fof(f47527,plain,
( spl0_1552
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f6329,plain,
( spl0_722
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f6861,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_722 ),
inference(resolution,[],[f6330,f1655]) ).
fof(f6330,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) )
| ~ spl0_722 ),
inference(avatar_component_clause,[],[f6329]) ).
fof(f47525,plain,
( spl0_1551
| ~ spl0_96
| ~ spl0_722 ),
inference(avatar_split_clause,[],[f6860,f6329,f1418,f47523]) ).
fof(f47523,plain,
( spl0_1551
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f6860,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X0,X2,tc_RealDef_Oreal),c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_722 ),
inference(resolution,[],[f6330,f1420]) ).
fof(f47521,plain,
( spl0_1550
| ~ spl0_55
| ~ spl0_716 ),
inference(avatar_split_clause,[],[f6809,f6290,f1213,f47519]) ).
fof(f47519,plain,
( spl0_1550
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f1213,plain,
( spl0_55
<=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f6290,plain,
( spl0_716
<=> ! [X2,X0,X9,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X9,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f6809,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_716 ),
inference(resolution,[],[f6291,f1215]) ).
fof(f1215,plain,
( class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f1213]) ).
fof(f6291,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X9,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) )
| ~ spl0_716 ),
inference(avatar_component_clause,[],[f6290]) ).
fof(f47436,plain,
( spl0_1549
| ~ spl0_55
| ~ spl0_715 ),
inference(avatar_split_clause,[],[f6808,f6286,f1213,f47434]) ).
fof(f47434,plain,
( spl0_1549
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f6286,plain,
( spl0_715
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X9,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f6808,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_715 ),
inference(resolution,[],[f6287,f1215]) ).
fof(f6287,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X9,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) )
| ~ spl0_715 ),
inference(avatar_component_clause,[],[f6286]) ).
fof(f47432,plain,
( spl0_1548
| ~ spl0_139
| ~ spl0_707 ),
inference(avatar_split_clause,[],[f6672,f6241,f1633,f47430]) ).
fof(f47430,plain,
( spl0_1548
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f6241,plain,
( spl0_707
<=> ! [X4,X0,X3,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f6672,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_139
| ~ spl0_707 ),
inference(resolution,[],[f6242,f1635]) ).
fof(f6242,plain,
( ! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) )
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f6241]) ).
fof(f47428,plain,
( spl0_1547
| ~ spl0_90
| ~ spl0_707 ),
inference(avatar_split_clause,[],[f6671,f6241,f1388,f47426]) ).
fof(f47426,plain,
( spl0_1547
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f6671,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_90
| ~ spl0_707 ),
inference(resolution,[],[f6242,f1390]) ).
fof(f47424,plain,
( spl0_1546
| ~ spl0_86
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f6589,f6225,f1368,f47422]) ).
fof(f47422,plain,
( spl0_1546
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f6225,plain,
( spl0_703
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f6589,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_703 ),
inference(resolution,[],[f6226,f1370]) ).
fof(f6226,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) )
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f6225]) ).
fof(f47420,plain,
( spl0_1545
| ~ spl0_28
| ~ spl0_703 ),
inference(avatar_split_clause,[],[f6588,f6225,f1078,f47418]) ).
fof(f47418,plain,
( spl0_1545
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f6588,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat)
| ~ spl0_28
| ~ spl0_703 ),
inference(resolution,[],[f6226,f1080]) ).
fof(f47416,plain,
( spl0_1544
| ~ spl0_86
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f6587,f6221,f1368,f47414]) ).
fof(f47414,plain,
( spl0_1544
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f6221,plain,
( spl0_702
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X18,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f6587,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_86
| ~ spl0_702 ),
inference(resolution,[],[f6222,f1370]) ).
fof(f6222,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X18,X3,X0),X0) )
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f6221]) ).
fof(f47412,plain,
( spl0_1543
| ~ spl0_28
| ~ spl0_702 ),
inference(avatar_split_clause,[],[f6586,f6221,f1078,f47410]) ).
fof(f47410,plain,
( spl0_1543
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f6586,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat)
| ~ spl0_28
| ~ spl0_702 ),
inference(resolution,[],[f6222,f1080]) ).
fof(f47408,plain,
( spl0_1542
| ~ spl0_63
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f6574,f6198,f1253,f47406]) ).
fof(f47406,plain,
( spl0_1542
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f6198,plain,
( spl0_700
<=> ! [X0,X23,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X23,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_Polynomial_Osmult(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f6574,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_700 ),
inference(resolution,[],[f6199,f1255]) ).
fof(f6199,plain,
( ! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X23,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_Polynomial_Osmult(X1,X23,X0),X0) )
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f6198]) ).
fof(f47404,plain,
( spl0_1541
| ~ spl0_118
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f6573,f6198,f1528,f47402]) ).
fof(f47402,plain,
( spl0_1541
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f6573,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_700 ),
inference(resolution,[],[f6199,f1530]) ).
fof(f47400,plain,
( spl0_1540
| ~ spl0_15
| ~ spl0_700 ),
inference(avatar_split_clause,[],[f6571,f6198,f1013,f47398]) ).
fof(f47398,plain,
( spl0_1540
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_nat),tc_nat) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Polynomial_Osmult(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f6571,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_OpCons(X1,X2,tc_nat),tc_nat) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Polynomial_Osmult(X0,X2,tc_nat),tc_nat)
| ~ spl0_15
| ~ spl0_700 ),
inference(resolution,[],[f6199,f1015]) ).
fof(f47396,plain,
( ~ spl0_99
| spl0_1539
| ~ spl0_242
| ~ spl0_933 ),
inference(avatar_split_clause,[],[f12808,f11891,f2077,f47394,f1433]) ).
fof(f1433,plain,
( spl0_99
<=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f2077,plain,
( spl0_242
<=> ! [X2,X0,X11] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f12808,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
| ~ spl0_242
| ~ spl0_933 ),
inference(superposition,[],[f2078,f11892]) ).
fof(f2078,plain,
( ! [X2,X0,X11] :
( c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X11,X0),X0)
| ~ class_Ring__and__Field_Odvd(X0) )
| ~ spl0_242 ),
inference(avatar_component_clause,[],[f2077]) ).
fof(f47392,plain,
( spl0_1538
| ~ spl0_14
| ~ spl0_698 ),
inference(avatar_split_clause,[],[f6563,f6190,f1008,f47390]) ).
fof(f47390,plain,
( spl0_1538
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f1008,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f6190,plain,
( spl0_698
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f6563,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_698 ),
inference(resolution,[],[f6191,f1010]) ).
fof(f1010,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f1008]) ).
fof(f6191,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) )
| ~ spl0_698 ),
inference(avatar_component_clause,[],[f6190]) ).
fof(f47388,plain,
( spl0_1537
| ~ spl0_119
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f6560,f6182,f1533,f47386]) ).
fof(f47386,plain,
( spl0_1537
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f6182,plain,
( spl0_696
<=> ! [X2,X20,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X20,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f6560,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_696 ),
inference(resolution,[],[f6183,f1535]) ).
fof(f6183,plain,
( ! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X20,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) )
| ~ spl0_696 ),
inference(avatar_component_clause,[],[f6182]) ).
fof(f47384,plain,
( spl0_1536
| ~ spl0_64
| ~ spl0_696 ),
inference(avatar_split_clause,[],[f6559,f6182,f1258,f47382]) ).
fof(f47382,plain,
( spl0_1536
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f6559,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_64
| ~ spl0_696 ),
inference(resolution,[],[f6183,f1260]) ).
fof(f47380,plain,
( spl0_1535
| ~ spl0_62
| ~ spl0_695 ),
inference(avatar_split_clause,[],[f6558,f6178,f1248,f47378]) ).
fof(f47378,plain,
( spl0_1535
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f1248,plain,
( spl0_62
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f6178,plain,
( spl0_695
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f6558,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_695 ),
inference(resolution,[],[f6179,f1250]) ).
fof(f1250,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f1248]) ).
fof(f6179,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) )
| ~ spl0_695 ),
inference(avatar_component_clause,[],[f6178]) ).
fof(f47376,plain,
( spl0_1534
| ~ spl0_117
| ~ spl0_695 ),
inference(avatar_split_clause,[],[f6557,f6178,f1523,f47374]) ).
fof(f47374,plain,
( spl0_1534
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f1523,plain,
( spl0_117
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f6557,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_695 ),
inference(resolution,[],[f6179,f1525]) ).
fof(f1525,plain,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1523]) ).
fof(f47372,plain,
( spl0_1533
| ~ spl0_14
| ~ spl0_695 ),
inference(avatar_split_clause,[],[f6555,f6178,f1008,f47370]) ).
fof(f47370,plain,
( spl0_1533
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f6555,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_695 ),
inference(resolution,[],[f6179,f1010]) ).
fof(f47368,plain,
( spl0_1532
| ~ spl0_31
| ~ spl0_694 ),
inference(avatar_split_clause,[],[f6512,f6174,f1093,f47366]) ).
fof(f47366,plain,
( spl0_1532
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f6174,plain,
( spl0_694
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f6512,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X2,tc_nat),X1,tc_nat),X2,tc_nat)
| ~ spl0_31
| ~ spl0_694 ),
inference(resolution,[],[f6175,f1095]) ).
fof(f6175,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) )
| ~ spl0_694 ),
inference(avatar_component_clause,[],[f6174]) ).
fof(f47364,plain,
( spl0_1531
| ~ spl0_62
| ~ spl0_692 ),
inference(avatar_split_clause,[],[f6507,f6166,f1248,f47362]) ).
fof(f47362,plain,
( spl0_1531
<=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_RealDef_Oreal),c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f6166,plain,
( spl0_692
<=> ! [X4,X0,X3,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X7,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X7,X0),c_Power_Opower__class_Opower(X4,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f6507,plain,
( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_RealDef_Oreal),c_Power_Opower__class_Opower(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_692 ),
inference(resolution,[],[f6167,f1250]) ).
fof(f6167,plain,
( ! [X3,X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X7,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X7,X0),c_Power_Opower__class_Opower(X4,X7,X0),X0) )
| ~ spl0_692 ),
inference(avatar_component_clause,[],[f6166]) ).
fof(f47360,plain,
( spl0_1530
| ~ spl0_117
| ~ spl0_692 ),
inference(avatar_split_clause,[],[f6506,f6166,f1523,f47358]) ).
fof(f47358,plain,
( spl0_1530
<=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f6506,plain,
( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_692 ),
inference(resolution,[],[f6167,f1525]) ).
fof(f47356,plain,
( spl0_1529
| ~ spl0_14
| ~ spl0_692 ),
inference(avatar_split_clause,[],[f6504,f6166,f1008,f47354]) ).
fof(f47354,plain,
( spl0_1529
<=> ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f6504,plain,
( ! [X2,X0,X1] : c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X2,tc_nat),c_Power_Opower__class_Opower(X1,X2,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_692 ),
inference(resolution,[],[f6167,f1010]) ).
fof(f47299,plain,
( spl0_1528
| ~ spl0_218
| ~ spl0_659 ),
inference(avatar_split_clause,[],[f5738,f5542,f1969,f47297]) ).
fof(f47297,plain,
( spl0_1528
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f1969,plain,
( spl0_218
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f5542,plain,
( spl0_659
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X2,X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f5738,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_218
| ~ spl0_659 ),
inference(resolution,[],[f5543,f1970]) ).
fof(f1970,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_218 ),
inference(avatar_component_clause,[],[f1969]) ).
fof(f5543,plain,
( ! [X2,X0,X1,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X2,X0)
| ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) )
| ~ spl0_659 ),
inference(avatar_component_clause,[],[f5542]) ).
fof(f47295,plain,
( spl0_1527
| ~ spl0_209
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f5262,f4839,f1929,f47293]) ).
fof(f47293,plain,
( spl0_1527
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Omod(X0,X1,X2),X1,X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Omod(X0,X1,X2),X0,X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f1929,plain,
( spl0_209
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f4839,plain,
( spl0_605
<=> ! [X11,X0,X27,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X27,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X27,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f5262,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Omod(X0,X1,X2),X1,X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Omod(X0,X1,X2),X0,X2)
| ~ class_Divides_Osemiring__div(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_209
| ~ spl0_605 ),
inference(resolution,[],[f4840,f1930]) ).
fof(f1930,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f1929]) ).
fof(f4840,plain,
( ! [X0,X11,X8,X27] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X27,X8,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X27,X0)
| ~ class_Divides_Osemiring__div(X0) )
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f4839]) ).
fof(f47291,plain,
( spl0_1526
| ~ spl0_283
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f4696,f4481,f2341,f47289]) ).
fof(f47289,plain,
( spl0_1526
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f2341,plain,
( spl0_283
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f4481,plain,
( spl0_574
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f4696,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_574 ),
inference(resolution,[],[f4482,f2342]) ).
fof(f2342,plain,
( ! [X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283 ),
inference(avatar_component_clause,[],[f2341]) ).
fof(f4482,plain,
( ! [X3,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) )
| ~ spl0_574 ),
inference(avatar_component_clause,[],[f4481]) ).
fof(f47287,plain,
( spl0_1525
| ~ spl0_284
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f4695,f4481,f2345,f47285]) ).
fof(f47285,plain,
( spl0_1525
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f2345,plain,
( spl0_284
<=> ! [X4,X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f4695,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_284
| ~ spl0_574 ),
inference(resolution,[],[f4482,f2346]) ).
fof(f2346,plain,
( ! [X3,X0,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0) )
| ~ spl0_284 ),
inference(avatar_component_clause,[],[f2345]) ).
fof(f47283,plain,
( spl0_1524
| ~ spl0_285
| ~ spl0_574 ),
inference(avatar_split_clause,[],[f4694,f4481,f2349,f47281]) ).
fof(f47281,plain,
( spl0_1524
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f2349,plain,
( spl0_285
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f4694,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_285
| ~ spl0_574 ),
inference(resolution,[],[f4482,f2350]) ).
fof(f2350,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_285 ),
inference(avatar_component_clause,[],[f2349]) ).
fof(f47279,plain,
( spl0_1523
| ~ spl0_283
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f4691,f4477,f2341,f47277]) ).
fof(f47277,plain,
( spl0_1523
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f4477,plain,
( spl0_573
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f4691,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_573 ),
inference(resolution,[],[f4478,f2342]) ).
fof(f4478,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
| ~ spl0_573 ),
inference(avatar_component_clause,[],[f4477]) ).
fof(f47275,plain,
( spl0_1522
| ~ spl0_284
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f4690,f4477,f2345,f47273]) ).
fof(f47273,plain,
( spl0_1522
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f4690,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
| ~ spl0_284
| ~ spl0_573 ),
inference(resolution,[],[f4478,f2346]) ).
fof(f47271,plain,
( spl0_1521
| ~ spl0_285
| ~ spl0_573 ),
inference(avatar_split_clause,[],[f4689,f4477,f2349,f47269]) ).
fof(f47269,plain,
( spl0_1521
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f4689,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
| ~ spl0_285
| ~ spl0_573 ),
inference(resolution,[],[f4478,f2350]) ).
fof(f47267,plain,
( spl0_1520
| ~ spl0_283
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f4679,f4473,f2341,f47265]) ).
fof(f47265,plain,
( spl0_1520
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f4473,plain,
( spl0_572
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f4679,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_572 ),
inference(resolution,[],[f4474,f2342]) ).
fof(f4474,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_572 ),
inference(avatar_component_clause,[],[f4473]) ).
fof(f47263,plain,
( spl0_1519
| ~ spl0_284
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f4678,f4473,f2345,f47261]) ).
fof(f47261,plain,
( spl0_1519
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f4678,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
| ~ spl0_284
| ~ spl0_572 ),
inference(resolution,[],[f4474,f2346]) ).
fof(f47259,plain,
( spl0_1518
| ~ spl0_1310
| ~ spl0_1477 ),
inference(avatar_split_clause,[],[f45122,f44033,f26660,f47257]) ).
fof(f47257,plain,
( spl0_1518
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f26660,plain,
( spl0_1310
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f44033,plain,
( spl0_1477
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f45122,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ~ spl0_1310
| ~ spl0_1477 ),
inference(superposition,[],[f44034,f26661]) ).
fof(f26661,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ~ spl0_1310 ),
inference(avatar_component_clause,[],[f26660]) ).
fof(f44034,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1477 ),
inference(avatar_component_clause,[],[f44033]) ).
fof(f47255,plain,
( spl0_1517
| ~ spl0_285
| ~ spl0_572 ),
inference(avatar_split_clause,[],[f4677,f4473,f2349,f47253]) ).
fof(f47253,plain,
( spl0_1517
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f4677,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X3,X2),c_HOL_Oplus__class_Oplus(X0,X3,X2),X2) )
| ~ spl0_285
| ~ spl0_572 ),
inference(resolution,[],[f4474,f2350]) ).
fof(f47251,plain,
( spl0_1516
| ~ spl0_283
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f4661,f4465,f2341,f47249]) ).
fof(f47249,plain,
( spl0_1516
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f4465,plain,
( spl0_570
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f4661,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_570 ),
inference(resolution,[],[f4466,f2342]) ).
fof(f4466,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0) )
| ~ spl0_570 ),
inference(avatar_component_clause,[],[f4465]) ).
fof(f47247,plain,
( spl0_1515
| ~ spl0_284
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f4660,f4465,f2345,f47245]) ).
fof(f47245,plain,
( spl0_1515
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f4660,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
| ~ spl0_284
| ~ spl0_570 ),
inference(resolution,[],[f4466,f2346]) ).
fof(f47243,plain,
( spl0_1514
| ~ spl0_285
| ~ spl0_570 ),
inference(avatar_split_clause,[],[f4659,f4465,f2349,f47241]) ).
fof(f47241,plain,
( spl0_1514
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f4659,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
| ~ spl0_285
| ~ spl0_570 ),
inference(resolution,[],[f4466,f2350]) ).
fof(f47239,plain,
( spl0_1513
| ~ spl0_283
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f4651,f4461,f2341,f47237]) ).
fof(f47237,plain,
( spl0_1513
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f4461,plain,
( spl0_569
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f4651,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_569 ),
inference(resolution,[],[f4462,f2342]) ).
fof(f4462,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_569 ),
inference(avatar_component_clause,[],[f4461]) ).
fof(f47235,plain,
( spl0_1512
| ~ spl0_284
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f4650,f4461,f2345,f47233]) ).
fof(f47233,plain,
( spl0_1512
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f4650,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
| ~ spl0_284
| ~ spl0_569 ),
inference(resolution,[],[f4462,f2346]) ).
fof(f47231,plain,
( spl0_1511
| ~ spl0_285
| ~ spl0_569 ),
inference(avatar_split_clause,[],[f4649,f4461,f2349,f47229]) ).
fof(f47229,plain,
( spl0_1511
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f4649,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X3,X1,X2),c_HOL_Oplus__class_Oplus(X3,X0,X2),X2) )
| ~ spl0_285
| ~ spl0_569 ),
inference(resolution,[],[f4462,f2350]) ).
fof(f47227,plain,
( spl0_1510
| ~ spl0_283
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f4638,f4453,f2341,f47225]) ).
fof(f47225,plain,
( spl0_1510
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f4453,plain,
( spl0_567
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X8),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f4638,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_567 ),
inference(resolution,[],[f4454,f2342]) ).
fof(f4454,plain,
( ! [X0,X1,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X8),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_567 ),
inference(avatar_component_clause,[],[f4453]) ).
fof(f47223,plain,
( spl0_1509
| ~ spl0_284
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f4637,f4453,f2345,f47221]) ).
fof(f47221,plain,
( spl0_1509
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f4637,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_284
| ~ spl0_567 ),
inference(resolution,[],[f4454,f2346]) ).
fof(f47219,plain,
( spl0_1508
| ~ spl0_285
| ~ spl0_567 ),
inference(avatar_split_clause,[],[f4636,f4453,f2349,f47217]) ).
fof(f47217,plain,
( spl0_1508
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f4636,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X2),X0),c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_285
| ~ spl0_567 ),
inference(resolution,[],[f4454,f2350]) ).
fof(f47161,plain,
( spl0_1507
| ~ spl0_525
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4349,f4155,f4076,f47159]) ).
fof(f47159,plain,
( spl0_1507
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(X1,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f4076,plain,
( spl0_525
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f4155,plain,
( spl0_542
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f4349,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(X1,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_525
| ~ spl0_542 ),
inference(duplicate_literal_removal,[],[f4342]) ).
fof(f4342,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(X1,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_525
| ~ spl0_542 ),
inference(resolution,[],[f4156,f4077]) ).
fof(f4077,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_525 ),
inference(avatar_component_clause,[],[f4076]) ).
fof(f4156,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0) )
| ~ spl0_542 ),
inference(avatar_component_clause,[],[f4155]) ).
fof(f47157,plain,
( spl0_1506
| ~ spl0_428
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f4290,f4112,f3180,f47155]) ).
fof(f47155,plain,
( spl0_1506
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Power_Opower__class_Opower(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f3180,plain,
( spl0_428
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f4112,plain,
( spl0_534
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f4290,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Power_Opower__class_Opower(X1,X2,X0),X0) )
| ~ spl0_428
| ~ spl0_534 ),
inference(resolution,[],[f4113,f3181]) ).
fof(f3181,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) )
| ~ spl0_428 ),
inference(avatar_component_clause,[],[f3180]) ).
fof(f4113,plain,
( ! [X0,X1,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X8,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_534 ),
inference(avatar_component_clause,[],[f4112]) ).
fof(f47153,plain,
( spl0_1505
| ~ spl0_207
| ~ spl0_529 ),
inference(avatar_split_clause,[],[f4275,f4092,f1921,f47151]) ).
fof(f47151,plain,
( spl0_1505
<=> ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f1921,plain,
( spl0_207
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Power_Opower(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f4092,plain,
( spl0_529
<=> ! [X0,X1,X8] :
( ~ class_Power_Opower(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f4275,plain,
( ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_207
| ~ spl0_529 ),
inference(resolution,[],[f4093,f1922]) ).
fof(f1922,plain,
( ! [X34] :
( class_Power_Opower(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X34) )
| ~ spl0_207 ),
inference(avatar_component_clause,[],[f1921]) ).
fof(f4093,plain,
( ! [X0,X1,X8] :
( ~ class_Power_Opower(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) )
| ~ spl0_529 ),
inference(avatar_component_clause,[],[f4092]) ).
fof(f47149,plain,
( spl0_1504
| ~ spl0_191
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f4271,f4088,f1857,f47147]) ).
fof(f47147,plain,
( spl0_1504
<=> ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_Polynomial_Opoly(X2)),X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f1857,plain,
( spl0_191
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f4088,plain,
( spl0_528
<=> ! [X0,X1,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f4271,plain,
( ! [X2,X0,X1] :
( c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_Polynomial_Opoly(X2)),X0,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_191
| ~ spl0_528 ),
inference(resolution,[],[f4089,f1858]) ).
fof(f1858,plain,
( ! [X34] :
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X34) )
| ~ spl0_191 ),
inference(avatar_component_clause,[],[f1857]) ).
fof(f4089,plain,
( ! [X0,X1,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) )
| ~ spl0_528 ),
inference(avatar_component_clause,[],[f4088]) ).
fof(f47145,plain,
( spl0_1503
| ~ spl0_198
| ~ spl0_511 ),
inference(avatar_split_clause,[],[f4211,f4020,f1885,f47143]) ).
fof(f47143,plain,
( spl0_1503
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X2
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f1885,plain,
( spl0_198
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f4020,plain,
( spl0_511
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f4211,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X2
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_511 ),
inference(resolution,[],[f4021,f1886]) ).
fof(f1886,plain,
( ! [X34] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ofield(X34) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f1885]) ).
fof(f4021,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) = X1 )
| ~ spl0_511 ),
inference(avatar_component_clause,[],[f4020]) ).
fof(f47141,plain,
( spl0_1502
| ~ spl0_198
| ~ spl0_510 ),
inference(avatar_split_clause,[],[f4209,f4016,f1885,f47139]) ).
fof(f47139,plain,
( spl0_1502
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X2
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f4016,plain,
( spl0_510
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f4209,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X2
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_510 ),
inference(resolution,[],[f4017,f1886]) ).
fof(f4017,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) = X1 )
| ~ spl0_510 ),
inference(avatar_component_clause,[],[f4016]) ).
fof(f47137,plain,
( spl0_1501
| ~ spl0_428
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f4190,f3984,f3180,f47135]) ).
fof(f47135,plain,
( spl0_1501
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f3984,plain,
( spl0_502
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f4190,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) )
| ~ spl0_428
| ~ spl0_502 ),
inference(resolution,[],[f3985,f3181]) ).
fof(f3985,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) )
| ~ spl0_502 ),
inference(avatar_component_clause,[],[f3984]) ).
fof(f47133,plain,
( spl0_1500
| ~ spl0_372
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3958,f3659,f2861,f47131]) ).
fof(f47131,plain,
( spl0_1500
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ouminus__class_Ouminus(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f3659,plain,
( spl0_487
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f3958,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1)
| c_HOL_Ouminus__class_Ouminus(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,X1),X1) )
| ~ spl0_372
| ~ spl0_487 ),
inference(resolution,[],[f3660,f2862]) ).
fof(f3660,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_487 ),
inference(avatar_component_clause,[],[f3659]) ).
fof(f47129,plain,
( spl0_1499
| ~ spl0_372
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3866,f3607,f2861,f47127]) ).
fof(f47127,plain,
( spl0_1499
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f3607,plain,
( spl0_474
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f3866,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_372
| ~ spl0_474 ),
inference(resolution,[],[f3608,f2862]) ).
fof(f3608,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0) )
| ~ spl0_474 ),
inference(avatar_component_clause,[],[f3607]) ).
fof(f47125,plain,
( spl0_1498
| ~ spl0_356
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3851,f3579,f2797,f47123]) ).
fof(f47123,plain,
( spl0_1498
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f3579,plain,
( spl0_467
<=> ! [X18,X4,X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X18,X0)
| c_HOL_Oord__class_Oless(X3,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f3851,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_356
| ~ spl0_467 ),
inference(resolution,[],[f3580,f2798]) ).
fof(f3580,plain,
( ! [X3,X0,X18,X4] :
( ~ c_HOL_Oord__class_Oless(X4,X18,X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X3,X18,X0) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f3579]) ).
fof(f47121,plain,
( spl0_1497
| ~ spl0_1144
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f42804,f41708,f18708,f47119]) ).
fof(f47119,plain,
( spl0_1497
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f18708,plain,
( spl0_1144
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f41708,plain,
( spl0_1475
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f42804,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1144
| ~ spl0_1475 ),
inference(superposition,[],[f41709,f18709]) ).
fof(f18709,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_1144 ),
inference(avatar_component_clause,[],[f18708]) ).
fof(f41709,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1475 ),
inference(avatar_component_clause,[],[f41708]) ).
fof(f47117,plain,
( spl0_1496
| ~ spl0_381
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3840,f3579,f2897,f47115]) ).
fof(f47115,plain,
( spl0_1496
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oabs__if(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f2897,plain,
( spl0_381
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f3840,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X2),X2)
| c_HOL_Oabs__class_Oabs(X1,X2) = X1
| ~ class_Ring__and__Field_Oabs__if(X2) )
| ~ spl0_381
| ~ spl0_467 ),
inference(resolution,[],[f3580,f2898]) ).
fof(f2898,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381 ),
inference(avatar_component_clause,[],[f2897]) ).
fof(f47113,plain,
( spl0_1495
| ~ spl0_356
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3832,f3575,f2797,f47111]) ).
fof(f47111,plain,
( spl0_1495
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f3832,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_356
| ~ spl0_466 ),
inference(resolution,[],[f3576,f2798]) ).
fof(f47109,plain,
( spl0_1494
| ~ spl0_381
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3821,f3575,f2897,f47107]) ).
fof(f47107,plain,
( spl0_1494
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2
| ~ class_Ring__and__Field_Oabs__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f3821,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oabs__class_Oabs(X2,X0) = X2
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381
| ~ spl0_466 ),
inference(resolution,[],[f3576,f2898]) ).
fof(f47105,plain,
( spl0_1493
| ~ spl0_381
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f3814,f3571,f2897,f47103]) ).
fof(f47103,plain,
( spl0_1493
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f3571,plain,
( spl0_465
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f3814,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381
| ~ spl0_465 ),
inference(resolution,[],[f3572,f2898]) ).
fof(f3572,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f3571]) ).
fof(f47101,plain,
( spl0_1492
| ~ spl0_372
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f3774,f3543,f2861,f47099]) ).
fof(f47099,plain,
( spl0_1492
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f3543,plain,
( spl0_458
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f3774,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Osgn__class_Osgn(X1,X0),X0) )
| ~ spl0_372
| ~ spl0_458 ),
inference(resolution,[],[f3544,f2862]) ).
fof(f3544,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_458 ),
inference(avatar_component_clause,[],[f3543]) ).
fof(f47097,plain,
( spl0_1491
| ~ spl0_381
| ~ spl0_453 ),
inference(avatar_split_clause,[],[f3758,f3523,f2897,f47095]) ).
fof(f47095,plain,
( spl0_1491
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Osgn__class_Osgn(X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f3523,plain,
( spl0_453
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f3758,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Osgn__class_Osgn(X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1) )
| ~ spl0_381
| ~ spl0_453 ),
inference(resolution,[],[f3524,f2898]) ).
fof(f3524,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f3523]) ).
fof(f47093,plain,
( spl0_1490
| ~ spl0_368
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3719,f3497,f2845,f47091]) ).
fof(f47091,plain,
( spl0_1490
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2845,plain,
( spl0_368
<=> ! [X27,X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f3497,plain,
( spl0_449
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f3719,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_368
| ~ spl0_449 ),
inference(resolution,[],[f3498,f2846]) ).
fof(f2846,plain,
( ! [X0,X11,X27] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_368 ),
inference(avatar_component_clause,[],[f2845]) ).
fof(f3498,plain,
( ! [X2,X0,X1,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0) )
| ~ spl0_449 ),
inference(avatar_component_clause,[],[f3497]) ).
fof(f47089,plain,
( spl0_1489
| ~ spl0_362
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3717,f3497,f2821,f47087]) ).
fof(f47087,plain,
( spl0_1489
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2821,plain,
( spl0_362
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f3717,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_362
| ~ spl0_449 ),
inference(resolution,[],[f3498,f2822]) ).
fof(f2822,plain,
( ! [X3,X0,X4] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_362 ),
inference(avatar_component_clause,[],[f2821]) ).
fof(f47085,plain,
( spl0_1488
| ~ spl0_371
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3712,f3497,f2857,f47083]) ).
fof(f47083,plain,
( spl0_1488
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f2857,plain,
( spl0_371
<=> ! [X27,X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f3712,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X3,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_371
| ~ spl0_449 ),
inference(resolution,[],[f3498,f2858]) ).
fof(f2858,plain,
( ! [X0,X11,X27] :
( c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_371 ),
inference(avatar_component_clause,[],[f2857]) ).
fof(f47081,plain,
( spl0_1487
| ~ spl0_360
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3711,f3497,f2813,f47079]) ).
fof(f47079,plain,
( spl0_1487
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f2813,plain,
( spl0_360
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f3711,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X3,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_360
| ~ spl0_449 ),
inference(resolution,[],[f3498,f2814]) ).
fof(f2814,plain,
( ! [X3,X0,X4] :
( c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_360 ),
inference(avatar_component_clause,[],[f2813]) ).
fof(f47009,plain,
( spl0_1486
| ~ spl0_394
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3444,f3180,f3042,f47007]) ).
fof(f47007,plain,
( spl0_1486
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f3444,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_394
| ~ spl0_428 ),
inference(resolution,[],[f3181,f3043]) ).
fof(f47005,plain,
( spl0_1485
| ~ spl0_395
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3443,f3180,f3046,f47003]) ).
fof(f47003,plain,
( spl0_1485
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f3443,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_Lattices_Oupper__semilattice(X0) )
| ~ spl0_395
| ~ spl0_428 ),
inference(resolution,[],[f3181,f3047]) ).
fof(f47001,plain,
( spl0_1484
| ~ spl0_381
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3441,f3180,f2897,f46999]) ).
fof(f46999,plain,
( spl0_1484
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f3441,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381
| ~ spl0_428 ),
inference(resolution,[],[f3181,f2898]) ).
fof(f46997,plain,
( spl0_1483
| ~ spl0_398
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3374,f3111,f3058,f46995]) ).
fof(f46995,plain,
( spl0_1483
<=> ! [X0,X3,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f3058,plain,
( spl0_398
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f3374,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_398
| ~ spl0_411 ),
inference(resolution,[],[f3112,f3059]) ).
fof(f3059,plain,
( ! [X2,X0,X1,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_398 ),
inference(avatar_component_clause,[],[f3058]) ).
fof(f46993,plain,
( spl0_1482
| ~ spl0_399
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3373,f3111,f3062,f46991]) ).
fof(f46991,plain,
( spl0_1482
<=> ! [X0,X3,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f3062,plain,
( spl0_399
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f3373,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_399
| ~ spl0_411 ),
inference(resolution,[],[f3112,f3063]) ).
fof(f3063,plain,
( ! [X2,X0,X1,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_399 ),
inference(avatar_component_clause,[],[f3062]) ).
fof(f46989,plain,
( spl0_1481
| ~ spl0_372
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f3338,f3091,f2861,f46987]) ).
fof(f46987,plain,
( spl0_1481
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f3338,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 )
| ~ spl0_372
| ~ spl0_406 ),
inference(resolution,[],[f3092,f2862]) ).
fof(f46985,plain,
( spl0_1480
| ~ spl0_372
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3311,f3087,f2861,f46983]) ).
fof(f46983,plain,
( spl0_1480
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f3311,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 )
| ~ spl0_372
| ~ spl0_405 ),
inference(resolution,[],[f3088,f2862]) ).
fof(f46981,plain,
( spl0_1479
| ~ spl0_366
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3026,f2897,f2837,f46979]) ).
fof(f46979,plain,
( spl0_1479
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2837,plain,
( spl0_366
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f3026,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_366
| ~ spl0_381 ),
inference(resolution,[],[f2898,f2838]) ).
fof(f2838,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_366 ),
inference(avatar_component_clause,[],[f2837]) ).
fof(f46401,plain,
( spl0_1478
| ~ spl0_1049
| ~ spl0_1477 ),
inference(avatar_split_clause,[],[f45114,f44033,f15192,f46399]) ).
fof(f46399,plain,
( spl0_1478
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f15192,plain,
( spl0_1049
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f45114,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1049
| ~ spl0_1477 ),
inference(superposition,[],[f44034,f15193]) ).
fof(f15193,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f15192]) ).
fof(f44035,plain,
( spl0_1477
| ~ spl0_932
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f42809,f41708,f11887,f44033]) ).
fof(f11887,plain,
( spl0_932
<=> ! [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_932])]) ).
fof(f42809,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_932
| ~ spl0_1475 ),
inference(superposition,[],[f41709,f11888]) ).
fof(f11888,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_932 ),
inference(avatar_component_clause,[],[f11887]) ).
fof(f43581,plain,
( spl0_1476
| ~ spl0_1207
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f42805,f41708,f23905,f43579]) ).
fof(f43579,plain,
( spl0_1476
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f23905,plain,
( spl0_1207
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f42805,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1207
| ~ spl0_1475 ),
inference(superposition,[],[f41709,f23906]) ).
fof(f23906,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_1207 ),
inference(avatar_component_clause,[],[f23905]) ).
fof(f41710,plain,
( ~ spl0_146
| spl0_1475
| ~ spl0_242
| ~ spl0_932 ),
inference(avatar_split_clause,[],[f12586,f11887,f2077,f41708,f1668]) ).
fof(f1668,plain,
( spl0_146
<=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f12586,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_242
| ~ spl0_932 ),
inference(superposition,[],[f2078,f11888]) ).
fof(f41706,plain,
( spl0_1474
| ~ spl0_212
| ~ spl0_896 ),
inference(avatar_split_clause,[],[f10084,f9902,f1942,f41704]) ).
fof(f41704,plain,
( spl0_1474
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f1942,plain,
( spl0_212
<=> ! [X0,X3] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f9902,plain,
( spl0_896
<=> ! [X2,X9,X0,X10,X28,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X28,X0),X10,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f10084,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_896 ),
inference(resolution,[],[f9903,f1943]) ).
fof(f1943,plain,
( ! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(X3,X3,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_212 ),
inference(avatar_component_clause,[],[f1942]) ).
fof(f9903,plain,
( ! [X2,X28,X10,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X28,X0),X10,X0),X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_896 ),
inference(avatar_component_clause,[],[f9902]) ).
fof(f41702,plain,
( spl0_1473
| ~ spl0_214
| ~ spl0_896 ),
inference(avatar_split_clause,[],[f10083,f9902,f1950,f41700]) ).
fof(f41700,plain,
( spl0_1473
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f1950,plain,
( spl0_214
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f10083,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_896 ),
inference(resolution,[],[f9903,f1951]) ).
fof(f1951,plain,
( ! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(X3,X3,X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f1950]) ).
fof(f41698,plain,
( spl0_1472
| ~ spl0_215
| ~ spl0_896 ),
inference(avatar_split_clause,[],[f10082,f9902,f1954,f41696]) ).
fof(f41696,plain,
( spl0_1472
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f1954,plain,
( spl0_215
<=> ! [X0,X3] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f10082,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X1,X2),X3,X2),X0,X2),X2)
| ~ class_Ring__and__Field_Opordered__ring(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_896 ),
inference(resolution,[],[f9903,f1955]) ).
fof(f1955,plain,
( ! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(X3,X3,X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_215 ),
inference(avatar_component_clause,[],[f1954]) ).
fof(f41694,plain,
( spl0_1471
| ~ spl0_212
| ~ spl0_894 ),
inference(avatar_split_clause,[],[f9993,f9894,f1942,f41692]) ).
fof(f41692,plain,
( spl0_1471
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f9894,plain,
( spl0_894
<=> ! [X2,X10,X0,X9,X28,X1] :
( ~ 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(X1,X2,X0),X28,X0),X9,X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f9993,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_212
| ~ spl0_894 ),
inference(resolution,[],[f9895,f1943]) ).
fof(f9895,plain,
( ! [X2,X28,X10,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0),X10,X0)
| ~ class_Ring__and__Field_Opordered__ring(X0) )
| ~ spl0_894 ),
inference(avatar_component_clause,[],[f9894]) ).
fof(f41690,plain,
( spl0_1470
| ~ spl0_214
| ~ spl0_894 ),
inference(avatar_split_clause,[],[f9992,f9894,f1950,f41688]) ).
fof(f41688,plain,
( spl0_1470
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f9992,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Oorder(X1) )
| ~ spl0_214
| ~ spl0_894 ),
inference(resolution,[],[f9895,f1951]) ).
fof(f41686,plain,
( spl0_1469
| ~ spl0_215
| ~ spl0_894 ),
inference(avatar_split_clause,[],[f9991,f9894,f1954,f41684]) ).
fof(f41684,plain,
( spl0_1469
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f9991,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1),X3,X1)
| ~ class_Ring__and__Field_Opordered__ring(X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_215
| ~ spl0_894 ),
inference(resolution,[],[f9895,f1955]) ).
fof(f41681,plain,
( spl0_1468
| ~ spl0_116
| ~ spl0_143
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f6160,f5880,f1653,f1518,f41679]) ).
fof(f41679,plain,
( spl0_1468
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f1518,plain,
( spl0_116
<=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f5880,plain,
( spl0_688
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X18,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f6160,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_688 ),
inference(resolution,[],[f5881,f1655]) ).
fof(f5881,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X18,X0),X4,X0) )
| ~ spl0_688 ),
inference(avatar_component_clause,[],[f5880]) ).
fof(f41676,plain,
( spl0_1467
| ~ spl0_60
| ~ spl0_96
| ~ spl0_688 ),
inference(avatar_split_clause,[],[f6159,f5880,f1418,f1238,f41674]) ).
fof(f41674,plain,
( spl0_1467
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f1238,plain,
( spl0_60
<=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f6159,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_688 ),
inference(resolution,[],[f5881,f1420]) ).
fof(f41535,plain,
( spl0_1466
| ~ spl0_126
| ~ spl0_149
| ~ spl0_687 ),
inference(avatar_split_clause,[],[f6158,f5876,f1683,f1568,f41533]) ).
fof(f41533,plain,
( spl0_1466
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f1568,plain,
( spl0_126
<=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1683,plain,
( spl0_149
<=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f5876,plain,
( spl0_687
<=> ! [X4,X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f6158,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_149
| ~ spl0_687 ),
inference(resolution,[],[f5877,f1685]) ).
fof(f1685,plain,
( class_SEQ_Obanach(tc_Complex_Ocomplex)
| ~ spl0_149 ),
inference(avatar_component_clause,[],[f1683]) ).
fof(f5877,plain,
( ! [X3,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) )
| ~ spl0_687 ),
inference(avatar_component_clause,[],[f5876]) ).
fof(f41326,plain,
( spl0_1465
| ~ spl0_73
| ~ spl0_106
| ~ spl0_687 ),
inference(avatar_split_clause,[],[f6157,f5876,f1468,f1303,f41324]) ).
fof(f41324,plain,
( spl0_1465
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f1303,plain,
( spl0_73
<=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1468,plain,
( spl0_106
<=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f6157,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_106
| ~ spl0_687 ),
inference(resolution,[],[f5877,f1470]) ).
fof(f1470,plain,
( class_SEQ_Obanach(tc_RealDef_Oreal)
| ~ spl0_106 ),
inference(avatar_component_clause,[],[f1468]) ).
fof(f41257,plain,
( spl0_1464
| ~ spl0_60
| ~ spl0_70
| ~ spl0_686 ),
inference(avatar_split_clause,[],[f6156,f5872,f1288,f1238,f41255]) ).
fof(f41255,plain,
( spl0_1464
<=> ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1288,plain,
( spl0_70
<=> class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f5872,plain,
( spl0_686
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f6156,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_70
| ~ spl0_686 ),
inference(resolution,[],[f5873,f1290]) ).
fof(f1290,plain,
( class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal)
| ~ spl0_70 ),
inference(avatar_component_clause,[],[f1288]) ).
fof(f5873,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) )
| ~ spl0_686 ),
inference(avatar_component_clause,[],[f5872]) ).
fof(f41209,plain,
( spl0_1463
| ~ spl0_126
| ~ spl0_149
| ~ spl0_674 ),
inference(avatar_split_clause,[],[f6017,f5819,f1683,f1568,f41207]) ).
fof(f41207,plain,
( spl0_1463
<=> ! [X0,X1] : c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f5819,plain,
( spl0_674
<=> ! [X4,X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f6017,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),c_Transcendental_Oexp(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_149
| ~ spl0_674 ),
inference(resolution,[],[f5820,f1685]) ).
fof(f5820,plain,
( ! [X3,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) )
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f5819]) ).
fof(f41161,plain,
( spl0_1462
| ~ spl0_73
| ~ spl0_106
| ~ spl0_674 ),
inference(avatar_split_clause,[],[f6016,f5819,f1468,f1303,f41159]) ).
fof(f41159,plain,
( spl0_1462
<=> ! [X0,X1] : c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f6016,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),c_Transcendental_Oexp(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_106
| ~ spl0_674 ),
inference(resolution,[],[f5820,f1470]) ).
fof(f41157,plain,
( spl0_1461
| ~ spl0_209
| ~ spl0_667 ),
inference(avatar_split_clause,[],[f5924,f5783,f1929,f41155]) ).
fof(f41155,plain,
( spl0_1461
<=> ! [X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X1,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f5783,plain,
( spl0_667
<=> ! [X4,X0,X3] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f5924,plain,
( ! [X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X1,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_209
| ~ spl0_667 ),
inference(resolution,[],[f5784,f1930]) ).
fof(f5784,plain,
( ! [X3,X0,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ class_Divides_Oring__div(X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) )
| ~ spl0_667 ),
inference(avatar_component_clause,[],[f5783]) ).
fof(f41153,plain,
( spl0_1460
| ~ spl0_209
| ~ spl0_666 ),
inference(avatar_split_clause,[],[f5900,f5779,f1929,f41151]) ).
fof(f41151,plain,
( spl0_1460
<=> ! [X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f5779,plain,
( spl0_666
<=> ! [X4,X0,X3] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Divides_Odiv__class_Odiv(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f5900,plain,
( ! [X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X1,X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_209
| ~ spl0_666 ),
inference(resolution,[],[f5780,f1930]) ).
fof(f5780,plain,
( ! [X3,X0,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Odiv(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) )
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f5779]) ).
fof(f41149,plain,
( spl0_1459
| ~ spl0_1321
| ~ spl0_1417 ),
inference(avatar_split_clause,[],[f40927,f40882,f26872,f41147]) ).
fof(f41147,plain,
( spl0_1459
<=> ! [X5,X3,X4,X2,X0,X8,X6,X1,X7] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X7,c_Polynomial_Osmult(X8,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f26872,plain,
( spl0_1321
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f40882,plain,
( spl0_1417
<=> ! [X5,X3,X4,X2,X0,X6,X1,X7] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X7,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f40927,plain,
( ! [X2,X3,X0,X1,X8,X6,X7,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X7,c_Polynomial_Osmult(X8,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1417 ),
inference(superposition,[],[f40883,f26873]) ).
fof(f26873,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f26872]) ).
fof(f40883,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X7,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1417 ),
inference(avatar_component_clause,[],[f40882]) ).
fof(f41145,plain,
( spl0_1458
| ~ spl0_220
| ~ spl0_659 ),
inference(avatar_split_clause,[],[f5718,f5542,f1977,f41143]) ).
fof(f41143,plain,
( spl0_1458
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0),X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f1977,plain,
( spl0_220
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f5718,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0),X2,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_220
| ~ spl0_659 ),
inference(resolution,[],[f5543,f1978]) ).
fof(f1978,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_220 ),
inference(avatar_component_clause,[],[f1977]) ).
fof(f41141,plain,
( spl0_1457
| ~ spl0_284
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f5149,f4749,f2345,f41139]) ).
fof(f41139,plain,
( spl0_1457
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f4749,plain,
( spl0_588
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f5149,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_284
| ~ spl0_588 ),
inference(duplicate_literal_removal,[],[f5130]) ).
fof(f5130,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_284
| ~ spl0_588 ),
inference(resolution,[],[f4750,f2346]) ).
fof(f4750,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_588 ),
inference(avatar_component_clause,[],[f4749]) ).
fof(f41137,plain,
( spl0_1456
| ~ spl0_225
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f5141,f4749,f1997,f41135]) ).
fof(f41135,plain,
( spl0_1456
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oone__class_Oone(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oone__class_Oone(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f1997,plain,
( spl0_225
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f5141,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oone__class_Oone(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oone__class_Oone(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_225
| ~ spl0_588 ),
inference(resolution,[],[f4750,f1998]) ).
fof(f1998,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_225 ),
inference(avatar_component_clause,[],[f1997]) ).
fof(f41133,plain,
( spl0_1455
| ~ spl0_454
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4348,f4155,f3527,f41131]) ).
fof(f41131,plain,
( spl0_1455
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f3527,plain,
( spl0_454
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f4348,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_454
| ~ spl0_542 ),
inference(duplicate_literal_removal,[],[f4347]) ).
fof(f4347,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_454
| ~ spl0_542 ),
inference(resolution,[],[f4156,f3528]) ).
fof(f3528,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_454 ),
inference(avatar_component_clause,[],[f3527]) ).
fof(f41129,plain,
( spl0_1454
| ~ spl0_381
| ~ spl0_542 ),
inference(avatar_split_clause,[],[f4335,f4155,f2897,f41127]) ).
fof(f41127,plain,
( spl0_1454
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_Ring__and__Field_Oabs__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f4335,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381
| ~ spl0_542 ),
inference(resolution,[],[f4156,f2898]) ).
fof(f41125,plain,
( spl0_1453
| ~ spl0_283
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f4296,f4112,f2341,f41123]) ).
fof(f41123,plain,
( spl0_1453
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f4296,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_534 ),
inference(resolution,[],[f4113,f2342]) ).
fof(f41121,plain,
( spl0_1452
| ~ spl0_284
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f4295,f4112,f2345,f41119]) ).
fof(f41119,plain,
( spl0_1452
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f4295,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_534 ),
inference(resolution,[],[f4113,f2346]) ).
fof(f41117,plain,
( spl0_1451
| ~ spl0_285
| ~ spl0_534 ),
inference(avatar_split_clause,[],[f4294,f4112,f2349,f41115]) ).
fof(f41115,plain,
( spl0_1451
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f4294,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_534 ),
inference(resolution,[],[f4113,f2350]) ).
fof(f41113,plain,
( spl0_1450
| ~ spl0_283
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f4264,f4076,f2341,f41111]) ).
fof(f41111,plain,
( spl0_1450
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f4264,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_525 ),
inference(resolution,[],[f4077,f2342]) ).
fof(f41109,plain,
( spl0_1449
| ~ spl0_284
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f4263,f4076,f2345,f41107]) ).
fof(f41107,plain,
( spl0_1449
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f4263,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) )
| ~ spl0_284
| ~ spl0_525 ),
inference(resolution,[],[f4077,f2346]) ).
fof(f41064,plain,
( spl0_1448
| ~ spl0_285
| ~ spl0_525 ),
inference(avatar_split_clause,[],[f4262,f4076,f2349,f41062]) ).
fof(f41062,plain,
( spl0_1448
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f4262,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) )
| ~ spl0_285
| ~ spl0_525 ),
inference(resolution,[],[f4077,f2350]) ).
fof(f41060,plain,
( spl0_1447
| ~ spl0_283
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f4238,f4064,f2341,f41058]) ).
fof(f41058,plain,
( spl0_1447
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f4064,plain,
( spl0_522
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f4238,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_522 ),
inference(resolution,[],[f4065,f2342]) ).
fof(f4065,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) )
| ~ spl0_522 ),
inference(avatar_component_clause,[],[f4064]) ).
fof(f41056,plain,
( spl0_1446
| ~ spl0_284
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f4237,f4064,f2345,f41054]) ).
fof(f41054,plain,
( spl0_1446
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f4237,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) )
| ~ spl0_284
| ~ spl0_522 ),
inference(resolution,[],[f4065,f2346]) ).
fof(f41052,plain,
( spl0_1445
| ~ spl0_285
| ~ spl0_522 ),
inference(avatar_split_clause,[],[f4236,f4064,f2349,f41050]) ).
fof(f41050,plain,
( spl0_1445
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f4236,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__add(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oplus__class_Oplus(X0,X0,X1),X1) )
| ~ spl0_285
| ~ spl0_522 ),
inference(resolution,[],[f4065,f2350]) ).
fof(f41048,plain,
( spl0_1444
| ~ spl0_283
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f4196,f3984,f2341,f41046]) ).
fof(f41046,plain,
( spl0_1444
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f4196,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_502 ),
inference(resolution,[],[f3985,f2342]) ).
fof(f41044,plain,
( spl0_1443
| ~ spl0_284
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f4195,f3984,f2345,f41042]) ).
fof(f41042,plain,
( spl0_1443
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f4195,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_502 ),
inference(resolution,[],[f3985,f2346]) ).
fof(f41040,plain,
( spl0_1442
| ~ spl0_285
| ~ spl0_502 ),
inference(avatar_split_clause,[],[f4194,f3984,f2349,f41038]) ).
fof(f41038,plain,
( spl0_1442
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f4194,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_502 ),
inference(resolution,[],[f3985,f2350]) ).
fof(f41036,plain,
( spl0_1441
| ~ spl0_428
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3957,f3659,f3180,f41034]) ).
fof(f41034,plain,
( spl0_1441
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,X1),X1) = c_HOL_Oone__class_Oone(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f3957,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,X1),X1) = c_HOL_Oone__class_Oone(X1) )
| ~ spl0_428
| ~ spl0_487 ),
inference(resolution,[],[f3660,f3181]) ).
fof(f41032,plain,
( spl0_1440
| ~ spl0_278
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f3938,f3651,f2321,f41030]) ).
fof(f41030,plain,
( spl0_1440
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f3651,plain,
( spl0_485
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f3938,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_278
| ~ spl0_485 ),
inference(resolution,[],[f3652,f2322]) ).
fof(f3652,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0) )
| ~ spl0_485 ),
inference(avatar_component_clause,[],[f3651]) ).
fof(f41028,plain,
( spl0_1439
| ~ spl0_428
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3865,f3607,f3180,f41026]) ).
fof(f41026,plain,
( spl0_1439
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f3865,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_428
| ~ spl0_474 ),
inference(resolution,[],[f3608,f3181]) ).
fof(f41024,plain,
( spl0_1438
| ~ spl0_1143
| ~ spl0_1336 ),
inference(avatar_split_clause,[],[f28042,f27631,f18704,f41022]) ).
fof(f41022,plain,
( spl0_1438
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f18704,plain,
( spl0_1143
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f27631,plain,
( spl0_1336
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f28042,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_1143
| ~ spl0_1336 ),
inference(superposition,[],[f27632,f18705]) ).
fof(f18705,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f18704]) ).
fof(f27632,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_1336 ),
inference(avatar_component_clause,[],[f27631]) ).
fof(f41020,plain,
( spl0_1437
| ~ spl0_198
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f3860,f3587,f1885,f41018]) ).
fof(f41018,plain,
( spl0_1437
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f3587,plain,
( spl0_469
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f3860,plain,
( ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) )
| ~ spl0_198
| ~ spl0_469 ),
inference(resolution,[],[f3588,f1886]) ).
fof(f3588,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) )
| ~ spl0_469 ),
inference(avatar_component_clause,[],[f3587]) ).
fof(f41016,plain,
( spl0_1436
| ~ spl0_307
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3850,f3579,f2497,f41014]) ).
fof(f41014,plain,
( spl0_1436
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2497,plain,
( spl0_307
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f3850,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_Power_Opower__class_Opower(X2,c_HOL_Ozero__class_Ozero(tc_nat),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_307
| ~ spl0_467 ),
inference(resolution,[],[f3580,f2498]) ).
fof(f2498,plain,
( ! [X3,X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_307 ),
inference(avatar_component_clause,[],[f2497]) ).
fof(f41012,plain,
( spl0_1435
| ~ spl0_307
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3831,f3575,f2497,f41010]) ).
fof(f41010,plain,
( spl0_1435
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f3831,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_307
| ~ spl0_466 ),
inference(resolution,[],[f3576,f2498]) ).
fof(f41008,plain,
( spl0_1434
| ~ spl0_427
| ~ spl0_451 ),
inference(avatar_split_clause,[],[f3740,f3515,f3176,f41006]) ).
fof(f41006,plain,
( spl0_1434
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f3515,plain,
( spl0_451
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f3740,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_427
| ~ spl0_451 ),
inference(resolution,[],[f3516,f3177]) ).
fof(f3516,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_451 ),
inference(avatar_component_clause,[],[f3515]) ).
fof(f41004,plain,
( spl0_1433
| ~ spl0_426
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f3732,f3511,f3172,f41002]) ).
fof(f41002,plain,
( spl0_1433
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f3172,plain,
( spl0_426
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f3511,plain,
( spl0_450
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f3732,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_426
| ~ spl0_450 ),
inference(resolution,[],[f3512,f3173]) ).
fof(f3173,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_426 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f3512,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_450 ),
inference(avatar_component_clause,[],[f3511]) ).
fof(f41000,plain,
( spl0_1432
| ~ spl0_399
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3722,f3497,f3062,f40998]) ).
fof(f40998,plain,
( spl0_1432
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f3722,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X2) )
| ~ spl0_399
| ~ spl0_449 ),
inference(duplicate_literal_removal,[],[f3713]) ).
fof(f3713,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X4,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_399
| ~ spl0_449 ),
inference(resolution,[],[f3498,f3063]) ).
fof(f40996,plain,
( spl0_1431
| ~ spl0_398
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3721,f3497,f3058,f40994]) ).
fof(f40994,plain,
( spl0_1431
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f3721,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2) )
| ~ spl0_398
| ~ spl0_449 ),
inference(duplicate_literal_removal,[],[f3714]) ).
fof(f3714,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_398
| ~ spl0_449 ),
inference(resolution,[],[f3498,f3059]) ).
fof(f40992,plain,
( spl0_1430
| ~ spl0_198
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f3698,f3485,f1885,f40990]) ).
fof(f40990,plain,
( spl0_1430
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f3485,plain,
( spl0_446
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f3698,plain,
( ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) )
| ~ spl0_198
| ~ spl0_446 ),
inference(resolution,[],[f3486,f1886]) ).
fof(f3486,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) )
| ~ spl0_446 ),
inference(avatar_component_clause,[],[f3485]) ).
fof(f40988,plain,
( spl0_1429
| ~ spl0_198
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f3696,f3481,f1885,f40986]) ).
fof(f40986,plain,
( spl0_1429
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f3481,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f3696,plain,
( ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X0,X1,tc_Polynomial_Opoly(X2)) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ofield(X2) )
| ~ spl0_198
| ~ spl0_445 ),
inference(resolution,[],[f3482,f1886]) ).
fof(f3482,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) )
| ~ spl0_445 ),
inference(avatar_component_clause,[],[f3481]) ).
fof(f40984,plain,
( spl0_1428
| ~ spl0_208
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f3692,f3469,f1925,f40982]) ).
fof(f40982,plain,
( spl0_1428
<=> ! [X0,X1] :
( c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1925,plain,
( spl0_208
<=> ! [X34] :
( ~ class_HOL_Ozero(X34)
| class_HOL_Ozero(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f3469,plain,
( spl0_442
<=> ! [X0,X1] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f3692,plain,
( ! [X0,X1] :
( c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X1)) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1))
| ~ class_HOL_Ozero(X1) )
| ~ spl0_208
| ~ spl0_442 ),
inference(resolution,[],[f3470,f1926]) ).
fof(f1926,plain,
( ! [X34] :
( class_HOL_Ozero(tc_Polynomial_Opoly(X34))
| ~ class_HOL_Ozero(X34) )
| ~ spl0_208 ),
inference(avatar_component_clause,[],[f1925]) ).
fof(f3470,plain,
( ! [X0,X1] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_442 ),
inference(avatar_component_clause,[],[f3469]) ).
fof(f40924,plain,
( spl0_1427
| ~ spl0_208
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3461,f3212,f1925,f40922]) ).
fof(f40922,plain,
( spl0_1427
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),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_1427])]) ).
fof(f3212,plain,
( spl0_436
<=> ! [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_436])]) ).
fof(f3461,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) )
| ~ spl0_208
| ~ spl0_436 ),
inference(resolution,[],[f3213,f1926]) ).
fof(f3213,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_436 ),
inference(avatar_component_clause,[],[f3212]) ).
fof(f40920,plain,
( spl0_1426
| ~ spl0_427
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3451,f3180,f3176,f40918]) ).
fof(f40918,plain,
( spl0_1426
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f3451,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_427
| ~ spl0_428 ),
inference(duplicate_literal_removal,[],[f3442]) ).
fof(f3442,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_427
| ~ spl0_428 ),
inference(resolution,[],[f3181,f3177]) ).
fof(f40916,plain,
( spl0_1425
| ~ spl0_405
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3450,f3180,f3087,f40914]) ).
fof(f40914,plain,
( spl0_1425
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f3450,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1 )
| ~ spl0_405
| ~ spl0_428 ),
inference(duplicate_literal_removal,[],[f3447]) ).
fof(f3447,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_405
| ~ spl0_428 ),
inference(resolution,[],[f3181,f3088]) ).
fof(f40912,plain,
( spl0_1424
| ~ spl0_366
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f3434,f3176,f2837,f40910]) ).
fof(f40910,plain,
( spl0_1424
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f3434,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,X1),X1),X1) )
| ~ spl0_366
| ~ spl0_427 ),
inference(duplicate_literal_removal,[],[f3433]) ).
fof(f3433,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(X0,X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_366
| ~ spl0_427 ),
inference(resolution,[],[f3177,f2838]) ).
fof(f40908,plain,
( spl0_1423
| ~ spl0_207
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f3384,f3124,f1921,f40906]) ).
fof(f40906,plain,
( spl0_1423
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Suc(X1),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f3124,plain,
( spl0_414
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X8),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f3384,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Suc(X1),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_207
| ~ spl0_414 ),
inference(resolution,[],[f3125,f1922]) ).
fof(f3125,plain,
( ! [X0,X8] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Osemiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X8),X0) )
| ~ spl0_414 ),
inference(avatar_component_clause,[],[f3124]) ).
fof(f40904,plain,
( spl0_1422
| ~ spl0_368
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3377,f3111,f2845,f40902]) ).
fof(f40902,plain,
( spl0_1422
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oabs__class_Oabs(X2,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f3377,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oabs__class_Oabs(X2,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_368
| ~ spl0_411 ),
inference(resolution,[],[f3112,f2846]) ).
fof(f40900,plain,
( spl0_1421
| ~ spl0_362
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3375,f3111,f2821,f40898]) ).
fof(f40898,plain,
( spl0_1421
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f3375,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_362
| ~ spl0_411 ),
inference(resolution,[],[f3112,f2822]) ).
fof(f40896,plain,
( spl0_1420
| ~ spl0_371
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3372,f3111,f2857,f40894]) ).
fof(f40894,plain,
( spl0_1420
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f3372,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_371
| ~ spl0_411 ),
inference(resolution,[],[f3112,f2858]) ).
fof(f40892,plain,
( spl0_1419
| ~ spl0_360
| ~ spl0_411 ),
inference(avatar_split_clause,[],[f3371,f3111,f2813,f40890]) ).
fof(f40890,plain,
( spl0_1419
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f3371,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_360
| ~ spl0_411 ),
inference(resolution,[],[f3112,f2814]) ).
fof(f40888,plain,
( spl0_1418
| ~ spl0_249
| ~ spl0_406 ),
inference(avatar_split_clause,[],[f3339,f3091,f2105,f40886]) ).
fof(f40886,plain,
( spl0_1418
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f2105,plain,
( spl0_249
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3339,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) )
| ~ spl0_249
| ~ spl0_406 ),
inference(resolution,[],[f3092,f2106]) ).
fof(f2106,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f2105]) ).
fof(f40884,plain,
( spl0_1417
| ~ spl0_1321
| ~ spl0_1402 ),
inference(avatar_split_clause,[],[f40797,f39004,f26872,f40882]) ).
fof(f39004,plain,
( spl0_1402
<=> ! [X5,X3,X4,X2,X0,X6,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f40797,plain,
( ! [X2,X3,X0,X1,X6,X7,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X7,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1402 ),
inference(superposition,[],[f39005,f26873]) ).
fof(f39005,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1402 ),
inference(avatar_component_clause,[],[f39004]) ).
fof(f40880,plain,
( spl0_1416
| ~ spl0_366
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3328,f3087,f2837,f40878]) ).
fof(f40878,plain,
( spl0_1416
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f3328,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1) )
| ~ spl0_366
| ~ spl0_405 ),
inference(duplicate_literal_removal,[],[f3313]) ).
fof(f3313,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = X2
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_366
| ~ spl0_405 ),
inference(resolution,[],[f3088,f2838]) ).
fof(f40876,plain,
( spl0_1415
| ~ spl0_249
| ~ spl0_405 ),
inference(avatar_split_clause,[],[f3312,f3087,f2105,f40874]) ).
fof(f40874,plain,
( spl0_1415
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f3312,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oabs__class_Oabs(X0,X1),X1)
| c_HOL_Oabs__class_Oabs(X0,X1) = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X1) )
| ~ spl0_249
| ~ spl0_405 ),
inference(resolution,[],[f3088,f2106]) ).
fof(f40872,plain,
( spl0_1414
| ~ spl0_367
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f3272,f3062,f2841,f40870]) ).
fof(f40870,plain,
( spl0_1414
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f2841,plain,
( spl0_367
<=> ! [X27,X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f3272,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_367
| ~ spl0_399 ),
inference(resolution,[],[f3063,f2842]) ).
fof(f2842,plain,
( ! [X0,X11,X27] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_367 ),
inference(avatar_component_clause,[],[f2841]) ).
fof(f40868,plain,
( spl0_1413
| ~ spl0_361
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f3270,f3062,f2817,f40866]) ).
fof(f40866,plain,
( spl0_1413
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f2817,plain,
( spl0_361
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f3270,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_361
| ~ spl0_399 ),
inference(resolution,[],[f3063,f2818]) ).
fof(f2818,plain,
( ! [X3,X0,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_361 ),
inference(avatar_component_clause,[],[f2817]) ).
fof(f40864,plain,
( spl0_1412
| ~ spl0_367
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f3264,f3058,f2841,f40862]) ).
fof(f40862,plain,
( spl0_1412
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f3264,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_367
| ~ spl0_398 ),
inference(resolution,[],[f3059,f2842]) ).
fof(f40860,plain,
( spl0_1411
| ~ spl0_361
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f3262,f3058,f2817,f40858]) ).
fof(f40858,plain,
( spl0_1411
<=> ! [X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f3262,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_361
| ~ spl0_398 ),
inference(resolution,[],[f3059,f2818]) ).
fof(f40856,plain,
( spl0_1410
| ~ spl0_371
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f3255,f3054,f2857,f40854]) ).
fof(f40854,plain,
( spl0_1410
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X3,X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f3054,plain,
( spl0_397
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f3255,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X3,X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_371
| ~ spl0_397 ),
inference(resolution,[],[f3055,f2858]) ).
fof(f3055,plain,
( ! [X2,X0,X1,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_397 ),
inference(avatar_component_clause,[],[f3054]) ).
fof(f40852,plain,
( spl0_1409
| ~ spl0_360
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f3254,f3054,f2813,f40850]) ).
fof(f40850,plain,
( spl0_1409
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X3,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f3254,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X3,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_360
| ~ spl0_397 ),
inference(resolution,[],[f3055,f2814]) ).
fof(f40848,plain,
( spl0_1408
| ~ spl0_371
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f3244,f3050,f2857,f40846]) ).
fof(f40846,plain,
( spl0_1408
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X0,X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f3050,plain,
( spl0_396
<=> ! [X9,X0,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f3244,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X0,X2),X1,X2)
| ~ class_Ring__and__Field_Oordered__idom(X2) )
| ~ spl0_371
| ~ spl0_396 ),
inference(resolution,[],[f3051,f2858]) ).
fof(f3051,plain,
( ! [X2,X0,X1,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_396 ),
inference(avatar_component_clause,[],[f3050]) ).
fof(f40844,plain,
( spl0_1407
| ~ spl0_360
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f3243,f3050,f2813,f40842]) ).
fof(f40842,plain,
( spl0_1407
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f3243,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X3,X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_360
| ~ spl0_396 ),
inference(resolution,[],[f3051,f2814]) ).
fof(f40794,plain,
( spl0_1406
| ~ spl0_366
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3235,f3046,f2837,f40792]) ).
fof(f40792,plain,
( spl0_1406
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_HOL_Oord__class_Oless(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f3235,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_HOL_Oord__class_Oless(X0,c_Lattices_Oupper__semilattice__class_Osup(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_366
| ~ spl0_395 ),
inference(resolution,[],[f3047,f2838]) ).
fof(f40790,plain,
( spl0_1405
| ~ spl0_366
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3225,f3042,f2837,f40788]) ).
fof(f40788,plain,
( spl0_1405
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_HOL_Oord__class_Oless(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f3225,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Lattices_Oupper__semilattice(X1)
| c_HOL_Oord__class_Oless(X0,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_366
| ~ spl0_394 ),
inference(resolution,[],[f3043,f2838]) ).
fof(f40786,plain,
( spl0_1404
| ~ spl0_206
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f3217,f3038,f1917,f40784]) ).
fof(f40784,plain,
( spl0_1404
<=> ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1917,plain,
( spl0_206
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Int_Onumber__ring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f3038,plain,
( spl0_393
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f3217,plain,
( ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_206
| ~ spl0_393 ),
inference(resolution,[],[f3039,f1918]) ).
fof(f1918,plain,
( ! [X34] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__ring__1(X34) )
| ~ spl0_206 ),
inference(avatar_component_clause,[],[f1917]) ).
fof(f3039,plain,
( ! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X3,X0) )
| ~ spl0_393 ),
inference(avatar_component_clause,[],[f3038]) ).
fof(f40782,plain,
( spl0_1403
| ~ spl0_307
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f2992,f2861,f2497,f40780]) ).
fof(f40780,plain,
( spl0_1403
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f2992,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_307
| ~ spl0_372 ),
inference(resolution,[],[f2862,f2498]) ).
fof(f39006,plain,
( spl0_1402
| ~ spl0_1321
| ~ spl0_1401 ),
inference(avatar_split_clause,[],[f38247,f37854,f26872,f39004]) ).
fof(f37854,plain,
( spl0_1401
<=> ! [X2,X3,X4,X0,X5,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f38247,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1401 ),
inference(superposition,[],[f37855,f26873]) ).
fof(f37855,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1401 ),
inference(avatar_component_clause,[],[f37854]) ).
fof(f37856,plain,
( spl0_1401
| ~ spl0_1321
| ~ spl0_1400 ),
inference(avatar_split_clause,[],[f37575,f37338,f26872,f37854]) ).
fof(f37338,plain,
( spl0_1400
<=> ! [X2,X4,X0,X3,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f37575,plain,
( ! [X2,X3,X0,X1,X4,X5] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1400 ),
inference(superposition,[],[f37339,f26873]) ).
fof(f37339,plain,
( ! [X2,X3,X0,X1,X4] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1400 ),
inference(avatar_component_clause,[],[f37338]) ).
fof(f37340,plain,
( spl0_1400
| ~ spl0_1321
| ~ spl0_1390 ),
inference(avatar_split_clause,[],[f36592,f36484,f26872,f37338]) ).
fof(f36484,plain,
( spl0_1390
<=> ! [X2,X0,X1,X3] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f36592,plain,
( ! [X2,X3,X0,X1,X4] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X4,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1390 ),
inference(superposition,[],[f36485,f26873]) ).
fof(f36485,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1390 ),
inference(avatar_component_clause,[],[f36484]) ).
fof(f36522,plain,
( spl0_1399
| ~ spl0_501
| ~ spl0_739 ),
inference(avatar_split_clause,[],[f7019,f6412,f3980,f36520]) ).
fof(f36520,plain,
( spl0_1399
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f3980,plain,
( spl0_501
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f6412,plain,
( spl0_739
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f7019,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) )
| ~ spl0_501
| ~ spl0_739 ),
inference(resolution,[],[f6413,f3981]) ).
fof(f3981,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) )
| ~ spl0_501 ),
inference(avatar_component_clause,[],[f3980]) ).
fof(f6413,plain,
( ! [X3,X0,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_739 ),
inference(avatar_component_clause,[],[f6412]) ).
fof(f36518,plain,
( spl0_1398
| ~ spl0_62
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f5691,f5530,f1248,f36516]) ).
fof(f36516,plain,
( spl0_1398
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f5530,plain,
( spl0_656
<=> ! [X0,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) = c_HOL_Oplus__class_Oplus(X27,c_HOL_Otimes__class_Otimes(X1,X27,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f5691,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_656 ),
inference(resolution,[],[f5531,f1250]) ).
fof(f5531,plain,
( ! [X0,X1,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) = c_HOL_Oplus__class_Oplus(X27,c_HOL_Otimes__class_Otimes(X1,X27,X0),X0) )
| ~ spl0_656 ),
inference(avatar_component_clause,[],[f5530]) ).
fof(f36514,plain,
( spl0_1397
| ~ spl0_117
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f5690,f5530,f1523,f36512]) ).
fof(f36512,plain,
( spl0_1397
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f5690,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_656 ),
inference(resolution,[],[f5531,f1525]) ).
fof(f36510,plain,
( spl0_1396
| ~ spl0_14
| ~ spl0_656 ),
inference(avatar_split_clause,[],[f5688,f5530,f1008,f36508]) ).
fof(f36508,plain,
( spl0_1396
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f5688,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_656 ),
inference(resolution,[],[f5531,f1010]) ).
fof(f36506,plain,
( spl0_1395
| ~ spl0_62
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f5687,f5526,f1248,f36504]) ).
fof(f36504,plain,
( spl0_1395
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f5526,plain,
( spl0_655
<=> ! [X0,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X27,X0),X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f5687,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_655 ),
inference(resolution,[],[f5527,f1250]) ).
fof(f5527,plain,
( ! [X0,X1,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X27,X0),X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) )
| ~ spl0_655 ),
inference(avatar_component_clause,[],[f5526]) ).
fof(f36502,plain,
( spl0_1394
| ~ spl0_117
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f5686,f5526,f1523,f36500]) ).
fof(f36500,plain,
( spl0_1394
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f5686,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_655 ),
inference(resolution,[],[f5527,f1525]) ).
fof(f36498,plain,
( spl0_1393
| ~ spl0_14
| ~ spl0_655 ),
inference(avatar_split_clause,[],[f5684,f5526,f1008,f36496]) ).
fof(f36496,plain,
( spl0_1393
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f5684,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_14
| ~ spl0_655 ),
inference(resolution,[],[f5527,f1010]) ).
fof(f36494,plain,
( spl0_1392
| ~ spl0_212
| ~ spl0_648 ),
inference(avatar_split_clause,[],[f5601,f5487,f1942,f36492]) ).
fof(f36492,plain,
( spl0_1392
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f5487,plain,
( spl0_648
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f5601,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_648 ),
inference(resolution,[],[f5488,f1943]) ).
fof(f5488,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_648 ),
inference(avatar_component_clause,[],[f5487]) ).
fof(f36490,plain,
( spl0_1391
| ~ spl0_214
| ~ spl0_648 ),
inference(avatar_split_clause,[],[f5600,f5487,f1950,f36488]) ).
fof(f36488,plain,
( spl0_1391
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f5600,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_648 ),
inference(resolution,[],[f5488,f1951]) ).
fof(f36486,plain,
( spl0_1390
| ~ spl0_1321
| ~ spl0_1369 ),
inference(avatar_split_clause,[],[f36429,f36384,f26872,f36484]) ).
fof(f36384,plain,
( spl0_1369
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f36429,plain,
( ! [X2,X3,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1369 ),
inference(superposition,[],[f36385,f26873]) ).
fof(f36385,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1369 ),
inference(avatar_component_clause,[],[f36384]) ).
fof(f36482,plain,
( spl0_1389
| ~ spl0_215
| ~ spl0_648 ),
inference(avatar_split_clause,[],[f5599,f5487,f1954,f36480]) ).
fof(f36480,plain,
( spl0_1389
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f5599,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,X2),X1,X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),X0,X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_648 ),
inference(resolution,[],[f5488,f1955]) ).
fof(f36478,plain,
( spl0_1388
| ~ spl0_226
| ~ spl0_591 ),
inference(avatar_split_clause,[],[f5163,f4783,f2001,f36476]) ).
fof(f36476,plain,
( spl0_1388
<=> ! [X0] :
( c_HOL_Oone__class_Oone(X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f2001,plain,
( spl0_226
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f4783,plain,
( spl0_591
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f5163,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_226
| ~ spl0_591 ),
inference(resolution,[],[f4784,f2002]) ).
fof(f2002,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_226 ),
inference(avatar_component_clause,[],[f2001]) ).
fof(f4784,plain,
( ! [X3,X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X3,X0) )
| ~ spl0_591 ),
inference(avatar_component_clause,[],[f4783]) ).
fof(f36474,plain,
( spl0_1387
| ~ spl0_485
| ~ spl0_556 ),
inference(avatar_split_clause,[],[f4578,f4409,f3651,f36472]) ).
fof(f36472,plain,
( spl0_1387
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f4409,plain,
( spl0_556
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f4578,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 )
| ~ spl0_485
| ~ spl0_556 ),
inference(duplicate_literal_removal,[],[f4562]) ).
fof(f4562,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0) )
| ~ spl0_485
| ~ spl0_556 ),
inference(resolution,[],[f4410,f3652]) ).
fof(f4410,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) )
| ~ spl0_556 ),
inference(avatar_component_clause,[],[f4409]) ).
fof(f36470,plain,
( spl0_1386
| ~ spl0_283
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3965,f3659,f2341,f36468]) ).
fof(f36468,plain,
( spl0_1386
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f3965,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_487 ),
inference(resolution,[],[f3660,f2342]) ).
fof(f36466,plain,
( spl0_1385
| ~ spl0_284
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3964,f3659,f2345,f36464]) ).
fof(f36464,plain,
( spl0_1385
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f3964,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_284
| ~ spl0_487 ),
inference(resolution,[],[f3660,f2346]) ).
fof(f36462,plain,
( spl0_1384
| ~ spl0_285
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3963,f3659,f2349,f36460]) ).
fof(f36460,plain,
( spl0_1384
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f3963,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),c_HOL_Ozero__class_Ozero(X1),X1) )
| ~ spl0_285
| ~ spl0_487 ),
inference(resolution,[],[f3660,f2350]) ).
fof(f36458,plain,
( spl0_1383
| ~ spl0_283
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f3911,f3631,f2341,f36456]) ).
fof(f36456,plain,
( spl0_1383
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f3631,plain,
( spl0_480
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f3911,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_480 ),
inference(resolution,[],[f3632,f2342]) ).
fof(f3632,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_480 ),
inference(avatar_component_clause,[],[f3631]) ).
fof(f36454,plain,
( spl0_1382
| ~ spl0_284
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f3910,f3631,f2345,f36452]) ).
fof(f36452,plain,
( spl0_1382
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f3910,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_284
| ~ spl0_480 ),
inference(resolution,[],[f3632,f2346]) ).
fof(f36450,plain,
( spl0_1381
| ~ spl0_285
| ~ spl0_480 ),
inference(avatar_split_clause,[],[f3909,f3631,f2349,f36448]) ).
fof(f36448,plain,
( spl0_1381
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f3909,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X2),c_HOL_Ominus__class_Ominus(X0,X1,X2),X2) )
| ~ spl0_285
| ~ spl0_480 ),
inference(resolution,[],[f3632,f2350]) ).
fof(f36446,plain,
( spl0_1380
| ~ spl0_283
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f3904,f3627,f2341,f36444]) ).
fof(f36444,plain,
( spl0_1380
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f3627,plain,
( spl0_479
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f3904,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_479 ),
inference(resolution,[],[f3628,f2342]) ).
fof(f3628,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__field(X0) )
| ~ spl0_479 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f36426,plain,
( spl0_1379
| ~ spl0_284
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f3903,f3627,f2345,f36424]) ).
fof(f36424,plain,
( spl0_1379
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f3903,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1) )
| ~ spl0_284
| ~ spl0_479 ),
inference(resolution,[],[f3628,f2346]) ).
fof(f36422,plain,
( spl0_1378
| ~ spl0_285
| ~ spl0_479 ),
inference(avatar_split_clause,[],[f3902,f3627,f2349,f36420]) ).
fof(f36420,plain,
( spl0_1378
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f3902,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Oinverse__class_Oinverse(X0,X1),X1) )
| ~ spl0_285
| ~ spl0_479 ),
inference(resolution,[],[f3628,f2350]) ).
fof(f36418,plain,
( spl0_1377
| ~ spl0_277
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f3878,f3619,f2317,f36416]) ).
fof(f36416,plain,
( spl0_1377
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oone__class_Oone(X0),X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f3619,plain,
( spl0_477
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f3878,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oone__class_Oone(X0),X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_477 ),
inference(resolution,[],[f3620,f2318]) ).
fof(f3620,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_477 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f36414,plain,
( spl0_1376
| ~ spl0_283
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3871,f3607,f2341,f36412]) ).
fof(f36412,plain,
( spl0_1376
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f3871,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_474 ),
inference(resolution,[],[f3608,f2342]) ).
fof(f36410,plain,
( spl0_1375
| ~ spl0_284
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3870,f3607,f2345,f36408]) ).
fof(f36408,plain,
( spl0_1375
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f3870,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_474 ),
inference(resolution,[],[f3608,f2346]) ).
fof(f36406,plain,
( spl0_1374
| ~ spl0_285
| ~ spl0_474 ),
inference(avatar_split_clause,[],[f3869,f3607,f2349,f36404]) ).
fof(f36404,plain,
( spl0_1374
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f3869,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_474 ),
inference(resolution,[],[f3608,f2350]) ).
fof(f36402,plain,
( spl0_1373
| ~ spl0_277
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3839,f3579,f2317,f36400]) ).
fof(f36400,plain,
( spl0_1373
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f3839,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Orderings_Opreorder(X2)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__semidom(X2) )
| ~ spl0_277
| ~ spl0_467 ),
inference(resolution,[],[f3580,f2318]) ).
fof(f36398,plain,
( spl0_1372
| ~ spl0_277
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3820,f3575,f2317,f36396]) ).
fof(f36396,plain,
( spl0_1372
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f3820,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X2,X1)
| ~ class_Orderings_Oorder(X1)
| c_HOL_Oord__class_Oless(X0,X2,X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_277
| ~ spl0_466 ),
inference(resolution,[],[f3576,f2318]) ).
fof(f36394,plain,
( spl0_1371
| ~ spl0_283
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f3812,f3567,f2341,f36392]) ).
fof(f36392,plain,
( spl0_1371
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f3567,plain,
( spl0_464
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f3812,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_464 ),
inference(resolution,[],[f3568,f2342]) ).
fof(f3568,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_464 ),
inference(avatar_component_clause,[],[f3567]) ).
fof(f36390,plain,
( spl0_1370
| ~ spl0_284
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f3811,f3567,f2345,f36388]) ).
fof(f36388,plain,
( spl0_1370
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f3811,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_284
| ~ spl0_464 ),
inference(resolution,[],[f3568,f2346]) ).
fof(f36386,plain,
( spl0_1369
| ~ spl0_1321
| ~ spl0_1348 ),
inference(avatar_split_clause,[],[f36334,f36289,f26872,f36384]) ).
fof(f36289,plain,
( spl0_1348
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f36334,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1348 ),
inference(superposition,[],[f36290,f26873]) ).
fof(f36290,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1348 ),
inference(avatar_component_clause,[],[f36289]) ).
fof(f36382,plain,
( spl0_1368
| ~ spl0_285
| ~ spl0_464 ),
inference(avatar_split_clause,[],[f3810,f3567,f2349,f36380]) ).
fof(f36380,plain,
( spl0_1368
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f3810,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_285
| ~ spl0_464 ),
inference(resolution,[],[f3568,f2350]) ).
fof(f36378,plain,
( spl0_1367
| ~ spl0_283
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f3777,f3543,f2341,f36376]) ).
fof(f36376,plain,
( spl0_1367
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f3777,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_458 ),
inference(resolution,[],[f3544,f2342]) ).
fof(f36374,plain,
( spl0_1366
| ~ spl0_284
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f3776,f3543,f2345,f36372]) ).
fof(f36372,plain,
( spl0_1366
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f3776,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_458 ),
inference(resolution,[],[f3544,f2346]) ).
fof(f36370,plain,
( spl0_1365
| ~ spl0_285
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f3775,f3543,f2349,f36368]) ).
fof(f36368,plain,
( spl0_1365
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f3775,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_458 ),
inference(resolution,[],[f3544,f2350]) ).
fof(f36366,plain,
( spl0_1364
| ~ spl0_283
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f3768,f3527,f2341,f36364]) ).
fof(f36364,plain,
( spl0_1364
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f3768,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_454 ),
inference(resolution,[],[f3528,f2342]) ).
fof(f36362,plain,
( spl0_1363
| ~ spl0_284
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f3767,f3527,f2345,f36360]) ).
fof(f36360,plain,
( spl0_1363
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f3767,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1) )
| ~ spl0_284
| ~ spl0_454 ),
inference(resolution,[],[f3528,f2346]) ).
fof(f36358,plain,
( spl0_1362
| ~ spl0_285
| ~ spl0_454 ),
inference(avatar_split_clause,[],[f3766,f3527,f2349,f36356]) ).
fof(f36356,plain,
( spl0_1362
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f3766,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),c_HOL_Osgn__class_Osgn(X0,X1),X1) )
| ~ spl0_285
| ~ spl0_454 ),
inference(resolution,[],[f3528,f2350]) ).
fof(f36354,plain,
( spl0_1361
| ~ spl0_277
| ~ spl0_452 ),
inference(avatar_split_clause,[],[f3746,f3519,f2317,f36352]) ).
fof(f36352,plain,
( spl0_1361
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f3746,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_452 ),
inference(resolution,[],[f3520,f2318]) ).
fof(f36350,plain,
( spl0_1360
| ~ spl0_283
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f3738,f3511,f2341,f36348]) ).
fof(f36348,plain,
( spl0_1360
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f3738,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_450 ),
inference(resolution,[],[f3512,f2342]) ).
fof(f36346,plain,
( spl0_1359
| ~ spl0_284
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f3737,f3511,f2345,f36344]) ).
fof(f36344,plain,
( spl0_1359
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f3737,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) )
| ~ spl0_284
| ~ spl0_450 ),
inference(resolution,[],[f3512,f2346]) ).
fof(f36331,plain,
( spl0_1358
| ~ spl0_285
| ~ spl0_450 ),
inference(avatar_split_clause,[],[f3736,f3511,f2349,f36329]) ).
fof(f36329,plain,
( spl0_1358
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f3736,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X2),c_HOL_Ouminus__class_Ouminus(X1,X2),X2) )
| ~ spl0_285
| ~ spl0_450 ),
inference(resolution,[],[f3512,f2350]) ).
fof(f36327,plain,
( spl0_1357
| ~ spl0_418
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3439,f3180,f3140,f36325]) ).
fof(f36325,plain,
( spl0_1357
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f3140,plain,
( spl0_418
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f3439,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_418
| ~ spl0_428 ),
inference(resolution,[],[f3181,f3141]) ).
fof(f3141,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_418 ),
inference(avatar_component_clause,[],[f3140]) ).
fof(f36323,plain,
( spl0_1356
| ~ spl0_194
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f3414,f3160,f1869,f36321]) ).
fof(f36321,plain,
( spl0_1356
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f1869,plain,
( spl0_194
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f3160,plain,
( spl0_423
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f3414,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_194
| ~ spl0_423 ),
inference(resolution,[],[f3161,f1870]) ).
fof(f1870,plain,
( ! [X34] :
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Oab__group__add(X34) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f1869]) ).
fof(f3161,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 )
| ~ spl0_423 ),
inference(avatar_component_clause,[],[f3160]) ).
fof(f36319,plain,
( spl0_1355
| ~ spl0_188
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f3411,f3156,f1845,f36317]) ).
fof(f36317,plain,
( spl0_1355
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oplus__class_Oplus(X2,X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f1845,plain,
( spl0_188
<=> ! [X34] :
( ~ class_OrderedGroup_Oab__group__add(X34)
| class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f3156,plain,
( spl0_422
<=> ! [X4,X0,X18] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X18,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f3411,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oplus__class_Oplus(X2,X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_188
| ~ spl0_422 ),
inference(resolution,[],[f3157,f1846]) ).
fof(f1846,plain,
( ! [X34] :
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Oab__group__add(X34) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f1845]) ).
fof(f3157,plain,
( ! [X0,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X18,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = X4 )
| ~ spl0_422 ),
inference(avatar_component_clause,[],[f3156]) ).
fof(f36315,plain,
( spl0_1354
| ~ spl0_188
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f3404,f3148,f1845,f36313]) ).
fof(f36313,plain,
( spl0_1354
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f3148,plain,
( spl0_420
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f3404,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_188
| ~ spl0_420 ),
inference(resolution,[],[f3149,f1846]) ).
fof(f3149,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) )
| ~ spl0_420 ),
inference(avatar_component_clause,[],[f3148]) ).
fof(f36311,plain,
( spl0_1353
| ~ spl0_194
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f3401,f3144,f1869,f36309]) ).
fof(f36309,plain,
( spl0_1353
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f3144,plain,
( spl0_419
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f3401,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_194
| ~ spl0_419 ),
inference(resolution,[],[f3145,f1870]) ).
fof(f3145,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_419 ),
inference(avatar_component_clause,[],[f3144]) ).
fof(f36307,plain,
( spl0_1352
| ~ spl0_198
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f3391,f3136,f1885,f36305]) ).
fof(f36305,plain,
( spl0_1352
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f3136,plain,
( spl0_417
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f3391,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
| c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_417 ),
inference(resolution,[],[f3137,f1886]) ).
fof(f3137,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) )
| ~ spl0_417 ),
inference(avatar_component_clause,[],[f3136]) ).
fof(f36303,plain,
( spl0_1351
| ~ spl0_206
| ~ spl0_409 ),
inference(avatar_split_clause,[],[f3362,f3103,f1917,f36301]) ).
fof(f36301,plain,
( spl0_1351
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f3103,plain,
( spl0_409
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(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_409])]) ).
fof(f3362,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_206
| ~ spl0_409 ),
inference(resolution,[],[f3104,f1918]) ).
fof(f3104,plain,
( ! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) )
| ~ spl0_409 ),
inference(avatar_component_clause,[],[f3103]) ).
fof(f36299,plain,
( spl0_1350
| ~ spl0_188
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f3359,f3099,f1845,f36297]) ).
fof(f36297,plain,
( spl0_1350
<=> ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f3099,plain,
( spl0_408
<=> ! [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_408])]) ).
fof(f3359,plain,
( ! [X2,X0,X1] :
( c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
| ~ class_OrderedGroup_Oab__group__add(X2) )
| ~ spl0_188
| ~ spl0_408 ),
inference(resolution,[],[f3100,f1846]) ).
fof(f3100,plain,
( ! [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) )
| ~ spl0_408 ),
inference(avatar_component_clause,[],[f3099]) ).
fof(f36295,plain,
( spl0_1349
| ~ spl0_194
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f3278,f3066,f1869,f36293]) ).
fof(f36293,plain,
( spl0_1349
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f3066,plain,
( spl0_400
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f3278,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X2
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_194
| ~ spl0_400 ),
inference(resolution,[],[f3067,f1870]) ).
fof(f3067,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 )
| ~ spl0_400 ),
inference(avatar_component_clause,[],[f3066]) ).
fof(f36291,plain,
( spl0_1348
| ~ spl0_1321
| ~ spl0_1339 ),
inference(avatar_split_clause,[],[f36184,f35604,f26872,f36289]) ).
fof(f36184,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1321
| ~ spl0_1339 ),
inference(superposition,[],[f35605,f26873]) ).
fof(f36287,plain,
( spl0_1347
| ~ spl0_397
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f3275,f3062,f3054,f36285]) ).
fof(f36285,plain,
( spl0_1347
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f3275,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) )
| ~ spl0_397
| ~ spl0_399 ),
inference(duplicate_literal_removal,[],[f3268]) ).
fof(f3268,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_397
| ~ spl0_399 ),
inference(resolution,[],[f3063,f3055]) ).
fof(f36283,plain,
( spl0_1346
| ~ spl0_396
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f3274,f3062,f3050,f36281]) ).
fof(f36281,plain,
( spl0_1346
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f3274,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2) )
| ~ spl0_396
| ~ spl0_399 ),
inference(duplicate_literal_removal,[],[f3269]) ).
fof(f3269,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X4,X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_396
| ~ spl0_399 ),
inference(resolution,[],[f3063,f3051]) ).
fof(f36279,plain,
( spl0_1345
| ~ spl0_397
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f3267,f3058,f3054,f36277]) ).
fof(f36277,plain,
( spl0_1345
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f3267,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) )
| ~ spl0_397
| ~ spl0_398 ),
inference(duplicate_literal_removal,[],[f3260]) ).
fof(f3260,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_397
| ~ spl0_398 ),
inference(resolution,[],[f3059,f3055]) ).
fof(f36275,plain,
( spl0_1344
| ~ spl0_396
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f3266,f3058,f3050,f36273]) ).
fof(f36273,plain,
( spl0_1344
<=> ! [X4,X0,X3,X2,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f3266,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2) )
| ~ spl0_396
| ~ spl0_398 ),
inference(duplicate_literal_removal,[],[f3261]) ).
fof(f3261,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X3,X4,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_396
| ~ spl0_398 ),
inference(resolution,[],[f3059,f3051]) ).
fof(f36271,plain,
( spl0_1343
| ~ spl0_361
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f2986,f2857,f2817,f36269]) ).
fof(f36269,plain,
( spl0_1343
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f2986,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_361
| ~ spl0_371 ),
inference(resolution,[],[f2858,f2818]) ).
fof(f36267,plain,
( spl0_1342
| ~ spl0_362
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f2981,f2853,f2821,f36265]) ).
fof(f36265,plain,
( spl0_1342
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f2853,plain,
( spl0_370
<=> ! [X27,X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2981,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_362
| ~ spl0_370 ),
inference(resolution,[],[f2854,f2822]) ).
fof(f2854,plain,
( ! [X0,X11,X27] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_370 ),
inference(avatar_component_clause,[],[f2853]) ).
fof(f36263,plain,
( spl0_1341
| ~ spl0_359
| ~ spl0_368 ),
inference(avatar_split_clause,[],[f2978,f2845,f2809,f36261]) ).
fof(f36261,plain,
( spl0_1341
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2809,plain,
( spl0_359
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2978,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_359
| ~ spl0_368 ),
inference(resolution,[],[f2846,f2810]) ).
fof(f2810,plain,
( ! [X3,X0,X4] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_359 ),
inference(avatar_component_clause,[],[f2809]) ).
fof(f36259,plain,
( spl0_1340
| ~ spl0_360
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f2976,f2841,f2813,f36257]) ).
fof(f36257,plain,
( spl0_1340
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f2976,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_360
| ~ spl0_367 ),
inference(resolution,[],[f2842,f2814]) ).
fof(f35606,plain,
( spl0_1339
| ~ spl0_1
| ~ spl0_845
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f35201,f26852,f8764,f943,f35604]) ).
fof(f943,plain,
( spl0_1
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f8764,plain,
( spl0_845
<=> ! [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_845])]) ).
fof(f26852,plain,
( spl0_1316
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f35201,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_845
| ~ spl0_1316 ),
inference(forward_demodulation,[],[f35041,f8765]) ).
fof(f8765,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_845 ),
inference(avatar_component_clause,[],[f8764]) ).
fof(f35041,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex)
| ~ spl0_1
| ~ spl0_1316 ),
inference(superposition,[],[f26853,f945]) ).
fof(f945,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f943]) ).
fof(f26853,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1316 ),
inference(avatar_component_clause,[],[f26852]) ).
fof(f31460,plain,
( spl0_1338
| ~ spl0_931
| ~ spl0_1336 ),
inference(avatar_split_clause,[],[f28046,f27631,f11883,f31458]) ).
fof(f31458,plain,
( spl0_1338
<=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f11883,plain,
( spl0_931
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f28046,plain,
( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_931
| ~ spl0_1336 ),
inference(superposition,[],[f27632,f11884]) ).
fof(f11884,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
| ~ spl0_931 ),
inference(avatar_component_clause,[],[f11883]) ).
fof(f30670,plain,
( spl0_1337
| ~ spl0_1206
| ~ spl0_1336 ),
inference(avatar_split_clause,[],[f28043,f27631,f23901,f30668]) ).
fof(f30668,plain,
( spl0_1337
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f23901,plain,
( spl0_1206
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f28043,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),tc_nat)
| ~ spl0_1206
| ~ spl0_1336 ),
inference(superposition,[],[f27632,f23902]) ).
fof(f23902,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f23901]) ).
fof(f27633,plain,
( ~ spl0_32
| spl0_1336
| ~ spl0_242
| ~ spl0_931 ),
inference(avatar_split_clause,[],[f12364,f11883,f2077,f27631,f1098]) ).
fof(f1098,plain,
( spl0_32
<=> class_Ring__and__Field_Odvd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f12364,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_242
| ~ spl0_931 ),
inference(superposition,[],[f2078,f11884]) ).
fof(f27184,plain,
( ~ spl0_149
| ~ spl0_126
| ~ spl0_1335
| ~ spl0_303
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f11905,f11901,f2421,f27181,f1568,f1683]) ).
fof(f27181,plain,
( spl0_1335
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f2421,plain,
( spl0_303
<=> ! [X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f11901,plain,
( spl0_935
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f11905,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| ~ class_SEQ_Obanach(tc_Complex_Ocomplex)
| ~ spl0_303
| ~ spl0_935 ),
inference(superposition,[],[f2422,f11903]) ).
fof(f11903,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_935 ),
inference(avatar_component_clause,[],[f11901]) ).
fof(f2422,plain,
( ! [X3,X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X3,X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| ~ class_SEQ_Obanach(X0) )
| ~ spl0_303 ),
inference(avatar_component_clause,[],[f2421]) ).
fof(f27048,plain,
( spl0_1334
| ~ spl0_711
| ~ spl0_781 ),
inference(avatar_split_clause,[],[f7811,f7447,f6257,f27046]) ).
fof(f27046,plain,
( spl0_1334
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f6257,plain,
( spl0_711
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f7447,plain,
( spl0_781
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f7811,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_711
| ~ spl0_781 ),
inference(duplicate_literal_removal,[],[f7784]) ).
fof(f7784,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_711
| ~ spl0_781 ),
inference(resolution,[],[f7448,f6258]) ).
fof(f6258,plain,
( ! [X2,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f6257]) ).
fof(f7448,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f7447]) ).
fof(f27044,plain,
( spl0_1333
| ~ spl0_711
| ~ spl0_780 ),
inference(avatar_split_clause,[],[f7779,f7443,f6257,f27042]) ).
fof(f27042,plain,
( spl0_1333
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f7443,plain,
( spl0_780
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f7779,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_711
| ~ spl0_780 ),
inference(duplicate_literal_removal,[],[f7754]) ).
fof(f7754,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_711
| ~ spl0_780 ),
inference(resolution,[],[f7444,f6258]) ).
fof(f7444,plain,
( ! [X2,X0,X1,X9] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f7443]) ).
fof(f26980,plain,
( ~ spl0_116
| spl0_1332
| ~ spl0_143
| ~ spl0_425
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f6002,f5811,f3168,f1653,f26978,f1518]) ).
fof(f26978,plain,
( spl0_1332
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f3168,plain,
( spl0_425
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f5811,plain,
( spl0_672
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f6002,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_425
| ~ spl0_672 ),
inference(forward_demodulation,[],[f6000,f3421]) ).
fof(f3421,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_425 ),
inference(resolution,[],[f3169,f1655]) ).
fof(f3169,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) )
| ~ spl0_425 ),
inference(avatar_component_clause,[],[f3168]) ).
fof(f6000,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_672 ),
inference(resolution,[],[f5812,f1655]) ).
fof(f5812,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) )
| ~ spl0_672 ),
inference(avatar_component_clause,[],[f5811]) ).
fof(f26915,plain,
( ~ spl0_60
| spl0_1331
| ~ spl0_96
| ~ spl0_425
| ~ spl0_672 ),
inference(avatar_split_clause,[],[f6001,f5811,f3168,f1418,f26913,f1238]) ).
fof(f26913,plain,
( spl0_1331
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f6001,plain,
( ! [X0,X1] :
( c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_425
| ~ spl0_672 ),
inference(forward_demodulation,[],[f5999,f3420]) ).
fof(f3420,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_425 ),
inference(resolution,[],[f3169,f1420]) ).
fof(f5999,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_672 ),
inference(resolution,[],[f5812,f1420]) ).
fof(f26911,plain,
( spl0_1330
| ~ spl0_348
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f5464,f5083,f2662,f26909]) ).
fof(f26909,plain,
( spl0_1330
<=> ! [X0,X1] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f2662,plain,
( spl0_348
<=> ! [X9,X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f5083,plain,
( spl0_646
<=> ! [X23] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X23,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X23),tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X23),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f5464,plain,
( ! [X0,X1] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = c_Polynomial_Opoly(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X0,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0),tc_Complex_Ocomplex) )
| ~ spl0_348
| ~ spl0_646 ),
inference(superposition,[],[f2663,f5084]) ).
fof(f5084,plain,
( ! [X23] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X23,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X23),tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X23),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X23 )
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f5083]) ).
fof(f2663,plain,
( ! [X3,X9] : c_Polynomial_Opoly(c_Polynomial_OpCons(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X9
| ~ spl0_348 ),
inference(avatar_component_clause,[],[f2662]) ).
fof(f26907,plain,
( spl0_1329
| ~ spl0_63
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f5459,f5079,f1253,f26905]) ).
fof(f26905,plain,
( spl0_1329
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f5079,plain,
( spl0_645
<=> ! [X23,X0,X3,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X23,X7,X0),X3,X0) = c_Polynomial_Opoly(X23,c_Polynomial_Opoly(X7,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f5459,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_645 ),
inference(resolution,[],[f5080,f1255]) ).
fof(f5080,plain,
( ! [X3,X0,X7,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X23,X7,X0),X3,X0) = c_Polynomial_Opoly(X23,c_Polynomial_Opoly(X7,X3,X0),X0) )
| ~ spl0_645 ),
inference(avatar_component_clause,[],[f5079]) ).
fof(f26903,plain,
( spl0_1328
| ~ spl0_118
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f5458,f5079,f1528,f26901]) ).
fof(f26901,plain,
( spl0_1328
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f5458,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_645 ),
inference(resolution,[],[f5080,f1530]) ).
fof(f26899,plain,
( spl0_1327
| ~ spl0_15
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f5456,f5079,f1013,f26897]) ).
fof(f26897,plain,
( spl0_1327
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_nat),X2,tc_nat) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f5456,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_nat),X2,tc_nat) = c_Polynomial_Opoly(X0,c_Polynomial_Opoly(X1,X2,tc_nat),tc_nat)
| ~ spl0_15
| ~ spl0_645 ),
inference(resolution,[],[f5080,f1015]) ).
fof(f26895,plain,
( spl0_1326
| ~ spl0_112
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f5420,f5032,f1498,f26893]) ).
fof(f26893,plain,
( spl0_1326
<=> ! [X0,X1] : c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Complex_Ocomplex),c_HOL_Osgn__class_Osgn(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1498,plain,
( spl0_112
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f5032,plain,
( spl0_639
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f5420,plain,
( ! [X0,X1] : c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Complex_Ocomplex),c_HOL_Osgn__class_Osgn(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_112
| ~ spl0_639 ),
inference(resolution,[],[f5033,f1500]) ).
fof(f1500,plain,
( class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1498]) ).
fof(f5033,plain,
( ! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) )
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f5032]) ).
fof(f26891,plain,
( spl0_1325
| ~ spl0_53
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f5419,f5032,f1203,f26889]) ).
fof(f26889,plain,
( spl0_1325
<=> ! [X0,X1] : c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1203,plain,
( spl0_53
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f5419,plain,
( ! [X0,X1] : c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Osgn__class_Osgn(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_53
| ~ spl0_639 ),
inference(resolution,[],[f5033,f1205]) ).
fof(f1205,plain,
( class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f1203]) ).
fof(f26887,plain,
( spl0_1324
| ~ spl0_14
| ~ spl0_31
| ~ spl0_316
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f5416,f5024,f2533,f1093,f1008,f26885]) ).
fof(f26885,plain,
( spl0_1324
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f2533,plain,
( spl0_316
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f5024,plain,
( spl0_637
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f5416,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat),tc_nat) = X0
| ~ spl0_14
| ~ spl0_31
| ~ spl0_316
| ~ spl0_637 ),
inference(forward_demodulation,[],[f5414,f2692]) ).
fof(f2692,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
| ~ spl0_14
| ~ spl0_316 ),
inference(resolution,[],[f2534,f1010]) ).
fof(f2534,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f2533]) ).
fof(f5414,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),X1,tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_637 ),
inference(resolution,[],[f5025,f1095]) ).
fof(f5025,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),X0) = X1 )
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f5024]) ).
fof(f26883,plain,
( spl0_1323
| ~ spl0_63
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f5408,f5016,f1253,f26881]) ).
fof(f26881,plain,
( spl0_1323
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f5016,plain,
( spl0_635
<=> ! [X0,X23,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X23,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f5408,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_635 ),
inference(resolution,[],[f5017,f1255]) ).
fof(f5017,plain,
( ! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X23,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X0),X23,X0) )
| ~ spl0_635 ),
inference(avatar_component_clause,[],[f5016]) ).
fof(f26879,plain,
( ~ spl0_106
| ~ spl0_73
| ~ spl0_1322
| ~ spl0_303
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f11899,f11895,f2421,f26876,f1303,f1468]) ).
fof(f26876,plain,
( spl0_1322
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f11895,plain,
( spl0_934
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f11899,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| ~ class_SEQ_Obanach(tc_RealDef_Oreal)
| ~ spl0_303
| ~ spl0_934 ),
inference(superposition,[],[f2422,f11897]) ).
fof(f11897,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_934 ),
inference(avatar_component_clause,[],[f11895]) ).
fof(f26874,plain,
( spl0_1321
| ~ spl0_118
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f5407,f5016,f1528,f26872]) ).
fof(f5407,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_635 ),
inference(resolution,[],[f5017,f1530]) ).
fof(f26870,plain,
( spl0_1320
| ~ spl0_15
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f5405,f5016,f1013,f26868]) ).
fof(f26868,plain,
( spl0_1320
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_nat),tc_nat) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f5405,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_nat),tc_nat) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_15
| ~ spl0_635 ),
inference(resolution,[],[f5017,f1015]) ).
fof(f26866,plain,
( spl0_1319
| ~ spl0_31
| ~ spl0_634 ),
inference(avatar_split_clause,[],[f5380,f5012,f1093,f26864]) ).
fof(f26864,plain,
( spl0_1319
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f5012,plain,
( spl0_634
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X9,X2,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f5380,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_634 ),
inference(resolution,[],[f5013,f1095]) ).
fof(f5013,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X9,X2,X0),X0),X2,X0) )
| ~ spl0_634 ),
inference(avatar_component_clause,[],[f5012]) ).
fof(f26862,plain,
( spl0_1318
| ~ spl0_31
| ~ spl0_633 ),
inference(avatar_split_clause,[],[f5378,f5008,f1093,f26860]) ).
fof(f26860,plain,
( spl0_1318
<=> ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f5008,plain,
( spl0_633
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f5378,plain,
( ! [X2,X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_633 ),
inference(resolution,[],[f5009,f1095]) ).
fof(f5009,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0),X2,X0) )
| ~ spl0_633 ),
inference(avatar_component_clause,[],[f5008]) ).
fof(f26858,plain,
( spl0_1317
| ~ spl0_63
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f5377,f5004,f1253,f26856]) ).
fof(f26856,plain,
( spl0_1317
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f26854,plain,
( spl0_1316
| ~ spl0_118
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f5376,f5004,f1528,f26852]) ).
fof(f26850,plain,
( spl0_1315
| ~ spl0_15
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f5374,f5004,f1013,f26848]) ).
fof(f26848,plain,
( spl0_1315
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Opoly(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f26846,plain,
( spl0_1314
| ~ spl0_55
| ~ spl0_631 ),
inference(avatar_split_clause,[],[f5373,f5000,f1213,f26844]) ).
fof(f26844,plain,
( spl0_1314
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f5000,plain,
( spl0_631
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f5373,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_631 ),
inference(resolution,[],[f5001,f1215]) ).
fof(f5001,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) )
| ~ spl0_631 ),
inference(avatar_component_clause,[],[f5000]) ).
fof(f26841,plain,
( spl0_1313
| ~ spl0_55
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f5372,f4996,f1213,f26839]) ).
fof(f26839,plain,
( spl0_1313
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f4996,plain,
( spl0_630
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f5372,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_630 ),
inference(resolution,[],[f4997,f1215]) ).
fof(f4997,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) )
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f4996]) ).
fof(f26837,plain,
( spl0_1312
| ~ spl0_76
| ~ spl0_629 ),
inference(avatar_split_clause,[],[f5370,f4969,f1318,f26835]) ).
fof(f26835,plain,
( spl0_1312
<=> ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1318,plain,
( spl0_76
<=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f4969,plain,
( spl0_629
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X8,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f5370,plain,
( ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_629 ),
inference(resolution,[],[f4970,f1320]) ).
fof(f1320,plain,
( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f1318]) ).
fof(f4970,plain,
( ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X8,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) )
| ~ spl0_629 ),
inference(avatar_component_clause,[],[f4969]) ).
fof(f26833,plain,
( spl0_1311
| ~ spl0_211
| ~ spl0_798 ),
inference(avatar_split_clause,[],[f10312,f7781,f1937,f26831]) ).
fof(f26831,plain,
( spl0_1311
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f1937,plain,
( spl0_211
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f7781,plain,
( spl0_798
<=> ! [X0,X1] :
( c_Complex_Ocnj(X1) != X0
| c_Complex_Ocnj(X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f10312,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) )
| ~ spl0_211
| ~ spl0_798 ),
inference(superposition,[],[f7782,f1939]) ).
fof(f1939,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| ~ spl0_211 ),
inference(avatar_component_clause,[],[f1937]) ).
fof(f7782,plain,
( ! [X0,X1] :
( c_Complex_Ocnj(X1) != X0
| c_Complex_Ocnj(X0) = X1 )
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7781]) ).
fof(f26662,plain,
( ~ spl0_116
| spl0_1310
| ~ spl0_117
| ~ spl0_143
| ~ spl0_316
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f5369,f4965,f2533,f1653,f1523,f26660,f1518]) ).
fof(f4965,plain,
( spl0_628
<=> ! [X9,X0,X2] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X9,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f5369,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
| ~ spl0_117
| ~ spl0_143
| ~ spl0_316
| ~ spl0_628 ),
inference(forward_demodulation,[],[f5367,f2694]) ).
fof(f2694,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_316 ),
inference(resolution,[],[f2534,f1525]) ).
fof(f5367,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X1 )
| ~ spl0_143
| ~ spl0_628 ),
inference(resolution,[],[f4966,f1655]) ).
fof(f4966,plain,
( ! [X2,X0,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X9,X0) = X2 )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f4965]) ).
fof(f26478,plain,
( ~ spl0_60
| spl0_1309
| ~ spl0_62
| ~ spl0_96
| ~ spl0_316
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f5368,f4965,f2533,f1418,f1248,f26476,f1238]) ).
fof(f5368,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
| ~ spl0_62
| ~ spl0_96
| ~ spl0_316
| ~ spl0_628 ),
inference(forward_demodulation,[],[f5366,f2695]) ).
fof(f2695,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_316 ),
inference(resolution,[],[f2534,f1250]) ).
fof(f5366,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X1 )
| ~ spl0_96
| ~ spl0_628 ),
inference(resolution,[],[f4966,f1420]) ).
fof(f26474,plain,
( spl0_1308
| ~ spl0_62
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f5363,f4957,f1248,f26472]) ).
fof(f26472,plain,
( spl0_1308
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f4957,plain,
( spl0_626
<=> ! [X0,X8,X3,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X8,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X3,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f5363,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_626 ),
inference(resolution,[],[f4958,f1250]) ).
fof(f4958,plain,
( ! [X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X8,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X3,X8,X0),X0) )
| ~ spl0_626 ),
inference(avatar_component_clause,[],[f4957]) ).
fof(f26470,plain,
( spl0_1307
| ~ spl0_117
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f5362,f4957,f1523,f26468]) ).
fof(f26468,plain,
( spl0_1307
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f5362,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_626 ),
inference(resolution,[],[f4958,f1525]) ).
fof(f26466,plain,
( spl0_1306
| ~ spl0_14
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f5360,f4957,f1008,f26464]) ).
fof(f26464,plain,
( spl0_1306
<=> ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f5360,plain,
( ! [X2,X0,X1] : c_Polynomial_Opoly(c_Polynomial_Omonom(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X2,X1,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_626 ),
inference(resolution,[],[f4958,f1010]) ).
fof(f26462,plain,
( spl0_1305
| ~ spl0_139
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f5353,f4945,f1633,f26460]) ).
fof(f26460,plain,
( spl0_1305
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f4945,plain,
( spl0_623
<=> ! [X0,X3,X2,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X3,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f5353,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_139
| ~ spl0_623 ),
inference(resolution,[],[f4946,f1635]) ).
fof(f4946,plain,
( ! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X3,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) )
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f4945]) ).
fof(f26458,plain,
( spl0_1304
| ~ spl0_90
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f5352,f4945,f1388,f26456]) ).
fof(f26456,plain,
( spl0_1304
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f5352,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_RealVector_OscaleR__class_OscaleR(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_90
| ~ spl0_623 ),
inference(resolution,[],[f4946,f1390]) ).
fof(f26454,plain,
( spl0_1303
| ~ spl0_126
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f5351,f4941,f1568,f26452]) ).
fof(f26452,plain,
( spl0_1303
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f4941,plain,
( spl0_622
<=> ! [X24,X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f5351,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_126
| ~ spl0_622 ),
inference(resolution,[],[f4942,f1570]) ).
fof(f1570,plain,
( class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| ~ spl0_126 ),
inference(avatar_component_clause,[],[f1568]) ).
fof(f4942,plain,
( ! [X3,X0,X4,X24] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) )
| ~ spl0_622 ),
inference(avatar_component_clause,[],[f4941]) ).
fof(f26408,plain,
( spl0_1302
| ~ spl0_73
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f5350,f4941,f1303,f26406]) ).
fof(f26406,plain,
( spl0_1302
<=> ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f5350,plain,
( ! [X2,X0,X1] : c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_73
| ~ spl0_622 ),
inference(resolution,[],[f4942,f1305]) ).
fof(f1305,plain,
( class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| ~ spl0_73 ),
inference(avatar_component_clause,[],[f1303]) ).
fof(f26404,plain,
( spl0_1301
| ~ spl0_78
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f5340,f4895,f1328,f26402]) ).
fof(f26402,plain,
( spl0_1301
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1328,plain,
( spl0_78
<=> class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f4895,plain,
( spl0_616
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f5340,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_616 ),
inference(resolution,[],[f4896,f1330]) ).
fof(f1330,plain,
( class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f4896,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X18,X0) )
| ~ spl0_616 ),
inference(avatar_component_clause,[],[f4895]) ).
fof(f26400,plain,
( spl0_1300
| ~ spl0_22
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f5339,f4895,f1048,f26398]) ).
fof(f26398,plain,
( spl0_1300
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1048,plain,
( spl0_22
<=> class_Lattices_Oupper__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f5339,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_22
| ~ spl0_616 ),
inference(resolution,[],[f4896,f1050]) ).
fof(f1050,plain,
( class_Lattices_Oupper__semilattice(tc_nat)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f1048]) ).
fof(f26396,plain,
( spl0_1299
| ~ spl0_78
| ~ spl0_615 ),
inference(avatar_split_clause,[],[f5338,f4891,f1328,f26394]) ).
fof(f26394,plain,
( spl0_1299
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f4891,plain,
( spl0_615
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f5338,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_615 ),
inference(resolution,[],[f4892,f1330]) ).
fof(f4892,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) )
| ~ spl0_615 ),
inference(avatar_component_clause,[],[f4891]) ).
fof(f26392,plain,
( spl0_1298
| ~ spl0_22
| ~ spl0_615 ),
inference(avatar_split_clause,[],[f5337,f4891,f1048,f26390]) ).
fof(f26390,plain,
( spl0_1298
<=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f5337,plain,
( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_nat),tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_615 ),
inference(resolution,[],[f4892,f1050]) ).
fof(f26388,plain,
( spl0_1297
| ~ spl0_62
| ~ spl0_74
| ~ spl0_609
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f5305,f4879,f4855,f1308,f1248,f26386]) ).
fof(f26386,plain,
( spl0_1297
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1308,plain,
( spl0_74
<=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f4855,plain,
( spl0_609
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f4879,plain,
( spl0_612
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f5305,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_74
| ~ spl0_609
| ~ spl0_612 ),
inference(forward_demodulation,[],[f5302,f5291]) ).
fof(f5291,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_74
| ~ spl0_609 ),
inference(resolution,[],[f4856,f1310]) ).
fof(f1310,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f1308]) ).
fof(f4856,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) )
| ~ spl0_609 ),
inference(avatar_component_clause,[],[f4855]) ).
fof(f5302,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_612 ),
inference(resolution,[],[f4880,f1250]) ).
fof(f4880,plain,
( ! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X2,X0) )
| ~ spl0_612 ),
inference(avatar_component_clause,[],[f4879]) ).
fof(f26384,plain,
( spl0_1296
| ~ spl0_117
| ~ spl0_127
| ~ spl0_609
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f5304,f4879,f4855,f1573,f1523,f26382]) ).
fof(f26382,plain,
( spl0_1296
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1573,plain,
( spl0_127
<=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f5304,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_127
| ~ spl0_609
| ~ spl0_612 ),
inference(forward_demodulation,[],[f5301,f5290]) ).
fof(f5290,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| ~ spl0_127
| ~ spl0_609 ),
inference(resolution,[],[f4856,f1575]) ).
fof(f1575,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1573]) ).
fof(f5301,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_612 ),
inference(resolution,[],[f4880,f1525]) ).
fof(f26380,plain,
( spl0_1295
| ~ spl0_14
| ~ spl0_20
| ~ spl0_609
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f5303,f4879,f4855,f1038,f1008,f26378]) ).
fof(f26378,plain,
( spl0_1295
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1038,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f5303,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)
| ~ spl0_14
| ~ spl0_20
| ~ spl0_609
| ~ spl0_612 ),
inference(forward_demodulation,[],[f5299,f5288]) ).
fof(f5288,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_20
| ~ spl0_609 ),
inference(resolution,[],[f4856,f1040]) ).
fof(f1040,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f5299,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_14
| ~ spl0_612 ),
inference(resolution,[],[f4880,f1010]) ).
fof(f26376,plain,
( spl0_1294
| ~ spl0_74
| ~ spl0_609 ),
inference(avatar_split_clause,[],[f5291,f4855,f1308,f26374]) ).
fof(f26374,plain,
( spl0_1294
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f26372,plain,
( spl0_1293
| ~ spl0_127
| ~ spl0_609 ),
inference(avatar_split_clause,[],[f5290,f4855,f1573,f26370]) ).
fof(f26370,plain,
( spl0_1293
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f26326,plain,
( spl0_1292
| ~ spl0_20
| ~ spl0_609 ),
inference(avatar_split_clause,[],[f5288,f4855,f1038,f26324]) ).
fof(f26324,plain,
( spl0_1292
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f26322,plain,
( spl0_1291
| ~ spl0_74
| ~ spl0_608 ),
inference(avatar_split_clause,[],[f5287,f4851,f1308,f26320]) ).
fof(f26320,plain,
( spl0_1291
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f4851,plain,
( spl0_608
<=> ! [X2,X0,X9,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f5287,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_74
| ~ spl0_608 ),
inference(resolution,[],[f4852,f1310]) ).
fof(f4852,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) )
| ~ spl0_608 ),
inference(avatar_component_clause,[],[f4851]) ).
fof(f26318,plain,
( spl0_1290
| ~ spl0_127
| ~ spl0_608 ),
inference(avatar_split_clause,[],[f5286,f4851,f1573,f26316]) ).
fof(f26316,plain,
( spl0_1290
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f5286,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_127
| ~ spl0_608 ),
inference(resolution,[],[f4852,f1575]) ).
fof(f26314,plain,
( spl0_1289
| ~ spl0_20
| ~ spl0_608 ),
inference(avatar_split_clause,[],[f5284,f4851,f1038,f26312]) ).
fof(f26312,plain,
( spl0_1289
<=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f5284,plain,
( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
| ~ spl0_20
| ~ spl0_608 ),
inference(resolution,[],[f4852,f1040]) ).
fof(f26310,plain,
( spl0_1288
| ~ spl0_55
| ~ spl0_607 ),
inference(avatar_split_clause,[],[f5283,f4847,f1213,f26308]) ).
fof(f26308,plain,
( spl0_1288
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f4847,plain,
( spl0_607
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f5283,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_607 ),
inference(resolution,[],[f4848,f1215]) ).
fof(f4848,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) )
| ~ spl0_607 ),
inference(avatar_component_clause,[],[f4847]) ).
fof(f26306,plain,
( spl0_1287
| ~ spl0_119
| ~ spl0_602 ),
inference(avatar_split_clause,[],[f5222,f4827,f1533,f26304]) ).
fof(f26304,plain,
( spl0_1287
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f4827,plain,
( spl0_602
<=> ! [X24,X0,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X24,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f5222,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_602 ),
inference(resolution,[],[f4828,f1535]) ).
fof(f4828,plain,
( ! [X2,X0,X1,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X24,X2,X0),X0) )
| ~ spl0_602 ),
inference(avatar_component_clause,[],[f4827]) ).
fof(f26302,plain,
( spl0_1286
| ~ spl0_64
| ~ spl0_602 ),
inference(avatar_split_clause,[],[f5221,f4827,f1258,f26300]) ).
fof(f26300,plain,
( spl0_1286
<=> ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f5221,plain,
( ! [X2,X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_64
| ~ spl0_602 ),
inference(resolution,[],[f4828,f1260]) ).
fof(f26298,plain,
( spl0_1285
| ~ spl0_119
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f5220,f4823,f1533,f26296]) ).
fof(f26296,plain,
( spl0_1285
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f4823,plain,
( spl0_601
<=> ! [X24,X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f5220,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_119
| ~ spl0_601 ),
inference(resolution,[],[f4824,f1535]) ).
fof(f4824,plain,
( ! [X3,X0,X4,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) )
| ~ spl0_601 ),
inference(avatar_component_clause,[],[f4823]) ).
fof(f26294,plain,
( spl0_1284
| ~ spl0_64
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f5219,f4823,f1258,f26292]) ).
fof(f26292,plain,
( spl0_1284
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f5219,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_64
| ~ spl0_601 ),
inference(resolution,[],[f4824,f1260]) ).
fof(f26290,plain,
( spl0_1283
| ~ spl0_55
| ~ spl0_598 ),
inference(avatar_split_clause,[],[f5205,f4811,f1213,f26288]) ).
fof(f26288,plain,
( spl0_1283
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f4811,plain,
( spl0_598
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f5205,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_598 ),
inference(resolution,[],[f4812,f1215]) ).
fof(f4812,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_598 ),
inference(avatar_component_clause,[],[f4811]) ).
fof(f26286,plain,
( spl0_1282
| ~ spl0_921
| ~ spl0_1138 ),
inference(avatar_split_clause,[],[f18744,f18684,f11791,f26284]) ).
fof(f26284,plain,
( spl0_1282
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f11791,plain,
( spl0_921
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f18684,plain,
( spl0_1138
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f18744,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_921
| ~ spl0_1138 ),
inference(superposition,[],[f18685,f11792]) ).
fof(f11792,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f11791]) ).
fof(f18685,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_1138 ),
inference(avatar_component_clause,[],[f18684]) ).
fof(f26282,plain,
( spl0_1281
| ~ spl0_63
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f5204,f4807,f1253,f26280]) ).
fof(f26280,plain,
( spl0_1281
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f4807,plain,
( spl0_597
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X8,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f5204,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_597 ),
inference(resolution,[],[f4808,f1255]) ).
fof(f4808,plain,
( ! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X8,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) )
| ~ spl0_597 ),
inference(avatar_component_clause,[],[f4807]) ).
fof(f26278,plain,
( spl0_1280
| ~ spl0_118
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f5203,f4807,f1528,f26276]) ).
fof(f26276,plain,
( spl0_1280
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f5203,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_597 ),
inference(resolution,[],[f4808,f1530]) ).
fof(f26274,plain,
( spl0_1279
| ~ spl0_15
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f5201,f4807,f1013,f26272]) ).
fof(f26272,plain,
( spl0_1279
<=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_nat),tc_nat) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f5201,plain,
( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_nat),tc_nat) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_15
| ~ spl0_597 ),
inference(resolution,[],[f4808,f1015]) ).
fof(f26270,plain,
( spl0_1278
| ~ spl0_79
| ~ spl0_593 ),
inference(avatar_split_clause,[],[f5184,f4791,f1333,f26268]) ).
fof(f26268,plain,
( spl0_1278
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1333,plain,
( spl0_79
<=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f4791,plain,
( spl0_593
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f5184,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
| ~ spl0_79
| ~ spl0_593 ),
inference(resolution,[],[f4792,f1335]) ).
fof(f1335,plain,
( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f4792,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X18,X0) )
| ~ spl0_593 ),
inference(avatar_component_clause,[],[f4791]) ).
fof(f26266,plain,
( spl0_1277
| ~ spl0_23
| ~ spl0_593 ),
inference(avatar_split_clause,[],[f5183,f4791,f1053,f26264]) ).
fof(f26264,plain,
( spl0_1277
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1053,plain,
( spl0_23
<=> class_Lattices_Olower__semilattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f5183,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),X2,tc_nat)
| ~ spl0_23
| ~ spl0_593 ),
inference(resolution,[],[f4792,f1055]) ).
fof(f1055,plain,
( class_Lattices_Olower__semilattice(tc_nat)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f1053]) ).
fof(f26262,plain,
( spl0_1276
| ~ spl0_79
| ~ spl0_592 ),
inference(avatar_split_clause,[],[f5182,f4787,f1333,f26260]) ).
fof(f26260,plain,
( spl0_1276
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f4787,plain,
( spl0_592
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f5182,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_79
| ~ spl0_592 ),
inference(resolution,[],[f4788,f1335]) ).
fof(f4788,plain,
( ! [X3,X0,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) )
| ~ spl0_592 ),
inference(avatar_component_clause,[],[f4787]) ).
fof(f26258,plain,
( spl0_1275
| ~ spl0_23
| ~ spl0_592 ),
inference(avatar_split_clause,[],[f5181,f4787,f1053,f26256]) ).
fof(f26256,plain,
( spl0_1275
<=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f5181,plain,
( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_nat),tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_nat),tc_nat)
| ~ spl0_23
| ~ spl0_592 ),
inference(resolution,[],[f4788,f1055]) ).
fof(f26254,plain,
( spl0_1274
| ~ spl0_76
| ~ spl0_590 ),
inference(avatar_split_clause,[],[f5155,f4779,f1318,f26252]) ).
fof(f26252,plain,
( spl0_1274
<=> ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f4779,plain,
( spl0_590
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f5155,plain,
( ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_590 ),
inference(resolution,[],[f4780,f1320]) ).
fof(f4780,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) )
| ~ spl0_590 ),
inference(avatar_component_clause,[],[f4779]) ).
fof(f26250,plain,
( spl0_1273
| ~ spl0_212
| ~ spl0_588 ),
inference(avatar_split_clause,[],[f5150,f4749,f1942,f26248]) ).
fof(f26248,plain,
( spl0_1273
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f5150,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0) )
| ~ spl0_212
| ~ spl0_588 ),
inference(duplicate_literal_removal,[],[f5126]) ).
fof(f5126,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_212
| ~ spl0_588 ),
inference(resolution,[],[f4750,f1943]) ).
fof(f26246,plain,
( spl0_1272
| ~ spl0_62
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f5119,f4745,f1248,f26244]) ).
fof(f26244,plain,
( spl0_1272
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f4745,plain,
( spl0_587
<=> ! [X17,X0,X14,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X14,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f5119,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_587 ),
inference(resolution,[],[f4746,f1250]) ).
fof(f4746,plain,
( ! [X0,X16,X14,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X14,X17,X0),X0) )
| ~ spl0_587 ),
inference(avatar_component_clause,[],[f4745]) ).
fof(f26242,plain,
( spl0_1271
| ~ spl0_921
| ~ spl0_1120 ),
inference(avatar_split_clause,[],[f18634,f18474,f11791,f26240]) ).
fof(f26240,plain,
( spl0_1271
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f18474,plain,
( spl0_1120
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f18634,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_921
| ~ spl0_1120 ),
inference(superposition,[],[f18475,f11792]) ).
fof(f18475,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1120 ),
inference(avatar_component_clause,[],[f18474]) ).
fof(f26238,plain,
( spl0_1270
| ~ spl0_117
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f5118,f4745,f1523,f26236]) ).
fof(f26236,plain,
( spl0_1270
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f5118,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_587 ),
inference(resolution,[],[f4746,f1525]) ).
fof(f26234,plain,
( spl0_1269
| ~ spl0_14
| ~ spl0_587 ),
inference(avatar_split_clause,[],[f5116,f4745,f1008,f26232]) ).
fof(f26232,plain,
( spl0_1269
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f5116,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_587 ),
inference(resolution,[],[f4746,f1010]) ).
fof(f26230,plain,
( spl0_1268
| ~ spl0_62
| ~ spl0_65
| ~ spl0_584
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f5111,f4737,f4733,f1263,f1248,f26228]) ).
fof(f26228,plain,
( spl0_1268
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1263,plain,
( spl0_65
<=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f4733,plain,
( spl0_584
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f4737,plain,
( spl0_585
<=> ! [X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X15,X0),X16,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),X15,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f5111,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_65
| ~ spl0_584
| ~ spl0_585 ),
inference(forward_demodulation,[],[f5108,f5104]) ).
fof(f5104,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_65
| ~ spl0_584 ),
inference(resolution,[],[f4734,f1265]) ).
fof(f1265,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f1263]) ).
fof(f4734,plain,
( ! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) )
| ~ spl0_584 ),
inference(avatar_component_clause,[],[f4733]) ).
fof(f5108,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_585 ),
inference(resolution,[],[f4738,f1250]) ).
fof(f4738,plain,
( ! [X0,X16,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X15,X0),X16,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),X15,X0) )
| ~ spl0_585 ),
inference(avatar_component_clause,[],[f4737]) ).
fof(f26226,plain,
( spl0_1267
| ~ spl0_117
| ~ spl0_120
| ~ spl0_584
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f5110,f4737,f4733,f1538,f1523,f26224]) ).
fof(f26224,plain,
( spl0_1267
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1538,plain,
( spl0_120
<=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f5110,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_120
| ~ spl0_584
| ~ spl0_585 ),
inference(forward_demodulation,[],[f5107,f5103]) ).
fof(f5103,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_120
| ~ spl0_584 ),
inference(resolution,[],[f4734,f1540]) ).
fof(f1540,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1538]) ).
fof(f5107,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_585 ),
inference(resolution,[],[f4738,f1525]) ).
fof(f26222,plain,
( spl0_1266
| ~ spl0_14
| ~ spl0_16
| ~ spl0_584
| ~ spl0_585 ),
inference(avatar_split_clause,[],[f5109,f4737,f4733,f1018,f1008,f26220]) ).
fof(f26220,plain,
( spl0_1266
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1018,plain,
( spl0_16
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f5109,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_16
| ~ spl0_584
| ~ spl0_585 ),
inference(forward_demodulation,[],[f5105,f5101]) ).
fof(f5101,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat)
| ~ spl0_16
| ~ spl0_584 ),
inference(resolution,[],[f4734,f1020]) ).
fof(f1020,plain,
( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f1018]) ).
fof(f5105,plain,
( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),X1,tc_nat)
| ~ spl0_14
| ~ spl0_585 ),
inference(resolution,[],[f4738,f1010]) ).
fof(f26218,plain,
( spl0_1265
| ~ spl0_65
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f5104,f4733,f1263,f26216]) ).
fof(f26216,plain,
( spl0_1265
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f26214,plain,
( spl0_1264
| ~ spl0_120
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f5103,f4733,f1538,f26212]) ).
fof(f26212,plain,
( spl0_1264
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f26210,plain,
( spl0_1263
| ~ spl0_16
| ~ spl0_584 ),
inference(avatar_split_clause,[],[f5101,f4733,f1018,f26208]) ).
fof(f26208,plain,
( spl0_1263
<=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f26168,plain,
( spl0_1262
| ~ spl0_124
| ~ spl0_116
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f5092,f4729,f1518,f1558,f26166]) ).
fof(f26166,plain,
( spl0_1262
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1558,plain,
( spl0_124
<=> class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f4729,plain,
( spl0_583
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f5092,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) )
| ~ spl0_116
| ~ spl0_583 ),
inference(resolution,[],[f4730,f1520]) ).
fof(f1520,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1518]) ).
fof(f4730,plain,
( ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X8,X0) )
| ~ spl0_583 ),
inference(avatar_component_clause,[],[f4729]) ).
fof(f26122,plain,
( spl0_1261
| ~ spl0_71
| ~ spl0_60
| ~ spl0_583 ),
inference(avatar_split_clause,[],[f5091,f4729,f1238,f1293,f26120]) ).
fof(f26120,plain,
( spl0_1261
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1293,plain,
( spl0_71
<=> class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f5091,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) )
| ~ spl0_60
| ~ spl0_583 ),
inference(resolution,[],[f4730,f1240]) ).
fof(f1240,plain,
( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f26118,plain,
( spl0_1260
| ~ spl0_14
| ~ spl0_31
| ~ spl0_316
| ~ spl0_581 ),
inference(avatar_split_clause,[],[f5088,f4721,f2533,f1093,f1008,f26116]) ).
fof(f26116,plain,
( spl0_1260
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f4721,plain,
( spl0_581
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f5088,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_14
| ~ spl0_31
| ~ spl0_316
| ~ spl0_581 ),
inference(forward_demodulation,[],[f5086,f2692]) ).
fof(f5086,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X0,X1,tc_nat),X1,tc_nat),c_Divides_Odiv__class_Omod(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_581 ),
inference(resolution,[],[f4722,f1095]) ).
fof(f4722,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 )
| ~ spl0_581 ),
inference(avatar_component_clause,[],[f4721]) ).
fof(f26114,plain,
( spl0_1259
| ~ spl0_218
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f4332,f4140,f1969,f26112]) ).
fof(f26112,plain,
( spl0_1259
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0),c_HOL_Oone__class_Oone(X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f4140,plain,
( spl0_541
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X1,X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f4332,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0),c_HOL_Oone__class_Oone(X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_218
| ~ spl0_541 ),
inference(resolution,[],[f4141,f1970]) ).
fof(f4141,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X1,X0) = X2 )
| ~ spl0_541 ),
inference(avatar_component_clause,[],[f4140]) ).
fof(f26110,plain,
( spl0_1258
| ~ spl0_220
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f4321,f4140,f1977,f26108]) ).
fof(f26108,plain,
( spl0_1258
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f4321,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_220
| ~ spl0_541 ),
inference(resolution,[],[f4141,f1978]) ).
fof(f26106,plain,
( spl0_1257
| ~ spl0_218
| ~ spl0_540 ),
inference(avatar_split_clause,[],[f4317,f4136,f1969,f26104]) ).
fof(f26104,plain,
( spl0_1257
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f4136,plain,
( spl0_540
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X0),X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f4317,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_218
| ~ spl0_540 ),
inference(resolution,[],[f4137,f1970]) ).
fof(f4137,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X0),X0) = X2 )
| ~ spl0_540 ),
inference(avatar_component_clause,[],[f4136]) ).
fof(f26102,plain,
( spl0_1256
| ~ spl0_220
| ~ spl0_540 ),
inference(avatar_split_clause,[],[f4306,f4136,f1977,f26100]) ).
fof(f26100,plain,
( spl0_1256
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f4306,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_220
| ~ spl0_540 ),
inference(resolution,[],[f4137,f1978]) ).
fof(f26098,plain,
( spl0_1255
| ~ spl0_428
| ~ spl0_458 ),
inference(avatar_split_clause,[],[f3778,f3543,f3180,f26096]) ).
fof(f26096,plain,
( spl0_1255
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f3778,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) )
| ~ spl0_428
| ~ spl0_458 ),
inference(duplicate_literal_removal,[],[f3773]) ).
fof(f3773,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) )
| ~ spl0_428
| ~ spl0_458 ),
inference(resolution,[],[f3544,f3181]) ).
fof(f26094,plain,
( spl0_1254
| ~ spl0_277
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3440,f3180,f2317,f26092]) ).
fof(f26092,plain,
( spl0_1254
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f3440,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_428 ),
inference(resolution,[],[f3181,f2318]) ).
fof(f26090,plain,
( spl0_1253
| ~ spl0_356
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3437,f3180,f2797,f26088]) ).
fof(f26088,plain,
( spl0_1253
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f3437,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_356
| ~ spl0_428 ),
inference(resolution,[],[f3181,f2798]) ).
fof(f26086,plain,
( ~ spl0_1251
| spl0_1252
| ~ spl0_359
| ~ spl0_566 ),
inference(avatar_split_clause,[],[f4492,f4449,f2809,f26084,f26080]) ).
fof(f26080,plain,
( spl0_1251
<=> class_Ring__and__Field_Ocomm__ring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f26084,plain,
( spl0_1252
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f4449,plain,
( spl0_566
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f4492,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Ocomm__ring__1(tc_nat) )
| ~ spl0_359
| ~ spl0_566 ),
inference(resolution,[],[f4450,f2810]) ).
fof(f4450,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
| ~ spl0_566 ),
inference(avatar_component_clause,[],[f4449]) ).
fof(f26078,plain,
( spl0_1250
| ~ spl0_283
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f3431,f3176,f2341,f26076]) ).
fof(f26076,plain,
( spl0_1250
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f3431,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_427 ),
inference(resolution,[],[f3177,f2342]) ).
fof(f26074,plain,
( spl0_1249
| ~ spl0_284
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f3430,f3176,f2345,f26072]) ).
fof(f26072,plain,
( spl0_1249
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f3430,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1) )
| ~ spl0_284
| ~ spl0_427 ),
inference(resolution,[],[f3177,f2346]) ).
fof(f26070,plain,
( spl0_1248
| ~ spl0_285
| ~ spl0_427 ),
inference(avatar_split_clause,[],[f3429,f3176,f2349,f26068]) ).
fof(f26068,plain,
( spl0_1248
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f3429,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1) )
| ~ spl0_285
| ~ spl0_427 ),
inference(resolution,[],[f3177,f2350]) ).
fof(f26066,plain,
( spl0_1247
| ~ spl0_283
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3299,f3083,f2341,f26064]) ).
fof(f26064,plain,
( spl0_1247
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f3083,plain,
( spl0_404
<=> ! [X0,X3,X2,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f3299,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_404 ),
inference(resolution,[],[f3084,f2342]) ).
fof(f3084,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_404 ),
inference(avatar_component_clause,[],[f3083]) ).
fof(f26062,plain,
( spl0_1246
| ~ spl0_284
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3298,f3083,f2345,f26060]) ).
fof(f26060,plain,
( spl0_1246
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f3298,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) )
| ~ spl0_284
| ~ spl0_404 ),
inference(resolution,[],[f3084,f2346]) ).
fof(f26058,plain,
( spl0_1245
| ~ spl0_285
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3297,f3083,f2349,f26056]) ).
fof(f26056,plain,
( spl0_1245
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f3297,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X3,X2),X2) )
| ~ spl0_285
| ~ spl0_404 ),
inference(resolution,[],[f3084,f2350]) ).
fof(f26054,plain,
( spl0_1244
| ~ spl0_283
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3291,f3079,f2341,f26052]) ).
fof(f26052,plain,
( spl0_1244
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f3079,plain,
( spl0_403
<=> ! [X2,X0,X1,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f3291,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_403 ),
inference(resolution,[],[f3080,f2342]) ).
fof(f3080,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| ~ class_Lattices_Olower__semilattice(X0) )
| ~ spl0_403 ),
inference(avatar_component_clause,[],[f3079]) ).
fof(f26050,plain,
( spl0_1243
| ~ spl0_284
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3290,f3079,f2345,f26048]) ).
fof(f26048,plain,
( spl0_1243
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f3290,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) )
| ~ spl0_284
| ~ spl0_403 ),
inference(resolution,[],[f3080,f2346]) ).
fof(f26046,plain,
( spl0_1242
| ~ spl0_285
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3289,f3079,f2349,f26044]) ).
fof(f26044,plain,
( spl0_1242
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f3289,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(X1,c_Lattices_Olower__semilattice__class_Oinf(X3,X0,X2),X2) )
| ~ spl0_285
| ~ spl0_403 ),
inference(resolution,[],[f3080,f2350]) ).
fof(f26042,plain,
( spl0_1241
| ~ spl0_283
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3233,f3046,f2341,f26040]) ).
fof(f26040,plain,
( spl0_1241
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f3233,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_395 ),
inference(resolution,[],[f3047,f2342]) ).
fof(f26019,plain,
( spl0_1240
| ~ spl0_284
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3232,f3046,f2345,f26017]) ).
fof(f26017,plain,
( spl0_1240
<=> ! [X2,X0,X1,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f3232,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) )
| ~ spl0_284
| ~ spl0_395 ),
inference(resolution,[],[f3047,f2346]) ).
fof(f26015,plain,
( spl0_1239
| ~ spl0_285
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3231,f3046,f2349,f26013]) ).
fof(f26013,plain,
( spl0_1239
<=> ! [X2,X0,X1,X3] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f3231,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X2),X0,X2) )
| ~ spl0_285
| ~ spl0_395 ),
inference(resolution,[],[f3047,f2350]) ).
fof(f26011,plain,
( spl0_1238
| ~ spl0_283
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3223,f3042,f2341,f26009]) ).
fof(f26009,plain,
( spl0_1238
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f3223,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_283
| ~ spl0_394 ),
inference(resolution,[],[f3043,f2342]) ).
fof(f26007,plain,
( spl0_1237
| ~ spl0_284
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3222,f3042,f2345,f26005]) ).
fof(f26005,plain,
( spl0_1237
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f3222,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) )
| ~ spl0_284
| ~ spl0_394 ),
inference(resolution,[],[f3043,f2346]) ).
fof(f26003,plain,
( spl0_1236
| ~ spl0_285
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3221,f3042,f2349,f26001]) ).
fof(f26001,plain,
( spl0_1236
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f3221,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2)
| ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X2),X0,X2) )
| ~ spl0_285
| ~ spl0_394 ),
inference(resolution,[],[f3043,f2350]) ).
fof(f25999,plain,
( spl0_1235
| ~ spl0_198
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f3031,f2905,f1885,f25997]) ).
fof(f25997,plain,
( spl0_1235
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f2905,plain,
( spl0_383
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f3031,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_383 ),
inference(resolution,[],[f2906,f1886]) ).
fof(f2906,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) )
| ~ spl0_383 ),
inference(avatar_component_clause,[],[f2905]) ).
fof(f25995,plain,
( spl0_1234
| ~ spl0_198
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f3029,f2901,f1885,f25993]) ).
fof(f25993,plain,
( spl0_1234
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f2901,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f3029,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_382 ),
inference(resolution,[],[f2902,f1886]) ).
fof(f2902,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) )
| ~ spl0_382 ),
inference(avatar_component_clause,[],[f2901]) ).
fof(f25991,plain,
( spl0_1233
| ~ spl0_278
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3022,f2897,f2321,f25989]) ).
fof(f25989,plain,
( spl0_1233
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f3022,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,X0,X1) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X0,X0,X1),X1)
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_278
| ~ spl0_381 ),
inference(resolution,[],[f2898,f2322]) ).
fof(f25987,plain,
( spl0_1232
| ~ spl0_176
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f3013,f2889,f1797,f25985]) ).
fof(f25985,plain,
( spl0_1232
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f1797,plain,
( spl0_176
<=> ! [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_176])]) ).
fof(f2889,plain,
( spl0_379
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f3013,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_176
| ~ spl0_379 ),
inference(resolution,[],[f2890,f1798]) ).
fof(f1798,plain,
( ! [X34] :
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X34) )
| ~ spl0_176 ),
inference(avatar_component_clause,[],[f1797]) ).
fof(f2890,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_379 ),
inference(avatar_component_clause,[],[f2889]) ).
fof(f25983,plain,
( spl0_1231
| ~ spl0_200
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f3011,f2885,f1893,f25981]) ).
fof(f25981,plain,
( spl0_1231
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f1893,plain,
( spl0_200
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f2885,plain,
( spl0_378
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f3011,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_200
| ~ spl0_378 ),
inference(resolution,[],[f2886,f1894]) ).
fof(f1894,plain,
( ! [X34] :
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oidom(X34) )
| ~ spl0_200 ),
inference(avatar_component_clause,[],[f1893]) ).
fof(f2886,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
| ~ spl0_378 ),
inference(avatar_component_clause,[],[f2885]) ).
fof(f25977,plain,
( spl0_1230
| ~ spl0_176
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3006,f2881,f1797,f25975]) ).
fof(f25975,plain,
( spl0_1230
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f2881,plain,
( spl0_377
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f3006,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_176
| ~ spl0_377 ),
inference(resolution,[],[f2882,f1798]) ).
fof(f2882,plain,
( ! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X9,X0) )
| ~ spl0_377 ),
inference(avatar_component_clause,[],[f2881]) ).
fof(f25973,plain,
( spl0_1229
| ~ spl0_337
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f2987,f2857,f2617,f25971]) ).
fof(f25971,plain,
( spl0_1229
<=> ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f2617,plain,
( spl0_337
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2987,plain,
( ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_337
| ~ spl0_371 ),
inference(resolution,[],[f2858,f2618]) ).
fof(f2618,plain,
( ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f2617]) ).
fof(f25969,plain,
( spl0_1228
| ~ spl0_198
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f2964,f2833,f1885,f25967]) ).
fof(f25967,plain,
( spl0_1228
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f2833,plain,
( spl0_365
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2964,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_365 ),
inference(resolution,[],[f2834,f1886]) ).
fof(f2834,plain,
( ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) )
| ~ spl0_365 ),
inference(avatar_component_clause,[],[f2833]) ).
fof(f25965,plain,
( spl0_1227
| ~ spl0_176
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f2960,f2829,f1797,f25963]) ).
fof(f25963,plain,
( spl0_1227
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f2829,plain,
( spl0_364
<=> ! [X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2960,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_176
| ~ spl0_364 ),
inference(resolution,[],[f2830,f1798]) ).
fof(f2830,plain,
( ! [X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X0) )
| ~ spl0_364 ),
inference(avatar_component_clause,[],[f2829]) ).
fof(f25961,plain,
( spl0_1226
| ~ spl0_184
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f2958,f2825,f1829,f25959]) ).
fof(f25959,plain,
( spl0_1226
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f1829,plain,
( spl0_184
<=> ! [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_184])]) ).
fof(f2825,plain,
( spl0_363
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2958,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_184
| ~ spl0_363 ),
inference(resolution,[],[f2826,f1830]) ).
fof(f1830,plain,
( ! [X34] :
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oordered__idom(X34) )
| ~ spl0_184 ),
inference(avatar_component_clause,[],[f1829]) ).
fof(f2826,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0) = X3 )
| ~ spl0_363 ),
inference(avatar_component_clause,[],[f2825]) ).
fof(f25957,plain,
( spl0_1225
| ~ spl0_337
| ~ spl0_360 ),
inference(avatar_split_clause,[],[f2943,f2813,f2617,f25955]) ).
fof(f25955,plain,
( spl0_1225
<=> ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f2943,plain,
( ! [X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_337
| ~ spl0_360 ),
inference(resolution,[],[f2814,f2618]) ).
fof(f25953,plain,
( spl0_1224
| ~ spl0_184
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f2940,f2801,f1829,f25951]) ).
fof(f25951,plain,
( spl0_1224
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f2801,plain,
( spl0_357
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X11,X0) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Osgn__class_Osgn(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2940,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_184
| ~ spl0_357 ),
inference(resolution,[],[f2802,f1830]) ).
fof(f2802,plain,
( ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X11,X0) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Osgn__class_Osgn(X11,X0),X0) )
| ~ spl0_357 ),
inference(avatar_component_clause,[],[f2801]) ).
fof(f25886,plain,
( spl0_1223
| spl0_152
| ~ spl0_1213 ),
inference(avatar_split_clause,[],[f25806,f23929,f1698,f25883]) ).
fof(f25883,plain,
( spl0_1223
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_x,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f23929,plain,
( spl0_1213
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X1,X0,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f25806,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_x,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_152
| ~ spl0_1213 ),
inference(trivial_inequality_removal,[],[f25805]) ).
fof(f25805,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(v_x,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_152
| ~ spl0_1213 ),
inference(superposition,[],[f1700,f23930]) ).
fof(f23930,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X1,X0,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Complex_Ocomplex) )
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f23929]) ).
fof(f24028,plain,
( spl0_1222
| ~ spl0_350
| ~ spl0_815
| ~ spl0_1145 ),
inference(avatar_split_clause,[],[f22370,f18712,f8226,f2701,f24026]) ).
fof(f24026,plain,
( spl0_1222
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f2701,plain,
( spl0_350
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f8226,plain,
( spl0_815
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f22370,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_RealDef_Oreal) = X0
| ~ spl0_350
| ~ spl0_815
| ~ spl0_1145 ),
inference(forward_demodulation,[],[f22249,f2702]) ).
fof(f2702,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_350 ),
inference(avatar_component_clause,[],[f2701]) ).
fof(f22249,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_RealDef_Oreal)
| ~ spl0_815
| ~ spl0_1145 ),
inference(superposition,[],[f18713,f8227]) ).
fof(f8227,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal)
| ~ spl0_815 ),
inference(avatar_component_clause,[],[f8226]) ).
fof(f23976,plain,
( spl0_1221
| ~ spl0_349
| ~ spl0_804
| ~ spl0_1144 ),
inference(avatar_split_clause,[],[f22225,f18708,f8182,f2671,f23974]) ).
fof(f23974,plain,
( spl0_1221
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2671,plain,
( spl0_349
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f8182,plain,
( spl0_804
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f22225,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Complex_Ocomplex) = X0
| ~ spl0_349
| ~ spl0_804
| ~ spl0_1144 ),
inference(forward_demodulation,[],[f22104,f2672]) ).
fof(f2672,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_349 ),
inference(avatar_component_clause,[],[f2671]) ).
fof(f22104,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_Complex_Ocomplex)
| ~ spl0_804
| ~ spl0_1144 ),
inference(superposition,[],[f18709,f8183]) ).
fof(f8183,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f8182]) ).
fof(f23959,plain,
( spl0_1220
| ~ spl0_883 ),
inference(avatar_split_clause,[],[f9638,f9609,f23957]) ).
fof(f23957,plain,
( spl0_1220
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1) = X3
| ~ class_Ring__and__Field_Oring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f9609,plain,
( spl0_883
<=> ! [X2,X10,X0,X9,X28,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0) = X10
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f9638,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X0,X1),X2,X1),X3,X1) = X3
| ~ class_Ring__and__Field_Oring(X1) )
| ~ spl0_883 ),
inference(equality_resolution,[],[f9610]) ).
fof(f9610,plain,
( ! [X2,X28,X10,X0,X1,X9] :
( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0) = X10
| ~ class_Ring__and__Field_Oring(X0) )
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f9609]) ).
fof(f23955,plain,
( spl0_1219
| ~ spl0_710
| ~ spl0_748 ),
inference(avatar_split_clause,[],[f7235,f6448,f6253,f23953]) ).
fof(f23953,plain,
( spl0_1219
<=> ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f6253,plain,
( spl0_710
<=> ! [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_710])]) ).
fof(f6448,plain,
( spl0_748
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f7235,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_710
| ~ spl0_748 ),
inference(duplicate_literal_removal,[],[f7220]) ).
fof(f7220,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_710
| ~ spl0_748 ),
inference(resolution,[],[f6449,f6254]) ).
fof(f6254,plain,
( ! [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)
| ~ class_Ring__and__Field_Oordered__ring__strict(X0) )
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f6253]) ).
fof(f6449,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ class_OrderedGroup_Opordered__comm__monoid__add(X0) )
| ~ spl0_748 ),
inference(avatar_component_clause,[],[f6448]) ).
fof(f23951,plain,
( spl0_1218
| ~ spl0_559
| ~ spl0_743 ),
inference(avatar_split_clause,[],[f7106,f6428,f4421,f23949]) ).
fof(f23949,plain,
( spl0_1218
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f4421,plain,
( spl0_559
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f6428,plain,
( spl0_743
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f7106,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) )
| ~ spl0_559
| ~ spl0_743 ),
inference(duplicate_literal_removal,[],[f7082]) ).
fof(f7082,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(X2,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_559
| ~ spl0_743 ),
inference(resolution,[],[f6429,f4422]) ).
fof(f4422,plain,
( ! [X2,X0,X1,X9] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_559 ),
inference(avatar_component_clause,[],[f4421]) ).
fof(f6429,plain,
( ! [X2,X0,X1,X9] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_743 ),
inference(avatar_component_clause,[],[f6428]) ).
fof(f23947,plain,
( spl0_1217
| ~ spl0_648
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f6696,f6253,f5487,f23945]) ).
fof(f23945,plain,
( spl0_1217
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f6696,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_648
| ~ spl0_710 ),
inference(duplicate_literal_removal,[],[f6691]) ).
fof(f6691,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_648
| ~ spl0_710 ),
inference(resolution,[],[f6254,f5488]) ).
fof(f23943,plain,
( spl0_1216
| ~ spl0_502
| ~ spl0_710 ),
inference(avatar_split_clause,[],[f6689,f6253,f3984,f23941]) ).
fof(f23941,plain,
( spl0_1216
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f6689,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add(X0) )
| ~ spl0_502
| ~ spl0_710 ),
inference(resolution,[],[f6254,f3985]) ).
fof(f23939,plain,
( spl0_1215
| ~ spl0_341
| ~ spl0_799
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f22084,f18704,f8022,f2633,f23937]) ).
fof(f23937,plain,
( spl0_1215
<=> ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f2633,plain,
( spl0_341
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f8022,plain,
( spl0_799
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f22084,plain,
( ! [X0] : c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| ~ spl0_341
| ~ spl0_799
| ~ spl0_1143 ),
inference(forward_demodulation,[],[f21964,f2634]) ).
fof(f2634,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f2633]) ).
fof(f21964,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = c_Power_Opower__class_Opower(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_799
| ~ spl0_1143 ),
inference(superposition,[],[f18705,f8023]) ).
fof(f8023,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f8022]) ).
fof(f23935,plain,
( spl0_1214
| ~ spl0_278
| ~ spl0_704 ),
inference(avatar_split_clause,[],[f6590,f6229,f2321,f23933]) ).
fof(f23933,plain,
( spl0_1214
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f6229,plain,
( spl0_704
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f6590,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X1)
| ~ class_Ring__and__Field_Oordered__ring__strict(X1) )
| ~ spl0_278
| ~ spl0_704 ),
inference(resolution,[],[f6230,f2322]) ).
fof(f6230,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semiring__strict(X0) )
| ~ spl0_704 ),
inference(avatar_component_clause,[],[f6229]) ).
fof(f23931,plain,
( spl0_1213
| ~ spl0_145
| ~ spl0_577 ),
inference(avatar_split_clause,[],[f4718,f4505,f1663,f23929]) ).
fof(f1663,plain,
( spl0_145
<=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f4505,plain,
( spl0_577
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X1,X23,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(X23,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f4718,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X1,X0,tc_Complex_Ocomplex) )
| ~ spl0_145
| ~ spl0_577 ),
inference(resolution,[],[f4506,f1665]) ).
fof(f1665,plain,
( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1663]) ).
fof(f4506,plain,
( ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X1,X23,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(X23,X1,X0) )
| ~ spl0_577 ),
inference(avatar_component_clause,[],[f4505]) ).
fof(f23927,plain,
( spl0_1212
| ~ spl0_98
| ~ spl0_577 ),
inference(avatar_split_clause,[],[f4717,f4505,f1428,f23925]) ).
fof(f23925,plain,
( spl0_1212
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(X1,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f1428,plain,
( spl0_98
<=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f4717,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(X1,X0,tc_RealDef_Oreal) )
| ~ spl0_98
| ~ spl0_577 ),
inference(resolution,[],[f4506,f1430]) ).
fof(f1430,plain,
( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f1428]) ).
fof(f23923,plain,
( spl0_1211
| ~ spl0_107
| ~ spl0_575 ),
inference(avatar_split_clause,[],[f4700,f4485,f1473,f23921]) ).
fof(f23921,plain,
( spl0_1211
<=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_RealDef_Oreal) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f1473,plain,
( spl0_107
<=> class_HOL_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f4485,plain,
( spl0_575
<=> ! [X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_Suc(X8),X0) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_Polynomial_Omonom(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f4700,plain,
( ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_RealDef_Oreal) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_107
| ~ spl0_575 ),
inference(resolution,[],[f4486,f1475]) ).
fof(f1475,plain,
( class_HOL_Ozero(tc_RealDef_Oreal)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1473]) ).
fof(f4486,plain,
( ! [X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_Suc(X8),X0) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_Polynomial_Omonom(X1,X8,X0),X0) )
| ~ spl0_575 ),
inference(avatar_component_clause,[],[f4485]) ).
fof(f23919,plain,
( spl0_1210
| ~ spl0_150
| ~ spl0_575 ),
inference(avatar_split_clause,[],[f4699,f4485,f1688,f23917]) ).
fof(f23917,plain,
( spl0_1210
<=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f1688,plain,
( spl0_150
<=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f4699,plain,
( ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_150
| ~ spl0_575 ),
inference(resolution,[],[f4486,f1690]) ).
fof(f1690,plain,
( class_HOL_Ozero(tc_Complex_Ocomplex)
| ~ spl0_150 ),
inference(avatar_component_clause,[],[f1688]) ).
fof(f23915,plain,
( spl0_1209
| ~ spl0_38
| ~ spl0_575 ),
inference(avatar_split_clause,[],[f4697,f4485,f1128,f23913]) ).
fof(f23913,plain,
( spl0_1209
<=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_nat) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1128,plain,
( spl0_38
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f4697,plain,
( ! [X0,X1] : c_Polynomial_Omonom(X0,c_Suc(X1),tc_nat) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_nat),c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat)
| ~ spl0_38
| ~ spl0_575 ),
inference(resolution,[],[f4486,f1130]) ).
fof(f1130,plain,
( class_HOL_Ozero(tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f1128]) ).
fof(f23911,plain,
( spl0_1208
| ~ spl0_62
| ~ spl0_561 ),
inference(avatar_split_clause,[],[f4610,f4429,f1248,f23909]) ).
fof(f4429,plain,
( spl0_561
<=> ! [X0,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X27,X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X27,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f4610,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_561 ),
inference(resolution,[],[f4430,f1250]) ).
fof(f4430,plain,
( ! [X0,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X27,X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X27,X0) )
| ~ spl0_561 ),
inference(avatar_component_clause,[],[f4429]) ).
fof(f23907,plain,
( spl0_1207
| ~ spl0_117
| ~ spl0_561 ),
inference(avatar_split_clause,[],[f4609,f4429,f1523,f23905]) ).
fof(f4609,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_561 ),
inference(resolution,[],[f4430,f1525]) ).
fof(f23903,plain,
( spl0_1206
| ~ spl0_14
| ~ spl0_561 ),
inference(avatar_split_clause,[],[f4607,f4429,f1008,f23901]) ).
fof(f4607,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat),X0,tc_nat)
| ~ spl0_14
| ~ spl0_561 ),
inference(resolution,[],[f4430,f1010]) ).
fof(f23857,plain,
( spl0_1205
| ~ spl0_81
| ~ spl0_105
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f4522,f4372,f1463,f1343,f23855]) ).
fof(f23855,plain,
( spl0_1205
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1343,plain,
( spl0_81
<=> class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1463,plain,
( spl0_105
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f4372,plain,
( spl0_550
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f4522,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_105
| ~ spl0_550 ),
inference(resolution,[],[f4373,f1465]) ).
fof(f1465,plain,
( class_Power_Opower(tc_RealDef_Oreal)
| ~ spl0_105 ),
inference(avatar_component_clause,[],[f1463]) ).
fof(f4373,plain,
( ! [X0,X8] :
( ~ class_Power_Opower(X0)
| ~ class_Ring__and__Field_Osemiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0) )
| ~ spl0_550 ),
inference(avatar_component_clause,[],[f4372]) ).
fof(f23827,plain,
( spl0_1204
| ~ spl0_131
| ~ spl0_148
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f4521,f4372,f1678,f1593,f23825]) ).
fof(f23825,plain,
( spl0_1204
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1593,plain,
( spl0_131
<=> class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1678,plain,
( spl0_148
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f4521,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) )
| ~ spl0_148
| ~ spl0_550 ),
inference(resolution,[],[f4373,f1680]) ).
fof(f1680,plain,
( class_Power_Opower(tc_Complex_Ocomplex)
| ~ spl0_148 ),
inference(avatar_component_clause,[],[f1678]) ).
fof(f23796,plain,
( spl0_1203
| ~ spl0_25
| ~ spl0_37
| ~ spl0_550 ),
inference(avatar_split_clause,[],[f4519,f4372,f1123,f1063,f23794]) ).
fof(f23794,plain,
( spl0_1203
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1063,plain,
( spl0_25
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1123,plain,
( spl0_37
<=> class_Power_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f4519,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_37
| ~ spl0_550 ),
inference(resolution,[],[f4373,f1125]) ).
fof(f1125,plain,
( class_Power_Opower(tc_nat)
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f1123]) ).
fof(f23792,plain,
( spl0_1202
| ~ spl0_478
| ~ spl0_487 ),
inference(avatar_split_clause,[],[f3966,f3659,f3623,f23790]) ).
fof(f23790,plain,
( spl0_1202
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f3623,plain,
( spl0_478
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f3966,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1),X1) )
| ~ spl0_478
| ~ spl0_487 ),
inference(duplicate_literal_removal,[],[f3960]) ).
fof(f3960,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X1),X1),X1) )
| ~ spl0_478
| ~ spl0_487 ),
inference(resolution,[],[f3660,f3624]) ).
fof(f3624,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_478 ),
inference(avatar_component_clause,[],[f3623]) ).
fof(f23788,plain,
( spl0_1201
| ~ spl0_284
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f3949,f3651,f2345,f23786]) ).
fof(f23786,plain,
( spl0_1201
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f3949,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_284
| ~ spl0_485 ),
inference(duplicate_literal_removal,[],[f3935]) ).
fof(f3935,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_284
| ~ spl0_485 ),
inference(resolution,[],[f3652,f2346]) ).
fof(f23784,plain,
( spl0_1200
| ~ spl0_450
| ~ spl0_478 ),
inference(avatar_split_clause,[],[f3897,f3623,f3511,f23782]) ).
fof(f23782,plain,
( spl0_1200
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f3897,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_450
| ~ spl0_478 ),
inference(duplicate_literal_removal,[],[f3894]) ).
fof(f3894,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_450
| ~ spl0_478 ),
inference(resolution,[],[f3624,f3512]) ).
fof(f23780,plain,
( spl0_1199
| ~ spl0_450
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f3888,f3619,f3511,f23778]) ).
fof(f23778,plain,
( spl0_1199
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f3888,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) )
| ~ spl0_450
| ~ spl0_477 ),
inference(duplicate_literal_removal,[],[f3876]) ).
fof(f3876,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_450
| ~ spl0_477 ),
inference(resolution,[],[f3620,f3512]) ).
fof(f23776,plain,
( spl0_1198
| ~ spl0_464
| ~ spl0_477 ),
inference(avatar_split_clause,[],[f3887,f3619,f3567,f23774]) ).
fof(f23774,plain,
( spl0_1198
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f3887,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_464
| ~ spl0_477 ),
inference(duplicate_literal_removal,[],[f3877]) ).
fof(f3877,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(X0),X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_464
| ~ spl0_477 ),
inference(resolution,[],[f3620,f3568]) ).
fof(f23771,plain,
( spl0_1197
| ~ spl0_226
| ~ spl0_467 ),
inference(avatar_split_clause,[],[f3852,f3579,f2001,f23769]) ).
fof(f23769,plain,
( spl0_1197
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f3852,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(X1),X1)
| ~ class_Orderings_Opreorder(X1)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_226
| ~ spl0_467 ),
inference(resolution,[],[f3580,f2002]) ).
fof(f23767,plain,
( spl0_1196
| ~ spl0_226
| ~ spl0_466 ),
inference(avatar_split_clause,[],[f3833,f3575,f2001,f23765]) ).
fof(f23765,plain,
( spl0_1196
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f3833,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| ~ class_Orderings_Oorder(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_226
| ~ spl0_466 ),
inference(resolution,[],[f3576,f2002]) ).
fof(f23763,plain,
( spl0_1195
| ~ spl0_381
| ~ spl0_462 ),
inference(avatar_split_clause,[],[f3806,f3559,f2897,f23761]) ).
fof(f23761,plain,
( spl0_1195
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f3559,plain,
( spl0_462
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f3806,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 )
| ~ spl0_381
| ~ spl0_462 ),
inference(duplicate_literal_removal,[],[f3798]) ).
fof(f3798,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| ~ class_Ring__and__Field_Oabs__if(X0) )
| ~ spl0_381
| ~ spl0_462 ),
inference(resolution,[],[f3560,f2898]) ).
fof(f3560,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) )
| ~ spl0_462 ),
inference(avatar_component_clause,[],[f3559]) ).
fof(f23759,plain,
( spl0_1194
| ~ spl0_337
| ~ spl0_399 ),
inference(avatar_split_clause,[],[f3273,f3062,f2617,f23757]) ).
fof(f23757,plain,
( spl0_1194
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f3273,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) )
| ~ spl0_337
| ~ spl0_399 ),
inference(duplicate_literal_removal,[],[f3271]) ).
fof(f3271,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_337
| ~ spl0_399 ),
inference(resolution,[],[f3063,f2618]) ).
fof(f23755,plain,
( spl0_1193
| ~ spl0_337
| ~ spl0_398 ),
inference(avatar_split_clause,[],[f3265,f3058,f2617,f23753]) ).
fof(f23753,plain,
( spl0_1193
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f3265,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Ozero__class_Ozero(X0) )
| ~ spl0_337
| ~ spl0_398 ),
inference(duplicate_literal_removal,[],[f3263]) ).
fof(f3263,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_337
| ~ spl0_398 ),
inference(resolution,[],[f3059,f2618]) ).
fof(f23751,plain,
( spl0_1192
| ~ spl0_283
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3021,f2897,f2341,f23749]) ).
fof(f23749,plain,
( spl0_1192
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f3021,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1)
| ~ class_Orderings_Opreorder(X1) )
| ~ spl0_283
| ~ spl0_381 ),
inference(resolution,[],[f2898,f2342]) ).
fof(f23747,plain,
( spl0_1191
| ~ spl0_284
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3020,f2897,f2345,f23745]) ).
fof(f23745,plain,
( spl0_1191
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f3020,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1) )
| ~ spl0_284
| ~ spl0_381 ),
inference(resolution,[],[f2898,f2346]) ).
fof(f23743,plain,
( spl0_1190
| ~ spl0_285
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3019,f2897,f2349,f23741]) ).
fof(f23741,plain,
( spl0_1190
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f3019,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,X1) = X0
| ~ class_Ring__and__Field_Oabs__if(X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X1),X0,X1) )
| ~ spl0_285
| ~ spl0_381 ),
inference(resolution,[],[f2898,f2350]) ).
fof(f23739,plain,
( spl0_1189
| ~ spl0_367
| ~ spl0_371 ),
inference(avatar_split_clause,[],[f2989,f2857,f2841,f23737]) ).
fof(f23737,plain,
( spl0_1189
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f2989,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1) )
| ~ spl0_367
| ~ spl0_371 ),
inference(duplicate_literal_removal,[],[f2988]) ).
fof(f2988,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_367
| ~ spl0_371 ),
inference(resolution,[],[f2858,f2842]) ).
fof(f23735,plain,
( spl0_1188
| ~ spl0_368
| ~ spl0_370 ),
inference(avatar_split_clause,[],[f2984,f2853,f2845,f23733]) ).
fof(f23733,plain,
( spl0_1188
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f2984,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1) )
| ~ spl0_368
| ~ spl0_370 ),
inference(duplicate_literal_removal,[],[f2983]) ).
fof(f2983,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_368
| ~ spl0_370 ),
inference(resolution,[],[f2854,f2846]) ).
fof(f23696,plain,
( spl0_1187
| ~ spl0_277
| ~ spl0_366 ),
inference(avatar_split_clause,[],[f2970,f2837,f2317,f23694]) ).
fof(f23694,plain,
( spl0_1187
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f2970,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X0,X1),c_HOL_Oone__class_Oone(X1),X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_277
| ~ spl0_366 ),
inference(resolution,[],[f2838,f2318]) ).
fof(f23692,plain,
( spl0_1186
| ~ spl0_359
| ~ spl0_362 ),
inference(avatar_split_clause,[],[f2955,f2821,f2809,f23690]) ).
fof(f23690,plain,
( spl0_1186
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f2955,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2) )
| ~ spl0_359
| ~ spl0_362 ),
inference(duplicate_literal_removal,[],[f2954]) ).
fof(f2954,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_359
| ~ spl0_362 ),
inference(resolution,[],[f2822,f2810]) ).
fof(f23688,plain,
( spl0_1185
| ~ spl0_360
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f2952,f2817,f2813,f23686]) ).
fof(f23686,plain,
( spl0_1185
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f2952,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2) )
| ~ spl0_360
| ~ spl0_361 ),
inference(duplicate_literal_removal,[],[f2951]) ).
fof(f2951,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2) )
| ~ spl0_360
| ~ spl0_361 ),
inference(resolution,[],[f2818,f2814]) ).
fof(f23684,plain,
( spl0_1184
| ~ spl0_283
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f2938,f2797,f2341,f23682]) ).
fof(f23682,plain,
( spl0_1184
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f2938,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_356 ),
inference(resolution,[],[f2798,f2342]) ).
fof(f23680,plain,
( spl0_1183
| ~ spl0_284
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f2937,f2797,f2345,f23678]) ).
fof(f23678,plain,
( spl0_1183
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f2937,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_356 ),
inference(resolution,[],[f2798,f2346]) ).
fof(f23676,plain,
( spl0_1182
| ~ spl0_285
| ~ spl0_356 ),
inference(avatar_split_clause,[],[f2936,f2797,f2349,f23674]) ).
fof(f23674,plain,
( spl0_1182
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f2936,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_356 ),
inference(resolution,[],[f2798,f2350]) ).
fof(f23672,plain,
( spl0_1181
| ~ spl0_200
| ~ spl0_347 ),
inference(avatar_split_clause,[],[f2783,f2658,f1893,f23670]) ).
fof(f23670,plain,
( spl0_1181
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f2658,plain,
( spl0_347
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2783,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_200
| ~ spl0_347 ),
inference(resolution,[],[f2659,f1894]) ).
fof(f2659,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) )
| ~ spl0_347 ),
inference(avatar_component_clause,[],[f2658]) ).
fof(f23668,plain,
( spl0_1180
| ~ spl0_176
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f2778,f2654,f1797,f23666]) ).
fof(f23666,plain,
( spl0_1180
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f2654,plain,
( spl0_346
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2778,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_176
| ~ spl0_346 ),
inference(resolution,[],[f2655,f1798]) ).
fof(f2655,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X0) )
| ~ spl0_346 ),
inference(avatar_component_clause,[],[f2654]) ).
fof(f23664,plain,
( spl0_1179
| ~ spl0_200
| ~ spl0_342 ),
inference(avatar_split_clause,[],[f2776,f2637,f1893,f23662]) ).
fof(f23662,plain,
( spl0_1179
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f2637,plain,
( spl0_342
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2776,plain,
( ! [X0,X1] :
( ~ class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_200
| ~ spl0_342 ),
inference(resolution,[],[f2638,f1894]) ).
fof(f2638,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f2637]) ).
fof(f23660,plain,
( spl0_1178
| ~ spl0_200
| ~ spl0_339 ),
inference(avatar_split_clause,[],[f2767,f2625,f1893,f23658]) ).
fof(f23658,plain,
( spl0_1178
<=> ! [X0,X1] :
( ~ class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f2625,plain,
( spl0_339
<=> ! [X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2767,plain,
( ! [X0,X1] :
( ~ class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ominus__class_Ominus(X1,X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_200
| ~ spl0_339 ),
inference(resolution,[],[f2626,f1894]) ).
fof(f2626,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Int_Onumber__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) )
| ~ spl0_339 ),
inference(avatar_component_clause,[],[f2625]) ).
fof(f23656,plain,
( spl0_1177
| ~ spl0_369
| ~ spl0_1167 ),
inference(avatar_split_clause,[],[f23548,f23041,f2849,f23654]) ).
fof(f23654,plain,
( spl0_1177
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f2849,plain,
( spl0_369
<=> ! [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_369])]) ).
fof(f23041,plain,
( spl0_1167
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f23548,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_369
| ~ spl0_1167 ),
inference(superposition,[],[f23042,f2850]) ).
fof(f2850,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_369 ),
inference(avatar_component_clause,[],[f2849]) ).
fof(f23042,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1167 ),
inference(avatar_component_clause,[],[f23041]) ).
fof(f23652,plain,
( spl0_1176
| ~ spl0_176
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f2753,f2613,f1797,f23650]) ).
fof(f23650,plain,
( spl0_1176
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(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_1176])]) ).
fof(f2613,plain,
( spl0_336
<=> ! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2753,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
| ~ spl0_176
| ~ spl0_336 ),
inference(resolution,[],[f2614,f1798]) ).
fof(f2614,plain,
( ! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) )
| ~ spl0_336 ),
inference(avatar_component_clause,[],[f2613]) ).
fof(f23648,plain,
( spl0_1175
| ~ spl0_200
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f2751,f2609,f1893,f23646]) ).
fof(f23646,plain,
( spl0_1175
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(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_1175])]) ).
fof(f2609,plain,
( spl0_335
<=> ! [X0,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2751,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_200
| ~ spl0_335 ),
inference(resolution,[],[f2610,f1894]) ).
fof(f2610,plain,
( ! [X0,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) )
| ~ spl0_335 ),
inference(avatar_component_clause,[],[f2609]) ).
fof(f23644,plain,
( spl0_1174
| ~ spl0_194
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f2721,f2569,f1869,f23642]) ).
fof(f23642,plain,
( spl0_1174
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f2569,plain,
( spl0_325
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2721,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_194
| ~ spl0_325 ),
inference(resolution,[],[f2570,f1870]) ).
fof(f2570,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_325 ),
inference(avatar_component_clause,[],[f2569]) ).
fof(f23640,plain,
( spl0_1173
| ~ spl0_188
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f2718,f2565,f1845,f23638]) ).
fof(f23638,plain,
( spl0_1173
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f2565,plain,
( spl0_324
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2718,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_188
| ~ spl0_324 ),
inference(resolution,[],[f2566,f1846]) ).
fof(f2566,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) )
| ~ spl0_324 ),
inference(avatar_component_clause,[],[f2565]) ).
fof(f23636,plain,
( spl0_1172
| ~ spl0_165
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f2699,f2541,f1753,f23634]) ).
fof(f23634,plain,
( spl0_1172
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1753,plain,
( spl0_165
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2541,plain,
( spl0_318
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2699,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_165
| ~ spl0_318 ),
inference(resolution,[],[f2542,f1754]) ).
fof(f1754,plain,
( ! [X34] :
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oordered__idom(X34) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1753]) ).
fof(f2542,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_318 ),
inference(avatar_component_clause,[],[f2541]) ).
fof(f23632,plain,
( spl0_1171
| ~ spl0_208
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f2682,f2517,f1925,f23630]) ).
fof(f23630,plain,
( spl0_1171
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f2517,plain,
( spl0_312
<=> ! [X0,X8] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2682,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_HOL_Ozero(X0) )
| ~ spl0_208
| ~ spl0_312 ),
inference(resolution,[],[f2518,f1926]) ).
fof(f2518,plain,
( ! [X0,X8] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X8,X0) )
| ~ spl0_312 ),
inference(avatar_component_clause,[],[f2517]) ).
fof(f23628,plain,
( spl0_1170
| ~ spl0_165
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f2680,f2513,f1753,f23626]) ).
fof(f23626,plain,
( spl0_1170
<=> ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f2513,plain,
( spl0_311
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2680,plain,
( ! [X0,X1] :
( c_HOL_Oabs__class_Oabs(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_165
| ~ spl0_311 ),
inference(resolution,[],[f2514,f1754]) ).
fof(f2514,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_311 ),
inference(avatar_component_clause,[],[f2513]) ).
fof(f23624,plain,
( spl0_1169
| ~ spl0_194
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f2678,f2509,f1869,f23622]) ).
fof(f23622,plain,
( spl0_1169
<=> ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f2509,plain,
( spl0_310
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2678,plain,
( ! [X0,X1] :
( c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_194
| ~ spl0_310 ),
inference(resolution,[],[f2510,f1870]) ).
fof(f2510,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f2509]) ).
fof(f23620,plain,
( spl0_1168
| ~ spl0_184
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f2675,f2505,f1829,f23618]) ).
fof(f23618,plain,
( spl0_1168
<=> ! [X0,X1] :
( c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f2505,plain,
( spl0_309
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2675,plain,
( ! [X0,X1] :
( c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_184
| ~ spl0_309 ),
inference(resolution,[],[f2506,f1830]) ).
fof(f2506,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) )
| ~ spl0_309 ),
inference(avatar_component_clause,[],[f2505]) ).
fof(f23043,plain,
( ~ spl0_117
| spl0_1167
| ~ spl0_240
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f15496,f14979,f2069,f23041,f1523]) ).
fof(f2069,plain,
( spl0_240
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f14979,plain,
( spl0_1010
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f15496,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
| ~ spl0_240
| ~ spl0_1010 ),
inference(superposition,[],[f2070,f14980]) ).
fof(f14980,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f14979]) ).
fof(f2070,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_240 ),
inference(avatar_component_clause,[],[f2069]) ).
fof(f20607,plain,
( spl0_1166
| ~ spl0_143
| ~ spl0_513
| ~ spl0_1119
| ~ spl0_1122
| ~ spl0_1133 ),
inference(avatar_split_clause,[],[f18666,f18663,f18557,f18470,f4028,f1653,f20605]) ).
fof(f20605,plain,
( spl0_1166
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f4028,plain,
( spl0_513
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f18470,plain,
( spl0_1119
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f18557,plain,
( spl0_1122
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f18663,plain,
( spl0_1133
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f18666,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_513
| ~ spl0_1119
| ~ spl0_1122
| ~ spl0_1133 ),
inference(forward_demodulation,[],[f18664,f18596]) ).
fof(f18596,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_513
| ~ spl0_1119
| ~ spl0_1122 ),
inference(forward_demodulation,[],[f18595,f18558]) ).
fof(f18558,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_1122 ),
inference(avatar_component_clause,[],[f18557]) ).
fof(f18595,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_513
| ~ spl0_1119
| ~ spl0_1122 ),
inference(forward_demodulation,[],[f18565,f4215]) ).
fof(f4215,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_513 ),
inference(resolution,[],[f4029,f1655]) ).
fof(f4029,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_513 ),
inference(avatar_component_clause,[],[f4028]) ).
fof(f18565,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1119
| ~ spl0_1122 ),
inference(superposition,[],[f18471,f18558]) ).
fof(f18471,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_1119 ),
inference(avatar_component_clause,[],[f18470]) ).
fof(f18664,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_1133 ),
inference(avatar_component_clause,[],[f18663]) ).
fof(f20603,plain,
( spl0_1165
| ~ spl0_96
| ~ spl0_513
| ~ spl0_1118
| ~ spl0_1121
| ~ spl0_1132 ),
inference(avatar_split_clause,[],[f18661,f18658,f18516,f18425,f4028,f1418,f20601]) ).
fof(f20601,plain,
( spl0_1165
<=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f18425,plain,
( spl0_1118
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f18516,plain,
( spl0_1121
<=> ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f18658,plain,
( spl0_1132
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f18661,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_513
| ~ spl0_1118
| ~ spl0_1121
| ~ spl0_1132 ),
inference(forward_demodulation,[],[f18659,f18555]) ).
fof(f18555,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_513
| ~ spl0_1118
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f18554,f18517]) ).
fof(f18517,plain,
( ! [X0,X1] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal)
| ~ spl0_1121 ),
inference(avatar_component_clause,[],[f18516]) ).
fof(f18554,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_513
| ~ spl0_1118
| ~ spl0_1121 ),
inference(forward_demodulation,[],[f18524,f4214]) ).
fof(f4214,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_513 ),
inference(resolution,[],[f4029,f1420]) ).
fof(f18524,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1118
| ~ spl0_1121 ),
inference(superposition,[],[f18426,f18517]) ).
fof(f18426,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1118 ),
inference(avatar_component_clause,[],[f18425]) ).
fof(f18659,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_1132 ),
inference(avatar_component_clause,[],[f18658]) ).
fof(f20503,plain,
( spl0_1164
| ~ spl0_358
| ~ spl0_1163 ),
inference(avatar_split_clause,[],[f19219,f19009,f2805,f20501]) ).
fof(f20501,plain,
( spl0_1164
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f2805,plain,
( spl0_358
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f19009,plain,
( spl0_1163
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f19219,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_358
| ~ spl0_1163 ),
inference(superposition,[],[f19010,f2806]) ).
fof(f2806,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_358 ),
inference(avatar_component_clause,[],[f2805]) ).
fof(f19010,plain,
( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_1163 ),
inference(avatar_component_clause,[],[f19009]) ).
fof(f19011,plain,
( ~ spl0_62
| spl0_1163
| ~ spl0_240
| ~ spl0_1009 ),
inference(avatar_split_clause,[],[f15300,f14968,f2069,f19009,f1248]) ).
fof(f14968,plain,
( spl0_1009
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f15300,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) )
| ~ spl0_240
| ~ spl0_1009 ),
inference(superposition,[],[f2070,f14969]) ).
fof(f14969,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_1009 ),
inference(avatar_component_clause,[],[f14968]) ).
fof(f18902,plain,
( spl0_1162
| ~ spl0_132
| ~ spl0_408
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f5432,f5067,f3099,f1598,f18900]) ).
fof(f18900,plain,
( spl0_1162
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f1598,plain,
( spl0_132
<=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f5067,plain,
( spl0_642
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f5432,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
| ~ spl0_132
| ~ spl0_408
| ~ spl0_642 ),
inference(forward_demodulation,[],[f5429,f3358]) ).
fof(f3358,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_132
| ~ spl0_408 ),
inference(resolution,[],[f3100,f1600]) ).
fof(f1600,plain,
( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1598]) ).
fof(f5429,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_132
| ~ spl0_642 ),
inference(resolution,[],[f5068,f1600]) ).
fof(f5068,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f5067]) ).
fof(f18898,plain,
( spl0_1161
| ~ spl0_82
| ~ spl0_408
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f5431,f5067,f3099,f1348,f18896]) ).
fof(f18896,plain,
( spl0_1161
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f1348,plain,
( spl0_82
<=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f5431,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_408
| ~ spl0_642 ),
inference(forward_demodulation,[],[f5428,f3357]) ).
fof(f3357,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_408 ),
inference(resolution,[],[f3100,f1350]) ).
fof(f1350,plain,
( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f1348]) ).
fof(f5428,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_642 ),
inference(resolution,[],[f5068,f1350]) ).
fof(f18894,plain,
( spl0_1160
| ~ spl0_132
| ~ spl0_140
| ~ spl0_408
| ~ spl0_641 ),
inference(avatar_split_clause,[],[f5427,f5063,f3099,f1638,f1598,f18892]) ).
fof(f18892,plain,
( spl0_1160
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f1638,plain,
( spl0_140
<=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f5063,plain,
( spl0_641
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f5427,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_132
| ~ spl0_140
| ~ spl0_408
| ~ spl0_641 ),
inference(forward_demodulation,[],[f5424,f3358]) ).
fof(f5424,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_140
| ~ spl0_641 ),
inference(resolution,[],[f5064,f1640]) ).
fof(f1640,plain,
( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1638]) ).
fof(f5064,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) )
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5063]) ).
fof(f18890,plain,
( spl0_1159
| ~ spl0_82
| ~ spl0_91
| ~ spl0_408
| ~ spl0_641 ),
inference(avatar_split_clause,[],[f5426,f5063,f3099,f1393,f1348,f18888]) ).
fof(f18888,plain,
( spl0_1159
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1393,plain,
( spl0_91
<=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f5426,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_91
| ~ spl0_408
| ~ spl0_641 ),
inference(forward_demodulation,[],[f5423,f3357]) ).
fof(f5423,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_91
| ~ spl0_641 ),
inference(resolution,[],[f5064,f1395]) ).
fof(f1395,plain,
( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f1393]) ).
fof(f18886,plain,
( spl0_1158
| ~ spl0_132
| ~ spl0_420
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f5413,f5020,f3148,f1598,f18884]) ).
fof(f18884,plain,
( spl0_1158
<=> ! [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_1158])]) ).
fof(f5020,plain,
( spl0_636
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f5413,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_132
| ~ spl0_420
| ~ spl0_636 ),
inference(forward_demodulation,[],[f5410,f3403]) ).
fof(f3403,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_132
| ~ spl0_420 ),
inference(resolution,[],[f3149,f1600]) ).
fof(f5410,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_132
| ~ spl0_636 ),
inference(resolution,[],[f5021,f1600]) ).
fof(f5021,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f5020]) ).
fof(f18882,plain,
( spl0_1157
| ~ spl0_82
| ~ spl0_420
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f5412,f5020,f3148,f1348,f18880]) ).
fof(f18880,plain,
( spl0_1157
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f5412,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_420
| ~ spl0_636 ),
inference(forward_demodulation,[],[f5409,f3402]) ).
fof(f3402,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_420 ),
inference(resolution,[],[f3149,f1350]) ).
fof(f5409,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_636 ),
inference(resolution,[],[f5021,f1350]) ).
fof(f18878,plain,
( ~ spl0_62
| spl0_1156
| ~ spl0_241
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f14658,f14252,f2073,f18876,f1248]) ).
fof(f18876,plain,
( spl0_1156
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2073,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f14252,plain,
( spl0_973
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f14658,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) )
| ~ spl0_241
| ~ spl0_973 ),
inference(superposition,[],[f2074,f14253]) ).
fof(f14253,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_973 ),
inference(avatar_component_clause,[],[f14252]) ).
fof(f2074,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_241 ),
inference(avatar_component_clause,[],[f2073]) ).
fof(f18844,plain,
( spl0_1155
| ~ spl0_126
| ~ spl0_149
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f4362,f4171,f1683,f1568,f18842]) ).
fof(f18842,plain,
( spl0_1155
<=> ! [X0] : c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f4171,plain,
( spl0_546
<=> ! [X0,X3] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f4362,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_149
| ~ spl0_546 ),
inference(resolution,[],[f4172,f1685]) ).
fof(f4172,plain,
( ! [X3,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X3,X0),X0) )
| ~ spl0_546 ),
inference(avatar_component_clause,[],[f4171]) ).
fof(f18810,plain,
( spl0_1154
| ~ spl0_73
| ~ spl0_106
| ~ spl0_546 ),
inference(avatar_split_clause,[],[f4361,f4171,f1468,f1303,f18808]) ).
fof(f18808,plain,
( spl0_1154
<=> ! [X0] : c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f4361,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_106
| ~ spl0_546 ),
inference(resolution,[],[f4172,f1470]) ).
fof(f18806,plain,
( spl0_1153
| ~ spl0_209
| ~ spl0_541 ),
inference(avatar_split_clause,[],[f4320,f4140,f1929,f18804]) ).
fof(f18804,plain,
( spl0_1153
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X1,X0),X1,X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f4320,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X1,X0),X1,X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_209
| ~ spl0_541 ),
inference(resolution,[],[f4141,f1930]) ).
fof(f18802,plain,
( spl0_1152
| ~ spl0_209
| ~ spl0_540 ),
inference(avatar_split_clause,[],[f4305,f4136,f1929,f18800]) ).
fof(f18800,plain,
( spl0_1152
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X1,X1,X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f4305,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X1,X1,X0),X0) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_209
| ~ spl0_540 ),
inference(resolution,[],[f4137,f1930]) ).
fof(f18763,plain,
( spl0_1151
| ~ spl0_60
| ~ spl0_70
| ~ spl0_538 ),
inference(avatar_split_clause,[],[f4303,f4128,f1288,f1238,f18761]) ).
fof(f18761,plain,
( spl0_1151
<=> ! [X0] : c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f4128,plain,
( spl0_538
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f4303,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_70
| ~ spl0_538 ),
inference(resolution,[],[f4129,f1290]) ).
fof(f4129,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_538 ),
inference(avatar_component_clause,[],[f4128]) ).
fof(f18759,plain,
( spl0_1150
| ~ spl0_76
| ~ spl0_537 ),
inference(avatar_split_clause,[],[f4301,f4124,f1318,f18757]) ).
fof(f18757,plain,
( spl0_1150
<=> ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f4124,plain,
( spl0_537
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f4301,plain,
( ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_537 ),
inference(resolution,[],[f4125,f1320]) ).
fof(f4125,plain,
( ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0) )
| ~ spl0_537 ),
inference(avatar_component_clause,[],[f4124]) ).
fof(f18755,plain,
( spl0_1149
| ~ spl0_76
| ~ spl0_535 ),
inference(avatar_split_clause,[],[f4297,f4116,f1318,f18753]) ).
fof(f18753,plain,
( spl0_1149
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f4116,plain,
( spl0_535
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f4297,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_535 ),
inference(resolution,[],[f4117,f1320]) ).
fof(f4117,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_535 ),
inference(avatar_component_clause,[],[f4116]) ).
fof(f18726,plain,
( spl0_1148
| ~ spl0_105
| ~ spl0_529 ),
inference(avatar_split_clause,[],[f4277,f4092,f1463,f18724]) ).
fof(f18724,plain,
( spl0_1148
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f4277,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_105
| ~ spl0_529 ),
inference(resolution,[],[f4093,f1465]) ).
fof(f18722,plain,
( spl0_1147
| ~ spl0_148
| ~ spl0_529 ),
inference(avatar_split_clause,[],[f4276,f4092,f1678,f18720]) ).
fof(f18720,plain,
( spl0_1147
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f4276,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_148
| ~ spl0_529 ),
inference(resolution,[],[f4093,f1680]) ).
fof(f18718,plain,
( spl0_1146
| ~ spl0_37
| ~ spl0_529 ),
inference(avatar_split_clause,[],[f4274,f4092,f1123,f18716]) ).
fof(f18716,plain,
( spl0_1146
<=> ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f4274,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,X1,tc_nat),tc_nat)
| ~ spl0_37
| ~ spl0_529 ),
inference(resolution,[],[f4093,f1125]) ).
fof(f18714,plain,
( spl0_1145
| ~ spl0_85
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f4273,f4088,f1363,f18712]) ).
fof(f1363,plain,
( spl0_85
<=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f4273,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_85
| ~ spl0_528 ),
inference(resolution,[],[f4089,f1365]) ).
fof(f1365,plain,
( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f1363]) ).
fof(f18710,plain,
( spl0_1144
| ~ spl0_135
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f4272,f4088,f1613,f18708]) ).
fof(f1613,plain,
( spl0_135
<=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f4272,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_135
| ~ spl0_528 ),
inference(resolution,[],[f4089,f1615]) ).
fof(f1615,plain,
( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| ~ spl0_135 ),
inference(avatar_component_clause,[],[f1613]) ).
fof(f18706,plain,
( spl0_1143
| ~ spl0_27
| ~ spl0_528 ),
inference(avatar_split_clause,[],[f4270,f4088,f1073,f18704]) ).
fof(f1073,plain,
( spl0_27
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f4270,plain,
( ! [X0,X1] : c_Power_Opower__class_Opower(X0,c_Suc(X1),tc_nat) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_27
| ~ spl0_528 ),
inference(resolution,[],[f4089,f1075]) ).
fof(f1075,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f1073]) ).
fof(f18702,plain,
( spl0_1142
| ~ spl0_139
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f4267,f4080,f1633,f18700]) ).
fof(f18700,plain,
( spl0_1142
<=> ! [X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f4080,plain,
( spl0_526
<=> ! [X0,X1,X3] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f4267,plain,
( ! [X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_139
| ~ spl0_526 ),
inference(resolution,[],[f4081,f1635]) ).
fof(f4081,plain,
( ! [X3,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) )
| ~ spl0_526 ),
inference(avatar_component_clause,[],[f4080]) ).
fof(f18698,plain,
( spl0_1141
| ~ spl0_90
| ~ spl0_526 ),
inference(avatar_split_clause,[],[f4266,f4080,f1388,f18696]) ).
fof(f18696,plain,
( spl0_1141
<=> ! [X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f4266,plain,
( ! [X0,X1] : c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_90
| ~ spl0_526 ),
inference(resolution,[],[f4081,f1390]) ).
fof(f18694,plain,
( spl0_1140
| ~ spl0_124
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f4231,f4060,f1558,f18692]) ).
fof(f18692,plain,
( spl0_1140
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f4060,plain,
( spl0_521
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f4231,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_124
| ~ spl0_521 ),
inference(resolution,[],[f4061,f1560]) ).
fof(f1560,plain,
( class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1558]) ).
fof(f4061,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_521 ),
inference(avatar_component_clause,[],[f4060]) ).
fof(f18690,plain,
( spl0_1139
| ~ spl0_71
| ~ spl0_521 ),
inference(avatar_split_clause,[],[f4230,f4060,f1293,f18688]) ).
fof(f18688,plain,
( spl0_1139
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f4230,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_71
| ~ spl0_521 ),
inference(resolution,[],[f4061,f1295]) ).
fof(f1295,plain,
( class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| ~ spl0_71 ),
inference(avatar_component_clause,[],[f1293]) ).
fof(f18686,plain,
( ~ spl0_62
| spl0_1138
| ~ spl0_240
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f14657,f14252,f2069,f18684,f1248]) ).
fof(f14657,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) )
| ~ spl0_240
| ~ spl0_973 ),
inference(superposition,[],[f2070,f14253]) ).
fof(f18682,plain,
( spl0_1137
| ~ spl0_143
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f4227,f4048,f1653,f18680]) ).
fof(f18680,plain,
( spl0_1137
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f4048,plain,
( spl0_518
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f4227,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_518 ),
inference(resolution,[],[f4049,f1655]) ).
fof(f4049,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) )
| ~ spl0_518 ),
inference(avatar_component_clause,[],[f4048]) ).
fof(f18678,plain,
( spl0_1136
| ~ spl0_96
| ~ spl0_518 ),
inference(avatar_split_clause,[],[f4226,f4048,f1418,f18676]) ).
fof(f18676,plain,
( spl0_1136
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f4226,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_518 ),
inference(resolution,[],[f4049,f1420]) ).
fof(f18674,plain,
( spl0_1135
| ~ spl0_144
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4224,f4044,f1658,f18672]) ).
fof(f18672,plain,
( spl0_1135
<=> ! [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_1135])]) ).
fof(f1658,plain,
( spl0_144
<=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f4044,plain,
( spl0_517
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f4224,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_144
| ~ spl0_517 ),
inference(resolution,[],[f4045,f1660]) ).
fof(f1660,plain,
( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1658]) ).
fof(f4045,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_517 ),
inference(avatar_component_clause,[],[f4044]) ).
fof(f18670,plain,
( spl0_1134
| ~ spl0_97
| ~ spl0_517 ),
inference(avatar_split_clause,[],[f4223,f4044,f1423,f18668]) ).
fof(f18668,plain,
( spl0_1134
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f1423,plain,
( spl0_97
<=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f4223,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_97
| ~ spl0_517 ),
inference(resolution,[],[f4045,f1425]) ).
fof(f1425,plain,
( class_Ring__and__Field_Oring(tc_RealDef_Oreal)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f18665,plain,
( spl0_1133
| ~ spl0_143
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4215,f4028,f1653,f18663]) ).
fof(f18660,plain,
( spl0_1132
| ~ spl0_96
| ~ spl0_513 ),
inference(avatar_split_clause,[],[f4214,f4028,f1418,f18658]) ).
fof(f18656,plain,
( spl0_1131
| ~ spl0_47
| ~ spl0_512 ),
inference(avatar_split_clause,[],[f4212,f4024,f1173,f18654]) ).
fof(f18654,plain,
( spl0_1131
<=> ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f1173,plain,
( spl0_47
<=> class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f4024,plain,
( spl0_512
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f4212,plain,
( ! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_47
| ~ spl0_512 ),
inference(resolution,[],[f4025,f1175]) ).
fof(f1175,plain,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f1173]) ).
fof(f4025,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) )
| ~ spl0_512 ),
inference(avatar_component_clause,[],[f4024]) ).
fof(f18652,plain,
( spl0_1130
| ~ spl0_31
| ~ spl0_511 ),
inference(avatar_split_clause,[],[f4210,f4020,f1093,f18650]) ).
fof(f18650,plain,
( spl0_1130
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f4210,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) = X1 )
| ~ spl0_31
| ~ spl0_511 ),
inference(resolution,[],[f4021,f1095]) ).
fof(f18648,plain,
( spl0_1129
| ~ spl0_31
| ~ spl0_510 ),
inference(avatar_split_clause,[],[f4208,f4016,f1093,f18646]) ).
fof(f18646,plain,
( spl0_1129
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f4208,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),X0,tc_nat) = X1 )
| ~ spl0_31
| ~ spl0_510 ),
inference(resolution,[],[f4017,f1095]) ).
fof(f18644,plain,
( spl0_1128
| ~ spl0_143
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f4207,f4004,f1653,f18642]) ).
fof(f18642,plain,
( spl0_1128
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f4004,plain,
( spl0_507
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X9,X0),X9,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f4207,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X1 )
| ~ spl0_143
| ~ spl0_507 ),
inference(resolution,[],[f4005,f1655]) ).
fof(f4005,plain,
( ! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X9,X0),X9,X0) = X1 )
| ~ spl0_507 ),
inference(avatar_component_clause,[],[f4004]) ).
fof(f18616,plain,
( spl0_1127
| ~ spl0_96
| ~ spl0_507 ),
inference(avatar_split_clause,[],[f4206,f4004,f1418,f18614]) ).
fof(f18614,plain,
( spl0_1127
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f4206,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X1 )
| ~ spl0_96
| ~ spl0_507 ),
inference(resolution,[],[f4005,f1420]) ).
fof(f18612,plain,
( spl0_1126
| ~ spl0_144
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f4204,f4000,f1658,f18610]) ).
fof(f18610,plain,
( spl0_1126
<=> ! [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_1126])]) ).
fof(f4000,plain,
( spl0_506
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f4204,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_144
| ~ spl0_506 ),
inference(resolution,[],[f4001,f1660]) ).
fof(f4001,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
| ~ spl0_506 ),
inference(avatar_component_clause,[],[f4000]) ).
fof(f18608,plain,
( spl0_1125
| ~ spl0_97
| ~ spl0_506 ),
inference(avatar_split_clause,[],[f4203,f4000,f1423,f18606]) ).
fof(f18606,plain,
( spl0_1125
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f4203,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
| ~ spl0_97
| ~ spl0_506 ),
inference(resolution,[],[f4001,f1425]) ).
fof(f18604,plain,
( spl0_1124
| ~ spl0_144
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f4201,f3996,f1658,f18602]) ).
fof(f18602,plain,
( spl0_1124
<=> ! [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_1124])]) ).
fof(f3996,plain,
( spl0_505
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f4201,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_144
| ~ spl0_505 ),
inference(resolution,[],[f3997,f1660]) ).
fof(f3997,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
| ~ spl0_505 ),
inference(avatar_component_clause,[],[f3996]) ).
fof(f18600,plain,
( spl0_1123
| ~ spl0_97
| ~ spl0_505 ),
inference(avatar_split_clause,[],[f4200,f3996,f1423,f18598]) ).
fof(f18598,plain,
( spl0_1123
<=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f4200,plain,
( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_97
| ~ spl0_505 ),
inference(resolution,[],[f3997,f1425]) ).
fof(f18559,plain,
( spl0_1122
| ~ spl0_116
| ~ spl0_143
| ~ spl0_504 ),
inference(avatar_split_clause,[],[f4199,f3992,f1653,f1518,f18557]) ).
fof(f3992,plain,
( spl0_504
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f4199,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_504 ),
inference(resolution,[],[f3993,f1655]) ).
fof(f3993,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,X1,X0) )
| ~ spl0_504 ),
inference(avatar_component_clause,[],[f3992]) ).
fof(f18518,plain,
( spl0_1121
| ~ spl0_60
| ~ spl0_96
| ~ spl0_504 ),
inference(avatar_split_clause,[],[f4198,f3992,f1418,f1238,f18516]) ).
fof(f4198,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X1,X0,tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_504 ),
inference(resolution,[],[f3993,f1420]) ).
fof(f18476,plain,
( ~ spl0_62
| spl0_1120
| ~ spl0_241
| ~ spl0_970 ),
inference(avatar_split_clause,[],[f14486,f14240,f2073,f18474,f1248]) ).
fof(f14486,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) )
| ~ spl0_241
| ~ spl0_970 ),
inference(superposition,[],[f2074,f14241]) ).
fof(f18472,plain,
( spl0_1119
| ~ spl0_124
| ~ spl0_116
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f4183,f3976,f1518,f1558,f18470]) ).
fof(f3976,plain,
( spl0_500
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f4183,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_116
| ~ spl0_500 ),
inference(resolution,[],[f3977,f1520]) ).
fof(f3977,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) )
| ~ spl0_500 ),
inference(avatar_component_clause,[],[f3976]) ).
fof(f18427,plain,
( spl0_1118
| ~ spl0_71
| ~ spl0_60
| ~ spl0_500 ),
inference(avatar_split_clause,[],[f4182,f3976,f1238,f1293,f18425]) ).
fof(f4182,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_60
| ~ spl0_500 ),
inference(resolution,[],[f3977,f1240]) ).
fof(f18423,plain,
( spl0_1117
| ~ spl0_225
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f3941,f3651,f1997,f18421]) ).
fof(f18421,plain,
( spl0_1117
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f3941,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_225
| ~ spl0_485 ),
inference(resolution,[],[f3652,f1998]) ).
fof(f18419,plain,
( spl0_1116
| ~ spl0_241
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f2975,f2841,f2073,f18417]) ).
fof(f18417,plain,
( spl0_1116
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f2975,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_241
| ~ spl0_367 ),
inference(resolution,[],[f2842,f2074]) ).
fof(f18415,plain,
( spl0_1115
| ~ spl0_242
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f2974,f2841,f2077,f18413]) ).
fof(f18413,plain,
( spl0_1115
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Odvd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f2974,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Odvd(X1) )
| ~ spl0_242
| ~ spl0_367 ),
inference(resolution,[],[f2842,f2078]) ).
fof(f18411,plain,
( spl0_1114
| ~ spl0_240
| ~ spl0_367 ),
inference(avatar_split_clause,[],[f2973,f2841,f2069,f18409]) ).
fof(f18409,plain,
( spl0_1114
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Oabs__class_Oabs(X0,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f2973,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Oabs__class_Oabs(X0,X2),X2),X2)
| ~ class_Ring__and__Field_Oordered__idom(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_240
| ~ spl0_367 ),
inference(resolution,[],[f2842,f2070]) ).
fof(f18407,plain,
( spl0_1113
| ~ spl0_241
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f2950,f2817,f2073,f18405]) ).
fof(f18405,plain,
( spl0_1113
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f2950,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_241
| ~ spl0_361 ),
inference(resolution,[],[f2818,f2074]) ).
fof(f18403,plain,
( spl0_1112
| ~ spl0_242
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f2949,f2817,f2077,f18401]) ).
fof(f18401,plain,
( spl0_1112
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Odvd(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f2949,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Odvd(X1) )
| ~ spl0_242
| ~ spl0_361 ),
inference(resolution,[],[f2818,f2078]) ).
fof(f18399,plain,
( spl0_1111
| ~ spl0_240
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f2948,f2817,f2069,f18397]) ).
fof(f18397,plain,
( spl0_1111
<=> ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X0,X2),X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f2948,plain,
( ! [X2,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X0,X2),X2),X2)
| ~ class_Ring__and__Field_Ocomm__ring__1(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_240
| ~ spl0_361 ),
inference(resolution,[],[f2818,f2070]) ).
fof(f18395,plain,
( spl0_1110
| ~ spl0_917
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f14475,f14236,f11754,f18393]) ).
fof(f18393,plain,
( spl0_1110
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f11754,plain,
( spl0_917
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f14236,plain,
( spl0_969
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f14475,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_917
| ~ spl0_969 ),
inference(superposition,[],[f11755,f14237]) ).
fof(f14237,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f14236]) ).
fof(f11755,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f11754]) ).
fof(f18391,plain,
( spl0_1109
| ~ spl0_194
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f2744,f2597,f1869,f18389]) ).
fof(f18389,plain,
( spl0_1109
<=> ! [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_1109])]) ).
fof(f2597,plain,
( spl0_332
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2744,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_194
| ~ spl0_332 ),
inference(resolution,[],[f2598,f1870]) ).
fof(f2598,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f2597]) ).
fof(f18387,plain,
( spl0_1108
| ~ spl0_182
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f2739,f2593,f1821,f18385]) ).
fof(f18385,plain,
( spl0_1108
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))) = X0
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f1821,plain,
( spl0_182
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2593,plain,
( spl0_331
<=> ! [X0,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2739,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))) = X0
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) )
| ~ spl0_182
| ~ spl0_331 ),
inference(resolution,[],[f2594,f1822]) ).
fof(f1822,plain,
( ! [X34] :
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X34))
| ~ class_OrderedGroup_Ocomm__monoid__add(X34) )
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f1821]) ).
fof(f2594,plain,
( ! [X0,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X23 )
| ~ spl0_331 ),
inference(avatar_component_clause,[],[f2593]) ).
fof(f18383,plain,
( spl0_1107
| ~ spl0_182
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f2730,f2585,f1821,f18381]) ).
fof(f18381,plain,
( spl0_1107
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f2585,plain,
( spl0_329
<=> ! [X0,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = X7 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2730,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = X1
| ~ class_OrderedGroup_Ocomm__monoid__add(X0) )
| ~ spl0_182
| ~ spl0_329 ),
inference(resolution,[],[f2586,f1822]) ).
fof(f2586,plain,
( ! [X0,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = X7 )
| ~ spl0_329 ),
inference(avatar_component_clause,[],[f2585]) ).
fof(f18379,plain,
( spl0_1106
| ~ spl0_182
| ~ spl0_321 ),
inference(avatar_split_clause,[],[f2709,f2553,f1821,f18377]) ).
fof(f18377,plain,
( spl0_1106
<=> ! [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_1106])]) ).
fof(f2553,plain,
( spl0_321
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2709,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_182
| ~ spl0_321 ),
inference(resolution,[],[f2554,f1822]) ).
fof(f2554,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) )
| ~ spl0_321 ),
inference(avatar_component_clause,[],[f2553]) ).
fof(f18375,plain,
( spl0_1105
| ~ spl0_175
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f2705,f2549,f1793,f18373]) ).
fof(f18373,plain,
( spl0_1105
<=> ! [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_1105])]) ).
fof(f1793,plain,
( spl0_175
<=> ! [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_175])]) ).
fof(f2549,plain,
( spl0_320
<=> ! [X9,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2705,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_175
| ~ spl0_320 ),
inference(resolution,[],[f2550,f1794]) ).
fof(f1794,plain,
( ! [X34] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X34) )
| ~ spl0_175 ),
inference(avatar_component_clause,[],[f1793]) ).
fof(f2550,plain,
( ! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f2549]) ).
fof(f18371,plain,
( spl0_1104
| ~ spl0_175
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f2693,f2533,f1793,f18369]) ).
fof(f18369,plain,
( spl0_1104
<=> ! [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_1104])]) ).
fof(f2693,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_175
| ~ spl0_316 ),
inference(resolution,[],[f2534,f1794]) ).
fof(f18367,plain,
( spl0_1103
| ~ spl0_194
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f2689,f2525,f1869,f18365]) ).
fof(f18365,plain,
( spl0_1103
<=> ! [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_1103])]) ).
fof(f2525,plain,
( spl0_314
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2689,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_194
| ~ spl0_314 ),
inference(resolution,[],[f2526,f1870]) ).
fof(f2526,plain,
( ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 )
| ~ spl0_314 ),
inference(avatar_component_clause,[],[f2525]) ).
fof(f18363,plain,
( spl0_1102
| ~ spl0_283
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f2669,f2497,f2341,f18361]) ).
fof(f18361,plain,
( spl0_1102
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f2669,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_283
| ~ spl0_307 ),
inference(resolution,[],[f2498,f2342]) ).
fof(f18359,plain,
( spl0_1101
| ~ spl0_284
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f2668,f2497,f2345,f18357]) ).
fof(f18357,plain,
( spl0_1101
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f2668,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_284
| ~ spl0_307 ),
inference(resolution,[],[f2498,f2346]) ).
fof(f18355,plain,
( spl0_1100
| ~ spl0_285
| ~ spl0_307 ),
inference(avatar_split_clause,[],[f2667,f2497,f2349,f18353]) ).
fof(f18353,plain,
( spl0_1100
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f2667,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_285
| ~ spl0_307 ),
inference(resolution,[],[f2498,f2350]) ).
fof(f18328,plain,
( spl0_1099
| ~ spl0_198
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2483,f2397,f1885,f18326]) ).
fof(f18326,plain,
( spl0_1099
<=> ! [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_1099])]) ).
fof(f2397,plain,
( spl0_297
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2483,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_198
| ~ spl0_297 ),
inference(resolution,[],[f2398,f1886]) ).
fof(f2398,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_297 ),
inference(avatar_component_clause,[],[f2397]) ).
fof(f18324,plain,
( spl0_1098
| ~ spl0_198
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f2481,f2393,f1885,f18322]) ).
fof(f18322,plain,
( spl0_1098
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(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_1098])]) ).
fof(f2393,plain,
( spl0_296
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2481,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_296 ),
inference(resolution,[],[f2394,f1886]) ).
fof(f2394,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_296 ),
inference(avatar_component_clause,[],[f2393]) ).
fof(f18320,plain,
( spl0_1097
| ~ spl0_198
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f2479,f2389,f1885,f18318]) ).
fof(f18318,plain,
( spl0_1097
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f2389,plain,
( spl0_295
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2479,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_295 ),
inference(resolution,[],[f2390,f1886]) ).
fof(f2390,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_295 ),
inference(avatar_component_clause,[],[f2389]) ).
fof(f18316,plain,
( spl0_1096
| ~ spl0_175
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f2471,f2385,f1793,f18314]) ).
fof(f18314,plain,
( spl0_1096
<=> ! [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_1096])]) ).
fof(f2385,plain,
( spl0_294
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2471,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_175
| ~ spl0_294 ),
inference(resolution,[],[f2386,f1794]) ).
fof(f2386,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f2385]) ).
fof(f18312,plain,
( spl0_1095
| ~ spl0_175
| ~ spl0_291 ),
inference(avatar_split_clause,[],[f2463,f2373,f1793,f18310]) ).
fof(f18310,plain,
( spl0_1095
<=> ! [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_1095])]) ).
fof(f2373,plain,
( spl0_291
<=> ! [X0,X3] :
( ~ 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),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2463,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_175
| ~ spl0_291 ),
inference(resolution,[],[f2374,f1794]) ).
fof(f2374,plain,
( ! [X3,X0] :
( ~ 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),X3,X0) )
| ~ spl0_291 ),
inference(avatar_component_clause,[],[f2373]) ).
fof(f18308,plain,
( spl0_1094
| ~ spl0_189
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f2459,f2365,f1849,f18306]) ).
fof(f18306,plain,
( spl0_1094
<=> ! [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_1094])]) ).
fof(f1849,plain,
( spl0_189
<=> ! [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_189])]) ).
fof(f2365,plain,
( spl0_289
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(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_289])]) ).
fof(f2459,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_189
| ~ spl0_289 ),
inference(resolution,[],[f2366,f1850]) ).
fof(f1850,plain,
( ! [X34] :
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Ocomm__semiring__0(X34) )
| ~ spl0_189 ),
inference(avatar_component_clause,[],[f1849]) ).
fof(f2366,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_289 ),
inference(avatar_component_clause,[],[f2365]) ).
fof(f18304,plain,
( spl0_1093
| ~ spl0_189
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f2455,f2361,f1849,f18302]) ).
fof(f18302,plain,
( spl0_1093
<=> ! [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_1093])]) ).
fof(f2361,plain,
( spl0_288
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2455,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_189
| ~ spl0_288 ),
inference(resolution,[],[f2362,f1850]) ).
fof(f2362,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f2361]) ).
fof(f18300,plain,
( spl0_1092
| ~ spl0_167
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2453,f2357,f1761,f18298]) ).
fof(f18298,plain,
( spl0_1092
<=> ! [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_1092])]) ).
fof(f1761,plain,
( spl0_167
<=> ! [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_167])]) ).
fof(f2357,plain,
( spl0_287
<=> ! [X2,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),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2453,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_167
| ~ spl0_287 ),
inference(resolution,[],[f2358,f1762]) ).
fof(f1762,plain,
( ! [X34] :
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oidom(X34) )
| ~ spl0_167 ),
inference(avatar_component_clause,[],[f1761]) ).
fof(f2358,plain,
( ! [X2,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),X2,X0) )
| ~ spl0_287 ),
inference(avatar_component_clause,[],[f2357]) ).
fof(f18296,plain,
( spl0_1091
| ~ spl0_167
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f2450,f2353,f1761,f18294]) ).
fof(f18294,plain,
( spl0_1091
<=> ! [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_1091])]) ).
fof(f2353,plain,
( spl0_286
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2450,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_167
| ~ spl0_286 ),
inference(resolution,[],[f2354,f1762]) ).
fof(f2354,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_286 ),
inference(avatar_component_clause,[],[f2353]) ).
fof(f18292,plain,
( spl0_1090
| ~ spl0_198
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f2437,f2333,f1885,f18290]) ).
fof(f18290,plain,
( spl0_1090
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f2333,plain,
( spl0_281
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2437,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ofield(X0) )
| ~ spl0_198
| ~ spl0_281 ),
inference(resolution,[],[f2334,f1886]) ).
fof(f2334,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_281 ),
inference(avatar_component_clause,[],[f2333]) ).
fof(f18265,plain,
( spl0_1089
| ~ spl0_191
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2433,f2329,f1857,f18263]) ).
fof(f18263,plain,
( spl0_1089
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f2329,plain,
( spl0_280
<=> ! [X0,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2433,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_191
| ~ spl0_280 ),
inference(resolution,[],[f2330,f1858]) ).
fof(f2330,plain,
( ! [X0,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X8,X0) )
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f2329]) ).
fof(f17639,plain,
( ~ spl0_13
| ~ spl0_226
| spl0_1067 ),
inference(avatar_split_clause,[],[f17514,f17430,f2001,f1003]) ).
fof(f1003,plain,
( spl0_13
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f17430,plain,
( spl0_1067
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f17514,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| ~ spl0_226
| spl0_1067 ),
inference(resolution,[],[f17431,f2002]) ).
fof(f17431,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| spl0_1067 ),
inference(avatar_component_clause,[],[f17430]) ).
fof(f17523,plain,
( spl0_1088
| ~ spl0_448
| ~ spl0_743 ),
inference(avatar_split_clause,[],[f7107,f6428,f3493,f17521]) ).
fof(f17521,plain,
( spl0_1088
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f7107,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_448
| ~ spl0_743 ),
inference(duplicate_literal_removal,[],[f7081]) ).
fof(f7081,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(X0) = X1
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oidom(X0)
| ~ class_Ring__and__Field_Oidom(X0) )
| ~ spl0_448
| ~ spl0_743 ),
inference(resolution,[],[f6429,f3494]) ).
fof(f17513,plain,
( spl0_1087
| ~ spl0_102
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f3924,f3643,f1448,f17511]) ).
fof(f17511,plain,
( spl0_1087
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1448,plain,
( spl0_102
<=> class_Lattices_Olattice(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f3643,plain,
( spl0_483
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f3924,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_102
| ~ spl0_483 ),
inference(resolution,[],[f3644,f1450]) ).
fof(f1450,plain,
( class_Lattices_Olattice(tc_RealDef_Oreal)
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f1448]) ).
fof(f3644,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) )
| ~ spl0_483 ),
inference(avatar_component_clause,[],[f3643]) ).
fof(f17509,plain,
( spl0_1086
| ~ spl0_35
| ~ spl0_483 ),
inference(avatar_split_clause,[],[f3923,f3643,f1113,f17507]) ).
fof(f17507,plain,
( spl0_1086
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f1113,plain,
( spl0_35
<=> class_Lattices_Olattice(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f3923,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat)
| ~ spl0_35
| ~ spl0_483 ),
inference(resolution,[],[f3644,f1115]) ).
fof(f1115,plain,
( class_Lattices_Olattice(tc_nat)
| ~ spl0_35 ),
inference(avatar_component_clause,[],[f1113]) ).
fof(f17505,plain,
( spl0_1085
| ~ spl0_78
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f3873,f3611,f1328,f17503]) ).
fof(f17503,plain,
( spl0_1085
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f3611,plain,
( spl0_475
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f3873,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_475 ),
inference(resolution,[],[f3612,f1330]) ).
fof(f3612,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) )
| ~ spl0_475 ),
inference(avatar_component_clause,[],[f3611]) ).
fof(f17501,plain,
( spl0_1084
| ~ spl0_22
| ~ spl0_475 ),
inference(avatar_split_clause,[],[f3872,f3611,f1048,f17499]) ).
fof(f17499,plain,
( spl0_1084
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f3872,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat)
| ~ spl0_22
| ~ spl0_475 ),
inference(resolution,[],[f3612,f1050]) ).
fof(f17497,plain,
( spl0_1083
| ~ spl0_31
| ~ spl0_469 ),
inference(avatar_split_clause,[],[f3859,f3587,f1093,f17495]) ).
fof(f17495,plain,
( spl0_1083
<=> ! [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_1083])]) ).
fof(f3859,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_31
| ~ spl0_469 ),
inference(resolution,[],[f3588,f1095]) ).
fof(f17493,plain,
( spl0_1082
| ~ spl0_48
| ~ spl0_463 ),
inference(avatar_split_clause,[],[f3807,f3563,f1178,f17491]) ).
fof(f17491,plain,
( spl0_1082
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f1178,plain,
( spl0_48
<=> class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f3563,plain,
( spl0_463
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f3807,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_48
| ~ spl0_463 ),
inference(resolution,[],[f3564,f1180]) ).
fof(f1180,plain,
( class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f1178]) ).
fof(f3564,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) )
| ~ spl0_463 ),
inference(avatar_component_clause,[],[f3563]) ).
fof(f17489,plain,
( spl0_1081
| ~ spl0_396
| ~ spl0_448 ),
inference(avatar_split_clause,[],[f3703,f3493,f3050,f17487]) ).
fof(f17487,plain,
( spl0_1081
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f3703,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_396
| ~ spl0_448 ),
inference(resolution,[],[f3494,f3051]) ).
fof(f17485,plain,
( spl0_1080
| ~ spl0_397
| ~ spl0_447 ),
inference(avatar_split_clause,[],[f3699,f3489,f3054,f17483]) ).
fof(f17483,plain,
( spl0_1080
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f3699,plain,
( ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_397
| ~ spl0_447 ),
inference(resolution,[],[f3490,f3055]) ).
fof(f17481,plain,
( spl0_1079
| ~ spl0_31
| ~ spl0_446 ),
inference(avatar_split_clause,[],[f3697,f3485,f1093,f17479]) ).
fof(f17479,plain,
( spl0_1079
<=> ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f3697,plain,
( ! [X0,X1] : c_Divides_Odiv__class_Omod(X0,X1,tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_446 ),
inference(resolution,[],[f3486,f1095]) ).
fof(f17477,plain,
( spl0_1078
| ~ spl0_31
| ~ spl0_445 ),
inference(avatar_split_clause,[],[f3695,f3481,f1093,f17475]) ).
fof(f17475,plain,
( spl0_1078
<=> ! [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_1078])]) ).
fof(f3695,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_31
| ~ spl0_445 ),
inference(resolution,[],[f3482,f1095]) ).
fof(f17473,plain,
( spl0_1077
| ~ spl0_107
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f3694,f3469,f1473,f17471]) ).
fof(f17471,plain,
( spl0_1077
<=> ! [X0] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f3694,plain,
( ! [X0] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_107
| ~ spl0_442 ),
inference(resolution,[],[f3470,f1475]) ).
fof(f17469,plain,
( spl0_1076
| ~ spl0_150
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f3693,f3469,f1688,f17467]) ).
fof(f17467,plain,
( spl0_1076
<=> ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f3693,plain,
( ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_150
| ~ spl0_442 ),
inference(resolution,[],[f3470,f1690]) ).
fof(f17465,plain,
( spl0_1075
| ~ spl0_38
| ~ spl0_442 ),
inference(avatar_split_clause,[],[f3691,f3469,f1128,f17463]) ).
fof(f17463,plain,
( spl0_1075
<=> ! [X0] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f3691,plain,
( ! [X0] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_38
| ~ spl0_442 ),
inference(resolution,[],[f3470,f1130]) ).
fof(f17461,plain,
( spl0_1074
| ~ spl0_307
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3452,f3180,f2497,f17459]) ).
fof(f17459,plain,
( spl0_1074
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f3452,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) )
| ~ spl0_307
| ~ spl0_428 ),
inference(duplicate_literal_removal,[],[f3436]) ).
fof(f3436,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_307
| ~ spl0_428 ),
inference(resolution,[],[f3181,f2498]) ).
fof(f17457,plain,
( spl0_1073
| ~ spl0_240
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f3257,f3054,f2069,f17455]) ).
fof(f17455,plain,
( spl0_1073
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f3257,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
| ~ spl0_240
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f3251]) ).
fof(f3251,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
| ~ spl0_240
| ~ spl0_397 ),
inference(resolution,[],[f3055,f2070]) ).
fof(f17453,plain,
( spl0_1072
| ~ spl0_241
| ~ spl0_397 ),
inference(avatar_split_clause,[],[f3256,f3054,f2073,f17451]) ).
fof(f17451,plain,
( spl0_1072
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f3256,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_241
| ~ spl0_397 ),
inference(duplicate_literal_removal,[],[f3253]) ).
fof(f3253,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_241
| ~ spl0_397 ),
inference(resolution,[],[f3055,f2074]) ).
fof(f17449,plain,
( spl0_1071
| ~ spl0_240
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f3246,f3050,f2069,f17447]) ).
fof(f17447,plain,
( spl0_1071
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X0,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f3246,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X0,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
| ~ spl0_240
| ~ spl0_396 ),
inference(duplicate_literal_removal,[],[f3240]) ).
fof(f3240,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X0,X3),X3),X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
| ~ spl0_240
| ~ spl0_396 ),
inference(resolution,[],[f3051,f2070]) ).
fof(f17445,plain,
( spl0_1070
| ~ spl0_241
| ~ spl0_396 ),
inference(avatar_split_clause,[],[f3245,f3050,f2073,f17443]) ).
fof(f17443,plain,
( spl0_1070
<=> ! [X0,X3,X2,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f3245,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_241
| ~ spl0_396 ),
inference(duplicate_literal_removal,[],[f3242]) ).
fof(f3242,plain,
( ! [X2,X3,X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X0,X2),X3,X2),X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
| ~ spl0_241
| ~ spl0_396 ),
inference(resolution,[],[f3051,f2074]) ).
fof(f17441,plain,
( spl0_1069
| ~ spl0_277
| ~ spl0_285 ),
inference(avatar_split_clause,[],[f2447,f2349,f2317,f17439]) ).
fof(f17439,plain,
( spl0_1069
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2447,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_285 ),
inference(resolution,[],[f2350,f2318]) ).
fof(f17437,plain,
( spl0_1068
| ~ spl0_277
| ~ spl0_284 ),
inference(avatar_split_clause,[],[f2445,f2345,f2317,f17435]) ).
fof(f17435,plain,
( spl0_1068
<=> ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f2445,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_277
| ~ spl0_284 ),
inference(resolution,[],[f2346,f2318]) ).
fof(f17433,plain,
( ~ spl0_1066
| spl0_1067
| ~ spl0_307
| ~ spl0_799 ),
inference(avatar_split_clause,[],[f10316,f8022,f2497,f17430,f17426]) ).
fof(f17426,plain,
( spl0_1066
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f10316,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat)
| ~ spl0_307
| ~ spl0_799 ),
inference(superposition,[],[f2498,f8023]) ).
fof(f17424,plain,
( spl0_1065
| ~ spl0_277
| ~ spl0_283 ),
inference(avatar_split_clause,[],[f2439,f2341,f2317,f17422]) ).
fof(f17422,plain,
( spl0_1065
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2439,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(X1),X1),X0,X1)
| ~ class_Orderings_Opreorder(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1) )
| ~ spl0_277
| ~ spl0_283 ),
inference(resolution,[],[f2342,f2318]) ).
fof(f17420,plain,
( spl0_1064
| ~ spl0_175
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2425,f2309,f1793,f17418]) ).
fof(f17418,plain,
( spl0_1064
<=> ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2309,plain,
( spl0_275
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2425,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_175
| ~ spl0_275 ),
inference(resolution,[],[f2310,f1794]) ).
fof(f2310,plain,
( ! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_275 ),
inference(avatar_component_clause,[],[f2309]) ).
fof(f17416,plain,
( spl0_1063
| ~ spl0_165
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2275,f2165,f1753,f17414]) ).
fof(f17414,plain,
( spl0_1063
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oabs__class_Oabs(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_1063])]) ).
fof(f2165,plain,
( spl0_264
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2275,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_165
| ~ spl0_264 ),
inference(resolution,[],[f2166,f1754]) ).
fof(f2166,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_264 ),
inference(avatar_component_clause,[],[f2165]) ).
fof(f17412,plain,
( spl0_1062
| ~ spl0_184
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2250,f2113,f1829,f17410]) ).
fof(f17410,plain,
( spl0_1062
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Osgn__class_Osgn(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_1062])]) ).
fof(f2113,plain,
( spl0_251
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2250,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_184
| ~ spl0_251 ),
inference(resolution,[],[f2114,f1830]) ).
fof(f2114,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_251 ),
inference(avatar_component_clause,[],[f2113]) ).
fof(f17408,plain,
( spl0_1061
| ~ spl0_194
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2248,f2109,f1869,f17406]) ).
fof(f17406,plain,
( spl0_1061
<=> ! [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_OrderedGroup_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f2109,plain,
( spl0_250
<=> ! [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_250])]) ).
fof(f2248,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_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_194
| ~ spl0_250 ),
inference(resolution,[],[f2110,f1870]) ).
fof(f2110,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_250 ),
inference(avatar_component_clause,[],[f2109]) ).
fof(f17404,plain,
( spl0_1060
| ~ spl0_171
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2240,f2093,f1777,f17402]) ).
fof(f17402,plain,
( spl0_1060
<=> ! [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_1060])]) ).
fof(f1777,plain,
( spl0_171
<=> ! [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_171])]) ).
fof(f2093,plain,
( spl0_246
<=> ! [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_246])]) ).
fof(f2240,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_171
| ~ spl0_246 ),
inference(resolution,[],[f2094,f1778]) ).
fof(f1778,plain,
( ! [X34] :
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X34))
| ~ class_Ring__and__Field_Oordered__idom(X34) )
| ~ spl0_171 ),
inference(avatar_component_clause,[],[f1777]) ).
fof(f2094,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_246 ),
inference(avatar_component_clause,[],[f2093]) ).
fof(f17400,plain,
( spl0_1059
| ~ spl0_184
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2205,f2029,f1829,f17398]) ).
fof(f17398,plain,
( spl0_1059
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f2029,plain,
( spl0_230
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f2205,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_184
| ~ spl0_230 ),
inference(resolution,[],[f2030,f1830]) ).
fof(f2030,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f2029]) ).
fof(f17356,plain,
( spl0_1058
| ~ spl0_157
| ~ spl0_798 ),
inference(avatar_split_clause,[],[f10311,f7781,f1721,f17354]) ).
fof(f17354,plain,
( spl0_1058
<=> ! [X0,X1] :
( X0 != X1
| c_Complex_Ocnj(X0) = c_Complex_Ocnj(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f1721,plain,
( spl0_157
<=> ! [X18] : c_Complex_Ocnj(c_Complex_Ocnj(X18)) = X18 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f10311,plain,
( ! [X0,X1] :
( X0 != X1
| c_Complex_Ocnj(X0) = c_Complex_Ocnj(X1) )
| ~ spl0_157
| ~ spl0_798 ),
inference(superposition,[],[f7782,f1722]) ).
fof(f1722,plain,
( ! [X18] : c_Complex_Ocnj(c_Complex_Ocnj(X18)) = X18
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1721]) ).
fof(f16111,plain,
( ~ spl0_47
| ~ spl0_1057
| ~ spl0_282
| ~ spl0_496 ),
inference(avatar_split_clause,[],[f6463,f3786,f2337,f16108,f1173]) ).
fof(f16108,plain,
( spl0_1057
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f2337,plain,
( spl0_282
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3786,plain,
( spl0_496
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f6463,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_282
| ~ spl0_496 ),
inference(superposition,[],[f2338,f3788]) ).
fof(f3788,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_496 ),
inference(avatar_component_clause,[],[f3786]) ).
fof(f2338,plain,
( ! [X0] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0) )
| ~ spl0_282 ),
inference(avatar_component_clause,[],[f2337]) ).
fof(f15276,plain,
( ~ spl0_1056
| ~ spl0_226
| spl0_1039 ),
inference(avatar_split_clause,[],[f15237,f15151,f2001,f15273]) ).
fof(f15273,plain,
( spl0_1056
<=> class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f15151,plain,
( spl0_1039
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f15237,plain,
( ~ class_Ring__and__Field_Oordered__semidom(tc_Complex_Ocomplex)
| ~ spl0_226
| spl0_1039 ),
inference(resolution,[],[f15152,f2002]) ).
fof(f15152,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| spl0_1039 ),
inference(avatar_component_clause,[],[f15151]) ).
fof(f15221,plain,
( spl0_1055
| ~ spl0_212
| ~ spl0_485 ),
inference(avatar_split_clause,[],[f3950,f3651,f1942,f15219]) ).
fof(f15219,plain,
( spl0_1055
<=> ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f3950,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0) )
| ~ spl0_212
| ~ spl0_485 ),
inference(duplicate_literal_removal,[],[f3931]) ).
fof(f3931,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_212
| ~ spl0_485 ),
inference(resolution,[],[f3652,f1943]) ).
fof(f15217,plain,
( spl0_1054
| ~ spl0_218
| ~ spl0_449 ),
inference(avatar_split_clause,[],[f3720,f3497,f1969,f15215]) ).
fof(f15215,plain,
( spl0_1054
<=> ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f3720,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X2,X1) )
| ~ spl0_218
| ~ spl0_449 ),
inference(duplicate_literal_removal,[],[f3718]) ).
fof(f3718,plain,
( ! [X2,X0,X1] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oone__class_Oone(X1),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
| c_Ring__and__Field_Odvd__class_Odvd(X0,X2,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_218
| ~ spl0_449 ),
inference(resolution,[],[f3498,f1970]) ).
fof(f15213,plain,
( spl0_1053
| ~ spl0_107
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3463,f3212,f1473,f15210]) ).
fof(f15210,plain,
( spl0_1053
<=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f3463,plain,
( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_107
| ~ spl0_436 ),
inference(resolution,[],[f3213,f1475]) ).
fof(f15208,plain,
( spl0_1052
| ~ spl0_150
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3462,f3212,f1688,f15205]) ).
fof(f15205,plain,
( spl0_1052
<=> 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_1052])]) ).
fof(f3462,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_150
| ~ spl0_436 ),
inference(resolution,[],[f3213,f1690]) ).
fof(f15203,plain,
( spl0_1051
| ~ spl0_38
| ~ spl0_436 ),
inference(avatar_split_clause,[],[f3460,f3212,f1128,f15200]) ).
fof(f15200,plain,
( spl0_1051
<=> 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_1051])]) ).
fof(f3460,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_38
| ~ spl0_436 ),
inference(resolution,[],[f3213,f1130]) ).
fof(f15198,plain,
( spl0_1050
| ~ spl0_226
| ~ spl0_428 ),
inference(avatar_split_clause,[],[f3438,f3180,f2001,f15196]) ).
fof(f15196,plain,
( spl0_1050
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f3438,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_226
| ~ spl0_428 ),
inference(resolution,[],[f3181,f2002]) ).
fof(f15194,plain,
( spl0_1049
| ~ spl0_143
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f3421,f3168,f1653,f15192]) ).
fof(f15190,plain,
( spl0_1048
| ~ spl0_96
| ~ spl0_425 ),
inference(avatar_split_clause,[],[f3420,f3168,f1418,f15188]) ).
fof(f15186,plain,
( spl0_1047
| ~ spl0_140
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f3413,f3160,f1638,f15184]) ).
fof(f15184,plain,
( spl0_1047
<=> ! [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_1047])]) ).
fof(f3413,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_140
| ~ spl0_423 ),
inference(resolution,[],[f3161,f1640]) ).
fof(f15182,plain,
( spl0_1046
| ~ spl0_91
| ~ spl0_423 ),
inference(avatar_split_clause,[],[f3412,f3160,f1393,f15180]) ).
fof(f15180,plain,
( spl0_1046
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f3412,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| ~ spl0_91
| ~ spl0_423 ),
inference(resolution,[],[f3161,f1395]) ).
fof(f15178,plain,
( spl0_1045
| ~ spl0_132
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f3410,f3156,f1598,f15176]) ).
fof(f15176,plain,
( spl0_1045
<=> ! [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_1045])]) ).
fof(f3410,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_132
| ~ spl0_422 ),
inference(resolution,[],[f3157,f1600]) ).
fof(f15174,plain,
( spl0_1044
| ~ spl0_82
| ~ spl0_422 ),
inference(avatar_split_clause,[],[f3409,f3156,f1348,f15172]) ).
fof(f15172,plain,
( spl0_1044
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3409,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| ~ spl0_82
| ~ spl0_422 ),
inference(resolution,[],[f3157,f1350]) ).
fof(f15170,plain,
( spl0_1043
| ~ spl0_132
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f3403,f3148,f1598,f15168]) ).
fof(f15168,plain,
( spl0_1043
<=> ! [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_1043])]) ).
fof(f15166,plain,
( spl0_1042
| ~ spl0_82
| ~ spl0_420 ),
inference(avatar_split_clause,[],[f3402,f3148,f1348,f15164]) ).
fof(f15164,plain,
( spl0_1042
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f15162,plain,
( spl0_1041
| ~ spl0_140
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f3400,f3144,f1638,f15160]) ).
fof(f15160,plain,
( spl0_1041
<=> ! [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_1041])]) ).
fof(f3400,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_140
| ~ spl0_419 ),
inference(resolution,[],[f3145,f1640]) ).
fof(f15158,plain,
( spl0_1040
| ~ spl0_91
| ~ spl0_419 ),
inference(avatar_split_clause,[],[f3399,f3144,f1393,f15156]) ).
fof(f15156,plain,
( spl0_1040
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f3399,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_91
| ~ spl0_419 ),
inference(resolution,[],[f3145,f1395]) ).
fof(f15154,plain,
( ~ spl0_1038
| spl0_1039
| ~ spl0_352
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f5192,f3184,f2770,f15151,f15147]) ).
fof(f15147,plain,
( spl0_1038
<=> class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f2770,plain,
( spl0_352
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f3184,plain,
( spl0_429
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f5192,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex)
| ~ spl0_352
| ~ spl0_429 ),
inference(trivial_inequality_removal,[],[f5187]) ).
fof(f5187,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oordered__idom(tc_Complex_Ocomplex)
| ~ spl0_352
| ~ spl0_429 ),
inference(superposition,[],[f3185,f2772]) ).
fof(f2772,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_352 ),
inference(avatar_component_clause,[],[f2770]) ).
fof(f3185,plain,
( ! [X0,X1] :
( c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_429 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f15145,plain,
( spl0_1037
| ~ spl0_31
| ~ spl0_417 ),
inference(avatar_split_clause,[],[f3390,f3136,f1093,f15143]) ).
fof(f15143,plain,
( spl0_1037
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Odiv(X0,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f3390,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_HOL_Oone__class_Oone(tc_nat) = c_Divides_Odiv__class_Odiv(X0,X0,tc_nat) )
| ~ spl0_31
| ~ spl0_417 ),
inference(resolution,[],[f3137,f1095]) ).
fof(f15141,plain,
( spl0_1036
| ~ spl0_55
| ~ spl0_416 ),
inference(avatar_split_clause,[],[f3389,f3132,f1213,f15139]) ).
fof(f15139,plain,
( spl0_1036
<=> ! [X0] : c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f3132,plain,
( spl0_416
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f3389,plain,
( ! [X0] : c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_416 ),
inference(resolution,[],[f3133,f1215]) ).
fof(f3133,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X3,X0),X0) )
| ~ spl0_416 ),
inference(avatar_component_clause,[],[f3132]) ).
fof(f15137,plain,
( spl0_1035
| ~ spl0_143
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f3388,f3128,f1653,f15135]) ).
fof(f15135,plain,
( spl0_1035
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3128,plain,
( spl0_415
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f3388,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_415 ),
inference(resolution,[],[f3129,f1655]) ).
fof(f3129,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) )
| ~ spl0_415 ),
inference(avatar_component_clause,[],[f3128]) ).
fof(f15133,plain,
( spl0_1034
| ~ spl0_96
| ~ spl0_415 ),
inference(avatar_split_clause,[],[f3387,f3128,f1418,f15131]) ).
fof(f15131,plain,
( spl0_1034
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_RealDef_Oreal) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f3387,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,X0,tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_415 ),
inference(resolution,[],[f3129,f1420]) ).
fof(f15114,plain,
( spl0_1033
| ~ spl0_81
| ~ spl0_105
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f3386,f3124,f1463,f1343,f15112]) ).
fof(f15112,plain,
( spl0_1033
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Suc(X0),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f3386,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Suc(X0),tc_RealDef_Oreal) )
| ~ spl0_105
| ~ spl0_414 ),
inference(resolution,[],[f3125,f1465]) ).
fof(f15095,plain,
( spl0_1032
| ~ spl0_131
| ~ spl0_148
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f3385,f3124,f1678,f1593,f15093]) ).
fof(f15093,plain,
( spl0_1032
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Suc(X0),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f3385,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Suc(X0),tc_Complex_Ocomplex) )
| ~ spl0_148
| ~ spl0_414 ),
inference(resolution,[],[f3125,f1680]) ).
fof(f15076,plain,
( spl0_1031
| ~ spl0_25
| ~ spl0_37
| ~ spl0_414 ),
inference(avatar_split_clause,[],[f3383,f3124,f1123,f1063,f15074]) ).
fof(f15074,plain,
( spl0_1031
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f3383,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__0(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X0),tc_nat) )
| ~ spl0_37
| ~ spl0_414 ),
inference(resolution,[],[f3125,f1125]) ).
fof(f15062,plain,
( spl0_1030
| ~ spl0_132
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f3358,f3099,f1598,f15060]) ).
fof(f15060,plain,
( spl0_1030
<=> ! [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_1030])]) ).
fof(f15058,plain,
( spl0_1029
| ~ spl0_82
| ~ spl0_408 ),
inference(avatar_split_clause,[],[f3357,f3099,f1348,f15056]) ).
fof(f15056,plain,
( spl0_1029
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f15054,plain,
( spl0_1028
| ~ spl0_55
| ~ spl0_407 ),
inference(avatar_split_clause,[],[f3356,f3095,f1213,f15052]) ).
fof(f15052,plain,
( spl0_1028
<=> ! [X0] : c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f3095,plain,
( spl0_407
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f3356,plain,
( ! [X0] : c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_407 ),
inference(resolution,[],[f3096,f1215]) ).
fof(f3096,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X3,X0),X0) )
| ~ spl0_407 ),
inference(avatar_component_clause,[],[f3095]) ).
fof(f15050,plain,
( spl0_1027
| ~ spl0_212
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3296,f3083,f1942,f15048]) ).
fof(f15048,plain,
( spl0_1027
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f3296,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_404 ),
inference(resolution,[],[f3084,f1943]) ).
fof(f15046,plain,
( spl0_1026
| ~ spl0_214
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3295,f3083,f1950,f15044]) ).
fof(f15044,plain,
( spl0_1026
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f3295,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_404 ),
inference(resolution,[],[f3084,f1951]) ).
fof(f15042,plain,
( spl0_1025
| ~ spl0_215
| ~ spl0_404 ),
inference(avatar_split_clause,[],[f3294,f3083,f1954,f15040]) ).
fof(f15040,plain,
( spl0_1025
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f3294,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_404 ),
inference(resolution,[],[f3084,f1955]) ).
fof(f15038,plain,
( spl0_1024
| ~ spl0_212
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3288,f3079,f1942,f15036]) ).
fof(f15036,plain,
( spl0_1024
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f3288,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_403 ),
inference(resolution,[],[f3080,f1943]) ).
fof(f15034,plain,
( spl0_1023
| ~ spl0_214
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3287,f3079,f1950,f15032]) ).
fof(f15032,plain,
( spl0_1023
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f3287,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_403 ),
inference(resolution,[],[f3080,f1951]) ).
fof(f15030,plain,
( spl0_1022
| ~ spl0_215
| ~ spl0_403 ),
inference(avatar_split_clause,[],[f3286,f3079,f1954,f15028]) ).
fof(f15028,plain,
( spl0_1022
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f3286,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X0,X2),X2)
| ~ class_Lattices_Olower__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_403 ),
inference(resolution,[],[f3080,f1955]) ).
fof(f15026,plain,
( spl0_1021
| ~ spl0_121
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f3280,f3070,f1543,f15024]) ).
fof(f15024,plain,
( spl0_1021
<=> ! [X0] : c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1543,plain,
( spl0_121
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f3070,plain,
( spl0_401
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f3280,plain,
( ! [X0] : c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_401 ),
inference(resolution,[],[f3071,f1545]) ).
fof(f1545,plain,
( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1543]) ).
fof(f3071,plain,
( ! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X3,X0),X0) )
| ~ spl0_401 ),
inference(avatar_component_clause,[],[f3070]) ).
fof(f15022,plain,
( ~ spl0_76
| spl0_1020
| ~ spl0_351
| ~ spl0_429 ),
inference(avatar_split_clause,[],[f5100,f3184,f2734,f15019,f1318]) ).
fof(f15019,plain,
( spl0_1020
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f2734,plain,
( spl0_351
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f5100,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_351
| ~ spl0_429 ),
inference(trivial_inequality_removal,[],[f5095]) ).
fof(f5095,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
| ~ spl0_351
| ~ spl0_429 ),
inference(superposition,[],[f3185,f2736]) ).
fof(f2736,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_351 ),
inference(avatar_component_clause,[],[f2734]) ).
fof(f15017,plain,
( spl0_1019
| ~ spl0_66
| ~ spl0_401 ),
inference(avatar_split_clause,[],[f3279,f3070,f1268,f15015]) ).
fof(f15015,plain,
( spl0_1019
<=> ! [X0] : c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1268,plain,
( spl0_66
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f3279,plain,
( ! [X0] : c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_66
| ~ spl0_401 ),
inference(resolution,[],[f3071,f1270]) ).
fof(f1270,plain,
( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f1268]) ).
fof(f15013,plain,
( spl0_1018
| ~ spl0_140
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f3277,f3066,f1638,f15011]) ).
fof(f15011,plain,
( spl0_1018
<=> ! [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_1018])]) ).
fof(f3277,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_140
| ~ spl0_400 ),
inference(resolution,[],[f3067,f1640]) ).
fof(f15009,plain,
( spl0_1017
| ~ spl0_91
| ~ spl0_400 ),
inference(avatar_split_clause,[],[f3276,f3066,f1393,f15007]) ).
fof(f15007,plain,
( spl0_1017
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f3276,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1
| ~ spl0_91
| ~ spl0_400 ),
inference(resolution,[],[f3067,f1395]) ).
fof(f15005,plain,
( spl0_1016
| ~ spl0_212
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3230,f3046,f1942,f15003]) ).
fof(f15003,plain,
( spl0_1016
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f3230,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_395 ),
inference(resolution,[],[f3047,f1943]) ).
fof(f15001,plain,
( spl0_1015
| ~ spl0_214
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3229,f3046,f1950,f14999]) ).
fof(f14999,plain,
( spl0_1015
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f3229,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_395 ),
inference(resolution,[],[f3047,f1951]) ).
fof(f14997,plain,
( spl0_1014
| ~ spl0_215
| ~ spl0_395 ),
inference(avatar_split_clause,[],[f3228,f3046,f1954,f14995]) ).
fof(f14995,plain,
( spl0_1014
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f3228,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X1,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_395 ),
inference(resolution,[],[f3047,f1955]) ).
fof(f14993,plain,
( spl0_1013
| ~ spl0_212
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3220,f3042,f1942,f14991]) ).
fof(f14991,plain,
( spl0_1013
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f3220,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl0_212
| ~ spl0_394 ),
inference(resolution,[],[f3043,f1943]) ).
fof(f14989,plain,
( spl0_1012
| ~ spl0_214
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3219,f3042,f1950,f14987]) ).
fof(f14987,plain,
( spl0_1012
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f3219,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Oorder(X2) )
| ~ spl0_214
| ~ spl0_394 ),
inference(resolution,[],[f3043,f1951]) ).
fof(f14985,plain,
( spl0_1011
| ~ spl0_215
| ~ spl0_394 ),
inference(avatar_split_clause,[],[f3218,f3042,f1954,f14983]) ).
fof(f14983,plain,
( spl0_1011
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f3218,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,X2),X0,X2)
| ~ class_Lattices_Oupper__semilattice(X2)
| ~ class_Orderings_Opreorder(X2) )
| ~ spl0_215
| ~ spl0_394 ),
inference(resolution,[],[f3043,f1955]) ).
fof(f14981,plain,
( spl0_1010
| ~ spl0_147
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f3216,f3038,f1673,f14979]) ).
fof(f1673,plain,
( spl0_147
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f3216,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_147
| ~ spl0_393 ),
inference(resolution,[],[f3039,f1675]) ).
fof(f1675,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1673]) ).
fof(f14970,plain,
( spl0_1009
| ~ spl0_104
| ~ spl0_393 ),
inference(avatar_split_clause,[],[f3215,f3038,f1458,f14968]) ).
fof(f1458,plain,
( spl0_104
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f3215,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_104
| ~ spl0_393 ),
inference(resolution,[],[f3039,f1460]) ).
fof(f1460,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl0_104 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f14966,plain,
( spl0_1008
| ~ spl0_225
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3023,f2897,f1997,f14964]) ).
fof(f14964,plain,
( spl0_1008
<=> ! [X0] :
( c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f3023,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_225
| ~ spl0_381 ),
inference(resolution,[],[f2898,f1998]) ).
fof(f14962,plain,
( spl0_1007
| ~ spl0_212
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3018,f2897,f1942,f14960]) ).
fof(f14960,plain,
( spl0_1007
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f3018,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_212
| ~ spl0_381 ),
inference(resolution,[],[f2898,f1943]) ).
fof(f14958,plain,
( spl0_1006
| ~ spl0_214
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3017,f2897,f1950,f14956]) ).
fof(f14956,plain,
( spl0_1006
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f3017,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Oorder(X0) )
| ~ spl0_214
| ~ spl0_381 ),
inference(resolution,[],[f2898,f1951]) ).
fof(f14954,plain,
( spl0_1005
| ~ spl0_215
| ~ spl0_381 ),
inference(avatar_split_clause,[],[f3016,f2897,f1954,f14952]) ).
fof(f14952,plain,
( spl0_1005
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Opreorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f3016,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0)
| ~ class_Ring__and__Field_Oabs__if(X0)
| ~ class_Orderings_Opreorder(X0) )
| ~ spl0_215
| ~ spl0_381 ),
inference(resolution,[],[f2898,f1955]) ).
fof(f14950,plain,
( spl0_1004
| ~ spl0_226
| ~ spl0_372 ),
inference(avatar_split_clause,[],[f2991,f2861,f2001,f14948]) ).
fof(f14948,plain,
( spl0_1004
<=> ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f2991,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_226
| ~ spl0_372 ),
inference(resolution,[],[f2862,f2002]) ).
fof(f14946,plain,
( spl0_1003
| ~ spl0_175
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f2302,f2193,f1793,f14944]) ).
fof(f14944,plain,
( spl0_1003
<=> ! [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_1003])]) ).
fof(f2193,plain,
( spl0_271
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2302,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_175
| ~ spl0_271 ),
inference(resolution,[],[f2194,f1794]) ).
fof(f2194,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f2193]) ).
fof(f14942,plain,
( spl0_1002
| ~ spl0_175
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f2294,f2185,f1793,f14940]) ).
fof(f14940,plain,
( spl0_1002
<=> ! [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_1002])]) ).
fof(f2185,plain,
( spl0_269
<=> ! [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_269])]) ).
fof(f2294,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_175
| ~ spl0_269 ),
inference(resolution,[],[f2186,f1794]) ).
fof(f2186,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_269 ),
inference(avatar_component_clause,[],[f2185]) ).
fof(f14938,plain,
( spl0_1001
| ~ spl0_194
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2272,f2157,f1869,f14936]) ).
fof(f14936,plain,
( spl0_1001
<=> ! [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_1001])]) ).
fof(f2157,plain,
( spl0_262
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2272,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_194
| ~ spl0_262 ),
inference(resolution,[],[f2158,f1870]) ).
fof(f2158,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_262 ),
inference(avatar_component_clause,[],[f2157]) ).
fof(f14934,plain,
( spl0_1000
| ~ spl0_188
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2266,f2149,f1845,f14932]) ).
fof(f14932,plain,
( spl0_1000
<=> ! [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_1000])]) ).
fof(f2149,plain,
( spl0_260
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2266,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_188
| ~ spl0_260 ),
inference(resolution,[],[f2150,f1846]) ).
fof(f2150,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) )
| ~ spl0_260 ),
inference(avatar_component_clause,[],[f2149]) ).
fof(f14930,plain,
( spl0_999
| ~ spl0_198
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2260,f2133,f1885,f14928]) ).
fof(f14928,plain,
( spl0_999
<=> ! [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_999])]) ).
fof(f2133,plain,
( spl0_256
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2260,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_198
| ~ spl0_256 ),
inference(resolution,[],[f2134,f1886]) ).
fof(f2134,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_256 ),
inference(avatar_component_clause,[],[f2133]) ).
fof(f14926,plain,
( spl0_998
| ~ spl0_198
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2258,f2129,f1885,f14924]) ).
fof(f14924,plain,
( spl0_998
<=> ! [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_998])]) ).
fof(f2129,plain,
( spl0_255
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2258,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_198
| ~ spl0_255 ),
inference(resolution,[],[f2130,f1886]) ).
fof(f2130,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f2129]) ).
fof(f14922,plain,
( spl0_997
| ~ spl0_198
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2238,f2089,f1885,f14920]) ).
fof(f14920,plain,
( spl0_997
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ofield(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f2089,plain,
( spl0_245
<=> ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2238,plain,
( ! [X0,X1] :
( c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ofield(X1) )
| ~ spl0_198
| ~ spl0_245 ),
inference(resolution,[],[f2090,f1886]) ).
fof(f2090,plain,
( ! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f2089]) ).
fof(f14918,plain,
( spl0_996
| ~ spl0_194
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2236,f2085,f1869,f14916]) ).
fof(f14916,plain,
( spl0_996
<=> ! [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_996])]) ).
fof(f2085,plain,
( spl0_244
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2236,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_194
| ~ spl0_244 ),
inference(resolution,[],[f2086,f1870]) ).
fof(f2086,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
| ~ spl0_244 ),
inference(avatar_component_clause,[],[f2085]) ).
fof(f14914,plain,
( spl0_995
| ~ spl0_191
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2217,f2049,f1857,f14912]) ).
fof(f14912,plain,
( spl0_995
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(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_995])]) ).
fof(f2049,plain,
( spl0_235
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f2217,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_191
| ~ spl0_235 ),
inference(resolution,[],[f2050,f1858]) ).
fof(f2050,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
| ~ spl0_235 ),
inference(avatar_component_clause,[],[f2049]) ).
fof(f14910,plain,
( spl0_994
| ~ spl0_191
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2213,f2045,f1857,f14908]) ).
fof(f14908,plain,
( spl0_994
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f2045,plain,
( spl0_234
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f2213,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_191
| ~ spl0_234 ),
inference(resolution,[],[f2046,f1858]) ).
fof(f2046,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_234 ),
inference(avatar_component_clause,[],[f2045]) ).
fof(f14906,plain,
( spl0_993
| ~ spl0_175
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2207,f2037,f1793,f14904]) ).
fof(f14904,plain,
( spl0_993
<=> ! [X0,X1] :
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(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_993])]) ).
fof(f2037,plain,
( spl0_232
<=> ! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X23,X0) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f2207,plain,
( ! [X0,X1] :
( c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
| ~ spl0_175
| ~ spl0_232 ),
inference(resolution,[],[f2038,f1794]) ).
fof(f2038,plain,
( ! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X23,X0) = X23 )
| ~ spl0_232 ),
inference(avatar_component_clause,[],[f2037]) ).
fof(f14816,plain,
( ~ spl0_991
| ~ spl0_992
| ~ spl0_278
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4547,f2545,f2321,f14813,f14809]) ).
fof(f14809,plain,
( spl0_991
<=> class_Ring__and__Field_Oordered__ring__strict(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f14813,plain,
( spl0_992
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f2545,plain,
( spl0_319
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f4547,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(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_278
| ~ spl0_319 ),
inference(superposition,[],[f2322,f2546]) ).
fof(f2546,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f2545]) ).
fof(f14429,plain,
( spl0_990
| ~ spl0_569
| ~ spl0_571 ),
inference(avatar_split_clause,[],[f4669,f4469,f4461,f14427]) ).
fof(f14427,plain,
( spl0_990
<=> ! [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_990])]) ).
fof(f4469,plain,
( spl0_571
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f4669,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_569
| ~ spl0_571 ),
inference(duplicate_literal_removal,[],[f4663]) ).
fof(f4663,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_569
| ~ spl0_571 ),
inference(resolution,[],[f4470,f4462]) ).
fof(f4470,plain,
( ! [X2,X0,X1,X9] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_571 ),
inference(avatar_component_clause,[],[f4469]) ).
fof(f14425,plain,
( spl0_989
| ~ spl0_31
| ~ spl0_383 ),
inference(avatar_split_clause,[],[f3030,f2905,f1093,f14423]) ).
fof(f14423,plain,
( spl0_989
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f3030,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_383 ),
inference(resolution,[],[f2906,f1095]) ).
fof(f14421,plain,
( spl0_988
| ~ spl0_31
| ~ spl0_382 ),
inference(avatar_split_clause,[],[f3028,f2901,f1093,f14419]) ).
fof(f14419,plain,
( spl0_988
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f3028,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_31
| ~ spl0_382 ),
inference(resolution,[],[f2902,f1095]) ).
fof(f14417,plain,
( spl0_987
| ~ spl0_15
| ~ spl0_379 ),
inference(avatar_split_clause,[],[f3012,f2889,f1013,f14415]) ).
fof(f14415,plain,
( spl0_987
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f3012,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
| ~ spl0_15
| ~ spl0_379 ),
inference(resolution,[],[f2890,f1015]) ).
fof(f14413,plain,
( spl0_986
| ~ spl0_145
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f3010,f2885,f1663,f14411]) ).
fof(f14411,plain,
( spl0_986
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f3010,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
| ~ spl0_145
| ~ spl0_378 ),
inference(resolution,[],[f2886,f1665]) ).
fof(f14409,plain,
( spl0_985
| ~ spl0_98
| ~ spl0_378 ),
inference(avatar_split_clause,[],[f3009,f2885,f1428,f14407]) ).
fof(f14407,plain,
( spl0_985
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f3009,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
| ~ spl0_98
| ~ spl0_378 ),
inference(resolution,[],[f2886,f1430]) ).
fof(f14405,plain,
( spl0_984
| ~ spl0_63
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3008,f2881,f1253,f14403]) ).
fof(f14403,plain,
( spl0_984
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f3008,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_377 ),
inference(resolution,[],[f2882,f1255]) ).
fof(f14401,plain,
( spl0_983
| ~ spl0_118
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3007,f2881,f1528,f14399]) ).
fof(f14399,plain,
( spl0_983
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f3007,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_377 ),
inference(resolution,[],[f2882,f1530]) ).
fof(f14397,plain,
( spl0_982
| ~ spl0_15
| ~ spl0_377 ),
inference(avatar_split_clause,[],[f3005,f2881,f1013,f14395]) ).
fof(f14395,plain,
( spl0_982
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f3005,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat)
| ~ spl0_15
| ~ spl0_377 ),
inference(resolution,[],[f2882,f1015]) ).
fof(f14340,plain,
( spl0_981
| ~ spl0_116
| ~ spl0_143
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f2996,f2865,f1653,f1518,f14338]) ).
fof(f14338,plain,
( spl0_981
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f2865,plain,
( spl0_373
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2996,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
| ~ spl0_143
| ~ spl0_373 ),
inference(resolution,[],[f2866,f1655]) ).
fof(f2866,plain,
( ! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_373 ),
inference(avatar_component_clause,[],[f2865]) ).
fof(f14283,plain,
( spl0_980
| ~ spl0_60
| ~ spl0_96
| ~ spl0_373 ),
inference(avatar_split_clause,[],[f2995,f2865,f1418,f1238,f14281]) ).
fof(f14281,plain,
( spl0_980
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f2995,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
| c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) )
| ~ spl0_96
| ~ spl0_373 ),
inference(resolution,[],[f2866,f1420]) ).
fof(f14279,plain,
( spl0_979
| ~ spl0_31
| ~ spl0_365 ),
inference(avatar_split_clause,[],[f2963,f2833,f1093,f14277]) ).
fof(f14277,plain,
( spl0_979
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f2963,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X0,X1,tc_nat),X1,tc_nat)
| ~ spl0_31
| ~ spl0_365 ),
inference(resolution,[],[f2834,f1095]) ).
fof(f14275,plain,
( ~ spl0_977
| ~ spl0_978
| ~ spl0_278
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4395,f2501,f2321,f14272,f14268]) ).
fof(f14268,plain,
( spl0_977
<=> class_Ring__and__Field_Oordered__ring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f14272,plain,
( spl0_978
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f2501,plain,
( spl0_308
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f4395,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Oordered__ring__strict(tc_nat)
| ~ spl0_278
| ~ spl0_308 ),
inference(superposition,[],[f2322,f2502]) ).
fof(f2502,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_308 ),
inference(avatar_component_clause,[],[f2501]) ).
fof(f14266,plain,
( spl0_976
| ~ spl0_63
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f2962,f2829,f1253,f14264]) ).
fof(f14264,plain,
( spl0_976
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2962,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_364 ),
inference(resolution,[],[f2830,f1255]) ).
fof(f14262,plain,
( spl0_975
| ~ spl0_118
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f2961,f2829,f1528,f14260]) ).
fof(f14260,plain,
( spl0_975
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2961,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex)
| ~ spl0_118
| ~ spl0_364 ),
inference(resolution,[],[f2830,f1530]) ).
fof(f14258,plain,
( spl0_974
| ~ spl0_15
| ~ spl0_364 ),
inference(avatar_split_clause,[],[f2959,f2829,f1013,f14256]) ).
fof(f14256,plain,
( spl0_974
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2959,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat)
| ~ spl0_15
| ~ spl0_364 ),
inference(resolution,[],[f2830,f1015]) ).
fof(f14254,plain,
( spl0_973
| ~ spl0_76
| ~ spl0_363 ),
inference(avatar_split_clause,[],[f2957,f2825,f1318,f14252]) ).
fof(f2957,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_76
| ~ spl0_363 ),
inference(resolution,[],[f2826,f1320]) ).
fof(f14250,plain,
( spl0_972
| ~ spl0_209
| ~ spl0_361 ),
inference(avatar_split_clause,[],[f2946,f2817,f1929,f14248]) ).
fof(f14248,plain,
( spl0_972
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f2946,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,X1),X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_209
| ~ spl0_361 ),
inference(resolution,[],[f2818,f1930]) ).
fof(f14246,plain,
( spl0_971
| ~ spl0_209
| ~ spl0_359 ),
inference(avatar_split_clause,[],[f2941,f2809,f1929,f14244]) ).
fof(f14244,plain,
( spl0_971
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2941,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X0,X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
| ~ spl0_209
| ~ spl0_359 ),
inference(resolution,[],[f2810,f1930]) ).
fof(f14242,plain,
( spl0_970
| ~ spl0_76
| ~ spl0_357 ),
inference(avatar_split_clause,[],[f2939,f2801,f1318,f14240]) ).
fof(f2939,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_357 ),
inference(resolution,[],[f2802,f1320]) ).
fof(f14238,plain,
( spl0_969
| ~ spl0_48
| ~ spl0_355 ),
inference(avatar_split_clause,[],[f2935,f2793,f1178,f14236]) ).
fof(f2793,plain,
( spl0_355
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2935,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_48
| ~ spl0_355 ),
inference(resolution,[],[f2794,f1180]) ).
fof(f2794,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0) )
| ~ spl0_355 ),
inference(avatar_component_clause,[],[f2793]) ).
fof(f14234,plain,
( spl0_968
| ~ spl0_55
| ~ spl0_353 ),
inference(avatar_split_clause,[],[f2928,f2785,f1213,f14232]) ).
fof(f14232,plain,
( spl0_968
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f2785,plain,
( spl0_353
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2928,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X0,tc_RealDef_Oreal),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_55
| ~ spl0_353 ),
inference(resolution,[],[f2786,f1215]) ).
fof(f2786,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 )
| ~ spl0_353 ),
inference(avatar_component_clause,[],[f2785]) ).
fof(f13996,plain,
( ~ spl0_47
| ~ spl0_967
| ~ spl0_249
| ~ spl0_274 ),
inference(avatar_split_clause,[],[f4143,f2285,f2105,f13993,f1173]) ).
fof(f13993,plain,
( spl0_967
<=> c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f2285,plain,
( spl0_274
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f4143,plain,
( ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal)
| ~ spl0_249
| ~ spl0_274 ),
inference(superposition,[],[f2106,f2287]) ).
fof(f2287,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_274 ),
inference(avatar_component_clause,[],[f2285]) ).
fof(f13444,plain,
( spl0_966
| ~ spl0_370
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f3509,f3457,f2853,f13442]) ).
fof(f13442,plain,
( spl0_966
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f3457,plain,
( spl0_440
<=> ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f3509,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0) )
| ~ spl0_370
| ~ spl0_440 ),
inference(duplicate_literal_removal,[],[f3501]) ).
fof(f3501,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X1,X0),X1,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_370
| ~ spl0_440 ),
inference(resolution,[],[f3458,f2854]) ).
fof(f3458,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_440 ),
inference(avatar_component_clause,[],[f3457]) ).
fof(f12305,plain,
( spl0_965
| ~ spl0_367
| ~ spl0_440 ),
inference(avatar_split_clause,[],[f3508,f3457,f2841,f12303]) ).
fof(f12303,plain,
( spl0_965
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f3508,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0) )
| ~ spl0_367
| ~ spl0_440 ),
inference(duplicate_literal_removal,[],[f3507]) ).
fof(f3507,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oabs__class_Oabs(X1,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_367
| ~ spl0_440 ),
inference(resolution,[],[f3458,f2842]) ).
fof(f12042,plain,
( spl0_964
| ~ spl0_63
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f2780,f2654,f1253,f12040]) ).
fof(f12040,plain,
( spl0_964
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2780,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal)
| ~ spl0_63
| ~ spl0_346 ),
inference(resolution,[],[f2655,f1255]) ).
fof(f12038,plain,
( spl0_963
| ~ spl0_15
| ~ spl0_346 ),
inference(avatar_split_clause,[],[f2777,f2654,f1013,f12036]) ).
fof(f12036,plain,
( spl0_963
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2777,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat)
| ~ spl0_15
| ~ spl0_346 ),
inference(resolution,[],[f2655,f1015]) ).
fof(f12034,plain,
( spl0_962
| ~ spl0_15
| ~ spl0_336 ),
inference(avatar_split_clause,[],[f2752,f2613,f1013,f12032]) ).
fof(f12032,plain,
( spl0_962
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2752,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_15
| ~ spl0_336 ),
inference(resolution,[],[f2614,f1015]) ).
fof(f12030,plain,
( spl0_961
| ~ spl0_145
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f2750,f2609,f1663,f12028]) ).
fof(f12028,plain,
( spl0_961
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2750,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_145
| ~ spl0_335 ),
inference(resolution,[],[f2610,f1665]) ).
fof(f12026,plain,
( spl0_960
| ~ spl0_98
| ~ spl0_335 ),
inference(avatar_split_clause,[],[f2749,f2609,f1428,f12024]) ).
fof(f12024,plain,
( spl0_960
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2749,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_98
| ~ spl0_335 ),
inference(resolution,[],[f2610,f1430]) ).
fof(f12022,plain,
( spl0_959
| ~ spl0_102
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f2746,f2601,f1448,f12020]) ).
fof(f12020,plain,
( spl0_959
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2601,plain,
( spl0_333
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2746,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_102
| ~ spl0_333 ),
inference(resolution,[],[f2602,f1450]) ).
fof(f2602,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 )
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f2601]) ).
fof(f12018,plain,
( ~ spl0_32
| spl0_958
| ~ spl0_242
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f11275,f9038,f2077,f12016,f1098]) ).
fof(f12016,plain,
( spl0_958
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f9038,plain,
( spl0_865
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f11275,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_242
| ~ spl0_865 ),
inference(superposition,[],[f2078,f9039]) ).
fof(f9039,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f9038]) ).
fof(f12014,plain,
( spl0_957
| ~ spl0_35
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f2745,f2601,f1113,f12012]) ).
fof(f12012,plain,
( spl0_957
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2745,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_35
| ~ spl0_333 ),
inference(resolution,[],[f2602,f1115]) ).
fof(f12010,plain,
( spl0_956
| ~ spl0_140
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f2743,f2597,f1638,f12008]) ).
fof(f12008,plain,
( spl0_956
<=> ! [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_956])]) ).
fof(f2743,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
| ~ spl0_140
| ~ spl0_332 ),
inference(resolution,[],[f2598,f1640]) ).
fof(f12006,plain,
( spl0_955
| ~ spl0_91
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f2742,f2597,f1393,f12004]) ).
fof(f12004,plain,
( spl0_955
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2742,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0
| ~ spl0_91
| ~ spl0_332 ),
inference(resolution,[],[f2598,f1395]) ).
fof(f12002,plain,
( spl0_954
| ~ spl0_74
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f2741,f2593,f1308,f12000]) ).
fof(f12000,plain,
( spl0_954
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2741,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
| ~ spl0_74
| ~ spl0_331 ),
inference(resolution,[],[f2594,f1310]) ).
fof(f11998,plain,
( spl0_953
| ~ spl0_127
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f2740,f2593,f1573,f11996]) ).
fof(f11996,plain,
( spl0_953
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2740,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| ~ spl0_127
| ~ spl0_331 ),
inference(resolution,[],[f2594,f1575]) ).
fof(f11994,plain,
( spl0_952
| ~ spl0_20
| ~ spl0_331 ),
inference(avatar_split_clause,[],[f2738,f2593,f1038,f11992]) ).
fof(f11992,plain,
( spl0_952
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_Polynomial_Opoly(tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2738,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_Polynomial_Opoly(tc_nat)) = X0
| ~ spl0_20
| ~ spl0_331 ),
inference(resolution,[],[f2594,f1040]) ).
fof(f11990,plain,
( spl0_951
| ~ spl0_74
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f2732,f2585,f1308,f11988]) ).
fof(f11988,plain,
( spl0_951
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f2732,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
| ~ spl0_74
| ~ spl0_329 ),
inference(resolution,[],[f2586,f1310]) ).
fof(f11986,plain,
( spl0_950
| ~ spl0_127
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f2731,f2585,f1573,f11984]) ).
fof(f11984,plain,
( spl0_950
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2731,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
| ~ spl0_127
| ~ spl0_329 ),
inference(resolution,[],[f2586,f1575]) ).
fof(f11982,plain,
( spl0_949
| ~ spl0_20
| ~ spl0_329 ),
inference(avatar_split_clause,[],[f2729,f2585,f1038,f11980]) ).
fof(f11980,plain,
( spl0_949
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_Polynomial_Opoly(tc_nat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2729,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_Polynomial_Opoly(tc_nat)) = X0
| ~ spl0_20
| ~ spl0_329 ),
inference(resolution,[],[f2586,f1040]) ).
fof(f11978,plain,
( spl0_948
| ~ spl0_78
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f2726,f2577,f1328,f11976]) ).
fof(f11976,plain,
( spl0_948
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2577,plain,
( spl0_327
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2726,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_RealDef_Oreal)
| ~ spl0_78
| ~ spl0_327 ),
inference(resolution,[],[f2578,f1330]) ).
fof(f2578,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) )
| ~ spl0_327 ),
inference(avatar_component_clause,[],[f2577]) ).
fof(f11953,plain,
( spl0_947
| ~ spl0_22
| ~ spl0_327 ),
inference(avatar_split_clause,[],[f2725,f2577,f1048,f11951]) ).
fof(f11951,plain,
( spl0_947
<=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f2725,plain,
( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
| ~ spl0_22
| ~ spl0_327 ),
inference(resolution,[],[f2578,f1050]) ).
fof(f11949,plain,
( spl0_946
| ~ spl0_140
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f2720,f2569,f1638,f11947]) ).
fof(f11947,plain,
( spl0_946
<=> ! [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_946])]) ).
fof(f2720,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_140
| ~ spl0_325 ),
inference(resolution,[],[f2570,f1640]) ).
fof(f11945,plain,
( spl0_945
| ~ spl0_91
| ~ spl0_325 ),
inference(avatar_split_clause,[],[f2719,f2569,f1393,f11943]) ).
fof(f11943,plain,
( spl0_945
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2719,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_91
| ~ spl0_325 ),
inference(resolution,[],[f2570,f1395]) ).
fof(f11941,plain,
( spl0_944
| ~ spl0_132
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f2717,f2565,f1598,f11939]) ).
fof(f11939,plain,
( spl0_944
<=> ! [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_944])]) ).
fof(f2717,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_132
| ~ spl0_324 ),
inference(resolution,[],[f2566,f1600]) ).
fof(f11937,plain,
( spl0_943
| ~ spl0_82
| ~ spl0_324 ),
inference(avatar_split_clause,[],[f2716,f2565,f1348,f11935]) ).
fof(f11935,plain,
( spl0_943
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f2716,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_324 ),
inference(resolution,[],[f2566,f1350]) ).
fof(f11933,plain,
( spl0_942
| ~ spl0_79
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f2713,f2557,f1333,f11931]) ).
fof(f11931,plain,
( spl0_942
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f2557,plain,
( spl0_322
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2713,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_RealDef_Oreal) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_RealDef_Oreal)
| ~ spl0_79
| ~ spl0_322 ),
inference(resolution,[],[f2558,f1335]) ).
fof(f2558,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f2557]) ).
fof(f11929,plain,
( spl0_941
| ~ spl0_23
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f2712,f2557,f1053,f11927]) ).
fof(f11927,plain,
( spl0_941
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f2712,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
| ~ spl0_23
| ~ spl0_322 ),
inference(resolution,[],[f2558,f1055]) ).
fof(f11925,plain,
( spl0_940
| ~ spl0_62
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f2707,f2549,f1248,f11923]) ).
fof(f11923,plain,
( spl0_940
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f2707,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_320 ),
inference(resolution,[],[f2550,f1250]) ).
fof(f11921,plain,
( spl0_939
| ~ spl0_117
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f2706,f2549,f1523,f11919]) ).
fof(f11919,plain,
( spl0_939
<=> ! [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_939])]) ).
fof(f2706,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_320 ),
inference(resolution,[],[f2550,f1525]) ).
fof(f11917,plain,
( spl0_938
| ~ spl0_14
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f2704,f2549,f1008,f11915]) ).
fof(f11915,plain,
( spl0_938
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f2704,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
| ~ spl0_14
| ~ spl0_320 ),
inference(resolution,[],[f2550,f1010]) ).
fof(f11913,plain,
( ~ spl0_146
| spl0_937
| ~ spl0_242
| ~ spl0_845 ),
inference(avatar_split_clause,[],[f10708,f8764,f2077,f11911,f1668]) ).
fof(f11911,plain,
( spl0_937
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f10708,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_242
| ~ spl0_845 ),
inference(superposition,[],[f2078,f8765]) ).
fof(f11909,plain,
( spl0_936
| ~ spl0_47
| ~ spl0_318 ),
inference(avatar_split_clause,[],[f2698,f2541,f1173,f11907]) ).
fof(f11907,plain,
( spl0_936
<=> ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2698,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_47
| ~ spl0_318 ),
inference(resolution,[],[f2542,f1175]) ).
fof(f11904,plain,
( spl0_935
| ~ spl0_126
| ~ spl0_149
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f2697,f2537,f1683,f1568,f11901]) ).
fof(f2537,plain,
( spl0_317
<=> ! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2697,plain,
( ~ class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_149
| ~ spl0_317 ),
inference(resolution,[],[f2538,f1685]) ).
fof(f2538,plain,
( ! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_317 ),
inference(avatar_component_clause,[],[f2537]) ).
fof(f11898,plain,
( spl0_934
| ~ spl0_73
| ~ spl0_106
| ~ spl0_317 ),
inference(avatar_split_clause,[],[f2696,f2537,f1468,f1303,f11895]) ).
fof(f2696,plain,
( ~ class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
| c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_106
| ~ spl0_317 ),
inference(resolution,[],[f2538,f1470]) ).
fof(f11893,plain,
( spl0_933
| ~ spl0_62
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f2695,f2533,f1248,f11891]) ).
fof(f11889,plain,
( spl0_932
| ~ spl0_117
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f2694,f2533,f1523,f11887]) ).
fof(f11885,plain,
( spl0_931
| ~ spl0_14
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f2692,f2533,f1008,f11883]) ).
fof(f11855,plain,
( spl0_930
| ~ spl0_124
| ~ spl0_116
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f2691,f2529,f1518,f1558,f11853]) ).
fof(f11853,plain,
( spl0_930
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f2529,plain,
( spl0_315
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2691,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 )
| ~ spl0_116
| ~ spl0_315 ),
inference(resolution,[],[f2530,f1520]) ).
fof(f2530,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 )
| ~ spl0_315 ),
inference(avatar_component_clause,[],[f2529]) ).
fof(f11825,plain,
( spl0_929
| ~ spl0_71
| ~ spl0_60
| ~ spl0_315 ),
inference(avatar_split_clause,[],[f2690,f2529,f1238,f1293,f11823]) ).
fof(f11823,plain,
( spl0_929
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f2690,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 )
| ~ spl0_60
| ~ spl0_315 ),
inference(resolution,[],[f2530,f1240]) ).
fof(f11821,plain,
( spl0_928
| ~ spl0_140
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f2688,f2525,f1638,f11819]) ).
fof(f11819,plain,
( spl0_928
<=> ! [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_928])]) ).
fof(f2688,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
| ~ spl0_140
| ~ spl0_314 ),
inference(resolution,[],[f2526,f1640]) ).
fof(f11817,plain,
( spl0_927
| ~ spl0_91
| ~ spl0_314 ),
inference(avatar_split_clause,[],[f2687,f2525,f1393,f11815]) ).
fof(f11815,plain,
( spl0_927
<=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2687,plain,
( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0
| ~ spl0_91
| ~ spl0_314 ),
inference(resolution,[],[f2526,f1395]) ).
fof(f11813,plain,
( spl0_926
| ~ spl0_143
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f2686,f2521,f1653,f11811]) ).
fof(f11811,plain,
( spl0_926
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2521,plain,
( spl0_313
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2686,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_313 ),
inference(resolution,[],[f2522,f1655]) ).
fof(f2522,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) )
| ~ spl0_313 ),
inference(avatar_component_clause,[],[f2521]) ).
fof(f11809,plain,
( spl0_925
| ~ spl0_96
| ~ spl0_313 ),
inference(avatar_split_clause,[],[f2685,f2521,f1418,f11807]) ).
fof(f11807,plain,
( spl0_925
<=> ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2685,plain,
( ! [X0] : c_HOL_Oinverse__class_Oinverse(X0,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_313 ),
inference(resolution,[],[f2522,f1420]) ).
fof(f11805,plain,
( spl0_924
| ~ spl0_107
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f2684,f2517,f1473,f11803]) ).
fof(f11803,plain,
( spl0_924
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2684,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_107
| ~ spl0_312 ),
inference(resolution,[],[f2518,f1475]) ).
fof(f11801,plain,
( spl0_923
| ~ spl0_150
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f2683,f2517,f1688,f11799]) ).
fof(f11799,plain,
( spl0_923
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2683,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_150
| ~ spl0_312 ),
inference(resolution,[],[f2518,f1690]) ).
fof(f11797,plain,
( spl0_922
| ~ spl0_38
| ~ spl0_312 ),
inference(avatar_split_clause,[],[f2681,f2517,f1128,f11795]) ).
fof(f11795,plain,
( spl0_922
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f2681,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_38
| ~ spl0_312 ),
inference(resolution,[],[f2518,f1130]) ).
fof(f11793,plain,
( spl0_921
| ~ spl0_47
| ~ spl0_311 ),
inference(avatar_split_clause,[],[f2679,f2513,f1173,f11791]) ).
fof(f2679,plain,
( ! [X0] : c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_47
| ~ spl0_311 ),
inference(resolution,[],[f2514,f1175]) ).
fof(f11789,plain,
( spl0_920
| ~ spl0_140
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f2677,f2509,f1638,f11787]) ).
fof(f11787,plain,
( spl0_920
<=> ! [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_920])]) ).
fof(f2677,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_140
| ~ spl0_310 ),
inference(resolution,[],[f2510,f1640]) ).
fof(f11764,plain,
( spl0_919
| ~ spl0_91
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f2676,f2509,f1393,f11762]) ).
fof(f11762,plain,
( spl0_919
<=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2676,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_91
| ~ spl0_310 ),
inference(resolution,[],[f2510,f1395]) ).
fof(f11760,plain,
( spl0_918
| ~ spl0_76
| ~ spl0_309 ),
inference(avatar_split_clause,[],[f2674,f2505,f1318,f11758]) ).
fof(f11758,plain,
( spl0_918
<=> ! [X0] : c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2674,plain,
( ! [X0] : c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_309 ),
inference(resolution,[],[f2506,f1320]) ).
fof(f11756,plain,
( spl0_917
| ~ spl0_102
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f2666,f2493,f1448,f11754]) ).
fof(f2493,plain,
( spl0_306
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2666,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_102
| ~ spl0_306 ),
inference(resolution,[],[f2494,f1450]) ).
fof(f2494,plain,
( ! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 )
| ~ spl0_306 ),
inference(avatar_component_clause,[],[f2493]) ).
fof(f11752,plain,
( spl0_916
| ~ spl0_35
| ~ spl0_306 ),
inference(avatar_split_clause,[],[f2665,f2493,f1113,f11750]) ).
fof(f11750,plain,
( spl0_916
<=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2665,plain,
( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_35
| ~ spl0_306 ),
inference(resolution,[],[f2494,f1115]) ).
fof(f11748,plain,
( spl0_915
| ~ spl0_157
| ~ spl0_272 ),
inference(avatar_split_clause,[],[f2305,f2197,f1721,f11746]) ).
fof(f11746,plain,
( spl0_915
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f2197,plain,
( spl0_272
<=> ! [X18] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X18
| c_Complex_Ocnj(X18) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2305,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) )
| ~ spl0_157
| ~ spl0_272 ),
inference(superposition,[],[f2198,f1722]) ).
fof(f2198,plain,
( ! [X18] :
( c_Complex_Ocnj(X18) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X18 )
| ~ spl0_272 ),
inference(avatar_component_clause,[],[f2197]) ).
fof(f11744,plain,
( spl0_914
| ~ spl0_211
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2020,f2005,f1937,f11742]) ).
fof(f11742,plain,
( spl0_914
<=> ! [X0] :
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Ocnj(X0)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2005,plain,
( spl0_227
<=> ! [X4,X3] :
( X3 = X4
| c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f2020,plain,
( ! [X0] :
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Ocnj(X0)
| c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = X0 )
| ~ spl0_211
| ~ spl0_227 ),
inference(superposition,[],[f2006,f1939]) ).
fof(f2006,plain,
( ! [X3,X4] :
( c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4)
| X3 = X4 )
| ~ spl0_227 ),
inference(avatar_component_clause,[],[f2005]) ).
fof(f11654,plain,
( ~ spl0_99
| spl0_913
| ~ spl0_242
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f10503,f8656,f2077,f11652,f1433]) ).
fof(f11652,plain,
( spl0_913
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f8656,plain,
( spl0_841
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f10503,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
| ~ spl0_242
| ~ spl0_841 ),
inference(superposition,[],[f2078,f8657]) ).
fof(f8657,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f8656]) ).
fof(f10300,plain,
spl0_912,
inference(avatar_split_clause,[],[f437,f10298]) ).
fof(f10298,plain,
( spl0_912
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f437,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X1,X0),X2,X0),X0),c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X4,X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).
fof(f10296,plain,
spl0_911,
inference(avatar_split_clause,[],[f62,f10294]) ).
fof(f10294,plain,
( spl0_911
<=> ! [X0,X25,X2,X1] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X25,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f62,axiom,
! [X2,X0,X1,X25] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X25,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X25,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__inverse__lemma_0) ).
fof(f10292,plain,
( spl0_910
| ~ spl0_143
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f2489,f2409,f1653,f10290]) ).
fof(f10290,plain,
( spl0_910
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2409,plain,
( spl0_300
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2489,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_143
| ~ spl0_300 ),
inference(resolution,[],[f2410,f1655]) ).
fof(f2410,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
| ~ spl0_300 ),
inference(avatar_component_clause,[],[f2409]) ).
fof(f10286,plain,
spl0_909,
inference(avatar_split_clause,[],[f361,f10284]) ).
fof(f10284,plain,
( spl0_909
<=> ! [X2,X10,X0,X9,X25,X1] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X9,X10,X0),X0),X25,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X10,X0),X25,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X9,X0),X25,X0),X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f361,axiom,
! [X2,X10,X0,X1,X9,X25] :
( ~ class_RealVector_Oreal__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X9,X10,X0),X0),X25,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X2,X10,X0),X25,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X9,X0),X25,X0),X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).
fof(f10278,plain,
spl0_908,
inference(avatar_split_clause,[],[f421,f10276]) ).
fof(f10276,plain,
( spl0_908
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X26,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X26,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f421,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X26,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X26,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).
fof(f10274,plain,
spl0_907,
inference(avatar_split_clause,[],[f149,f10272]) ).
fof(f10272,plain,
( spl0_907
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X26,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X26,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f149,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X26,X18,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X26,X4,X0),X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).
fof(f10217,plain,
( spl0_906
| ~ spl0_96
| ~ spl0_300 ),
inference(avatar_split_clause,[],[f2488,f2409,f1418,f10215]) ).
fof(f10215,plain,
( spl0_906
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2488,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_96
| ~ spl0_300 ),
inference(resolution,[],[f2410,f1420]) ).
fof(f10213,plain,
spl0_905,
inference(avatar_split_clause,[],[f544,f10211]) ).
fof(f10211,plain,
( spl0_905
<=> ! [X2,X0,X20,X9,X22,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X22,X20,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f544,axiom,
! [X2,X0,X1,X9,X22,X20] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X22,X20,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).
fof(f10209,plain,
spl0_904,
inference(avatar_split_clause,[],[f420,f10207]) ).
fof(f10207,plain,
( spl0_904
<=> ! [X2,X0,X20,X9,X22,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X22,X20,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f420,axiom,
! [X2,X0,X1,X9,X22,X20] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X22,X20,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).
fof(f10205,plain,
spl0_903,
inference(avatar_split_clause,[],[f407,f10203]) ).
fof(f10203,plain,
( spl0_903
<=> ! [X2,X0,X20,X9,X22,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X22,X20,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f407,axiom,
! [X2,X0,X1,X9,X22,X20] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) != c_Divides_Odiv__class_Omod(X22,X9,X0)
| c_Divides_Odiv__class_Omod(X2,X9,X0) != c_Divides_Odiv__class_Omod(X20,X9,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X22,X20,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).
fof(f10201,plain,
spl0_902,
inference(avatar_split_clause,[],[f197,f10199]) ).
fof(f10199,plain,
( spl0_902
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f197,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oinverse__diff__inverse_0) ).
fof(f10189,plain,
spl0_901,
inference(avatar_split_clause,[],[f605,f10187]) ).
fof(f10187,plain,
( spl0_901
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X2,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f605,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ominus__class_Ominus(X2,X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).
fof(f10185,plain,
spl0_900,
inference(avatar_split_clause,[],[f189,f10183]) ).
fof(f10183,plain,
( spl0_900
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f189,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).
fof(f10181,plain,
spl0_899,
inference(avatar_split_clause,[],[f188,f10179]) ).
fof(f10179,plain,
( spl0_899
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f188,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).
fof(f10177,plain,
( spl0_898
| ~ spl0_121
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f2485,f2401,f1543,f10175]) ).
fof(f10175,plain,
( spl0_898
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2401,plain,
( spl0_298
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2485,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_298 ),
inference(resolution,[],[f2402,f1545]) ).
fof(f2402,plain,
( ! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_298 ),
inference(avatar_component_clause,[],[f2401]) ).
fof(f9908,plain,
spl0_897,
inference(avatar_split_clause,[],[f416,f9906]) ).
fof(f9906,plain,
( spl0_897
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X26
| X4 = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X18,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f416,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X26
| X4 = X18
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X26,X18,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).
fof(f9904,plain,
spl0_896,
inference(avatar_split_clause,[],[f405,f9902]) ).
fof(f405,axiom,
! [X2,X28,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X28,X0),X10,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).
fof(f9900,plain,
spl0_895,
inference(avatar_split_clause,[],[f404,f9898]) ).
fof(f9898,plain,
( spl0_895
<=> ! [X2,X9,X0,X10,X28,X1] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X28,X0),X10,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f404,axiom,
! [X2,X28,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Opordered__ring(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X2,X1,X0),X28,X0),X10,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).
fof(f9896,plain,
spl0_894,
inference(avatar_split_clause,[],[f403,f9894]) ).
fof(f403,axiom,
! [X2,X28,X10,X0,X1,X9] :
( ~ 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(X1,X2,X0),X28,X0),X9,X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).
fof(f9892,plain,
( spl0_893
| ~ spl0_66
| ~ spl0_298 ),
inference(avatar_split_clause,[],[f2484,f2401,f1268,f9890]) ).
fof(f9890,plain,
( spl0_893
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2484,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_OscaleR__class_OscaleR(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_66
| ~ spl0_298 ),
inference(resolution,[],[f2402,f1270]) ).
fof(f9888,plain,
spl0_892,
inference(avatar_split_clause,[],[f402,f9886]) ).
fof(f9886,plain,
( spl0_892
<=> ! [X2,X10,X0,X9,X28,X1] :
( ~ 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(X1,X2,X0),X28,X0),X9,X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f402,axiom,
! [X2,X28,X10,X0,X1,X9] :
( ~ 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(X1,X2,X0),X28,X0),X9,X0),X10,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).
fof(f9884,plain,
spl0_891,
inference(avatar_split_clause,[],[f84,f9882]) ).
fof(f9882,plain,
( spl0_891
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X26,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X0),c_Divides_Odiv__class_Odiv(X26,X18,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X26,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f84,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X26,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X3,X4,X0),c_Divides_Odiv__class_Odiv(X26,X18,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X3,X26,X0),c_HOL_Otimes__class_Otimes(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__div__if__dvd_0) ).
fof(f9729,plain,
spl0_890,
inference(avatar_split_clause,[],[f170,f9727]) ).
fof(f9727,plain,
( spl0_890
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f170,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).
fof(f9725,plain,
spl0_889,
inference(avatar_split_clause,[],[f169,f9723]) ).
fof(f9723,plain,
( spl0_889
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f169,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).
fof(f9721,plain,
spl0_888,
inference(avatar_split_clause,[],[f166,f9719]) ).
fof(f9719,plain,
( spl0_888
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f166,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).
fof(f9717,plain,
spl0_887,
inference(avatar_split_clause,[],[f165,f9715]) ).
fof(f9715,plain,
( spl0_887
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f165,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).
fof(f9713,plain,
( spl0_886
| ~ spl0_31
| ~ spl0_297 ),
inference(avatar_split_clause,[],[f2482,f2397,f1093,f9711]) ).
fof(f9711,plain,
( spl0_886
<=> ! [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_886])]) ).
fof(f2482,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_31
| ~ spl0_297 ),
inference(resolution,[],[f2398,f1095]) ).
fof(f9619,plain,
spl0_885,
inference(avatar_split_clause,[],[f561,f9617]) ).
fof(f9617,plain,
( spl0_885
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X1,X0),c_HOL_Oinverse__class_Odivide(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f561,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X1,X0),c_HOL_Oinverse__class_Odivide(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).
fof(f9615,plain,
spl0_884,
inference(avatar_split_clause,[],[f560,f9613]) ).
fof(f9613,plain,
( spl0_884
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X1,X0),c_HOL_Oinverse__class_Odivide(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f560,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X9,X1,X0),c_HOL_Oinverse__class_Odivide(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).
fof(f9611,plain,
spl0_883,
inference(avatar_split_clause,[],[f369,f9609]) ).
fof(f369,axiom,
! [X2,X28,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0) = X10
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X10,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).
fof(f9503,plain,
( spl0_882
| ~ spl0_31
| ~ spl0_296 ),
inference(avatar_split_clause,[],[f2480,f2393,f1093,f9501]) ).
fof(f9501,plain,
( spl0_882
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2480,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_31
| ~ spl0_296 ),
inference(resolution,[],[f2394,f1095]) ).
fof(f9164,plain,
( spl0_881
| ~ spl0_31
| ~ spl0_295 ),
inference(avatar_split_clause,[],[f2478,f2389,f1093,f9162]) ).
fof(f9162,plain,
( spl0_881
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2478,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Odiv(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_31
| ~ spl0_295 ),
inference(resolution,[],[f2390,f1095]) ).
fof(f9160,plain,
spl0_880,
inference(avatar_split_clause,[],[f618,f9158]) ).
fof(f9158,plain,
( spl0_880
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Otimes__class_Otimes(X3,X18,X0) != c_HOL_Otimes__class_Otimes(X26,X4,X0)
| c_HOL_Oinverse__class_Odivide(X3,X4,X0) = c_HOL_Oinverse__class_Odivide(X26,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f618,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Otimes__class_Otimes(X3,X18,X0) != c_HOL_Otimes__class_Otimes(X26,X4,X0)
| c_HOL_Oinverse__class_Odivide(X3,X4,X0) = c_HOL_Oinverse__class_Odivide(X26,X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).
fof(f9156,plain,
spl0_879,
inference(avatar_split_clause,[],[f617,f9154]) ).
fof(f9154,plain,
( spl0_879
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Oinverse__class_Odivide(X3,X4,X0) != c_HOL_Oinverse__class_Odivide(X26,X18,X0)
| c_HOL_Otimes__class_Otimes(X3,X18,X0) = c_HOL_Otimes__class_Otimes(X26,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f617,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) = X18
| c_HOL_Oinverse__class_Odivide(X3,X4,X0) != c_HOL_Oinverse__class_Odivide(X26,X18,X0)
| c_HOL_Otimes__class_Otimes(X3,X18,X0) = c_HOL_Otimes__class_Otimes(X26,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).
fof(f9152,plain,
spl0_878,
inference(avatar_split_clause,[],[f397,f9150]) ).
fof(f9150,plain,
( spl0_878
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f397,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).
fof(f9148,plain,
spl0_877,
inference(avatar_split_clause,[],[f396,f9146]) ).
fof(f9146,plain,
( spl0_877
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f396,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).
fof(f9144,plain,
spl0_876,
inference(avatar_split_clause,[],[f395,f9142]) ).
fof(f9142,plain,
( spl0_876
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f395,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).
fof(f9140,plain,
spl0_875,
inference(avatar_split_clause,[],[f394,f9138]) ).
fof(f9138,plain,
( spl0_875
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f394,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).
fof(f9136,plain,
spl0_874,
inference(avatar_split_clause,[],[f393,f9134]) ).
fof(f9134,plain,
( spl0_874
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f393,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).
fof(f9132,plain,
spl0_873,
inference(avatar_split_clause,[],[f392,f9130]) ).
fof(f9130,plain,
( spl0_873
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f392,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).
fof(f9128,plain,
spl0_872,
inference(avatar_split_clause,[],[f391,f9126]) ).
fof(f9126,plain,
( spl0_872
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f391,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).
fof(f9124,plain,
spl0_871,
inference(avatar_split_clause,[],[f390,f9122]) ).
fof(f9122,plain,
( spl0_871
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f390,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).
fof(f9120,plain,
( spl0_870
| ~ spl0_26
| ~ spl0_289 ),
inference(avatar_split_clause,[],[f2458,f2365,f1068,f9118]) ).
fof(f9118,plain,
( spl0_870
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f1068,plain,
( spl0_26
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f2458,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ spl0_26
| ~ spl0_289 ),
inference(resolution,[],[f2366,f1070]) ).
fof(f1070,plain,
( class_Ring__and__Field_Omult__zero(tc_nat)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f1068]) ).
fof(f9116,plain,
spl0_869,
inference(avatar_split_clause,[],[f291,f9114]) ).
fof(f9114,plain,
( spl0_869
<=> ! [X2,X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f291,axiom,
! [X2,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X2,X0),X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),c_HOL_Otimes__class_Otimes(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).
fof(f9112,plain,
spl0_868,
inference(avatar_split_clause,[],[f268,f9110]) ).
fof(f9110,plain,
( spl0_868
<=> ! [X18,X4,X0,X3] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X4,X0)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X4,X0),X18,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X18,X0),c_Divides_Odiv__class_Odiv(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f268,axiom,
! [X3,X0,X18,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X3,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X18,X4,X0)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X3,X4,X0),X18,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X3,X18,X0),c_Divides_Odiv__class_Odiv(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add_0) ).
fof(f9108,plain,
spl0_867,
inference(avatar_split_clause,[],[f9,f9106]) ).
fof(f9106,plain,
( spl0_867
<=> ! [X10,X11,X13,X0,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X12,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X3,X13,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X11,X12,X0),X0),X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f9,axiom,
! [X3,X10,X0,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X12,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X3,X13,X0),X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X11,X12,X0),X0),X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).
fof(f9104,plain,
spl0_866,
inference(avatar_split_clause,[],[f8,f9102]) ).
fof(f9102,plain,
( spl0_866
<=> ! [X10,X11,X13,X0,X12,X3] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X12,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X3,X13,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X11,X12,X0),X0),X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f8,axiom,
! [X3,X10,X0,X11,X12,X13] :
( ~ class_Ring__and__Field_Ocomm__ring(X0)
| ~ class_Ring__and__Field_Odvd(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,X12,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(X3,X13,X0),X0)
| c_Ring__and__Field_Odvd__class_Odvd(X10,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Otimes__class_Otimes(X11,X12,X0),X0),X13,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).
fof(f9040,plain,
( spl0_865
| ~ spl0_26
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f2454,f2361,f1068,f9038]) ).
fof(f2454,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_26
| ~ spl0_288 ),
inference(resolution,[],[f2362,f1070]) ).
fof(f8908,plain,
spl0_864,
inference(avatar_split_clause,[],[f543,f8906]) ).
fof(f8906,plain,
( spl0_864
<=> ! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f543,axiom,
! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_2) ).
fof(f8904,plain,
spl0_863,
inference(avatar_split_clause,[],[f440,f8902]) ).
fof(f8902,plain,
( spl0_863
<=> ! [X2,X0,X9,X28,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X28,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f440,axiom,
! [X2,X28,X0,X1,X9] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X28,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f8900,plain,
spl0_862,
inference(avatar_split_clause,[],[f364,f8898]) ).
fof(f8898,plain,
( spl0_862
<=> ! [X2,X0,X9,X28,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f364,axiom,
! [X2,X28,X0,X1,X9] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X28,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X28,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X2,X0),X28,X0),X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).
fof(f8896,plain,
spl0_861,
inference(avatar_split_clause,[],[f195,f8894]) ).
fof(f8894,plain,
( spl0_861
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0),X4,X0) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f195,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0),X4,X0) = c_HOL_Oplus__class_Oplus(X18,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).
fof(f8892,plain,
spl0_860,
inference(avatar_split_clause,[],[f194,f8890]) ).
fof(f8890,plain,
( spl0_860
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f194,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).
fof(f8888,plain,
( spl0_859
| ~ spl0_110
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2452,f2357,f1488,f8886]) ).
fof(f8886,plain,
( spl0_859
<=> ! [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_859])]) ).
fof(f1488,plain,
( spl0_110
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2452,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_110
| ~ spl0_287 ),
inference(resolution,[],[f2358,f1490]) ).
fof(f1490,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1488]) ).
fof(f8884,plain,
spl0_858,
inference(avatar_split_clause,[],[f168,f8882]) ).
fof(f8882,plain,
( spl0_858
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f168,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).
fof(f8880,plain,
spl0_857,
inference(avatar_split_clause,[],[f167,f8878]) ).
fof(f8878,plain,
( spl0_857
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f167,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).
fof(f8876,plain,
spl0_856,
inference(avatar_split_clause,[],[f164,f8874]) ).
fof(f8874,plain,
( spl0_856
<=> ! [X9,X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f164,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).
fof(f8872,plain,
spl0_855,
inference(avatar_split_clause,[],[f163,f8870]) ).
fof(f8870,plain,
( spl0_855
<=> ! [X9,X0,X1,X2] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f163,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).
fof(f8868,plain,
spl0_854,
inference(avatar_split_clause,[],[f63,f8866]) ).
fof(f8866,plain,
( spl0_854
<=> ! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f63,axiom,
! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_2) ).
fof(f8864,plain,
spl0_853,
inference(avatar_split_clause,[],[f56,f8862]) ).
fof(f8862,plain,
( spl0_853
<=> ! [X24,X10,X0,X9,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X9 = X10
| c_HOL_Ozero__class_Ozero(X0) = X24
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X24,X9,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X24,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f56,axiom,
! [X3,X10,X0,X9,X24] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X9 = X10
| c_HOL_Ozero__class_Ozero(X0) = X24
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X24,X9,X0),X0) != c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X24,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).
fof(f8814,plain,
( spl0_852
| ~ spl0_50
| ~ spl0_287 ),
inference(avatar_split_clause,[],[f2451,f2357,f1188,f8812]) ).
fof(f8812,plain,
( spl0_852
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1188,plain,
( spl0_50
<=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f2451,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_50
| ~ spl0_287 ),
inference(resolution,[],[f2358,f1190]) ).
fof(f1190,plain,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f1188]) ).
fof(f8796,plain,
spl0_851,
inference(avatar_split_clause,[],[f515,f8794]) ).
fof(f8794,plain,
( spl0_851
<=> ! [X24,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X24,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X24,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f515,axiom,
! [X3,X0,X1,X24] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X24,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X24,X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).
fof(f8792,plain,
spl0_850,
inference(avatar_split_clause,[],[f401,f8790]) ).
fof(f8790,plain,
( spl0_850
<=> ! [X1,X0,X23,X2,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f401,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).
fof(f8788,plain,
spl0_849,
inference(avatar_split_clause,[],[f289,f8786]) ).
fof(f8786,plain,
( spl0_849
<=> ! [X18,X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f289,axiom,
! [X3,X0,X18,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).
fof(f8784,plain,
spl0_848,
inference(avatar_split_clause,[],[f224,f8782]) ).
fof(f8782,plain,
( spl0_848
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f224,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).
fof(f8780,plain,
spl0_847,
inference(avatar_split_clause,[],[f172,f8778]) ).
fof(f8778,plain,
( spl0_847
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f172,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).
fof(f8776,plain,
spl0_846,
inference(avatar_split_clause,[],[f93,f8774]) ).
fof(f8774,plain,
( spl0_846
<=> ! [X18,X4,X0,X3,X26] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X18,X26,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X4,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f93,axiom,
! [X3,X0,X18,X26,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Oinverse__class_Odivide(X18,X26,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X18,X0),c_HOL_Otimes__class_Otimes(X4,X26,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).
fof(f8766,plain,
( spl0_845
| ~ spl0_110
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f2449,f2353,f1488,f8764]) ).
fof(f2449,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_110
| ~ spl0_286 ),
inference(resolution,[],[f2354,f1490]) ).
fof(f8670,plain,
spl0_844,
inference(avatar_split_clause,[],[f586,f8668]) ).
fof(f8668,plain,
( spl0_844
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f586,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
fof(f8666,plain,
spl0_843,
inference(avatar_split_clause,[],[f510,f8664]) ).
fof(f8664,plain,
( spl0_843
<=> ! [X9,X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,c_Polynomial_Osynthetic__div(X23,X9,X0),X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X23,X9,X0),c_Polynomial_Osynthetic__div(X23,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f510,axiom,
! [X0,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,c_Polynomial_Osynthetic__div(X23,X9,X0),X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_Polynomial_Opoly(X23,X9,X0),c_Polynomial_Osynthetic__div(X23,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_0) ).
fof(f8662,plain,
spl0_842,
inference(avatar_split_clause,[],[f412,f8660]) ).
fof(f8660,plain,
( spl0_842
<=> ! [X4,X0,X3,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X3,X8,X0),c_Power_Opower__class_Opower(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f412,axiom,
! [X3,X0,X8,X4] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(X3,X4,X0),X8,X0) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(X3,X8,X0),c_Power_Opower__class_Opower(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__power_0) ).
fof(f8658,plain,
( spl0_841
| ~ spl0_50
| ~ spl0_286 ),
inference(avatar_split_clause,[],[f2448,f2353,f1188,f8656]) ).
fof(f2448,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_50
| ~ spl0_286 ),
inference(resolution,[],[f2354,f1190]) ).
fof(f8654,plain,
spl0_840,
inference(avatar_split_clause,[],[f389,f8652]) ).
fof(f8652,plain,
( spl0_840
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f389,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2_0) ).
fof(f8650,plain,
spl0_839,
inference(avatar_split_clause,[],[f388,f8648]) ).
fof(f8648,plain,
( spl0_839
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X9,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f388,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X9,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X9,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1_0) ).
fof(f8646,plain,
spl0_838,
inference(avatar_split_clause,[],[f385,f8644]) ).
fof(f8644,plain,
( spl0_838
<=> ! [X2,X0,X22,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) != c_Divides_Odiv__class_Omod(X22,X2,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X22,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f385,axiom,
! [X2,X0,X1,X22] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) != c_Divides_Odiv__class_Omod(X22,X2,X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X22,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__cong_0) ).
fof(f8642,plain,
spl0_837,
inference(avatar_split_clause,[],[f262,f8640]) ).
fof(f8640,plain,
( spl0_837
<=> ! [X0,X7,X23,X2,X1] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f262,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| ~ c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0))
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_2) ).
fof(f8638,plain,
spl0_836,
inference(avatar_split_clause,[],[f204,f8636]) ).
fof(f8636,plain,
( spl0_836
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X9,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f204,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X9,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_1) ).
fof(f8634,plain,
spl0_835,
inference(avatar_split_clause,[],[f203,f8632]) ).
fof(f8632,plain,
( spl0_835
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X9,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f203,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(X2,X1,X0),c_Divides_Odiv__class_Odiv(X9,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__dvd__div_0) ).
fof(f8621,plain,
( spl0_834
| ~ spl0_31
| ~ spl0_281 ),
inference(avatar_split_clause,[],[f2436,f2333,f1093,f8619]) ).
fof(f8619,plain,
( spl0_834
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2436,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_31
| ~ spl0_281 ),
inference(resolution,[],[f2334,f1095]) ).
fof(f8538,plain,
spl0_833,
inference(avatar_split_clause,[],[f482,f8536]) ).
fof(f8536,plain,
( spl0_833
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f482,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).
fof(f8534,plain,
spl0_832,
inference(avatar_split_clause,[],[f481,f8532]) ).
fof(f8532,plain,
( spl0_832
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f481,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).
fof(f8530,plain,
( spl0_831
| ~ spl0_85
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2435,f2329,f1363,f8528]) ).
fof(f8528,plain,
( spl0_831
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2435,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ spl0_85
| ~ spl0_280 ),
inference(resolution,[],[f2330,f1365]) ).
fof(f8526,plain,
spl0_830,
inference(avatar_split_clause,[],[f450,f8524]) ).
fof(f8524,plain,
( spl0_830
<=> ! [X10,X0,X9,X2,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X9,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f450,axiom,
! [X2,X10,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ominus__class_Ominus(X9,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).
fof(f8522,plain,
spl0_829,
inference(avatar_split_clause,[],[f386,f8520]) ).
fof(f8520,plain,
( spl0_829
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f386,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).
fof(f8518,plain,
spl0_828,
inference(avatar_split_clause,[],[f372,f8516]) ).
fof(f8516,plain,
( spl0_828
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f372,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality2_0) ).
fof(f8514,plain,
spl0_827,
inference(avatar_split_clause,[],[f371,f8512]) ).
fof(f8512,plain,
( spl0_827
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f371,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mod__equality_0) ).
fof(f8510,plain,
spl0_826,
inference(avatar_split_clause,[],[f303,f8508]) ).
fof(f8508,plain,
( spl0_826
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f303,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).
fof(f8506,plain,
spl0_825,
inference(avatar_split_clause,[],[f214,f8504]) ).
fof(f8504,plain,
( spl0_825
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f214,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X9,X0),c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).
fof(f8502,plain,
spl0_824,
inference(avatar_split_clause,[],[f196,f8500]) ).
fof(f8500,plain,
( spl0_824
<=> ! [X10,X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f196,axiom,
! [X2,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f8498,plain,
spl0_823,
inference(avatar_split_clause,[],[f120,f8496]) ).
fof(f8496,plain,
( spl0_823
<=> ! [X17,X0,X14,X16,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X15,X0),c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),c_HOL_Otimes__class_Otimes(X15,X17,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f120,axiom,
! [X0,X16,X14,X17,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X15,X0),c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),c_HOL_Otimes__class_Otimes(X15,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f8494,plain,
spl0_822,
inference(avatar_split_clause,[],[f50,f8492]) ).
fof(f8492,plain,
( spl0_822
<=> ! [X2,X0,X9,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f50,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).
fof(f8490,plain,
spl0_821,
inference(avatar_split_clause,[],[f48,f8488]) ).
fof(f48,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).
fof(f8486,plain,
( spl0_820
| ~ spl0_135
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2434,f2329,f1613,f8484]) ).
fof(f8484,plain,
( spl0_820
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2434,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ spl0_135
| ~ spl0_280 ),
inference(resolution,[],[f2330,f1615]) ).
fof(f8344,plain,
( spl0_819
| ~ spl0_27
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f2432,f2329,f1073,f8342]) ).
fof(f8342,plain,
( spl0_819
<=> ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2432,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ spl0_27
| ~ spl0_280 ),
inference(resolution,[],[f2330,f1075]) ).
fof(f8240,plain,
spl0_818,
inference(avatar_split_clause,[],[f478,f8238]) ).
fof(f8238,plain,
( spl0_818
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f478,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).
fof(f8236,plain,
spl0_817,
inference(avatar_split_clause,[],[f477,f8234]) ).
fof(f8234,plain,
( spl0_817
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f477,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).
fof(f8232,plain,
spl0_816,
inference(avatar_split_clause,[],[f476,f8230]) ).
fof(f8230,plain,
( spl0_816
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f476,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).
fof(f8228,plain,
( spl0_815
| ~ spl0_62
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2427,f2309,f1248,f8226]) ).
fof(f2427,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal)
| ~ spl0_62
| ~ spl0_275 ),
inference(resolution,[],[f2310,f1250]) ).
fof(f8224,plain,
spl0_814,
inference(avatar_split_clause,[],[f475,f8222]) ).
fof(f8222,plain,
( spl0_814
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f475,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).
fof(f8220,plain,
spl0_813,
inference(avatar_split_clause,[],[f383,f8218]) ).
fof(f8218,plain,
( spl0_813
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X8,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f383,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X8,X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).
fof(f8216,plain,
spl0_812,
inference(avatar_split_clause,[],[f256,f8214]) ).
fof(f8214,plain,
( spl0_812
<=> ! [X0,X23,X1,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X23,X0),c_Polynomial_Osmult(X1,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f256,axiom,
! [X0,X1,X7,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X23,X0),c_Polynomial_Osmult(X1,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).
fof(f8212,plain,
spl0_811,
inference(avatar_split_clause,[],[f243,f8210]) ).
fof(f8210,plain,
( spl0_811
<=> ! [X23,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X9,X23,X0),c_Polynomial_OpCons(X1,X23,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f243,axiom,
! [X0,X1,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X9,X23,X0),c_Polynomial_OpCons(X1,X23,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).
fof(f8208,plain,
spl0_810,
inference(avatar_split_clause,[],[f175,f8206]) ).
fof(f8206,plain,
( spl0_810
<=> ! [X9,X0,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f175,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).
fof(f8204,plain,
spl0_809,
inference(avatar_split_clause,[],[f173,f8202]) ).
fof(f8202,plain,
( spl0_809
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f173,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).
fof(f8200,plain,
spl0_808,
inference(avatar_split_clause,[],[f144,f8198]) ).
fof(f8198,plain,
( spl0_808
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f144,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self2_0) ).
fof(f8196,plain,
spl0_807,
inference(avatar_split_clause,[],[f143,f8194]) ).
fof(f8194,plain,
( spl0_807
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f143,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(X1,X2,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__add__self1_0) ).
fof(f8192,plain,
spl0_806,
inference(avatar_split_clause,[],[f126,f8190]) ).
fof(f8190,plain,
( spl0_806
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X0),X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f126,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X3,X0),X4,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).
fof(f8188,plain,
spl0_805,
inference(avatar_split_clause,[],[f110,f8186]) ).
fof(f8186,plain,
( spl0_805
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f110,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X8,X0) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).
fof(f8184,plain,
( spl0_804
| ~ spl0_117
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2426,f2309,f1523,f8182]) ).
fof(f2426,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)
| ~ spl0_117
| ~ spl0_275 ),
inference(resolution,[],[f2310,f1525]) ).
fof(f8180,plain,
spl0_803,
inference(avatar_split_clause,[],[f41,f8178]) ).
fof(f8178,plain,
( spl0_803
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f41,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).
fof(f8176,plain,
spl0_802,
inference(avatar_split_clause,[],[f40,f8174]) ).
fof(f8174,plain,
( spl0_802
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f40,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).
fof(f8172,plain,
spl0_801,
inference(avatar_split_clause,[],[f39,f8170]) ).
fof(f8170,plain,
( spl0_801
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f39,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).
fof(f8168,plain,
spl0_800,
inference(avatar_split_clause,[],[f38,f8166]) ).
fof(f8166,plain,
( spl0_800
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f38,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).
fof(f8024,plain,
( spl0_799
| ~ spl0_14
| ~ spl0_275 ),
inference(avatar_split_clause,[],[f2424,f2309,f1008,f8022]) ).
fof(f2424,plain,
( ! [X0] : c_HOL_Oone__class_Oone(tc_nat) = c_Power_Opower__class_Opower(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_275 ),
inference(resolution,[],[f2310,f1010]) ).
fof(f7783,plain,
( spl0_798
| ~ spl0_157
| ~ spl0_227 ),
inference(avatar_split_clause,[],[f2019,f2005,f1721,f7781]) ).
fof(f2019,plain,
( ! [X0,X1] :
( c_Complex_Ocnj(X1) != X0
| c_Complex_Ocnj(X0) = X1 )
| ~ spl0_157
| ~ spl0_227 ),
inference(superposition,[],[f2006,f1722]) ).
fof(f7525,plain,
( ~ spl0_99
| spl0_797
| ~ spl0_242
| ~ spl0_350 ),
inference(avatar_split_clause,[],[f5040,f2701,f2077,f7523,f1433]) ).
fof(f7523,plain,
( spl0_797
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f5040,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
| ~ spl0_242
| ~ spl0_350 ),
inference(superposition,[],[f2078,f2702]) ).
fof(f7521,plain,
spl0_796,
inference(avatar_split_clause,[],[f716,f7519]) ).
fof(f7519,plain,
( spl0_796
<=> ! [X24,X23,X0,X9,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(X23,X9,X0) = X24
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X24,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f716,axiom,
! [X0,X9,X7,X24,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(X23,X9,X0) = X24
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X24,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).
fof(f7517,plain,
spl0_795,
inference(avatar_split_clause,[],[f611,f7515]) ).
fof(f7515,plain,
( spl0_795
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f611,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).
fof(f7513,plain,
spl0_794,
inference(avatar_split_clause,[],[f610,f7511]) ).
fof(f7511,plain,
( spl0_794
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f610,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).
fof(f7509,plain,
spl0_793,
inference(avatar_split_clause,[],[f609,f7507]) ).
fof(f7507,plain,
( spl0_793
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f609,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).
fof(f7505,plain,
spl0_792,
inference(avatar_split_clause,[],[f608,f7503]) ).
fof(f7503,plain,
( spl0_792
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f608,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).
fof(f7501,plain,
spl0_791,
inference(avatar_split_clause,[],[f588,f7499]) ).
fof(f7499,plain,
( spl0_791
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f588,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).
fof(f7497,plain,
spl0_790,
inference(avatar_split_clause,[],[f576,f7495]) ).
fof(f7495,plain,
( spl0_790
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X1,X23,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Polynomial_Opoly(X23,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f576,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X1,X23,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Polynomial_Opoly(X23,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_0) ).
fof(f7493,plain,
spl0_789,
inference(avatar_split_clause,[],[f575,f7491]) ).
fof(f7491,plain,
( spl0_789
<=> ! [X24,X23,X0,X9,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osynthetic__div(X23,X9,X0) = X7
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X24,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f575,axiom,
! [X0,X9,X7,X24,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osynthetic__div(X23,X9,X0) = X7
| c_HOL_Oplus__class_Oplus(X23,c_Polynomial_Osmult(X9,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X24,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).
fof(f7489,plain,
spl0_788,
inference(avatar_split_clause,[],[f549,f7487]) ).
fof(f7487,plain,
( spl0_788
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f549,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).
fof(f7485,plain,
spl0_787,
inference(avatar_split_clause,[],[f501,f7483]) ).
fof(f7483,plain,
( spl0_787
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f501,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).
fof(f7469,plain,
spl0_786,
inference(avatar_split_clause,[],[f499,f7467]) ).
fof(f7467,plain,
( spl0_786
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f499,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).
fof(f7465,plain,
spl0_785,
inference(avatar_split_clause,[],[f497,f7463]) ).
fof(f7463,plain,
( spl0_785
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f497,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).
fof(f7461,plain,
spl0_784,
inference(avatar_split_clause,[],[f496,f7459]) ).
fof(f7459,plain,
( spl0_784
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f496,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f7457,plain,
spl0_783,
inference(avatar_split_clause,[],[f495,f7455]) ).
fof(f7455,plain,
( spl0_783
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f495,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).
fof(f7453,plain,
spl0_782,
inference(avatar_split_clause,[],[f492,f7451]) ).
fof(f7451,plain,
( spl0_782
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f492,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f7449,plain,
spl0_781,
inference(avatar_split_clause,[],[f491,f7447]) ).
fof(f491,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).
fof(f7445,plain,
spl0_780,
inference(avatar_split_clause,[],[f490,f7443]) ).
fof(f490,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).
fof(f7441,plain,
spl0_779,
inference(avatar_split_clause,[],[f489,f7439]) ).
fof(f7439,plain,
( spl0_779
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f489,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f7437,plain,
spl0_778,
inference(avatar_split_clause,[],[f452,f7435]) ).
fof(f7435,plain,
( spl0_778
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X9,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X9,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f452,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X9,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X9,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult_0) ).
fof(f7433,plain,
spl0_777,
inference(avatar_split_clause,[],[f426,f7431]) ).
fof(f7431,plain,
( spl0_777
<=> ! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f426,axiom,
! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_1) ).
fof(f7429,plain,
( ~ spl0_146
| spl0_776
| ~ spl0_242
| ~ spl0_349 ),
inference(avatar_split_clause,[],[f4977,f2671,f2077,f7427,f1668]) ).
fof(f7427,plain,
( spl0_776
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f4977,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_242
| ~ spl0_349 ),
inference(superposition,[],[f2078,f2672]) ).
fof(f7425,plain,
spl0_775,
inference(avatar_split_clause,[],[f374,f7423]) ).
fof(f7423,plain,
( spl0_775
<=> ! [X23,X0,X3,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X3,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X23,X3,X0),c_Polynomial_Opoly(X7,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f374,axiom,
! [X3,X0,X7,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X3,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(X23,X3,X0),c_Polynomial_Opoly(X7,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).
fof(f7421,plain,
spl0_774,
inference(avatar_split_clause,[],[f347,f7419]) ).
fof(f7419,plain,
( spl0_774
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X8),X0),c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f347,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,c_Suc(X8),X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).
fof(f7417,plain,
spl0_773,
inference(avatar_split_clause,[],[f339,f7415]) ).
fof(f7415,plain,
( spl0_773
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f339,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).
fof(f7413,plain,
spl0_772,
inference(avatar_split_clause,[],[f309,f7411]) ).
fof(f7411,plain,
( spl0_772
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f309,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).
fof(f7409,plain,
spl0_771,
inference(avatar_split_clause,[],[f285,f7407]) ).
fof(f7407,plain,
( spl0_771
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f285,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).
fof(f7405,plain,
spl0_770,
inference(avatar_split_clause,[],[f255,f7403]) ).
fof(f7403,plain,
( spl0_770
<=> ! [X0,X23,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X0),X23,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X23,X0),c_Polynomial_Osmult(X2,X23,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f255,axiom,
! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X1,X2,X0),X23,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X1,X23,X0),c_Polynomial_Osmult(X2,X23,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).
fof(f7401,plain,
spl0_769,
inference(avatar_split_clause,[],[f213,f7399]) ).
fof(f7399,plain,
( spl0_769
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f213,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X9,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).
fof(f7397,plain,
spl0_768,
inference(avatar_split_clause,[],[f212,f7395]) ).
fof(f7395,plain,
( spl0_768
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f212,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).
fof(f7393,plain,
spl0_767,
inference(avatar_split_clause,[],[f209,f7391]) ).
fof(f7391,plain,
( spl0_767
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X1,X8,X0),c_Polynomial_Omonom(X2,X8,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f209,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X1,X8,X0),c_Polynomial_Omonom(X2,X8,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__monom_0) ).
fof(f7389,plain,
spl0_766,
inference(avatar_split_clause,[],[f193,f7387]) ).
fof(f7387,plain,
( spl0_766
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f193,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).
fof(f7370,plain,
spl0_765,
inference(avatar_split_clause,[],[f192,f7368]) ).
fof(f7368,plain,
( spl0_765
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f192,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).
fof(f7366,plain,
spl0_764,
inference(avatar_split_clause,[],[f161,f7364]) ).
fof(f7364,plain,
( spl0_764
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f161,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).
fof(f7362,plain,
spl0_763,
inference(avatar_split_clause,[],[f160,f7360]) ).
fof(f7360,plain,
( spl0_763
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f160,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Divides_Odiv__class_Odiv(X1,X2,X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).
fof(f7358,plain,
spl0_762,
inference(avatar_split_clause,[],[f85,f7356]) ).
fof(f7356,plain,
( spl0_762
<=> ! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f85,axiom,
! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_1) ).
fof(f7354,plain,
spl0_761,
inference(avatar_split_clause,[],[f46,f7352]) ).
fof(f7352,plain,
( spl0_761
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f46,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(X3,c_HOL_Otimes__class_Otimes(X18,X4,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).
fof(f7350,plain,
spl0_760,
inference(avatar_split_clause,[],[f45,f7348]) ).
fof(f7348,plain,
( spl0_760
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X4,X0),X3,X0)
| c_HOL_Oord__class_Oless(X18,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f45,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X4,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X18,X4,X0),X3,X0)
| c_HOL_Oord__class_Oless(X18,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).
fof(f7320,plain,
( ~ spl0_32
| spl0_759
| ~ spl0_242
| ~ spl0_341 ),
inference(avatar_split_clause,[],[f4915,f2633,f2077,f7318,f1098]) ).
fof(f7318,plain,
( spl0_759
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f4915,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_242
| ~ spl0_341 ),
inference(superposition,[],[f2078,f2634]) ).
fof(f6503,plain,
spl0_758,
inference(avatar_split_clause,[],[f729,f6501]) ).
fof(f729,axiom,
! [X0,X1,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_OpCons(c_Polynomial_Opoly(X23,X9,X0),c_Polynomial_Osynthetic__div(X23,X9,X0),X0) = c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X1,X23,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).
fof(f6499,plain,
spl0_757,
inference(avatar_split_clause,[],[f715,f6497]) ).
fof(f715,axiom,
! [X3,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_OpCons(X1,X23,X0),X3,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Opoly(X23,X3,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).
fof(f6495,plain,
spl0_756,
inference(avatar_split_clause,[],[f712,f6493]) ).
fof(f6493,plain,
( spl0_756
<=> ! [X1,X0,X23,X2,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f712,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_1) ).
fof(f6491,plain,
spl0_755,
inference(avatar_split_clause,[],[f663,f6489]) ).
fof(f6489,plain,
( spl0_755
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f663,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).
fof(f6487,plain,
spl0_754,
inference(avatar_split_clause,[],[f622,f6485]) ).
fof(f622,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).
fof(f6483,plain,
spl0_753,
inference(avatar_split_clause,[],[f621,f6481]) ).
fof(f621,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X9,c_Divides_Odiv__class_Omod(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).
fof(f6479,plain,
spl0_752,
inference(avatar_split_clause,[],[f592,f6477]) ).
fof(f6477,plain,
( spl0_752
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f592,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).
fof(f6462,plain,
spl0_751,
inference(avatar_split_clause,[],[f591,f6460]) ).
fof(f6460,plain,
( spl0_751
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(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),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f591,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(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),X4,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(X3,X4,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).
fof(f6458,plain,
spl0_750,
inference(avatar_split_clause,[],[f587,f6456]) ).
fof(f6456,plain,
( spl0_750
<=> ! [X9,X0,X10,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f587,axiom,
! [X2,X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X10,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).
fof(f6454,plain,
spl0_749,
inference(avatar_split_clause,[],[f545,f6452]) ).
fof(f6452,plain,
( spl0_749
<=> ! [X9,X0,X10,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f545,axiom,
! [X2,X10,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X9,X10,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f6450,plain,
spl0_748,
inference(avatar_split_clause,[],[f539,f6448]) ).
fof(f539,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f6446,plain,
spl0_747,
inference(avatar_split_clause,[],[f516,f6444]) ).
fof(f6444,plain,
( spl0_747
<=> ! [X0,X27,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X27,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X27,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f516,axiom,
! [X0,X8,X27] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X27,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X27,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).
fof(f6442,plain,
spl0_746,
inference(avatar_split_clause,[],[f514,f6440]) ).
fof(f6440,plain,
( spl0_746
<=> ! [X4,X0,X3,X21] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,X4,X0),X21,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X21,X0),c_HOL_Oinverse__class_Odivide(X4,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f514,axiom,
! [X21,X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X3,X4,X0),X21,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X3,X21,X0),c_HOL_Oinverse__class_Odivide(X4,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).
fof(f6438,plain,
spl0_745,
inference(avatar_split_clause,[],[f513,f6436]) ).
fof(f513,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).
fof(f6434,plain,
spl0_744,
inference(avatar_split_clause,[],[f507,f6432]) ).
fof(f6432,plain,
( spl0_744
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f507,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).
fof(f6430,plain,
spl0_743,
inference(avatar_split_clause,[],[f506,f6428]) ).
fof(f506,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).
fof(f6426,plain,
spl0_742,
inference(avatar_split_clause,[],[f468,f6424]) ).
fof(f6424,plain,
( spl0_742
<=> ! [X2,X20,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X2,X20,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X20,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f468,axiom,
! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X2,X20,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).
fof(f6422,plain,
spl0_741,
inference(avatar_split_clause,[],[f467,f6420]) ).
fof(f467,axiom,
! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).
fof(f6418,plain,
spl0_740,
inference(avatar_split_clause,[],[f466,f6416]) ).
fof(f6416,plain,
( spl0_740
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f466,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).
fof(f6414,plain,
spl0_739,
inference(avatar_split_clause,[],[f465,f6412]) ).
fof(f465,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).
fof(f6410,plain,
spl0_738,
inference(avatar_split_clause,[],[f463,f6408]) ).
fof(f463,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).
fof(f6406,plain,
spl0_737,
inference(avatar_split_clause,[],[f449,f6404]) ).
fof(f449,axiom,
! [X21,X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,X0),X21,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X21,X0),c_HOL_Otimes__class_Otimes(X4,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).
fof(f6402,plain,
spl0_736,
inference(avatar_split_clause,[],[f447,f6400]) ).
fof(f447,axiom,
! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ominus__class_Ominus(X2,X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).
fof(f6398,plain,
spl0_735,
inference(avatar_split_clause,[],[f445,f6396]) ).
fof(f6396,plain,
( spl0_735
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f445,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f6394,plain,
spl0_734,
inference(avatar_split_clause,[],[f345,f6392]) ).
fof(f6392,plain,
( spl0_734
<=> ! [X18,X4,X0,X3,X30] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X18,X0) = X30
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f345,axiom,
! [X3,X0,X18,X4,X30] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,X18,X0) = X30
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) != c_HOL_Oplus__class_Oplus(X4,X30,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).
fof(f6390,plain,
spl0_733,
inference(avatar_split_clause,[],[f342,f6388]) ).
fof(f6388,plain,
( spl0_733
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f342,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).
fof(f6386,plain,
spl0_732,
inference(avatar_split_clause,[],[f341,f6384]) ).
fof(f6384,plain,
( spl0_732
<=> ! [X0,X9,X2,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f341,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).
fof(f6367,plain,
spl0_731,
inference(avatar_split_clause,[],[f325,f6365]) ).
fof(f325,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_Divides_Odiv__class_Omod(X2,X9,X0),X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).
fof(f6363,plain,
spl0_730,
inference(avatar_split_clause,[],[f307,f6361]) ).
fof(f6361,plain,
( spl0_730
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f307,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).
fof(f6359,plain,
spl0_729,
inference(avatar_split_clause,[],[f306,f6357]) ).
fof(f6357,plain,
( spl0_729
<=> ! [X2,X0,X9,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X9,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f306,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X9,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).
fof(f6355,plain,
spl0_728,
inference(avatar_split_clause,[],[f305,f6353]) ).
fof(f305,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X9,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).
fof(f6351,plain,
spl0_727,
inference(avatar_split_clause,[],[f304,f6349]) ).
fof(f304,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X9,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).
fof(f6347,plain,
spl0_726,
inference(avatar_split_clause,[],[f300,f6345]) ).
fof(f300,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
fof(f6343,plain,
spl0_725,
inference(avatar_split_clause,[],[f299,f6341]) ).
fof(f299,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0),c_Lattices_Olower__semilattice__class_Oinf(X18,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
fof(f6339,plain,
spl0_724,
inference(avatar_split_clause,[],[f273,f6337]) ).
fof(f273,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).
fof(f6335,plain,
spl0_723,
inference(avatar_split_clause,[],[f245,f6333]) ).
fof(f6333,plain,
( spl0_723
<=> ! [X4,X0,X3,X21] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X4,X0),X21,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X3,X21,X0),c_HOL_Oinverse__class_Odivide(X4,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f245,axiom,
! [X21,X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X3,X4,X0),X21,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X3,X21,X0),c_HOL_Oinverse__class_Odivide(X4,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).
fof(f6331,plain,
spl0_722,
inference(avatar_split_clause,[],[f244,f6329]) ).
fof(f244,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X9,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X9,X0),c_HOL_Oinverse__class_Odivide(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).
fof(f6312,plain,
spl0_721,
inference(avatar_split_clause,[],[f238,f6310]) ).
fof(f6310,plain,
( spl0_721
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f238,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).
fof(f6308,plain,
spl0_720,
inference(avatar_split_clause,[],[f237,f6306]) ).
fof(f6306,plain,
( spl0_720
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f237,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f6304,plain,
spl0_719,
inference(avatar_split_clause,[],[f236,f6302]) ).
fof(f6302,plain,
( spl0_719
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f236,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f6300,plain,
spl0_718,
inference(avatar_split_clause,[],[f230,f6298]) ).
fof(f6298,plain,
( spl0_718
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X9,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f230,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X9,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).
fof(f6296,plain,
spl0_717,
inference(avatar_split_clause,[],[f229,f6294]) ).
fof(f6294,plain,
( spl0_717
<=> ! [X2,X0,X9,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X9,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f229,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X9,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).
fof(f6292,plain,
spl0_716,
inference(avatar_split_clause,[],[f228,f6290]) ).
fof(f228,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X9,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).
fof(f6288,plain,
spl0_715,
inference(avatar_split_clause,[],[f227,f6286]) ).
fof(f227,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X9,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).
fof(f6284,plain,
spl0_714,
inference(avatar_split_clause,[],[f182,f6282]) ).
fof(f6282,plain,
( spl0_714
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f182,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).
fof(f6280,plain,
spl0_713,
inference(avatar_split_clause,[],[f181,f6278]) ).
fof(f6278,plain,
( spl0_713
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f181,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__field(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_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).
fof(f6276,plain,
spl0_712,
inference(avatar_split_clause,[],[f176,f6274]) ).
fof(f6274,plain,
( spl0_712
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f176,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).
fof(f6259,plain,
spl0_711,
inference(avatar_split_clause,[],[f174,f6257]) ).
fof(f174,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).
fof(f6255,plain,
spl0_710,
inference(avatar_split_clause,[],[f141,f6253]) ).
fof(f141,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(f6251,plain,
spl0_709,
inference(avatar_split_clause,[],[f135,f6249]) ).
fof(f6249,plain,
( spl0_709
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f135,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f6247,plain,
spl0_708,
inference(avatar_split_clause,[],[f100,f6245]) ).
fof(f6245,plain,
( spl0_708
<=> ! [X2,X20,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X2,X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X20,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f100,axiom,
! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X2,X20,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),c_RealVector_OscaleR__class_OscaleR(X1,X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Odiff__right_0) ).
fof(f6243,plain,
spl0_707,
inference(avatar_split_clause,[],[f99,f6241]) ).
fof(f99,axiom,
! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Odiff_0) ).
fof(f6239,plain,
spl0_706,
inference(avatar_split_clause,[],[f80,f6237]) ).
fof(f6237,plain,
( spl0_706
<=> ! [X0,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f80,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).
fof(f6235,plain,
spl0_705,
inference(avatar_split_clause,[],[f74,f6233]) ).
fof(f6233,plain,
( spl0_705
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f74,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f6231,plain,
spl0_704,
inference(avatar_split_clause,[],[f73,f6229]) ).
fof(f73,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f6227,plain,
spl0_703,
inference(avatar_split_clause,[],[f70,f6225]) ).
fof(f70,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
fof(f6223,plain,
spl0_702,
inference(avatar_split_clause,[],[f69,f6221]) ).
fof(f69,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Odistrib__lattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X3,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0),c_Lattices_Oupper__semilattice__class_Osup(X18,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
fof(f6204,plain,
spl0_701,
inference(avatar_split_clause,[],[f60,f6202]) ).
fof(f6202,plain,
( spl0_701
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X8,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f60,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(X1,X8,X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).
fof(f6200,plain,
spl0_700,
inference(avatar_split_clause,[],[f42,f6198]) ).
fof(f42,axiom,
! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_OpCons(X2,X23,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_Polynomial_Osmult(X1,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).
fof(f6196,plain,
spl0_699,
inference(avatar_split_clause,[],[f31,f6194]) ).
fof(f6194,plain,
( spl0_699
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f31,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f6192,plain,
spl0_698,
inference(avatar_split_clause,[],[f30,f6190]) ).
fof(f30,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X4,X0),c_HOL_Otimes__class_Otimes(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f6188,plain,
spl0_697,
inference(avatar_split_clause,[],[f28,f6186]) ).
fof(f6186,plain,
( spl0_697
<=> ! [X4,X0,X3,X21] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X21,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X21,X0),c_HOL_Otimes__class_Otimes(X4,X21,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f28,axiom,
! [X21,X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,X0),X21,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X21,X0),c_HOL_Otimes__class_Otimes(X4,X21,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).
fof(f6184,plain,
spl0_696,
inference(avatar_split_clause,[],[f27,f6182]) ).
fof(f27,axiom,
! [X2,X0,X1,X20] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X20,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X20,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).
fof(f6180,plain,
spl0_695,
inference(avatar_split_clause,[],[f25,f6178]) ).
fof(f25,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f6176,plain,
spl0_694,
inference(avatar_split_clause,[],[f7,f6174]) ).
fof(f7,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X9,X0),X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).
fof(f6172,plain,
spl0_693,
inference(avatar_split_clause,[],[f5,f6170]) ).
fof(f6170,plain,
( spl0_693
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f5,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),c_Power_Opower__class_Opower(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).
fof(f6168,plain,
spl0_692,
inference(avatar_split_clause,[],[f4,f6166]) ).
fof(f4,axiom,
! [X3,X0,X7,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(X3,X4,X0),X7,X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X7,X0),c_Power_Opower__class_Opower(X4,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).
fof(f5897,plain,
spl0_691,
inference(avatar_split_clause,[],[f666,f5895]) ).
fof(f5895,plain,
( spl0_691
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X8,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f666,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X8,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).
fof(f5893,plain,
spl0_690,
inference(avatar_split_clause,[],[f607,f5891]) ).
fof(f5891,plain,
( spl0_690
<=> ! [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_690])]) ).
fof(f607,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(f5889,plain,
spl0_689,
inference(avatar_split_clause,[],[f562,f5887]) ).
fof(f5887,plain,
( spl0_689
<=> ! [X0,X27,X8,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X8 = X27
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X8,X0) != c_Power_Opower__class_Opower(X1,X27,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f562,axiom,
! [X0,X1,X8,X27] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X8 = X27
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_Power_Opower__class_Opower(X1,X8,X0) != c_Power_Opower__class_Opower(X1,X27,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).
fof(f5882,plain,
spl0_688,
inference(avatar_split_clause,[],[f486,f5880]) ).
fof(f486,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X18,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X3,X18,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).
fof(f5878,plain,
spl0_687,
inference(avatar_split_clause,[],[f485,f5876]) ).
fof(f485,axiom,
! [X3,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__add_0) ).
fof(f5874,plain,
spl0_686,
inference(avatar_split_clause,[],[f458,f5872]) ).
fof(f458,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).
fof(f5870,plain,
spl0_685,
inference(avatar_split_clause,[],[f425,f5868]) ).
fof(f5868,plain,
( spl0_685
<=> ! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f425,axiom,
! [X0,X1,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_0) ).
fof(f5866,plain,
spl0_684,
inference(avatar_split_clause,[],[f418,f5864]) ).
fof(f5864,plain,
( spl0_684
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f418,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).
fof(f5862,plain,
spl0_683,
inference(avatar_split_clause,[],[f367,f5860]) ).
fof(f5860,plain,
( spl0_683
<=> ! [X0,X7,X23,X2,X1] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f367,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X1,X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(X1,X23,X0),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_0) ).
fof(f5858,plain,
spl0_682,
inference(avatar_split_clause,[],[f356,f5856]) ).
fof(f5856,plain,
( spl0_682
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f356,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__if_0) ).
fof(f5854,plain,
spl0_681,
inference(avatar_split_clause,[],[f352,f5852]) ).
fof(f5852,plain,
( spl0_681
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f352,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).
fof(f5850,plain,
spl0_680,
inference(avatar_split_clause,[],[f351,f5848]) ).
fof(f5848,plain,
( spl0_680
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f351,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).
fof(f5846,plain,
spl0_679,
inference(avatar_split_clause,[],[f350,f5844]) ).
fof(f5844,plain,
( spl0_679
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f350,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X2,X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).
fof(f5837,plain,
spl0_678,
inference(avatar_split_clause,[],[f349,f5835]) ).
fof(f5835,plain,
( spl0_678
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f349,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).
fof(f5833,plain,
spl0_677,
inference(avatar_split_clause,[],[f346,f5831]) ).
fof(f5831,plain,
( spl0_677
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f346,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_2) ).
fof(f5829,plain,
spl0_676,
inference(avatar_split_clause,[],[f343,f5827]) ).
fof(f5827,plain,
( spl0_676
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f343,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).
fof(f5825,plain,
spl0_675,
inference(avatar_split_clause,[],[f286,f5823]) ).
fof(f5823,plain,
( spl0_675
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f286,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).
fof(f5821,plain,
spl0_674,
inference(avatar_split_clause,[],[f274,f5819]) ).
fof(f274,axiom,
! [X3,X0,X4] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X3,X4,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X3,X0),c_Transcendental_Oexp(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__diff_0) ).
fof(f5817,plain,
spl0_673,
inference(avatar_split_clause,[],[f252,f5815]) ).
fof(f5815,plain,
( spl0_673
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X2,X2,X0) != c_HOL_Otimes__class_Otimes(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f252,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Otimes__class_Otimes(X2,X2,X0) != c_HOL_Otimes__class_Otimes(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).
fof(f5813,plain,
spl0_672,
inference(avatar_split_clause,[],[f223,f5811]) ).
fof(f223,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).
fof(f5809,plain,
spl0_671,
inference(avatar_split_clause,[],[f202,f5807]) ).
fof(f5807,plain,
( spl0_671
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f202,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).
fof(f5805,plain,
spl0_670,
inference(avatar_split_clause,[],[f86,f5803]) ).
fof(f5803,plain,
( spl0_670
<=> ! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f86,axiom,
! [X2,X0,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X2,X7,X0),tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_0) ).
fof(f5801,plain,
spl0_669,
inference(avatar_split_clause,[],[f55,f5799]) ).
fof(f5799,plain,
( spl0_669
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f55,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).
fof(f5789,plain,
spl0_668,
inference(avatar_split_clause,[],[f54,f5787]) ).
fof(f5787,plain,
( spl0_668
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f54,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_HOL_Ozero__class_Ozero(X0) = X4
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).
fof(f5785,plain,
spl0_667,
inference(avatar_split_clause,[],[f18,f5783]) ).
fof(f18,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__neg__div_0) ).
fof(f5781,plain,
spl0_666,
inference(avatar_split_clause,[],[f17,f5779]) ).
fof(f17,axiom,
! [X3,X0,X4] :
( ~ class_Divides_Oring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X3,X0)
| c_Divides_Odiv__class_Odiv(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__neg_0) ).
fof(f5777,plain,
spl0_665,
inference(avatar_split_clause,[],[f2,f5775]) ).
fof(f5775,plain,
( spl0_665
<=> ! [X5,X4,X0,X6,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f2,axiom,
! [X3,X0,X6,X4,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
fof(f5564,plain,
( spl0_663
| ~ spl0_664 ),
inference(avatar_split_clause,[],[f728,f5561,f5558]) ).
fof(f5558,plain,
( spl0_663
<=> ! [X18,X23] :
( c_HOL_Ozero__class_Ozero(t_a) = X18
| c_HOL_Ozero__class_Ozero(t_a) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X23)
| c_HOL_Ozero__class_Ozero(t_a) = c_Polynomial_Opoly(X23,X18,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f5561,plain,
( spl0_664
<=> class_Ring__and__Field_Oidom(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f728,axiom,
! [X18,X23] :
( ~ class_Ring__and__Field_Oidom(t_a)
| c_HOL_Ozero__class_Ozero(t_a) = X18
| c_HOL_Ozero__class_Ozero(t_a) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(X23)
| c_HOL_Ozero__class_Ozero(t_a) = c_Polynomial_Opoly(X23,X18,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose__lemma_0) ).
fof(f5556,plain,
spl0_662,
inference(avatar_split_clause,[],[f612,f5554]) ).
fof(f5554,plain,
( spl0_662
<=> ! [X24,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X24,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f612,axiom,
! [X3,X0,X1,X24] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,X24,X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).
fof(f5552,plain,
spl0_661,
inference(avatar_split_clause,[],[f578,f5550]) ).
fof(f578,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).
fof(f5548,plain,
spl0_660,
inference(avatar_split_clause,[],[f577,f5546]) ).
fof(f5546,plain,
( spl0_660
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f577,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).
fof(f5544,plain,
spl0_659,
inference(avatar_split_clause,[],[f574,f5542]) ).
fof(f574,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X9,X2,X0)
| c_Divides_Odiv__class_Omod(X1,X9,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).
fof(f5540,plain,
spl0_658,
inference(avatar_split_clause,[],[f529,f5538]) ).
fof(f5538,plain,
( spl0_658
<=> ! [X0,X3,X2,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_RealVector_OscaleR__class_OscaleR(X1,X3,X0) != c_RealVector_OscaleR__class_OscaleR(X2,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f529,axiom,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_RealVector_OscaleR__class_OscaleR(X1,X3,X0) != c_RealVector_OscaleR__class_OscaleR(X2,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).
fof(f5536,plain,
spl0_657,
inference(avatar_split_clause,[],[f456,f5534]) ).
fof(f5534,plain,
( spl0_657
<=> ! [X24,X0,X3,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X24,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f456,axiom,
! [X3,X0,X1,X24] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X24,X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X3,X1,X0),X0),X24,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).
fof(f5532,plain,
spl0_656,
inference(avatar_split_clause,[],[f429,f5530]) ).
fof(f429,axiom,
! [X0,X1,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) = c_HOL_Oplus__class_Oplus(X27,c_HOL_Otimes__class_Otimes(X1,X27,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).
fof(f5528,plain,
spl0_655,
inference(avatar_split_clause,[],[f428,f5526]) ).
fof(f428,axiom,
! [X0,X1,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X27,X0),X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X27,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).
fof(f5513,plain,
spl0_654,
inference(avatar_split_clause,[],[f360,f5511]) ).
fof(f5511,plain,
( spl0_654
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f360,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).
fof(f5509,plain,
spl0_653,
inference(avatar_split_clause,[],[f359,f5507]) ).
fof(f5507,plain,
( spl0_653
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f359,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).
fof(f5505,plain,
spl0_652,
inference(avatar_split_clause,[],[f340,f5503]) ).
fof(f5503,plain,
( spl0_652
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f340,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).
fof(f5501,plain,
spl0_651,
inference(avatar_split_clause,[],[f178,f5499]) ).
fof(f5499,plain,
( spl0_651
<=> ! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f178,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Oring__div(X0)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(X1,X2,X0),X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__minus__eq_0) ).
fof(f5497,plain,
spl0_650,
inference(avatar_split_clause,[],[f109,f5495]) ).
fof(f5495,plain,
( spl0_650
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f109,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).
fof(f5493,plain,
spl0_649,
inference(avatar_split_clause,[],[f77,f5491]) ).
fof(f5491,plain,
( spl0_649
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f77,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).
fof(f5489,plain,
spl0_648,
inference(avatar_split_clause,[],[f64,f5487]) ).
fof(f64,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X9,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f5485,plain,
spl0_647,
inference(avatar_split_clause,[],[f61,f5483]) ).
fof(f5483,plain,
( spl0_647
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f61,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).
fof(f5085,plain,
spl0_646,
inference(avatar_split_clause,[],[f722,f5083]) ).
fof(f722,axiom,
! [X23] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X23,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X23),tc_Complex_Ocomplex)
| c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X23),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).
fof(f5081,plain,
spl0_645,
inference(avatar_split_clause,[],[f717,f5079]) ).
fof(f717,axiom,
! [X3,X0,X7,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(X23,X7,X0),X3,X0) = c_Polynomial_Opoly(X23,c_Polynomial_Opoly(X7,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).
fof(f5077,plain,
spl0_644,
inference(avatar_split_clause,[],[f670,f5075]) ).
fof(f5075,plain,
( spl0_644
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f670,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f5073,plain,
spl0_643,
inference(avatar_split_clause,[],[f669,f5071]) ).
fof(f5071,plain,
( spl0_643
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f669,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).
fof(f5069,plain,
spl0_642,
inference(avatar_split_clause,[],[f631,f5067]) ).
fof(f631,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).
fof(f5065,plain,
spl0_641,
inference(avatar_split_clause,[],[f630,f5063]) ).
fof(f630,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).
fof(f5061,plain,
spl0_640,
inference(avatar_split_clause,[],[f620,f5059]) ).
fof(f5059,plain,
( spl0_640
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f620,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Osgn__class_Osgn(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).
fof(f5034,plain,
spl0_639,
inference(avatar_split_clause,[],[f619,f5032]) ).
fof(f619,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__div__algebra(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Osgn__class_Osgn(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).
fof(f5030,plain,
spl0_638,
inference(avatar_split_clause,[],[f614,f5028]) ).
fof(f5028,plain,
( spl0_638
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f614,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
fof(f5026,plain,
spl0_637,
inference(avatar_split_clause,[],[f606,f5024]) ).
fof(f606,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(X1,X2,X0),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__div__class_Omod__div__equality_H_0) ).
fof(f5022,plain,
spl0_636,
inference(avatar_split_clause,[],[f585,f5020]) ).
fof(f585,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).
fof(f5018,plain,
spl0_635,
inference(avatar_split_clause,[],[f505,f5016]) ).
fof(f505,axiom,
! [X2,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X23,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X1,X2,X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).
fof(f5014,plain,
spl0_634,
inference(avatar_split_clause,[],[f504,f5012]) ).
fof(f504,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X9,X2,X0),X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).
fof(f5010,plain,
spl0_633,
inference(avatar_split_clause,[],[f503,f5008]) ).
fof(f503,axiom,
! [X2,X0,X1,X9] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).
fof(f5006,plain,
spl0_632,
inference(avatar_split_clause,[],[f474,f5004]) ).
fof(f474,axiom,
! [X3,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X23,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X23,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f5002,plain,
spl0_631,
inference(avatar_split_clause,[],[f472,f5000]) ).
fof(f472,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
fof(f4998,plain,
spl0_630,
inference(avatar_split_clause,[],[f469,f4996]) ).
fof(f469,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
fof(f4971,plain,
spl0_629,
inference(avatar_split_clause,[],[f424,f4969]) ).
fof(f424,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(X1,X0),X8,X0),X0) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).
fof(f4967,plain,
spl0_628,
inference(avatar_split_clause,[],[f422,f4965]) ).
fof(f422,axiom,
! [X2,X0,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X2,X9,X0),X9,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
fof(f4963,plain,
spl0_627,
inference(avatar_split_clause,[],[f419,f4961]) ).
fof(f4961,plain,
( spl0_627
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f419,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).
fof(f4959,plain,
spl0_626,
inference(avatar_split_clause,[],[f409,f4957]) ).
fof(f409,axiom,
! [X3,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Opoly(c_Polynomial_Omonom(X1,X8,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X3,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__monom_0) ).
fof(f4955,plain,
spl0_625,
inference(avatar_split_clause,[],[f387,f4953]) ).
fof(f4953,plain,
( spl0_625
<=> ! [X0,X1,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f387,axiom,
! [X0,X1,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).
fof(f4951,plain,
spl0_624,
inference(avatar_split_clause,[],[f378,f4949]) ).
fof(f4949,plain,
( spl0_624
<=> ! [X24,X0,X31,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X31,c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_RealVector_OscaleR__class_OscaleR(X31,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f378,axiom,
! [X31,X3,X0,X24] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X31,c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_RealVector_OscaleR__class_OscaleR(X31,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).
fof(f4947,plain,
spl0_623,
inference(avatar_split_clause,[],[f377,f4945]) ).
fof(f377,axiom,
! [X2,X3,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_RealVector_OscaleR__class_OscaleR(X2,X3,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).
fof(f4943,plain,
spl0_622,
inference(avatar_split_clause,[],[f355,f4941]) ).
fof(f355,axiom,
! [X3,X0,X4,X24] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OscaleR_0) ).
fof(f4939,plain,
spl0_621,
inference(avatar_split_clause,[],[f337,f4937]) ).
fof(f4937,plain,
( spl0_621
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f337,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).
fof(f4935,plain,
spl0_620,
inference(avatar_split_clause,[],[f336,f4933]) ).
fof(f4933,plain,
( spl0_620
<=> ! [X4,X0,X3,X1] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f336,axiom,
! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) = c_HOL_Otimes__class_Otimes(X3,c_RealVector_OscaleR__class_OscaleR(X1,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).
fof(f4909,plain,
spl0_619,
inference(avatar_split_clause,[],[f335,f4907]) ).
fof(f4907,plain,
( spl0_619
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f335,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).
fof(f4905,plain,
spl0_618,
inference(avatar_split_clause,[],[f334,f4903]) ).
fof(f4903,plain,
( spl0_618
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f334,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
fof(f4901,plain,
spl0_617,
inference(avatar_split_clause,[],[f333,f4899]) ).
fof(f4899,plain,
( spl0_617
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f333,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
fof(f4897,plain,
spl0_616,
inference(avatar_split_clause,[],[f332,f4895]) ).
fof(f332,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
fof(f4893,plain,
spl0_615,
inference(avatar_split_clause,[],[f331,f4891]) ).
fof(f331,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X4,X18,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X4,c_Lattices_Oupper__semilattice__class_Osup(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
fof(f4889,plain,
spl0_614,
inference(avatar_split_clause,[],[f320,f4887]) ).
fof(f4887,plain,
( spl0_614
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f320,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).
fof(f4885,plain,
spl0_613,
inference(avatar_split_clause,[],[f319,f4883]) ).
fof(f4883,plain,
( spl0_613
<=> ! [X10,X0,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f319,axiom,
! [X10,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X9,X10,X0),X0) = c_HOL_Oplus__class_Oplus(X9,c_HOL_Oplus__class_Oplus(X1,X10,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f4881,plain,
spl0_612,
inference(avatar_split_clause,[],[f318,f4879]) ).
fof(f318,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X9,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f4877,plain,
spl0_611,
inference(avatar_split_clause,[],[f316,f4875]) ).
fof(f4875,plain,
( spl0_611
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f316,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f4873,plain,
spl0_610,
inference(avatar_split_clause,[],[f315,f4871]) ).
fof(f4871,plain,
( spl0_610
<=> ! [X18,X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f315,axiom,
! [X3,X0,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Oplus__class_Oplus(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).
fof(f4857,plain,
spl0_609,
inference(avatar_split_clause,[],[f313,f4855]) ).
fof(f313,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f4853,plain,
spl0_608,
inference(avatar_split_clause,[],[f312,f4851]) ).
fof(f312,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f4849,plain,
spl0_607,
inference(avatar_split_clause,[],[f261,f4847]) ).
fof(f261,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).
fof(f4845,plain,
spl0_606,
inference(avatar_split_clause,[],[f260,f4843]) ).
fof(f4843,plain,
( spl0_606
<=> ! [X11,X0,X27,X8] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X27,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X27,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f260,axiom,
! [X0,X11,X8,X27] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X27,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X27,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).
fof(f4841,plain,
spl0_605,
inference(avatar_split_clause,[],[f259,f4839]) ).
fof(f259,axiom,
! [X0,X11,X8,X27] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,X8,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X11,X27,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X11,c_Divides_Odiv__class_Omod(X27,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).
fof(f4837,plain,
spl0_604,
inference(avatar_split_clause,[],[f248,f4835]) ).
fof(f4835,plain,
( spl0_604
<=> ! [X18,X4,X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X18,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ominus__class_Ominus(X4,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f248,axiom,
! [X3,X0,X18,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X18,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ominus__class_Ominus(X4,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).
fof(f4833,plain,
spl0_603,
inference(avatar_split_clause,[],[f235,f4831]) ).
fof(f4831,plain,
( spl0_603
<=> ! [X4,X0,X3,X1] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f235,axiom,
! [X3,X0,X1,X4] :
( ~ class_RealVector_Oreal__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).
fof(f4829,plain,
spl0_602,
inference(avatar_split_clause,[],[f233,f4827]) ).
fof(f233,axiom,
! [X2,X0,X1,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X24,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).
fof(f4825,plain,
spl0_601,
inference(avatar_split_clause,[],[f232,f4823]) ).
fof(f232,axiom,
! [X3,X0,X4,X24] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X24,X3,X0),X4,X0) = c_RealVector_OscaleR__class_OscaleR(X24,c_HOL_Otimes__class_Otimes(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).
fof(f4821,plain,
spl0_600,
inference(avatar_split_clause,[],[f187,f4819]) ).
fof(f4819,plain,
( spl0_600
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f187,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).
fof(f4817,plain,
( ~ spl0_99
| spl0_599
| ~ spl0_242
| ~ spl0_330 ),
inference(avatar_split_clause,[],[f4757,f2589,f2077,f4815,f1433]) ).
fof(f4815,plain,
( spl0_599
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2589,plain,
( spl0_330
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f4757,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_RealDef_Oreal)
| ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
| ~ spl0_242
| ~ spl0_330 ),
inference(superposition,[],[f2078,f2590]) ).
fof(f2590,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_330 ),
inference(avatar_component_clause,[],[f2589]) ).
fof(f4813,plain,
spl0_598,
inference(avatar_split_clause,[],[f180,f4811]) ).
fof(f180,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
fof(f4809,plain,
spl0_597,
inference(avatar_split_clause,[],[f171,f4807]) ).
fof(f171,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_Polynomial_Osmult(X1,c_Polynomial_Omonom(X2,X8,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__monom_0) ).
fof(f4805,plain,
spl0_596,
inference(avatar_split_clause,[],[f137,f4803]) ).
fof(f4803,plain,
( spl0_596
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f137,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).
fof(f4801,plain,
spl0_595,
inference(avatar_split_clause,[],[f132,f4799]) ).
fof(f4799,plain,
( spl0_595
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f132,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
fof(f4797,plain,
spl0_594,
inference(avatar_split_clause,[],[f131,f4795]) ).
fof(f4795,plain,
( spl0_594
<=> ! [X18,X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f131,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
fof(f4793,plain,
spl0_593,
inference(avatar_split_clause,[],[f130,f4791]) ).
fof(f130,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
fof(f4789,plain,
spl0_592,
inference(avatar_split_clause,[],[f129,f4787]) ).
fof(f129,axiom,
! [X3,X0,X18,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X4,X18,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,c_Lattices_Olower__semilattice__class_Oinf(X3,X18,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
fof(f4785,plain,
spl0_591,
inference(avatar_split_clause,[],[f128,f4783]) ).
fof(f128,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__if_1) ).
fof(f4781,plain,
spl0_590,
inference(avatar_split_clause,[],[f94,f4779]) ).
fof(f94,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).
fof(f4777,plain,
spl0_589,
inference(avatar_split_clause,[],[f78,f4775]) ).
fof(f4775,plain,
( spl0_589
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f78,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).
fof(f4751,plain,
spl0_588,
inference(avatar_split_clause,[],[f58,f4749]) ).
fof(f58,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__if_1) ).
fof(f4747,plain,
spl0_587,
inference(avatar_split_clause,[],[f23,f4745]) ).
fof(f23,axiom,
! [X0,X16,X14,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(X16,c_HOL_Otimes__class_Otimes(X14,X17,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f4743,plain,
spl0_586,
inference(avatar_split_clause,[],[f22,f4741]) ).
fof(f4741,plain,
( spl0_586
<=> ! [X17,X0,X14,X16] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),X17,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f22,axiom,
! [X0,X16,X14,X17] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X14,c_HOL_Otimes__class_Otimes(X16,X17,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),X17,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f4739,plain,
spl0_585,
inference(avatar_split_clause,[],[f20,f4737]) ).
fof(f20,axiom,
! [X0,X16,X14,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X15,X0),X16,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X14,X16,X0),X15,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f4735,plain,
spl0_584,
inference(avatar_split_clause,[],[f19,f4733]) ).
fof(f19,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f4731,plain,
spl0_583,
inference(avatar_split_clause,[],[f13,f4729]) ).
fof(f13,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(X1,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).
fof(f4727,plain,
spl0_582,
inference(avatar_split_clause,[],[f12,f4725]) ).
fof(f4725,plain,
( spl0_582
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,c_Divides_Odiv__class_Odiv(X1,X2,X0),X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality2_0) ).
fof(f4723,plain,
spl0_581,
inference(avatar_split_clause,[],[f11,f4721]) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X1,X2,X0),X2,X0),c_Divides_Odiv__class_Omod(X1,X2,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__equality_0) ).
fof(f4625,plain,
( ~ spl0_146
| spl0_580
| ~ spl0_242
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f4550,f2545,f2077,f4623,f1668]) ).
fof(f4623,plain,
( spl0_580
<=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f4550,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
| ~ spl0_242
| ~ spl0_319 ),
inference(superposition,[],[f2078,f2546]) ).
fof(f4516,plain,
( spl0_579
| ~ spl0_150
| ~ spl0_442
| ~ spl0_578 ),
inference(avatar_split_clause,[],[f4512,f4509,f3469,f1688,f4514]) ).
fof(f4514,plain,
( spl0_579
<=> ! [X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f4509,plain,
( spl0_578
<=> ! [X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f4512,plain,
( ! [X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X3
| ~ spl0_150
| ~ spl0_442
| ~ spl0_578 ),
inference(forward_demodulation,[],[f4510,f3693]) ).
fof(f4510,plain,
( ! [X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X3
| ~ spl0_578 ),
inference(avatar_component_clause,[],[f4509]) ).
fof(f4511,plain,
spl0_578,
inference(avatar_split_clause,[],[f723,f4509]) ).
fof(f723,axiom,
! [X3] : c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mpoly__base__conv_I3_J_0) ).
fof(f4507,plain,
spl0_577,
inference(avatar_split_clause,[],[f710,f4505]) ).
fof(f710,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X1,X23,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(X23,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_2) ).
fof(f4491,plain,
spl0_576,
inference(avatar_split_clause,[],[f707,f4489]) ).
fof(f4489,plain,
( spl0_576
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X23,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f707,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X23,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_1) ).
fof(f4487,plain,
spl0_575,
inference(avatar_split_clause,[],[f706,f4485]) ).
fof(f706,axiom,
! [X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_Suc(X8),X0) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_Polynomial_Omonom(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__Suc_0) ).
fof(f4483,plain,
spl0_574,
inference(avatar_split_clause,[],[f601,f4481]) ).
fof(f601,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X3,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X3,X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).
fof(f4479,plain,
spl0_573,
inference(avatar_split_clause,[],[f600,f4477]) ).
fof(f600,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f4475,plain,
spl0_572,
inference(avatar_split_clause,[],[f599,f4473]) ).
fof(f599,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f4471,plain,
spl0_571,
inference(avatar_split_clause,[],[f598,f4469]) ).
fof(f598,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X9,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f4467,plain,
spl0_570,
inference(avatar_split_clause,[],[f597,f4465]) ).
fof(f597,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f4463,plain,
spl0_569,
inference(avatar_split_clause,[],[f596,f4461]) ).
fof(f596,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f4459,plain,
spl0_568,
inference(avatar_split_clause,[],[f595,f4457]) ).
fof(f4457,plain,
( spl0_568
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f595,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X9,X1,X0),c_HOL_Oplus__class_Oplus(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f4455,plain,
spl0_567,
inference(avatar_split_clause,[],[f555,f4453]) ).
fof(f555,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_Power_Opower__class_Opower(X1,c_Suc(X8),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).
fof(f4451,plain,
( ~ spl0_32
| spl0_566
| ~ spl0_242
| ~ spl0_308 ),
inference(avatar_split_clause,[],[f4398,f2501,f2077,f4449,f1098]) ).
fof(f4398,plain,
( ! [X0] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
| ~ class_Ring__and__Field_Odvd(tc_nat) )
| ~ spl0_242
| ~ spl0_308 ),
inference(superposition,[],[f2078,f2502]) ).
fof(f4447,plain,
spl0_565,
inference(avatar_split_clause,[],[f540,f4445]) ).
fof(f4445,plain,
( spl0_565
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f540,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).
fof(f4443,plain,
spl0_564,
inference(avatar_split_clause,[],[f480,f4441]) ).
fof(f4441,plain,
( spl0_564
<=> ! [X18,X4,X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X18,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f480,axiom,
! [X3,X0,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ouminus__class_Ouminus(X18,X0) = X3
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) != X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).
fof(f4439,plain,
spl0_563,
inference(avatar_split_clause,[],[f462,f4437]) ).
fof(f4437,plain,
( spl0_563
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f462,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).
fof(f4435,plain,
spl0_562,
inference(avatar_split_clause,[],[f455,f4433]) ).
fof(f4433,plain,
( spl0_562
<=> ! [X4,X0,X3,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X8,X0),c_Power_Opower__class_Opower(X4,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f455,axiom,
! [X3,X0,X8,X4] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(X3,X8,X0),c_Power_Opower__class_Opower(X4,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__power__same_0) ).
fof(f4431,plain,
spl0_561,
inference(avatar_split_clause,[],[f398,f4429]) ).
fof(f398,axiom,
! [X0,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X27,X27,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X27,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).
fof(f4427,plain,
spl0_560,
inference(avatar_split_clause,[],[f366,f4425]) ).
fof(f4425,plain,
( spl0_560
<=> ! [X0,X9,X2,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f366,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X9,X0),c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).
fof(f4423,plain,
spl0_559,
inference(avatar_split_clause,[],[f365,f4421]) ).
fof(f365,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Oidom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X9,X1,X0),c_HOL_Otimes__class_Otimes(X9,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).
fof(f4419,plain,
spl0_558,
inference(avatar_split_clause,[],[f353,f4417]) ).
fof(f4417,plain,
( spl0_558
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X23,X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f353,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Polynomial_Opos__poly(X23,X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_0) ).
fof(f4415,plain,
spl0_557,
inference(avatar_split_clause,[],[f321,f4413]) ).
fof(f4413,plain,
( spl0_557
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f321,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| ~ class_Ring__and__Field_Omult__zero(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).
fof(f4411,plain,
spl0_556,
inference(avatar_split_clause,[],[f251,f4409]) ).
fof(f251,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).
fof(f4394,plain,
spl0_555,
inference(avatar_split_clause,[],[f218,f4392]) ).
fof(f4392,plain,
( spl0_555
<=> ! [X18,X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X18
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X18,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f218,axiom,
! [X3,X0,X18,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X4 = X18
| c_HOL_Oplus__class_Oplus(X3,X4,X0) != c_HOL_Oplus__class_Oplus(X3,X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).
fof(f4390,plain,
spl0_554,
inference(avatar_split_clause,[],[f186,f4388]) ).
fof(f4388,plain,
( spl0_554
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f186,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(X3,c_HOL_Oone__class_Oone(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).
fof(f4386,plain,
spl0_553,
inference(avatar_split_clause,[],[f139,f4384]) ).
fof(f4384,plain,
( spl0_553
<=> ! [X9,X0,X1,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_Polynomial_Osmult(X9,X23,X0) != c_Polynomial_OpCons(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f139,axiom,
! [X0,X1,X9,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_Polynomial_Osmult(X9,X23,X0) != c_Polynomial_OpCons(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).
fof(f4382,plain,
spl0_552,
inference(avatar_split_clause,[],[f127,f4380]) ).
fof(f4380,plain,
( spl0_552
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f127,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X3,X0),c_HOL_Otimes__class_Otimes(X4,X4,X0),X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).
fof(f4378,plain,
spl0_551,
inference(avatar_split_clause,[],[f87,f4376]) ).
fof(f4376,plain,
( spl0_551
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f87,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X3,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Oinverse__class_Oinverse(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).
fof(f4374,plain,
spl0_550,
inference(avatar_split_clause,[],[f79,f4372]) ).
fof(f79,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X8
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).
fof(f4370,plain,
spl0_549,
inference(avatar_split_clause,[],[f15,f4368]) ).
fof(f4368,plain,
( spl0_549
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).
fof(f4181,plain,
spl0_548,
inference(avatar_split_clause,[],[f711,f4179]) ).
fof(f4179,plain,
( spl0_548
<=> ! [X0,X1,X23] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f711,axiom,
! [X0,X1,X23] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X23
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).
fof(f4177,plain,
spl0_547,
inference(avatar_split_clause,[],[f625,f4175]) ).
fof(f4175,plain,
( spl0_547
<=> ! [X9,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X9,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f625,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X9,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).
fof(f4173,plain,
spl0_546,
inference(avatar_split_clause,[],[f604,f4171]) ).
fof(f604,axiom,
! [X3,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_Transcendental_Oexp(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_Transcendental_Oexp(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__minus_0) ).
fof(f4169,plain,
spl0_545,
inference(avatar_split_clause,[],[f569,f4167]) ).
fof(f4167,plain,
( spl0_545
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f569,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).
fof(f4165,plain,
spl0_544,
inference(avatar_split_clause,[],[f568,f4163]) ).
fof(f4163,plain,
( spl0_544
<=> ! [X0,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X3,c_Suc(X7),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X7,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f568,axiom,
! [X3,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X3,c_Suc(X7),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X3,X7,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).
fof(f4161,plain,
spl0_543,
inference(avatar_split_clause,[],[f566,f4159]) ).
fof(f4159,plain,
( spl0_543
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f566,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__neg_0) ).
fof(f4157,plain,
spl0_542,
inference(avatar_split_clause,[],[f565,f4155]) ).
fof(f565,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0) = c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__neg_0) ).
fof(f4142,plain,
spl0_541,
inference(avatar_split_clause,[],[f488,f4140]) ).
fof(f488,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(X2,X1,X0),X1,X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__div__mult__self_0) ).
fof(f4138,plain,
spl0_540,
inference(avatar_split_clause,[],[f487,f4136]) ).
fof(f487,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Otimes__class_Otimes(X1,c_Divides_Odiv__class_Odiv(X2,X1,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__div__cancel_0) ).
fof(f4134,plain,
spl0_539,
inference(avatar_split_clause,[],[f479,f4132]) ).
fof(f4132,plain,
( spl0_539
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f479,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_3) ).
fof(f4130,plain,
spl0_538,
inference(avatar_split_clause,[],[f457,f4128]) ).
fof(f457,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__inverse_0) ).
fof(f4126,plain,
spl0_537,
inference(avatar_split_clause,[],[f454,f4124]) ).
fof(f454,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(X1,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).
fof(f4122,plain,
spl0_536,
inference(avatar_split_clause,[],[f436,f4120]) ).
fof(f4120,plain,
( spl0_536
<=> ! [X4,X0,X3] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f436,axiom,
! [X3,X0,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).
fof(f4118,plain,
spl0_535,
inference(avatar_split_clause,[],[f417,f4116]) ).
fof(f417,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(X1,X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).
fof(f4114,plain,
spl0_534,
inference(avatar_split_clause,[],[f408,f4112]) ).
fof(f408,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).
fof(f4110,plain,
spl0_533,
inference(avatar_split_clause,[],[f357,f4108]) ).
fof(f4108,plain,
( spl0_533
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f357,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).
fof(f4106,plain,
spl0_532,
inference(avatar_split_clause,[],[f329,f4104]) ).
fof(f4104,plain,
( spl0_532
<=> ! [X0,X8,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_Power_Opower__class_Opower(X3,X8,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f329,axiom,
! [X3,X0,X8] :
( ~ 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_Power_Opower__class_Opower(X3,X8,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).
fof(f4102,plain,
( spl0_531
| ~ spl0_89
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f2283,f2173,f1383,f4100]) ).
fof(f4100,plain,
( spl0_531
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f1383,plain,
( spl0_89
<=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f2173,plain,
( spl0_266
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2283,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_89
| ~ spl0_266 ),
inference(resolution,[],[f2174,f1385]) ).
fof(f1385,plain,
( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f1383]) ).
fof(f2174,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f2173]) ).
fof(f4098,plain,
spl0_530,
inference(avatar_split_clause,[],[f298,f4096]) ).
fof(f4096,plain,
( spl0_530
<=> ! [X0,X7,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X3,c_Suc(X7),X0) = c_HOL_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f298,axiom,
! [X3,X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Power_Opower__class_Opower(X3,c_Suc(X7),X0) = c_HOL_Otimes__class_Otimes(X3,c_Power_Opower__class_Opower(X3,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).
fof(f4094,plain,
spl0_529,
inference(avatar_split_clause,[],[f297,f4092]) ).
fof(f297,axiom,
! [X0,X1,X8] :
( ~ class_Power_Opower(X0)
| c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,X8,X0),X0) = c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).
fof(f4090,plain,
spl0_528,
inference(avatar_split_clause,[],[f296,f4088]) ).
fof(f296,axiom,
! [X0,X1,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(X1,c_Suc(X8),X0) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(X1,X8,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).
fof(f4086,plain,
spl0_527,
inference(avatar_split_clause,[],[f264,f4084]) ).
fof(f4084,plain,
( spl0_527
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f264,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).
fof(f4082,plain,
spl0_526,
inference(avatar_split_clause,[],[f263,f4080]) ).
fof(f263,axiom,
! [X3,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X1,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).
fof(f4078,plain,
spl0_525,
inference(avatar_split_clause,[],[f242,f4076]) ).
fof(f242,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).
fof(f4074,plain,
spl0_524,
inference(avatar_split_clause,[],[f241,f4072]) ).
fof(f4072,plain,
( spl0_524
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f241,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).
fof(f4070,plain,
spl0_523,
inference(avatar_split_clause,[],[f240,f4068]) ).
fof(f4068,plain,
( spl0_523
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f240,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).
fof(f4066,plain,
spl0_522,
inference(avatar_split_clause,[],[f239,f4064]) ).
fof(f239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).
fof(f4062,plain,
spl0_521,
inference(avatar_split_clause,[],[f159,f4060]) ).
fof(f159,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).
fof(f4058,plain,
( spl0_520
| ~ spl0_138
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f2282,f2173,f1628,f4056]) ).
fof(f4056,plain,
( spl0_520
<=> ! [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_520])]) ).
fof(f1628,plain,
( spl0_138
<=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f2282,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_138
| ~ spl0_266 ),
inference(resolution,[],[f2174,f1630]) ).
fof(f1630,plain,
( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1628]) ).
fof(f4054,plain,
spl0_519,
inference(avatar_split_clause,[],[f158,f4052]) ).
fof(f4052,plain,
( spl0_519
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f158,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).
fof(f4050,plain,
spl0_518,
inference(avatar_split_clause,[],[f157,f4048]) ).
fof(f157,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).
fof(f4046,plain,
spl0_517,
inference(avatar_split_clause,[],[f156,f4044]) ).
fof(f156,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).
fof(f4042,plain,
spl0_516,
inference(avatar_split_clause,[],[f155,f4040]) ).
fof(f4040,plain,
( spl0_516
<=> ! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f155,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) = c_HOL_Otimes__class_Otimes(X2,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).
fof(f4038,plain,
spl0_515,
inference(avatar_split_clause,[],[f153,f4036]) ).
fof(f4036,plain,
( spl0_515
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f153,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).
fof(f4034,plain,
spl0_514,
inference(avatar_split_clause,[],[f151,f4032]) ).
fof(f4032,plain,
( spl0_514
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__normed__algebra(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).
fof(f4030,plain,
spl0_513,
inference(avatar_split_clause,[],[f138,f4028]) ).
fof(f138,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).
fof(f4026,plain,
spl0_512,
inference(avatar_split_clause,[],[f136,f4024]) ).
fof(f136,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).
fof(f4022,plain,
spl0_511,
inference(avatar_split_clause,[],[f123,f4020]) ).
fof(f123,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).
fof(f4018,plain,
spl0_510,
inference(avatar_split_clause,[],[f122,f4016]) ).
fof(f122,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).
fof(f4014,plain,
( spl0_509
| ~ spl0_30
| ~ spl0_266 ),
inference(avatar_split_clause,[],[f2280,f2173,f1088,f4012]) ).
fof(f4012,plain,
( spl0_509
<=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f1088,plain,
( spl0_30
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2280,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0
| ~ spl0_30
| ~ spl0_266 ),
inference(resolution,[],[f2174,f1090]) ).
fof(f1090,plain,
( class_OrderedGroup_Omonoid__add(tc_nat)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f1088]) ).
fof(f4010,plain,
spl0_508,
inference(avatar_split_clause,[],[f121,f4008]) ).
fof(f4008,plain,
( spl0_508
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f121,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).
fof(f4006,plain,
spl0_507,
inference(avatar_split_clause,[],[f114,f4004]) ).
fof(f114,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X9
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X9,X0),X9,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).
fof(f4002,plain,
spl0_506,
inference(avatar_split_clause,[],[f91,f4000]) ).
fof(f91,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).
fof(f3998,plain,
spl0_505,
inference(avatar_split_clause,[],[f90,f3996]) ).
fof(f90,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).
fof(f3994,plain,
spl0_504,
inference(avatar_split_clause,[],[f59,f3992]) ).
fof(f59,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).
fof(f3990,plain,
spl0_503,
inference(avatar_split_clause,[],[f44,f3988]) ).
fof(f3988,plain,
( spl0_503
<=> ! [X0,X23,X7] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X23,X0)
| ~ c_Polynomial_Opos__poly(X7,X0)
| c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f44,axiom,
! [X0,X7,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X23,X0)
| ~ c_Polynomial_Opos__poly(X7,X0)
| c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X23,X7,tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__add_0) ).
fof(f3986,plain,
spl0_502,
inference(avatar_split_clause,[],[f33,f3984]) ).
fof(f33,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).
fof(f3982,plain,
spl0_501,
inference(avatar_split_clause,[],[f32,f3980]) ).
fof(f32,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).
fof(f3978,plain,
spl0_500,
inference(avatar_split_clause,[],[f14,f3976]) ).
fof(f14,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).
fof(f3973,plain,
( spl0_499
| ~ spl0_89
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2279,f2169,f1383,f3971]) ).
fof(f3971,plain,
( spl0_499
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2169,plain,
( spl0_265
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2279,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_89
| ~ spl0_265 ),
inference(resolution,[],[f2170,f1385]) ).
fof(f2170,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f2169]) ).
fof(f3922,plain,
( spl0_498
| ~ spl0_138
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2278,f2169,f1628,f3920]) ).
fof(f2278,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_138
| ~ spl0_265 ),
inference(resolution,[],[f2170,f1630]) ).
fof(f3864,plain,
( spl0_497
| ~ spl0_30
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f2276,f2169,f1088,f3862]) ).
fof(f3862,plain,
( spl0_497
<=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2276,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_30
| ~ spl0_265 ),
inference(resolution,[],[f2170,f1090]) ).
fof(f3789,plain,
( spl0_496
| ~ spl0_47
| ~ spl0_264 ),
inference(avatar_split_clause,[],[f2274,f2165,f1173,f3786]) ).
fof(f2274,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_47
| ~ spl0_264 ),
inference(resolution,[],[f2166,f1175]) ).
fof(f3731,plain,
( spl0_495
| ~ spl0_55
| ~ spl0_263 ),
inference(avatar_split_clause,[],[f2273,f2161,f1213,f3728]) ).
fof(f3728,plain,
( spl0_495
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2161,plain,
( spl0_263
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2273,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_263 ),
inference(resolution,[],[f2162,f1215]) ).
fof(f2162,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f2161]) ).
fof(f3689,plain,
spl0_494,
inference(avatar_split_clause,[],[f735,f3687]) ).
fof(f3687,plain,
( spl0_494
<=> ! [X2,X0,X23,X1,X7] :
( ~ class_HOL_Ozero(X0)
| X7 = X23
| c_Polynomial_OpCons(X2,X7,X0) != c_Polynomial_OpCons(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f735,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_HOL_Ozero(X0)
| X7 = X23
| c_Polynomial_OpCons(X2,X7,X0) != c_Polynomial_OpCons(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).
fof(f3685,plain,
( spl0_493
| ~ spl0_140
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2271,f2157,f1638,f3683]) ).
fof(f3683,plain,
( spl0_493
<=> ! [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_493])]) ).
fof(f2271,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_140
| ~ spl0_262 ),
inference(resolution,[],[f2158,f1640]) ).
fof(f3681,plain,
spl0_492,
inference(avatar_split_clause,[],[f734,f3679]) ).
fof(f3679,plain,
( spl0_492
<=> ! [X0,X7,X23,X2,X1] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_OpCons(X2,X7,X0) != c_Polynomial_OpCons(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f734,axiom,
! [X2,X0,X1,X7,X23] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_OpCons(X2,X7,X0) != c_Polynomial_OpCons(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).
fof(f3677,plain,
spl0_491,
inference(avatar_split_clause,[],[f724,f3675]) ).
fof(f3675,plain,
( spl0_491
<=> ! [X0,X1,X23] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f724,axiom,
! [X0,X1,X23] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X1,X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).
fof(f3673,plain,
spl0_490,
inference(avatar_split_clause,[],[f690,f3671]) ).
fof(f3671,plain,
( spl0_490
<=> ! [X4,X0,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f690,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| X3 = X4
| c_HOL_Ominus__class_Ominus(X3,X4,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).
fof(f3669,plain,
spl0_489,
inference(avatar_split_clause,[],[f680,f3667]) ).
fof(f3667,plain,
( spl0_489
<=> ! [X0,X1,X3] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f680,axiom,
! [X3,X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oplus__class_Oplus(X3,X1,X0) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).
fof(f3665,plain,
spl0_488,
inference(avatar_split_clause,[],[f626,f3663]) ).
fof(f3663,plain,
( spl0_488
<=> ! [X0,X8,X2,X1] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_Omonom(X1,X8,X0) != c_Polynomial_Omonom(X2,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f626,axiom,
! [X2,X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| X1 = X2
| c_Polynomial_Omonom(X1,X8,X0) != c_Polynomial_Omonom(X2,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).
fof(f3661,plain,
spl0_487,
inference(avatar_split_clause,[],[f616,f3659]) ).
fof(f616,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).
fof(f3657,plain,
spl0_486,
inference(avatar_split_clause,[],[f615,f3655]) ).
fof(f3655,plain,
( spl0_486
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f615,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).
fof(f3653,plain,
spl0_485,
inference(avatar_split_clause,[],[f583,f3651]) ).
fof(f583,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| ~ class_Orderings_Olinorder(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).
fof(f3649,plain,
spl0_484,
inference(avatar_split_clause,[],[f573,f3647]) ).
fof(f3647,plain,
( spl0_484
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f573,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
fof(f3645,plain,
spl0_483,
inference(avatar_split_clause,[],[f572,f3643]) ).
fof(f572,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
fof(f3641,plain,
( spl0_482
| ~ spl0_91
| ~ spl0_262 ),
inference(avatar_split_clause,[],[f2270,f2157,f1393,f3639]) ).
fof(f3639,plain,
( spl0_482
<=> ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2270,plain,
( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_91
| ~ spl0_262 ),
inference(resolution,[],[f2158,f1395]) ).
fof(f3637,plain,
spl0_481,
inference(avatar_split_clause,[],[f557,f3635]) ).
fof(f3635,plain,
( spl0_481
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f557,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).
fof(f3633,plain,
spl0_480,
inference(avatar_split_clause,[],[f556,f3631]) ).
fof(f556,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).
fof(f3629,plain,
spl0_479,
inference(avatar_split_clause,[],[f542,f3627]) ).
fof(f542,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).
fof(f3625,plain,
spl0_478,
inference(avatar_split_clause,[],[f527,f3623]) ).
fof(f527,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
fof(f3621,plain,
spl0_477,
inference(avatar_split_clause,[],[f524,f3619]) ).
fof(f524,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
fof(f3617,plain,
spl0_476,
inference(avatar_split_clause,[],[f484,f3615]) ).
fof(f3615,plain,
( spl0_476
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f484,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
fof(f3613,plain,
spl0_475,
inference(avatar_split_clause,[],[f483,f3611]) ).
fof(f483,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
fof(f3609,plain,
spl0_474,
inference(avatar_split_clause,[],[f460,f3607]) ).
fof(f460,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__field(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oinverse__class_Oinverse(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).
fof(f3605,plain,
spl0_473,
inference(avatar_split_clause,[],[f453,f3603]) ).
fof(f3603,plain,
( spl0_473
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f453,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = X3
| c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Oinverse(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).
fof(f3601,plain,
spl0_472,
inference(avatar_split_clause,[],[f411,f3599]) ).
fof(f3599,plain,
( spl0_472
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f411,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X2,X0) = X1
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).
fof(f3597,plain,
( spl0_471
| ~ spl0_132
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2265,f2149,f1598,f3595]) ).
fof(f3595,plain,
( spl0_471
<=> ! [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_471])]) ).
fof(f2265,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
| ~ spl0_132
| ~ spl0_260 ),
inference(resolution,[],[f2150,f1600]) ).
fof(f3593,plain,
spl0_470,
inference(avatar_split_clause,[],[f410,f3591]) ).
fof(f3591,plain,
( spl0_470
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f410,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = X2
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).
fof(f3589,plain,
spl0_469,
inference(avatar_split_clause,[],[f362,f3587]) ).
fof(f362,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).
fof(f3585,plain,
spl0_468,
inference(avatar_split_clause,[],[f327,f3583]) ).
fof(f3583,plain,
( spl0_468
<=> ! [X5,X0,X6,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X5 = X6
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f327,axiom,
! [X3,X0,X6,X5] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X5 = X6
| c_HOL_Ominus__class_Ominus(X5,X6,X0) != c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
fof(f3581,plain,
spl0_467,
inference(avatar_split_clause,[],[f311,f3579]) ).
fof(f311,axiom,
! [X3,X0,X18,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X18,X0)
| c_HOL_Oord__class_Oless(X3,X18,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f3577,plain,
spl0_466,
inference(avatar_split_clause,[],[f310,f3575]) ).
fof(f310,axiom,
! [X3,X0,X18,X4] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0)
| ~ c_HOL_Oord__class_Oless(X18,X4,X0)
| c_HOL_Oord__class_Oless(X18,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f3573,plain,
spl0_465,
inference(avatar_split_clause,[],[f288,f3571]) ).
fof(f288,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).
fof(f3569,plain,
spl0_464,
inference(avatar_split_clause,[],[f287,f3567]) ).
fof(f287,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).
fof(f3565,plain,
spl0_463,
inference(avatar_split_clause,[],[f284,f3563]) ).
fof(f284,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__prts_0) ).
fof(f3561,plain,
spl0_462,
inference(avatar_split_clause,[],[f250,f3559]) ).
fof(f250,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).
fof(f3557,plain,
spl0_461,
inference(avatar_split_clause,[],[f249,f3555]) ).
fof(f3555,plain,
( spl0_461
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f249,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).
fof(f3553,plain,
( spl0_460
| ~ spl0_82
| ~ spl0_260 ),
inference(avatar_split_clause,[],[f2264,f2149,f1348,f3551]) ).
fof(f3551,plain,
( spl0_460
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2264,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
| ~ spl0_82
| ~ spl0_260 ),
inference(resolution,[],[f2150,f1350]) ).
fof(f3549,plain,
spl0_459,
inference(avatar_split_clause,[],[f247,f3547]) ).
fof(f3547,plain,
( spl0_459
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f247,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).
fof(f3545,plain,
spl0_458,
inference(avatar_split_clause,[],[f246,f3543]) ).
fof(f246,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).
fof(f3541,plain,
spl0_457,
inference(avatar_split_clause,[],[f221,f3539]) ).
fof(f3539,plain,
( spl0_457
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f221,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X2,X1,X0) != c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f3537,plain,
spl0_456,
inference(avatar_split_clause,[],[f220,f3535]) ).
fof(f3535,plain,
( spl0_456
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f220,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f3533,plain,
spl0_455,
inference(avatar_split_clause,[],[f219,f3531]) ).
fof(f3531,plain,
( spl0_455
<=> ! [X0,X9,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f219,axiom,
! [X2,X0,X1,X9] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X9
| c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f3529,plain,
spl0_454,
inference(avatar_split_clause,[],[f211,f3527]) ).
fof(f211,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).
fof(f3525,plain,
spl0_453,
inference(avatar_split_clause,[],[f210,f3523]) ).
fof(f210,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).
fof(f3521,plain,
spl0_452,
inference(avatar_split_clause,[],[f134,f3519]) ).
fof(f134,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).
fof(f3517,plain,
spl0_451,
inference(avatar_split_clause,[],[f125,f3515]) ).
fof(f125,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
fof(f3513,plain,
spl0_450,
inference(avatar_split_clause,[],[f124,f3511]) ).
fof(f124,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(X2,X0),c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
fof(f3499,plain,
spl0_449,
inference(avatar_split_clause,[],[f97,f3497]) ).
fof(f97,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).
fof(f3495,plain,
spl0_448,
inference(avatar_split_clause,[],[f96,f3493]) ).
fof(f96,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).
fof(f3491,plain,
spl0_447,
inference(avatar_split_clause,[],[f95,f3489]) ).
fof(f95,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).
fof(f3487,plain,
spl0_446,
inference(avatar_split_clause,[],[f76,f3485]) ).
fof(f76,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X2,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).
fof(f3483,plain,
spl0_445,
inference(avatar_split_clause,[],[f75,f3481]) ).
fof(f75,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,X2,X0) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).
fof(f3479,plain,
spl0_444,
inference(avatar_split_clause,[],[f51,f3477]) ).
fof(f3477,plain,
( spl0_444
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f51,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).
fof(f3475,plain,
spl0_443,
inference(avatar_split_clause,[],[f43,f3473]) ).
fof(f3473,plain,
( spl0_443
<=> ! [X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Omonom(X1,X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f43,axiom,
! [X0,X1,X8] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Omonom(X1,X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).
fof(f3471,plain,
spl0_442,
inference(avatar_split_clause,[],[f36,f3469]) ).
fof(f36,axiom,
! [X0,X1] :
( ~ class_HOL_Ozero(X0)
| c_Polynomial_Omonom(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).
fof(f3467,plain,
spl0_441,
inference(avatar_split_clause,[],[f1,f3465]) ).
fof(f3465,plain,
( spl0_441
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = X2
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Oinverse__class_Oinverse(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).
fof(f3459,plain,
( spl0_440
| ~ spl0_430 ),
inference(avatar_split_clause,[],[f3453,f3188,f3457]) ).
fof(f3188,plain,
( spl0_430
<=> ! [X0,X11,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X33,X11,X0)
| c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f3453,plain,
( ! [X0,X1] :
( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_430 ),
inference(equality_resolution,[],[f3189]) ).
fof(f3189,plain,
( ! [X0,X11,X33] :
( c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X33,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X33,X11,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_430 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f3419,plain,
( spl0_439
| ~ spl0_55
| ~ spl0_259 ),
inference(avatar_split_clause,[],[f2263,f2145,f1213,f3416]) ).
fof(f3416,plain,
( spl0_439
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2145,plain,
( spl0_259
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2263,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_55
| ~ spl0_259 ),
inference(resolution,[],[f2146,f1215]) ).
fof(f2146,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_259 ),
inference(avatar_component_clause,[],[f2145]) ).
fof(f3382,plain,
( spl0_438
| ~ spl0_116
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2262,f2141,f1518,f3379]) ).
fof(f3379,plain,
( spl0_438
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2141,plain,
( spl0_258
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2262,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_116
| ~ spl0_258 ),
inference(resolution,[],[f2142,f1520]) ).
fof(f2142,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_258 ),
inference(avatar_component_clause,[],[f2141]) ).
fof(f3285,plain,
( spl0_437
| ~ spl0_60
| ~ spl0_258 ),
inference(avatar_split_clause,[],[f2261,f2141,f1238,f3282]) ).
fof(f3282,plain,
( spl0_437
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2261,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_60
| ~ spl0_258 ),
inference(resolution,[],[f2142,f1240]) ).
fof(f3214,plain,
spl0_436,
inference(avatar_split_clause,[],[f725,f3212]) ).
fof(f725,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(f3210,plain,
( spl0_435
| ~ spl0_31
| ~ spl0_256 ),
inference(avatar_split_clause,[],[f2259,f2133,f1093,f3208]) ).
fof(f3208,plain,
( spl0_435
<=> ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2259,plain,
( ! [X0] : c_Divides_Odiv__class_Omod(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_256 ),
inference(resolution,[],[f2134,f1095]) ).
fof(f3206,plain,
spl0_434,
inference(avatar_split_clause,[],[f718,f3204]) ).
fof(f3204,plain,
( spl0_434
<=> ! [X23] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X23) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X23,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X23),tc_Complex_Ocomplex) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f718,axiom,
! [X23] :
( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X23) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(X23,v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X23),tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_0) ).
fof(f3202,plain,
spl0_433,
inference(avatar_split_clause,[],[f674,f3200]) ).
fof(f3200,plain,
( spl0_433
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f674,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).
fof(f3198,plain,
spl0_432,
inference(avatar_split_clause,[],[f665,f3196]) ).
fof(f3196,plain,
( spl0_432
<=> ! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X8,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f665,axiom,
! [X0,X1,X8] :
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_Power_Opower__class_Opower(X1,X8,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
fof(f3194,plain,
spl0_431,
inference(avatar_split_clause,[],[f657,f3192]) ).
fof(f3192,plain,
( spl0_431
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f657,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).
fof(f3190,plain,
spl0_430,
inference(avatar_split_clause,[],[f629,f3188]) ).
fof(f629,axiom,
! [X0,X11,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X33,X11,X0)
| c_HOL_Oabs__class_Oabs(X11,X0) != c_HOL_Oabs__class_Oabs(X33,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__if__abs__eq_0) ).
fof(f3186,plain,
spl0_429,
inference(avatar_split_clause,[],[f628,f3184]) ).
fof(f628,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__1__pos_0) ).
fof(f3182,plain,
spl0_428,
inference(avatar_split_clause,[],[f627,f3180]) ).
fof(f627,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__pos_0) ).
fof(f3178,plain,
spl0_427,
inference(avatar_split_clause,[],[f624,f3176]) ).
fof(f624,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).
fof(f3174,plain,
spl0_426,
inference(avatar_split_clause,[],[f623,f3172]) ).
fof(f623,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).
fof(f3170,plain,
spl0_425,
inference(avatar_split_clause,[],[f570,f3168]) ).
fof(f570,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oinverse__class_Oinverse(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).
fof(f3166,plain,
( spl0_424
| ~ spl0_31
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f2257,f2129,f1093,f3164]) ).
fof(f3164,plain,
( spl0_424
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2257,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Divides_Odiv__class_Omod(X0,X0,tc_nat)
| ~ spl0_31
| ~ spl0_255 ),
inference(resolution,[],[f2130,f1095]) ).
fof(f3162,plain,
spl0_423,
inference(avatar_split_clause,[],[f547,f3160]) ).
fof(f547,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).
fof(f3158,plain,
spl0_422,
inference(avatar_split_clause,[],[f546,f3156]) ).
fof(f546,axiom,
! [X0,X18,X4] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X18,X0),c_HOL_Oplus__class_Oplus(X4,X18,X0),X0) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).
fof(f3154,plain,
spl0_421,
inference(avatar_split_clause,[],[f530,f3152]) ).
fof(f3152,plain,
( spl0_421
<=> ! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f530,axiom,
! [X2,X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).
fof(f3150,plain,
spl0_420,
inference(avatar_split_clause,[],[f523,f3148]) ).
fof(f523,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ominus__class_Ominus(X2,X1,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
fof(f3146,plain,
spl0_419,
inference(avatar_split_clause,[],[f502,f3144]) ).
fof(f502,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Ominus__class_Ominus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).
fof(f3142,plain,
spl0_418,
inference(avatar_split_clause,[],[f373,f3140]) ).
fof(f373,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).
fof(f3138,plain,
spl0_417,
inference(avatar_split_clause,[],[f363,f3136]) ).
fof(f363,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_Divides_Odiv__class_Odiv(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__self_0) ).
fof(f3134,plain,
spl0_416,
inference(avatar_split_clause,[],[f348,f3132]) ).
fof(f348,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nprt__neg_0) ).
fof(f3130,plain,
spl0_415,
inference(avatar_split_clause,[],[f323,f3128]) ).
fof(f323,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).
fof(f3126,plain,
spl0_414,
inference(avatar_split_clause,[],[f269,f3124]) ).
fof(f269,axiom,
! [X0,X8] :
( ~ class_Ring__and__Field_Osemiring__0(X0)
| ~ class_Power_Opower(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(X0),c_Suc(X8),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).
fof(f3122,plain,
( spl0_413
| ~ spl0_121
| ~ spl0_253 ),
inference(avatar_split_clause,[],[f2254,f2121,f1543,f3119]) ).
fof(f3119,plain,
( spl0_413
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2121,plain,
( spl0_253
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2254,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_121
| ~ spl0_253 ),
inference(resolution,[],[f2122,f1545]) ).
fof(f2122,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) )
| ~ spl0_253 ),
inference(avatar_component_clause,[],[f2121]) ).
fof(f3117,plain,
spl0_412,
inference(avatar_split_clause,[],[f226,f3115]) ).
fof(f3115,plain,
( spl0_412
<=> ! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f226,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Divides_Odiv__class_Omod(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).
fof(f3113,plain,
spl0_411,
inference(avatar_split_clause,[],[f225,f3111]) ).
fof(f225,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).
fof(f3109,plain,
spl0_410,
inference(avatar_split_clause,[],[f200,f3107]) ).
fof(f3107,plain,
( spl0_410
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(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_410])]) ).
fof(f200,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(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_diff__minus_0) ).
fof(f3105,plain,
spl0_409,
inference(avatar_split_clause,[],[f199,f3103]) ).
fof(f199,axiom,
! [X3,X0,X4] :
( ~ class_Int_Onumber__ring(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_class__ring_Osub__add_0) ).
fof(f3101,plain,
spl0_408,
inference(avatar_split_clause,[],[f198,f3099]) ).
fof(f198,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_diff__def_0) ).
fof(f3097,plain,
spl0_407,
inference(avatar_split_clause,[],[f177,f3095]) ).
fof(f177,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pprt__neg_0) ).
fof(f3093,plain,
spl0_406,
inference(avatar_split_clause,[],[f105,f3091]) ).
fof(f105,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f3089,plain,
spl0_405,
inference(avatar_split_clause,[],[f104,f3087]) ).
fof(f104,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,X0)
| c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
fof(f3085,plain,
spl0_404,
inference(avatar_split_clause,[],[f102,f3083]) ).
fof(f102,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X1,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
fof(f3081,plain,
spl0_403,
inference(avatar_split_clause,[],[f101,f3079]) ).
fof(f101,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Olower__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X2,X3,X0)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
fof(f3077,plain,
( spl0_402
| ~ spl0_76
| ~ spl0_251 ),
inference(avatar_split_clause,[],[f2249,f2113,f1318,f3074]) ).
fof(f3074,plain,
( spl0_402
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2249,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_251 ),
inference(resolution,[],[f2114,f1320]) ).
fof(f3072,plain,
spl0_401,
inference(avatar_split_clause,[],[f92,f3070]) ).
fof(f92,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X3,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__minus_0) ).
fof(f3068,plain,
spl0_400,
inference(avatar_split_clause,[],[f71,f3066]) ).
fof(f71,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0),X0) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).
fof(f3064,plain,
spl0_399,
inference(avatar_split_clause,[],[f68,f3062]) ).
fof(f68,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).
fof(f3060,plain,
spl0_398,
inference(avatar_split_clause,[],[f67,f3058]) ).
fof(f67,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).
fof(f3056,plain,
spl0_397,
inference(avatar_split_clause,[],[f66,f3054]) ).
fof(f66,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).
fof(f3052,plain,
spl0_396,
inference(avatar_split_clause,[],[f65,f3050]) ).
fof(f65,axiom,
! [X2,X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,X9,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).
fof(f3048,plain,
spl0_395,
inference(avatar_split_clause,[],[f35,f3046]) ).
fof(f35,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X3,X2,X0)
| c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
fof(f3044,plain,
spl0_394,
inference(avatar_split_clause,[],[f34,f3042]) ).
fof(f34,axiom,
! [X2,X3,X0,X1] :
( ~ class_Lattices_Oupper__semilattice(X0)
| ~ c_HOL_Oord__class_Oless(X3,X1,X0)
| c_HOL_Oord__class_Oless(X3,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
fof(f3040,plain,
spl0_393,
inference(avatar_split_clause,[],[f16,f3038]) ).
fof(f16,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| c_HOL_Ouminus__class_Ouminus(X3,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).
fof(f3036,plain,
( spl0_392
| ~ spl0_140
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f2247,f2109,f1638,f3033]) ).
fof(f3033,plain,
( spl0_392
<=> 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_392])]) ).
fof(f2247,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_140
| ~ spl0_250 ),
inference(resolution,[],[f2110,f1640]) ).
fof(f3004,plain,
( spl0_391
| ~ spl0_124
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2242,f2097,f1558,f3001]) ).
fof(f3001,plain,
( spl0_391
<=> c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2097,plain,
( spl0_247
<=> ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2242,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_124
| ~ spl0_247 ),
inference(resolution,[],[f2098,f1560]) ).
fof(f2098,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_247 ),
inference(avatar_component_clause,[],[f2097]) ).
fof(f2969,plain,
( spl0_390
| ~ spl0_71
| ~ spl0_247 ),
inference(avatar_split_clause,[],[f2241,f2097,f1293,f2966]) ).
fof(f2966,plain,
( spl0_390
<=> c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2241,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_71
| ~ spl0_247 ),
inference(resolution,[],[f2098,f1295]) ).
fof(f2934,plain,
( spl0_389
| ~ spl0_56
| ~ spl0_246 ),
inference(avatar_split_clause,[],[f2239,f2093,f1218,f2931]) ).
fof(f2931,plain,
( spl0_389
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f1218,plain,
( spl0_56
<=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f2239,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_56
| ~ spl0_246 ),
inference(resolution,[],[f2094,f1220]) ).
fof(f1220,plain,
( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f1218]) ).
fof(f2927,plain,
spl0_388,
inference(avatar_split_clause,[],[f696,f2925]) ).
fof(f2925,plain,
( spl0_388
<=> ! [X0,X3] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f696,axiom,
! [X3,X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = X3
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).
fof(f2923,plain,
spl0_387,
inference(avatar_split_clause,[],[f695,f2921]) ).
fof(f2921,plain,
( spl0_387
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f695,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).
fof(f2919,plain,
spl0_386,
inference(avatar_split_clause,[],[f689,f2917]) ).
fof(f2917,plain,
( spl0_386
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f689,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(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_right__minus__eq_0) ).
fof(f2915,plain,
spl0_385,
inference(avatar_split_clause,[],[f688,f2913]) ).
fof(f2913,plain,
( spl0_385
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X2
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f688,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(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_eq__iff__diff__eq__0_1) ).
fof(f2911,plain,
spl0_384,
inference(avatar_split_clause,[],[f685,f2909]) ).
fof(f2909,plain,
( spl0_384
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f685,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).
fof(f2907,plain,
spl0_383,
inference(avatar_split_clause,[],[f603,f2905]) ).
fof(f603,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).
fof(f2903,plain,
spl0_382,
inference(avatar_split_clause,[],[f602,f2901]) ).
fof(f602,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(X2,X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).
fof(f2899,plain,
spl0_381,
inference(avatar_split_clause,[],[f584,f2897]) ).
fof(f584,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oabs__if(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1
| c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).
fof(f2895,plain,
( spl0_380
| ~ spl0_31
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f2237,f2089,f1093,f2893]) ).
fof(f2893,plain,
( spl0_380
<=> ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2237,plain,
( ! [X0] : c_Divides_Odiv__class_Odiv(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_31
| ~ spl0_245 ),
inference(resolution,[],[f2090,f1095]) ).
fof(f2891,plain,
spl0_379,
inference(avatar_split_clause,[],[f581,f2889]) ).
fof(f581,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).
fof(f2887,plain,
spl0_378,
inference(avatar_split_clause,[],[f579,f2885]) ).
fof(f579,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).
fof(f2883,plain,
spl0_377,
inference(avatar_split_clause,[],[f564,f2881]) ).
fof(f564,axiom,
! [X0,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).
fof(f2879,plain,
spl0_376,
inference(avatar_split_clause,[],[f553,f2877]) ).
fof(f2877,plain,
( spl0_376
<=> ! [X0,X23,X7] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| X7 = X23
| ~ c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f553,axiom,
! [X0,X7,X23] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| X7 = X23
| ~ c_HOL_Oeq__class_Oeq(X23,X7,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_0) ).
fof(f2875,plain,
spl0_375,
inference(avatar_split_clause,[],[f535,f2873]) ).
fof(f2873,plain,
( spl0_375
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f535,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Oinverse__class_Oinverse(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).
fof(f2871,plain,
spl0_374,
inference(avatar_split_clause,[],[f531,f2869]) ).
fof(f2869,plain,
( spl0_374
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f531,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).
fof(f2867,plain,
spl0_373,
inference(avatar_split_clause,[],[f528,f2865]) ).
fof(f528,axiom,
! [X2,X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X2,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).
fof(f2863,plain,
spl0_372,
inference(avatar_split_clause,[],[f459,f2861]) ).
fof(f459,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).
fof(f2859,plain,
spl0_371,
inference(avatar_split_clause,[],[f434,f2857]) ).
fof(f434,axiom,
! [X0,X11,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_1) ).
fof(f2855,plain,
spl0_370,
inference(avatar_split_clause,[],[f433,f2853]) ).
fof(f433,axiom,
! [X0,X11,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oabs__class_Oabs(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__abs__iff_0) ).
fof(f2851,plain,
( spl0_369
| ~ spl0_140
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2235,f2085,f1638,f2849]) ).
fof(f2235,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_140
| ~ spl0_244 ),
inference(resolution,[],[f2086,f1640]) ).
fof(f2847,plain,
spl0_368,
inference(avatar_split_clause,[],[f432,f2845]) ).
fof(f432,axiom,
! [X0,X11,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_1) ).
fof(f2843,plain,
spl0_367,
inference(avatar_split_clause,[],[f431,f2841]) ).
fof(f431,axiom,
! [X0,X11,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X27,X11,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(X27,X0),X11,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__dvd__iff_0) ).
fof(f2839,plain,
spl0_366,
inference(avatar_split_clause,[],[f414,f2837]) ).
fof(f414,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).
fof(f2835,plain,
spl0_365,
inference(avatar_split_clause,[],[f384,f2833]) ).
fof(f384,axiom,
! [X2,X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(X1,X2,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__div__trivial_0) ).
fof(f2831,plain,
spl0_364,
inference(avatar_split_clause,[],[f294,f2829]) ).
fof(f294,axiom,
! [X0,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pcompose__0_0) ).
fof(f2827,plain,
spl0_363,
inference(avatar_split_clause,[],[f254,f2825]) ).
fof(f254,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X3,X0),c_HOL_Oabs__class_Oabs(X3,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__sgn__abs_0) ).
fof(f2823,plain,
spl0_362,
inference(avatar_split_clause,[],[f208,f2821]) ).
fof(f208,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).
fof(f2819,plain,
spl0_361,
inference(avatar_split_clause,[],[f207,f2817]) ).
fof(f207,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X3,X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).
fof(f2815,plain,
spl0_360,
inference(avatar_split_clause,[],[f206,f2813]) ).
fof(f206,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).
fof(f2811,plain,
spl0_359,
inference(avatar_split_clause,[],[f205,f2809]) ).
fof(f205,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X3,X4,X0)
| ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Ouminus__class_Ouminus(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).
fof(f2807,plain,
( spl0_358
| ~ spl0_91
| ~ spl0_244 ),
inference(avatar_split_clause,[],[f2234,f2085,f1393,f2805]) ).
fof(f2234,plain,
( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_91
| ~ spl0_244 ),
inference(resolution,[],[f2086,f1395]) ).
fof(f2803,plain,
spl0_357,
inference(avatar_split_clause,[],[f190,f2801]) ).
fof(f190,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs__class_Oabs(X11,X0) = c_HOL_Otimes__class_Otimes(X11,c_HOL_Osgn__class_Osgn(X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sgn_0) ).
fof(f2799,plain,
spl0_356,
inference(avatar_split_clause,[],[f150,f2797]) ).
fof(f150,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f2795,plain,
spl0_355,
inference(avatar_split_clause,[],[f117,f2793]) ).
fof(f117,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Oabs__class_Oabs(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__lattice_0) ).
fof(f2791,plain,
spl0_354,
inference(avatar_split_clause,[],[f112,f2789]) ).
fof(f2789,plain,
( spl0_354
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f112,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| X1 = X2
| c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
fof(f2787,plain,
spl0_353,
inference(avatar_split_clause,[],[f57,f2785]) ).
fof(f57,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prts_0) ).
fof(f2773,plain,
( spl0_352
| ~ spl0_114
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2233,f2081,f1508,f2770]) ).
fof(f1508,plain,
( spl0_114
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f2081,plain,
( spl0_243
<=> ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2233,plain,
( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ spl0_114
| ~ spl0_243 ),
inference(resolution,[],[f2082,f1510]) ).
fof(f1510,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f1508]) ).
fof(f2082,plain,
( ! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f2081]) ).
fof(f2737,plain,
( spl0_351
| ~ spl0_58
| ~ spl0_243 ),
inference(avatar_split_clause,[],[f2232,f2081,f1228,f2734]) ).
fof(f1228,plain,
( spl0_58
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f2232,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_58
| ~ spl0_243 ),
inference(resolution,[],[f2082,f1230]) ).
fof(f1230,plain,
( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f1228]) ).
fof(f2703,plain,
( spl0_350
| ~ spl0_85
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2219,f2049,f1363,f2701]) ).
fof(f2219,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_85
| ~ spl0_235 ),
inference(resolution,[],[f2050,f1365]) ).
fof(f2673,plain,
( spl0_349
| ~ spl0_135
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2218,f2049,f1613,f2671]) ).
fof(f2218,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_135
| ~ spl0_235 ),
inference(resolution,[],[f2050,f1615]) ).
fof(f2664,plain,
spl0_348,
inference(avatar_split_clause,[],[f732,f2662]) ).
fof(f732,axiom,
! [X3,X9] : c_Polynomial_Opoly(c_Polynomial_OpCons(X9,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X3,tc_Complex_Ocomplex) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mpoly__base__conv_I2_J_0) ).
fof(f2660,plain,
spl0_347,
inference(avatar_split_clause,[],[f727,f2658]) ).
fof(f727,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).
fof(f2656,plain,
spl0_346,
inference(avatar_split_clause,[],[f726,f2654]) ).
fof(f726,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).
fof(f2652,plain,
spl0_345,
inference(avatar_split_clause,[],[f713,f2650]) ).
fof(f2650,plain,
( spl0_345
<=> ! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X23,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f713,axiom,
! [X0,X1,X23] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(X23,X0)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(X1,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).
fof(f2648,plain,
( spl0_343
| ~ spl0_344 ),
inference(avatar_split_clause,[],[f708,f2645,f2641]) ).
fof(f2641,plain,
( spl0_343
<=> c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2645,plain,
( spl0_344
<=> class_OrderedGroup_Olordered__ab__group__add(t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f708,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pprt__def__raw_0) ).
fof(f2639,plain,
spl0_342,
inference(avatar_split_clause,[],[f701,f2637]) ).
fof(f701,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).
fof(f2635,plain,
( spl0_341
| ~ spl0_27
| ~ spl0_235 ),
inference(avatar_split_clause,[],[f2216,f2049,f1073,f2633]) ).
fof(f2216,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_27
| ~ spl0_235 ),
inference(resolution,[],[f2050,f1075]) ).
fof(f2631,plain,
spl0_340,
inference(avatar_split_clause,[],[f683,f2629]) ).
fof(f2629,plain,
( spl0_340
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f683,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).
fof(f2627,plain,
spl0_339,
inference(avatar_split_clause,[],[f679,f2625]) ).
fof(f679,axiom,
! [X3,X0] :
( ~ class_Int_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).
fof(f2623,plain,
spl0_338,
inference(avatar_split_clause,[],[f660,f2621]) ).
fof(f2621,plain,
( spl0_338
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f660,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ouminus__class_Ouminus(X1,X0) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).
fof(f2619,plain,
spl0_337,
inference(avatar_split_clause,[],[f658,f2617]) ).
fof(f658,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).
fof(f2615,plain,
spl0_336,
inference(avatar_split_clause,[],[f582,f2613]) ).
fof(f582,axiom,
! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).
fof(f2611,plain,
spl0_335,
inference(avatar_split_clause,[],[f580,f2609]) ).
fof(f580,axiom,
! [X0,X23] :
( ~ class_Ring__and__Field_Oidom(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).
fof(f2607,plain,
spl0_334,
inference(avatar_split_clause,[],[f548,f2605]) ).
fof(f2605,plain,
( spl0_334
<=> ! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f548,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).
fof(f2603,plain,
spl0_333,
inference(avatar_split_clause,[],[f538,f2601]) ).
fof(f538,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
fof(f2599,plain,
spl0_332,
inference(avatar_split_clause,[],[f512,f2597]) ).
fof(f512,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).
fof(f2595,plain,
spl0_331,
inference(avatar_split_clause,[],[f509,f2593]) ).
fof(f509,axiom,
! [X0,X23] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X23,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).
fof(f2591,plain,
( spl0_330
| ~ spl0_85
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2215,f2045,f1363,f2589]) ).
fof(f2215,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_85
| ~ spl0_234 ),
inference(resolution,[],[f2046,f1365]) ).
fof(f2587,plain,
spl0_329,
inference(avatar_split_clause,[],[f508,f2585]) ).
fof(f508,axiom,
! [X0,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I1_J_0) ).
fof(f2583,plain,
spl0_328,
inference(avatar_split_clause,[],[f471,f2581]) ).
fof(f2581,plain,
( spl0_328
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f471,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
fof(f2579,plain,
spl0_327,
inference(avatar_split_clause,[],[f470,f2577]) ).
fof(f470,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X4,X3,X0) = c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
fof(f2575,plain,
spl0_326,
inference(avatar_split_clause,[],[f444,f2573]) ).
fof(f2573,plain,
( spl0_326
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f444,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).
fof(f2571,plain,
spl0_325,
inference(avatar_split_clause,[],[f443,f2569]) ).
fof(f443,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).
fof(f2567,plain,
spl0_324,
inference(avatar_split_clause,[],[f442,f2565]) ).
fof(f442,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).
fof(f2563,plain,
spl0_323,
inference(avatar_split_clause,[],[f439,f2561]) ).
fof(f2561,plain,
( spl0_323
<=> ! [X4,X0,X3] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f439,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
fof(f2559,plain,
spl0_322,
inference(avatar_split_clause,[],[f438,f2557]) ).
fof(f438,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X4,X0) = c_Lattices_Olower__semilattice__class_Oinf(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
fof(f2555,plain,
spl0_321,
inference(avatar_split_clause,[],[f382,f2553]) ).
fof(f382,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f2551,plain,
spl0_320,
inference(avatar_split_clause,[],[f380,f2549]) ).
fof(f380,axiom,
! [X0,X1,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X9,X0) = c_HOL_Oplus__class_Oplus(X9,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f2547,plain,
( spl0_319
| ~ spl0_135
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2214,f2045,f1613,f2545]) ).
fof(f2214,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_135
| ~ spl0_234 ),
inference(resolution,[],[f2046,f1615]) ).
fof(f2543,plain,
spl0_318,
inference(avatar_split_clause,[],[f368,f2541]) ).
fof(f368,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).
fof(f2539,plain,
spl0_317,
inference(avatar_split_clause,[],[f354,f2537]) ).
fof(f354,axiom,
! [X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Oone__class_Oone(X0) = c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__zero_0) ).
fof(f2535,plain,
spl0_316,
inference(avatar_split_clause,[],[f302,f2533]) ).
fof(f302,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f2531,plain,
spl0_315,
inference(avatar_split_clause,[],[f293,f2529]) ).
fof(f293,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).
fof(f2527,plain,
spl0_314,
inference(avatar_split_clause,[],[f292,f2525]) ).
fof(f292,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,X2,X0),X2,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).
fof(f2523,plain,
spl0_313,
inference(avatar_split_clause,[],[f271,f2521]) ).
fof(f271,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Oinverse(X1,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).
fof(f2519,plain,
spl0_312,
inference(avatar_split_clause,[],[f270,f2517]) ).
fof(f270,axiom,
! [X0,X8] :
( ~ class_HOL_Ozero(X0)
| c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).
fof(f2515,plain,
spl0_311,
inference(avatar_split_clause,[],[f217,f2513]) ).
fof(f217,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Oabs__class_Oabs(X1,X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).
fof(f2511,plain,
spl0_310,
inference(avatar_split_clause,[],[f191,f2509]) ).
fof(f191,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).
fof(f2507,plain,
spl0_309,
inference(avatar_split_clause,[],[f162,f2505]) ).
fof(f162,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Osgn__class_Osgn(X1,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).
fof(f2503,plain,
( spl0_308
| ~ spl0_27
| ~ spl0_234 ),
inference(avatar_split_clause,[],[f2212,f2045,f1073,f2501]) ).
fof(f2212,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
| ~ spl0_27
| ~ spl0_234 ),
inference(resolution,[],[f2046,f1075]) ).
fof(f2499,plain,
spl0_307,
inference(avatar_split_clause,[],[f140,f2497]) ).
fof(f140,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).
fof(f2495,plain,
spl0_306,
inference(avatar_split_clause,[],[f103,f2493]) ).
fof(f103,axiom,
! [X3,X0,X4] :
( ~ class_Lattices_Olattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,c_Lattices_Oupper__semilattice__class_Osup(X3,X4,X0),X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
fof(f2477,plain,
( spl0_305
| ~ spl0_143
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2211,f2041,f1653,f2475]) ).
fof(f2475,plain,
( spl0_305
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2041,plain,
( spl0_233
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f2211,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
| ~ spl0_143
| ~ spl0_233 ),
inference(resolution,[],[f2042,f1655]) ).
fof(f2042,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 )
| ~ spl0_233 ),
inference(avatar_component_clause,[],[f2041]) ).
fof(f2443,plain,
( spl0_304
| ~ spl0_96
| ~ spl0_233 ),
inference(avatar_split_clause,[],[f2210,f2041,f1418,f2441]) ).
fof(f2441,plain,
( spl0_304
<=> ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2210,plain,
( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
| ~ spl0_96
| ~ spl0_233 ),
inference(resolution,[],[f2042,f1420]) ).
fof(f2423,plain,
spl0_303,
inference(avatar_split_clause,[],[f697,f2421]) ).
fof(f697,axiom,
! [X3,X0] :
( ~ class_SEQ_Obanach(X0)
| ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).
fof(f2419,plain,
spl0_302,
inference(avatar_split_clause,[],[f694,f2417]) ).
fof(f2417,plain,
( spl0_302
<=> ! [X4,X0] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f694,axiom,
! [X0,X4] :
( ~ class_RealVector_Oreal__normed__field(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).
fof(f2415,plain,
( spl0_301
| ~ spl0_62
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2209,f2037,f1248,f2413]) ).
fof(f2413,plain,
( spl0_301
<=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2209,plain,
( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
| ~ spl0_62
| ~ spl0_232 ),
inference(resolution,[],[f2038,f1250]) ).
fof(f2411,plain,
spl0_300,
inference(avatar_split_clause,[],[f691,f2409]) ).
fof(f691,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).
fof(f2407,plain,
spl0_299,
inference(avatar_split_clause,[],[f687,f2405]) ).
fof(f2405,plain,
( spl0_299
<=> ! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f687,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).
fof(f2403,plain,
spl0_298,
inference(avatar_split_clause,[],[f686,f2401]) ).
fof(f686,axiom,
! [X0,X1] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).
fof(f2399,plain,
spl0_297,
inference(avatar_split_clause,[],[f682,f2397]) ).
fof(f682,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).
fof(f2395,plain,
spl0_296,
inference(avatar_split_clause,[],[f673,f2393]) ).
fof(f673,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__0_0) ).
fof(f2391,plain,
spl0_295,
inference(avatar_split_clause,[],[f672,f2389]) ).
fof(f672,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Odiv(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__0_0) ).
fof(f2387,plain,
spl0_294,
inference(avatar_split_clause,[],[f651,f2385]) ).
fof(f651,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f2383,plain,
spl0_293,
inference(avatar_split_clause,[],[f650,f2381]) ).
fof(f2381,plain,
( spl0_293
<=> ! [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_293])]) ).
fof(f650,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__left_Ozero_0) ).
fof(f2379,plain,
spl0_292,
inference(avatar_split_clause,[],[f647,f2377]) ).
fof(f2377,plain,
( spl0_292
<=> ! [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_292])]) ).
fof(f647,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__right_Ozero_0) ).
fof(f2375,plain,
spl0_291,
inference(avatar_split_clause,[],[f646,f2373]) ).
fof(f646,axiom,
! [X3,X0] :
( ~ 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),X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f2371,plain,
( spl0_290
| ~ spl0_117
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2208,f2037,f1523,f2369]) ).
fof(f2369,plain,
( spl0_290
<=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2208,plain,
( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
| ~ spl0_117
| ~ spl0_232 ),
inference(resolution,[],[f2038,f1525]) ).
fof(f2367,plain,
spl0_289,
inference(avatar_split_clause,[],[f645,f2365]) ).
fof(f645,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(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_mult__zero__left_0) ).
fof(f2363,plain,
spl0_288,
inference(avatar_split_clause,[],[f644,f2361]) ).
fof(f644,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f2359,plain,
spl0_287,
inference(avatar_split_clause,[],[f643,f2357]) ).
fof(f643,axiom,
! [X2,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),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f2355,plain,
spl0_286,
inference(avatar_split_clause,[],[f642,f2353]) ).
fof(f642,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).
fof(f2351,plain,
spl0_285,
inference(avatar_split_clause,[],[f635,f2349]) ).
fof(f635,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(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_xt1_I9_J_0) ).
fof(f2347,plain,
spl0_284,
inference(avatar_split_clause,[],[f634,f2345]) ).
fof(f634,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Olinorder(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_not__less__iff__gr__or__eq_1) ).
fof(f2343,plain,
spl0_283,
inference(avatar_split_clause,[],[f633,f2341]) ).
fof(f633,axiom,
! [X3,X0,X4] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,X0)
| ~ c_HOL_Oord__class_Oless(X4,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f2339,plain,
spl0_282,
inference(avatar_split_clause,[],[f590,f2337]) ).
fof(f590,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).
fof(f2335,plain,
spl0_281,
inference(avatar_split_clause,[],[f430,f2333]) ).
fof(f430,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).
fof(f2331,plain,
spl0_280,
inference(avatar_split_clause,[],[f338,f2329]) ).
fof(f338,axiom,
! [X0,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f2327,plain,
( spl0_279
| ~ spl0_14
| ~ spl0_232 ),
inference(avatar_split_clause,[],[f2206,f2037,f1008,f2325]) ).
fof(f2325,plain,
( spl0_279
<=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2206,plain,
( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
| ~ spl0_14
| ~ spl0_232 ),
inference(resolution,[],[f2038,f1010]) ).
fof(f2323,plain,
spl0_278,
inference(avatar_split_clause,[],[f222,f2321]) ).
fof(f222,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).
fof(f2319,plain,
spl0_277,
inference(avatar_split_clause,[],[f89,f2317]) ).
fof(f89,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oone__class_Oone(X0),X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f2315,plain,
spl0_276,
inference(avatar_split_clause,[],[f82,f2313]) ).
fof(f2313,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f82,axiom,
! [X0,X1] :
( ~ class_Power_Opower(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X1,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).
fof(f2311,plain,
spl0_275,
inference(avatar_split_clause,[],[f81,f2309]) ).
fof(f81,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(X3,c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).
fof(f2288,plain,
( spl0_274
| ~ spl0_76
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f2204,f2029,f1318,f2285]) ).
fof(f2204,plain,
( c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_76
| ~ spl0_230 ),
inference(resolution,[],[f2030,f1320]) ).
fof(f2203,plain,
spl0_273,
inference(avatar_split_clause,[],[f730,f2201]) ).
fof(f2201,plain,
( spl0_273
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X3,tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f730,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X3,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mpoly__base__conv_I1_J_0) ).
fof(f2199,plain,
spl0_272,
inference(avatar_split_clause,[],[f720,f2197]) ).
fof(f720,axiom,
! [X18] :
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X18
| c_Complex_Ocnj(X18) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).
fof(f2195,plain,
spl0_271,
inference(avatar_split_clause,[],[f704,f2193]) ).
fof(f704,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f2191,plain,
spl0_270,
inference(avatar_split_clause,[],[f703,f2189]) ).
fof(f2189,plain,
( spl0_270
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f703,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f2187,plain,
spl0_269,
inference(avatar_split_clause,[],[f702,f2185]) ).
fof(f702,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_Oadd__0_0) ).
fof(f2183,plain,
( spl0_268
| ~ spl0_79
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2027,f2009,f1333,f2181]) ).
fof(f2181,plain,
( spl0_268
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2009,plain,
( spl0_228
<=> ! [X0,X3] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f2027,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_79
| ~ spl0_228 ),
inference(resolution,[],[f2010,f1335]) ).
fof(f2010,plain,
( ! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f2009]) ).
fof(f2179,plain,
spl0_267,
inference(avatar_split_clause,[],[f700,f2177]) ).
fof(f2177,plain,
( spl0_267
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f700,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f2175,plain,
spl0_266,
inference(avatar_split_clause,[],[f699,f2173]) ).
fof(f699,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f2171,plain,
spl0_265,
inference(avatar_split_clause,[],[f698,f2169]) ).
fof(f698,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f2167,plain,
spl0_264,
inference(avatar_split_clause,[],[f684,f2165]) ).
fof(f684,axiom,
! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).
fof(f2163,plain,
spl0_263,
inference(avatar_split_clause,[],[f681,f2161]) ).
fof(f681,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pprt__0_0) ).
fof(f2159,plain,
spl0_262,
inference(avatar_split_clause,[],[f677,f2157]) ).
fof(f677,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ominus__class_Ominus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).
fof(f2155,plain,
spl0_261,
inference(avatar_split_clause,[],[f676,f2153]) ).
fof(f2153,plain,
( spl0_261
<=> ! [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_261])]) ).
fof(f676,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_right__minus__eq_1) ).
fof(f2151,plain,
spl0_260,
inference(avatar_split_clause,[],[f675,f2149]) ).
fof(f675,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).
fof(f2147,plain,
spl0_259,
inference(avatar_split_clause,[],[f664,f2145]) ).
fof(f664,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nprt__0_0) ).
fof(f2143,plain,
spl0_258,
inference(avatar_split_clause,[],[f661,f2141]) ).
fof(f661,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__by__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).
fof(f2139,plain,
( spl0_257
| ~ spl0_23
| ~ spl0_228 ),
inference(avatar_split_clause,[],[f2026,f2009,f1053,f2137]) ).
fof(f2137,plain,
( spl0_257
<=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2026,plain,
( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
| ~ spl0_23
| ~ spl0_228 ),
inference(resolution,[],[f2010,f1055]) ).
fof(f2135,plain,
spl0_256,
inference(avatar_split_clause,[],[f655,f2133]) ).
fof(f655,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Omod(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).
fof(f2131,plain,
spl0_255,
inference(avatar_split_clause,[],[f654,f2129]) ).
fof(f654,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Divides_Odiv__class_Omod(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).
fof(f2127,plain,
spl0_254,
inference(avatar_split_clause,[],[f641,f2125]) ).
fof(f2125,plain,
( spl0_254
<=> ! [X18,X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(X18,X0)
| c_HOL_Ozero__class_Ozero(X0) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f641,axiom,
! [X0,X18] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(X18,X0)
| c_HOL_Ozero__class_Ozero(X0) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__def_0) ).
fof(f2123,plain,
spl0_253,
inference(avatar_split_clause,[],[f640,f2121]) ).
fof(f640,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__vector(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).
fof(f2119,plain,
spl0_252,
inference(avatar_split_clause,[],[f639,f2117]) ).
fof(f2117,plain,
( spl0_252
<=> ! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f639,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osgn__if(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).
fof(f2115,plain,
spl0_251,
inference(avatar_split_clause,[],[f638,f2113]) ).
fof(f638,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).
fof(f2111,plain,
spl0_250,
inference(avatar_split_clause,[],[f637,f2109]) ).
fof(f637,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_neg__0__equal__iff__equal_1) ).
fof(f2107,plain,
spl0_249,
inference(avatar_split_clause,[],[f558,f2105]) ).
fof(f558,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(X1,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).
fof(f2103,plain,
spl0_248,
inference(avatar_split_clause,[],[f554,f2101]) ).
fof(f2101,plain,
( spl0_248
<=> ! [X4,X0,X3] :
( ~ class_HOL_Oeq(X0)
| X3 = X4
| ~ c_HOL_Oeq__class_Oeq(X3,X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f554,axiom,
! [X3,X0,X4] :
( ~ class_HOL_Oeq(X0)
| X3 = X4
| ~ c_HOL_Oeq__class_Oeq(X3,X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equals_0) ).
fof(f2099,plain,
spl0_247,
inference(avatar_split_clause,[],[f550,f2097]) ).
fof(f550,axiom,
! [X0] :
( ~ class_Ring__and__Field_Odivision__ring(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).
fof(f2095,plain,
spl0_246,
inference(avatar_split_clause,[],[f533,f2093]) ).
fof(f533,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(f2091,plain,
spl0_245,
inference(avatar_split_clause,[],[f522,f2089]) ).
fof(f522,axiom,
! [X0,X1] :
( ~ class_Divides_Osemiring__div(X0)
| c_Divides_Odiv__class_Odiv(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_div__by__1_0) ).
fof(f2087,plain,
spl0_244,
inference(avatar_split_clause,[],[f518,f2085]) ).
fof(f518,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ogroup__add(X0)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
fof(f2083,plain,
spl0_243,
inference(avatar_split_clause,[],[f451,f2081]) ).
fof(f451,axiom,
! [X0] :
( ~ class_RealVector_Oreal__normed__algebra__1(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__one_0) ).
fof(f2079,plain,
spl0_242,
inference(avatar_split_clause,[],[f283,f2077]) ).
fof(f283,axiom,
! [X2,X0,X11] :
( ~ class_Ring__and__Field_Odvd(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X2,X11,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).
fof(f2075,plain,
spl0_241,
inference(avatar_split_clause,[],[f282,f2073]) ).
fof(f282,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).
fof(f2071,plain,
spl0_240,
inference(avatar_split_clause,[],[f281,f2069]) ).
fof(f281,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).
fof(f2067,plain,
spl0_239,
inference(avatar_split_clause,[],[f280,f2065]) ).
fof(f2065,plain,
( spl0_239
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f280,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).
fof(f2063,plain,
spl0_238,
inference(avatar_split_clause,[],[f279,f2061]) ).
fof(f2061,plain,
( spl0_238
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f279,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).
fof(f2059,plain,
spl0_237,
inference(avatar_split_clause,[],[f277,f2057]) ).
fof(f2057,plain,
( spl0_237
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f277,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).
fof(f2055,plain,
( spl0_236
| ~ spl0_78
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2013,f1989,f1328,f2053]) ).
fof(f2053,plain,
( spl0_236
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1989,plain,
( spl0_223
<=> ! [X0,X3] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f2013,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0
| ~ spl0_78
| ~ spl0_223 ),
inference(resolution,[],[f1990,f1330]) ).
fof(f1990,plain,
( ! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 )
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f1989]) ).
fof(f2051,plain,
spl0_235,
inference(avatar_split_clause,[],[f276,f2049]) ).
fof(f276,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f2047,plain,
spl0_234,
inference(avatar_split_clause,[],[f275,f2045]) ).
fof(f275,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).
fof(f2043,plain,
spl0_233,
inference(avatar_split_clause,[],[f215,f2041]) ).
fof(f215,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Oinverse__class_Odivide(X1,c_HOL_Oone__class_Oone(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).
fof(f2039,plain,
spl0_232,
inference(avatar_split_clause,[],[f185,f2037]) ).
fof(f185,axiom,
! [X0,X23] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X23,X0) = X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).
fof(f2035,plain,
spl0_231,
inference(avatar_split_clause,[],[f146,f2033]) ).
fof(f2033,plain,
( spl0_231
<=> ! [X0,X3] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,tc_Polynomial_Opoly(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f146,axiom,
! [X3,X0] :
( ~ class_HOL_Oeq(X0)
| ~ class_HOL_Ozero(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,tc_Polynomial_Opoly(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_1) ).
fof(f2031,plain,
spl0_230,
inference(avatar_split_clause,[],[f145,f2029]) ).
fof(f145,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oone__class_Oone(X0) = c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).
fof(f2018,plain,
( spl0_229
| ~ spl0_22
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f2012,f1989,f1048,f2016]) ).
fof(f2016,plain,
( spl0_229
<=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f2012,plain,
( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
| ~ spl0_22
| ~ spl0_223 ),
inference(resolution,[],[f1990,f1050]) ).
fof(f2011,plain,
spl0_228,
inference(avatar_split_clause,[],[f589,f2009]) ).
fof(f589,axiom,
! [X3,X0] :
( ~ class_Lattices_Olower__semilattice(X0)
| c_Lattices_Olower__semilattice__class_Oinf(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
fof(f2007,plain,
spl0_227,
inference(avatar_split_clause,[],[f563,f2005]) ).
fof(f563,axiom,
! [X3,X4] :
( X3 = X4
| c_Complex_Ocnj(X3) != c_Complex_Ocnj(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).
fof(f2003,plain,
spl0_226,
inference(avatar_split_clause,[],[f559,f2001]) ).
fof(f559,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f1999,plain,
spl0_225,
inference(avatar_split_clause,[],[f413,f1997]) ).
fof(f413,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f1995,plain,
spl0_224,
inference(avatar_split_clause,[],[f399,f1993]) ).
fof(f1993,plain,
( spl0_224
<=> ! [X29,X32] :
( X29 = X32
| c_Suc(X29) != c_Suc(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f399,axiom,
! [X29,X32] :
( X29 = X32
| c_Suc(X29) != c_Suc(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
fof(f1991,plain,
spl0_223,
inference(avatar_split_clause,[],[f308,f1989]) ).
fof(f308,axiom,
! [X3,X0] :
( ~ class_Lattices_Oupper__semilattice(X0)
| c_Lattices_Oupper__semilattice__class_Osup(X3,X3,X0) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
fof(f1987,plain,
spl0_222,
inference(avatar_split_clause,[],[f938,f1985]) ).
fof(f1985,plain,
( spl0_222
<=> ! [X34] :
( ~ class_HOL_Oeq(X34)
| ~ class_HOL_Ozero(X34)
| class_HOL_Oeq(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f938,axiom,
! [X34] :
( ~ class_HOL_Oeq(X34)
| ~ class_HOL_Ozero(X34)
| class_HOL_Oeq(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Oeq) ).
fof(f1983,plain,
spl0_221,
inference(avatar_split_clause,[],[f668,f1981]) ).
fof(f1981,plain,
( spl0_221
<=> ! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f668,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ozero__neq__one(X0)
| c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f1979,plain,
spl0_220,
inference(avatar_split_clause,[],[f653,f1977]) ).
fof(f653,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).
fof(f1975,plain,
spl0_219,
inference(avatar_split_clause,[],[f133,f1973]) ).
fof(f1973,plain,
( spl0_219
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f133,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__pos__poly__0_0) ).
fof(f1971,plain,
spl0_218,
inference(avatar_split_clause,[],[f83,f1969]) ).
fof(f83,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).
fof(f1965,plain,
spl0_217,
inference(avatar_split_clause,[],[f721,f1962]) ).
fof(f1962,plain,
( spl0_217
<=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f721,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cnj_Ozero_0) ).
fof(f1960,plain,
spl0_216,
inference(avatar_split_clause,[],[f613,f1958]) ).
fof(f1958,plain,
( spl0_216
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f613,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| ~ c_Int_Oiszero(c_HOL_Oone__class_Oone(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__iszero__1_0) ).
fof(f1956,plain,
spl0_215,
inference(avatar_split_clause,[],[f537,f1954]) ).
fof(f537,axiom,
! [X3,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f1952,plain,
spl0_214,
inference(avatar_split_clause,[],[f536,f1950]) ).
fof(f536,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f1948,plain,
spl0_213,
inference(avatar_split_clause,[],[f532,f1946]) ).
fof(f1946,plain,
( spl0_213
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f532,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Int_Oiszero(c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_iszero__0_0) ).
fof(f1944,plain,
spl0_212,
inference(avatar_split_clause,[],[f435,f1942]) ).
fof(f435,axiom,
! [X3,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f1940,plain,
spl0_211,
inference(avatar_split_clause,[],[f427,f1937]) ).
fof(f427,axiom,
c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__one_0) ).
fof(f1935,plain,
spl0_210,
inference(avatar_split_clause,[],[f147,f1933]) ).
fof(f1933,plain,
( spl0_210
<=> ! [X0,X3] :
( ~ class_HOL_Oeq(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f147,axiom,
! [X3,X0] :
( ~ class_HOL_Oeq(X0)
| c_HOL_Oeq__class_Oeq(X3,X3,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).
fof(f1931,plain,
spl0_209,
inference(avatar_split_clause,[],[f98,f1929]) ).
fof(f98,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_Ring__and__Field_Odvd__class_Odvd(X1,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).
fof(f1927,plain,
spl0_208,
inference(avatar_split_clause,[],[f937,f1925]) ).
fof(f937,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(f1923,plain,
spl0_207,
inference(avatar_split_clause,[],[f936,f1921]) ).
fof(f936,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Power_Opower(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).
fof(f1919,plain,
spl0_206,
inference(avatar_split_clause,[],[f935,f1917]) ).
fof(f935,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(f1915,plain,
spl0_205,
inference(avatar_split_clause,[],[f934,f1913]) ).
fof(f1913,plain,
( spl0_205
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Oorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f934,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(f1911,plain,
spl0_204,
inference(avatar_split_clause,[],[f933,f1909]) ).
fof(f1909,plain,
( spl0_204
<=> ! [X34] :
( ~ class_Ring__and__Field_Ofield(X34)
| class_Divides_Oring__div(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f933,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(f1907,plain,
spl0_203,
inference(avatar_split_clause,[],[f932,f1905]) ).
fof(f1905,plain,
( spl0_203
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Olinorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f932,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(f1903,plain,
spl0_202,
inference(avatar_split_clause,[],[f931,f1901]) ).
fof(f1901,plain,
( spl0_202
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Orderings_Opreorder(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f931,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(f1899,plain,
spl0_201,
inference(avatar_split_clause,[],[f930,f1897]) ).
fof(f1897,plain,
( spl0_201
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f930,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).
fof(f1895,plain,
spl0_200,
inference(avatar_split_clause,[],[f929,f1893]) ).
fof(f929,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(f1891,plain,
spl0_199,
inference(avatar_split_clause,[],[f928,f1889]) ).
fof(f1889,plain,
( spl0_199
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring(X34)
| class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f928,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(f1887,plain,
spl0_198,
inference(avatar_split_clause,[],[f927,f1885]) ).
fof(f927,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(f1883,plain,
spl0_197,
inference(avatar_split_clause,[],[f926,f1881]) ).
fof(f1881,plain,
( spl0_197
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f926,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).
fof(f1879,plain,
spl0_196,
inference(avatar_split_clause,[],[f925,f1877]) ).
fof(f1877,plain,
( spl0_196
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f925,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X34)
| class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1) ).
fof(f1875,plain,
spl0_195,
inference(avatar_split_clause,[],[f924,f1873]) ).
fof(f1873,plain,
( spl0_195
<=> ! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f924,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).
fof(f1871,plain,
spl0_194,
inference(avatar_split_clause,[],[f923,f1869]) ).
fof(f923,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(f1867,plain,
spl0_193,
inference(avatar_split_clause,[],[f922,f1865]) ).
fof(f1865,plain,
( spl0_193
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f922,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(f1863,plain,
spl0_192,
inference(avatar_split_clause,[],[f921,f1861]) ).
fof(f1861,plain,
( spl0_192
<=> ! [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_192])]) ).
fof(f921,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(f1859,plain,
spl0_191,
inference(avatar_split_clause,[],[f920,f1857]) ).
fof(f920,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).
fof(f1855,plain,
spl0_190,
inference(avatar_split_clause,[],[f919,f1853]) ).
fof(f1853,plain,
( spl0_190
<=> ! [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_190])]) ).
fof(f919,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(f1851,plain,
spl0_189,
inference(avatar_split_clause,[],[f918,f1849]) ).
fof(f918,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(f1847,plain,
spl0_188,
inference(avatar_split_clause,[],[f917,f1845]) ).
fof(f917,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(f1843,plain,
spl0_187,
inference(avatar_split_clause,[],[f916,f1841]) ).
fof(f1841,plain,
( spl0_187
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f916,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X34)
| class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0) ).
fof(f1839,plain,
spl0_186,
inference(avatar_split_clause,[],[f915,f1837]) ).
fof(f1837,plain,
( spl0_186
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f915,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1) ).
fof(f1835,plain,
spl0_185,
inference(avatar_split_clause,[],[f914,f1833]) ).
fof(f1833,plain,
( spl0_185
<=> ! [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_185])]) ).
fof(f914,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(f1831,plain,
spl0_184,
inference(avatar_split_clause,[],[f913,f1829]) ).
fof(f913,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(f1827,plain,
spl0_183,
inference(avatar_split_clause,[],[f912,f1825]) ).
fof(f1825,plain,
( spl0_183
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f912,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).
fof(f1823,plain,
spl0_182,
inference(avatar_split_clause,[],[f911,f1821]) ).
fof(f911,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(f1819,plain,
spl0_181,
inference(avatar_split_clause,[],[f910,f1817]) ).
fof(f1817,plain,
( spl0_181
<=> ! [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_181])]) ).
fof(f910,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(f1815,plain,
spl0_180,
inference(avatar_split_clause,[],[f909,f1813]) ).
fof(f1813,plain,
( spl0_180
<=> ! [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_180])]) ).
fof(f909,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(f1811,plain,
spl0_179,
inference(avatar_split_clause,[],[f908,f1809]) ).
fof(f1809,plain,
( spl0_179
<=> ! [X34] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X34)
| class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f908,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(f1807,plain,
spl0_178,
inference(avatar_split_clause,[],[f907,f1805]) ).
fof(f1805,plain,
( spl0_178
<=> ! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f907,axiom,
! [X34] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X34)
| class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1803,plain,
spl0_177,
inference(avatar_split_clause,[],[f906,f1801]) ).
fof(f1801,plain,
( spl0_177
<=> ! [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_177])]) ).
fof(f906,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(f1799,plain,
spl0_176,
inference(avatar_split_clause,[],[f905,f1797]) ).
fof(f905,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(f1795,plain,
spl0_175,
inference(avatar_split_clause,[],[f904,f1793]) ).
fof(f904,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(f1791,plain,
spl0_174,
inference(avatar_split_clause,[],[f903,f1789]) ).
fof(f1789,plain,
( spl0_174
<=> ! [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_174])]) ).
fof(f903,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(f1787,plain,
spl0_173,
inference(avatar_split_clause,[],[f902,f1785]) ).
fof(f1785,plain,
( spl0_173
<=> ! [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_173])]) ).
fof(f902,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(f1783,plain,
spl0_172,
inference(avatar_split_clause,[],[f901,f1781]) ).
fof(f1781,plain,
( spl0_172
<=> ! [X34] :
( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X34)
| class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f901,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(f1779,plain,
spl0_171,
inference(avatar_split_clause,[],[f900,f1777]) ).
fof(f900,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(f1775,plain,
spl0_170,
inference(avatar_split_clause,[],[f899,f1773]) ).
fof(f1773,plain,
( spl0_170
<=> ! [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_170])]) ).
fof(f899,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(f1771,plain,
spl0_169,
inference(avatar_split_clause,[],[f898,f1769]) ).
fof(f1769,plain,
( spl0_169
<=> ! [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_169])]) ).
fof(f898,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(f1767,plain,
spl0_168,
inference(avatar_split_clause,[],[f897,f1765]) ).
fof(f1765,plain,
( spl0_168
<=> ! [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_168])]) ).
fof(f897,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(f1763,plain,
spl0_167,
inference(avatar_split_clause,[],[f896,f1761]) ).
fof(f896,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(f1759,plain,
spl0_166,
inference(avatar_split_clause,[],[f895,f1757]) ).
fof(f1757,plain,
( spl0_166
<=> ! [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_166])]) ).
fof(f895,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(f1755,plain,
spl0_165,
inference(avatar_split_clause,[],[f894,f1753]) ).
fof(f894,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oordered__idom(X34)
| class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1751,plain,
spl0_164,
inference(avatar_split_clause,[],[f893,f1749]) ).
fof(f1749,plain,
( spl0_164
<=> ! [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_164])]) ).
fof(f893,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(f1747,plain,
spl0_163,
inference(avatar_split_clause,[],[f892,f1745]) ).
fof(f1745,plain,
( spl0_163
<=> ! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f892,axiom,
! [X34] :
( ~ class_Ring__and__Field_Oidom(X34)
| class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1743,plain,
spl0_162,
inference(avatar_split_clause,[],[f891,f1741]) ).
fof(f1741,plain,
( spl0_162
<=> ! [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_162])]) ).
fof(f891,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(f1739,plain,
spl0_161,
inference(avatar_split_clause,[],[f890,f1737]) ).
fof(f1737,plain,
( spl0_161
<=> ! [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_161])]) ).
fof(f890,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(f1735,plain,
spl0_160,
inference(avatar_split_clause,[],[f889,f1733]) ).
fof(f1733,plain,
( spl0_160
<=> ! [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_160])]) ).
fof(f889,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(f1731,plain,
spl0_159,
inference(avatar_split_clause,[],[f738,f1729]) ).
fof(f1729,plain,
( spl0_159
<=> ! [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_159])]) ).
fof(f738,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(f1727,plain,
spl0_158,
inference(avatar_split_clause,[],[f511,f1725]) ).
fof(f1725,plain,
( spl0_158
<=> ! [X0,X3] : c_Fun_Oid(X3,X0) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f511,axiom,
! [X3,X0] : c_Fun_Oid(X3,X0) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f1723,plain,
spl0_157,
inference(avatar_split_clause,[],[f375,f1721]) ).
fof(f375,axiom,
! [X18] : c_Complex_Ocnj(c_Complex_Ocnj(X18)) = X18,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).
fof(f1719,plain,
spl0_156,
inference(avatar_split_clause,[],[f267,f1717]) ).
fof(f1717,plain,
( spl0_156
<=> ! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f267,axiom,
! [X27] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X27),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f1715,plain,
~ spl0_155,
inference(avatar_split_clause,[],[f719,f1712]) ).
fof(f1712,plain,
( spl0_155
<=> c_Complex_Oii = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f719,axiom,
c_Complex_Oii != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__zero_0) ).
fof(f1710,plain,
~ spl0_154,
inference(avatar_split_clause,[],[f379,f1707]) ).
fof(f1707,plain,
( spl0_154
<=> c_Complex_Oii = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f379,axiom,
c_Complex_Oii != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__i__not__one_0) ).
fof(f1705,plain,
spl0_153,
inference(avatar_split_clause,[],[f52,f1703]) ).
fof(f1703,plain,
( spl0_153
<=> ! [X8] : c_Suc(X8) != X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f52,axiom,
! [X8] : c_Suc(X8) != X8,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f1701,plain,
~ spl0_152,
inference(avatar_split_clause,[],[f737,f1698]) ).
fof(f737,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1696,plain,
spl0_151,
inference(avatar_split_clause,[],[f888,f1693]) ).
fof(f1693,plain,
( spl0_151
<=> class_HOL_Oeq(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f888,axiom,
class_HOL_Oeq(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Oeq) ).
fof(f1691,plain,
spl0_150,
inference(avatar_split_clause,[],[f887,f1688]) ).
fof(f887,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).
fof(f1686,plain,
spl0_149,
inference(avatar_split_clause,[],[f886,f1683]) ).
fof(f886,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).
fof(f1681,plain,
spl0_148,
inference(avatar_split_clause,[],[f885,f1678]) ).
fof(f885,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).
fof(f1676,plain,
spl0_147,
inference(avatar_split_clause,[],[f884,f1673]) ).
fof(f884,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f1671,plain,
spl0_146,
inference(avatar_split_clause,[],[f883,f1668]) ).
fof(f883,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).
fof(f1666,plain,
spl0_145,
inference(avatar_split_clause,[],[f882,f1663]) ).
fof(f882,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).
fof(f1661,plain,
spl0_144,
inference(avatar_split_clause,[],[f881,f1658]) ).
fof(f881,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).
fof(f1656,plain,
spl0_143,
inference(avatar_split_clause,[],[f880,f1653]) ).
fof(f880,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1651,plain,
spl0_142,
inference(avatar_split_clause,[],[f879,f1648]) ).
fof(f1648,plain,
( spl0_142
<=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f879,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).
fof(f1646,plain,
spl0_141,
inference(avatar_split_clause,[],[f878,f1643]) ).
fof(f1643,plain,
( spl0_141
<=> class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f878,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).
fof(f1641,plain,
spl0_140,
inference(avatar_split_clause,[],[f877,f1638]) ).
fof(f877,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).
fof(f1636,plain,
spl0_139,
inference(avatar_split_clause,[],[f876,f1633]) ).
fof(f876,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).
fof(f1631,plain,
spl0_138,
inference(avatar_split_clause,[],[f875,f1628]) ).
fof(f875,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).
fof(f1626,plain,
spl0_137,
inference(avatar_split_clause,[],[f874,f1623]) ).
fof(f1623,plain,
( spl0_137
<=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f874,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).
fof(f1621,plain,
spl0_136,
inference(avatar_split_clause,[],[f873,f1618]) ).
fof(f1618,plain,
( spl0_136
<=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f873,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).
fof(f1616,plain,
spl0_135,
inference(avatar_split_clause,[],[f872,f1613]) ).
fof(f872,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1611,plain,
spl0_134,
inference(avatar_split_clause,[],[f871,f1608]) ).
fof(f1608,plain,
( spl0_134
<=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f871,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(f1606,plain,
spl0_133,
inference(avatar_split_clause,[],[f870,f1603]) ).
fof(f1603,plain,
( spl0_133
<=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f870,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(f1601,plain,
spl0_132,
inference(avatar_split_clause,[],[f869,f1598]) ).
fof(f869,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).
fof(f1596,plain,
spl0_131,
inference(avatar_split_clause,[],[f868,f1593]) ).
fof(f868,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).
fof(f1591,plain,
spl0_130,
inference(avatar_split_clause,[],[f867,f1588]) ).
fof(f1588,plain,
( spl0_130
<=> class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f867,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).
fof(f1586,plain,
spl0_129,
inference(avatar_split_clause,[],[f866,f1583]) ).
fof(f1583,plain,
( spl0_129
<=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f866,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(f1581,plain,
spl0_128,
inference(avatar_split_clause,[],[f865,f1578]) ).
fof(f1578,plain,
( spl0_128
<=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f865,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1576,plain,
spl0_127,
inference(avatar_split_clause,[],[f864,f1573]) ).
fof(f864,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).
fof(f1571,plain,
spl0_126,
inference(avatar_split_clause,[],[f863,f1568]) ).
fof(f863,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).
fof(f1566,plain,
spl0_125,
inference(avatar_split_clause,[],[f862,f1563]) ).
fof(f1563,plain,
( spl0_125
<=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f862,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(f1561,plain,
spl0_124,
inference(avatar_split_clause,[],[f861,f1558]) ).
fof(f861,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).
fof(f1556,plain,
spl0_123,
inference(avatar_split_clause,[],[f860,f1553]) ).
fof(f1553,plain,
( spl0_123
<=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f860,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).
fof(f1551,plain,
spl0_122,
inference(avatar_split_clause,[],[f859,f1548]) ).
fof(f1548,plain,
( spl0_122
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f859,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1546,plain,
spl0_121,
inference(avatar_split_clause,[],[f858,f1543]) ).
fof(f858,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f1541,plain,
spl0_120,
inference(avatar_split_clause,[],[f857,f1538]) ).
fof(f857,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).
fof(f1536,plain,
spl0_119,
inference(avatar_split_clause,[],[f856,f1533]) ).
fof(f856,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f1531,plain,
spl0_118,
inference(avatar_split_clause,[],[f855,f1528]) ).
fof(f855,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(f1526,plain,
spl0_117,
inference(avatar_split_clause,[],[f854,f1523]) ).
fof(f854,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(f1521,plain,
spl0_116,
inference(avatar_split_clause,[],[f853,f1518]) ).
fof(f853,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1516,plain,
spl0_115,
inference(avatar_split_clause,[],[f852,f1513]) ).
fof(f1513,plain,
( spl0_115
<=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f852,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(f1511,plain,
spl0_114,
inference(avatar_split_clause,[],[f851,f1508]) ).
fof(f851,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f1506,plain,
spl0_113,
inference(avatar_split_clause,[],[f850,f1503]) ).
fof(f1503,plain,
( spl0_113
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f850,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1501,plain,
spl0_112,
inference(avatar_split_clause,[],[f849,f1498]) ).
fof(f849,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f1496,plain,
spl0_111,
inference(avatar_split_clause,[],[f848,f1493]) ).
fof(f1493,plain,
( spl0_111
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f848,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(f1491,plain,
spl0_110,
inference(avatar_split_clause,[],[f847,f1488]) ).
fof(f847,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(f1486,plain,
spl0_109,
inference(avatar_split_clause,[],[f846,f1483]) ).
fof(f1483,plain,
( spl0_109
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f846,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1481,plain,
spl0_108,
inference(avatar_split_clause,[],[f845,f1478]) ).
fof(f1478,plain,
( spl0_108
<=> class_HOL_Oeq(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f845,axiom,
class_HOL_Oeq(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oeq) ).
fof(f1476,plain,
spl0_107,
inference(avatar_split_clause,[],[f844,f1473]) ).
fof(f844,axiom,
class_HOL_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).
fof(f1471,plain,
spl0_106,
inference(avatar_split_clause,[],[f843,f1468]) ).
fof(f843,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).
fof(f1466,plain,
spl0_105,
inference(avatar_split_clause,[],[f842,f1463]) ).
fof(f842,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).
fof(f1461,plain,
spl0_104,
inference(avatar_split_clause,[],[f841,f1458]) ).
fof(f841,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f1456,plain,
spl0_103,
inference(avatar_split_clause,[],[f840,f1453]) ).
fof(f1453,plain,
( spl0_103
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f840,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).
fof(f1451,plain,
spl0_102,
inference(avatar_split_clause,[],[f839,f1448]) ).
fof(f839,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).
fof(f1446,plain,
spl0_101,
inference(avatar_split_clause,[],[f838,f1443]) ).
fof(f1443,plain,
( spl0_101
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f838,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f1441,plain,
spl0_100,
inference(avatar_split_clause,[],[f837,f1438]) ).
fof(f1438,plain,
( spl0_100
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f837,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f1436,plain,
spl0_99,
inference(avatar_split_clause,[],[f836,f1433]) ).
fof(f836,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).
fof(f1431,plain,
spl0_98,
inference(avatar_split_clause,[],[f835,f1428]) ).
fof(f835,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).
fof(f1426,plain,
spl0_97,
inference(avatar_split_clause,[],[f834,f1423]) ).
fof(f834,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).
fof(f1421,plain,
spl0_96,
inference(avatar_split_clause,[],[f833,f1418]) ).
fof(f833,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).
fof(f1416,plain,
spl0_95,
inference(avatar_split_clause,[],[f832,f1413]) ).
fof(f1413,plain,
( spl0_95
<=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f832,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).
fof(f1411,plain,
spl0_94,
inference(avatar_split_clause,[],[f831,f1408]) ).
fof(f1408,plain,
( spl0_94
<=> class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f831,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).
fof(f1406,plain,
spl0_93,
inference(avatar_split_clause,[],[f830,f1403]) ).
fof(f1403,plain,
( spl0_93
<=> class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f830,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).
fof(f1401,plain,
spl0_92,
inference(avatar_split_clause,[],[f829,f1398]) ).
fof(f1398,plain,
( spl0_92
<=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f829,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).
fof(f1396,plain,
spl0_91,
inference(avatar_split_clause,[],[f828,f1393]) ).
fof(f828,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).
fof(f1391,plain,
spl0_90,
inference(avatar_split_clause,[],[f827,f1388]) ).
fof(f827,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).
fof(f1386,plain,
spl0_89,
inference(avatar_split_clause,[],[f826,f1383]) ).
fof(f826,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).
fof(f1381,plain,
spl0_88,
inference(avatar_split_clause,[],[f825,f1378]) ).
fof(f1378,plain,
( spl0_88
<=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f825,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).
fof(f1376,plain,
spl0_87,
inference(avatar_split_clause,[],[f824,f1373]) ).
fof(f1373,plain,
( spl0_87
<=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f824,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).
fof(f1371,plain,
spl0_86,
inference(avatar_split_clause,[],[f823,f1368]) ).
fof(f823,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).
fof(f1366,plain,
spl0_85,
inference(avatar_split_clause,[],[f822,f1363]) ).
fof(f822,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).
fof(f1361,plain,
spl0_84,
inference(avatar_split_clause,[],[f821,f1358]) ).
fof(f1358,plain,
( spl0_84
<=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f821,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring) ).
fof(f1356,plain,
spl0_83,
inference(avatar_split_clause,[],[f820,f1353]) ).
fof(f1353,plain,
( spl0_83
<=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f820,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).
fof(f1351,plain,
spl0_82,
inference(avatar_split_clause,[],[f819,f1348]) ).
fof(f819,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).
fof(f1346,plain,
spl0_81,
inference(avatar_split_clause,[],[f818,f1343]) ).
fof(f818,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0) ).
fof(f1341,plain,
spl0_80,
inference(avatar_split_clause,[],[f817,f1338]) ).
fof(f1338,plain,
( spl0_80
<=> class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f817,axiom,
class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1) ).
fof(f1336,plain,
spl0_79,
inference(avatar_split_clause,[],[f816,f1333]) ).
fof(f816,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).
fof(f1331,plain,
spl0_78,
inference(avatar_split_clause,[],[f815,f1328]) ).
fof(f815,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).
fof(f1326,plain,
spl0_77,
inference(avatar_split_clause,[],[f814,f1323]) ).
fof(f1323,plain,
( spl0_77
<=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f814,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).
fof(f1321,plain,
spl0_76,
inference(avatar_split_clause,[],[f813,f1318]) ).
fof(f813,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).
fof(f1316,plain,
spl0_75,
inference(avatar_split_clause,[],[f812,f1313]) ).
fof(f1313,plain,
( spl0_75
<=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f812,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).
fof(f1311,plain,
spl0_74,
inference(avatar_split_clause,[],[f811,f1308]) ).
fof(f811,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).
fof(f1306,plain,
spl0_73,
inference(avatar_split_clause,[],[f810,f1303]) ).
fof(f810,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).
fof(f1301,plain,
spl0_72,
inference(avatar_split_clause,[],[f809,f1298]) ).
fof(f1298,plain,
( spl0_72
<=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f809,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).
fof(f1296,plain,
spl0_71,
inference(avatar_split_clause,[],[f808,f1293]) ).
fof(f808,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).
fof(f1291,plain,
spl0_70,
inference(avatar_split_clause,[],[f807,f1288]) ).
fof(f807,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).
fof(f1286,plain,
spl0_69,
inference(avatar_split_clause,[],[f806,f1283]) ).
fof(f1283,plain,
( spl0_69
<=> class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f806,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).
fof(f1281,plain,
spl0_68,
inference(avatar_split_clause,[],[f805,f1278]) ).
fof(f1278,plain,
( spl0_68
<=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f805,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).
fof(f1276,plain,
spl0_67,
inference(avatar_split_clause,[],[f804,f1273]) ).
fof(f1273,plain,
( spl0_67
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f804,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1271,plain,
spl0_66,
inference(avatar_split_clause,[],[f803,f1268]) ).
fof(f803,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f1266,plain,
spl0_65,
inference(avatar_split_clause,[],[f802,f1263]) ).
fof(f802,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).
fof(f1261,plain,
spl0_64,
inference(avatar_split_clause,[],[f801,f1258]) ).
fof(f801,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f1256,plain,
spl0_63,
inference(avatar_split_clause,[],[f800,f1253]) ).
fof(f800,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1251,plain,
spl0_62,
inference(avatar_split_clause,[],[f799,f1248]) ).
fof(f799,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1246,plain,
spl0_61,
inference(avatar_split_clause,[],[f798,f1243]) ).
fof(f1243,plain,
( spl0_61
<=> class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f798,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).
fof(f1241,plain,
spl0_60,
inference(avatar_split_clause,[],[f797,f1238]) ).
fof(f797,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).
fof(f1236,plain,
spl0_59,
inference(avatar_split_clause,[],[f796,f1233]) ).
fof(f1233,plain,
( spl0_59
<=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f796,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).
fof(f1231,plain,
spl0_58,
inference(avatar_split_clause,[],[f795,f1228]) ).
fof(f795,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f1226,plain,
spl0_57,
inference(avatar_split_clause,[],[f794,f1223]) ).
fof(f1223,plain,
( spl0_57
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f794,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).
fof(f1221,plain,
spl0_56,
inference(avatar_split_clause,[],[f793,f1218]) ).
fof(f793,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).
fof(f1216,plain,
spl0_55,
inference(avatar_split_clause,[],[f792,f1213]) ).
fof(f792,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).
fof(f1211,plain,
spl0_54,
inference(avatar_split_clause,[],[f791,f1208]) ).
fof(f1208,plain,
( spl0_54
<=> class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f791,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).
fof(f1206,plain,
spl0_53,
inference(avatar_split_clause,[],[f790,f1203]) ).
fof(f790,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f1201,plain,
spl0_52,
inference(avatar_split_clause,[],[f789,f1198]) ).
fof(f1198,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f789,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).
fof(f1196,plain,
spl0_51,
inference(avatar_split_clause,[],[f788,f1193]) ).
fof(f1193,plain,
( spl0_51
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f788,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f1191,plain,
spl0_50,
inference(avatar_split_clause,[],[f787,f1188]) ).
fof(f787,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1186,plain,
spl0_49,
inference(avatar_split_clause,[],[f786,f1183]) ).
fof(f1183,plain,
( spl0_49
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f786,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f1181,plain,
spl0_48,
inference(avatar_split_clause,[],[f785,f1178]) ).
fof(f785,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).
fof(f1176,plain,
spl0_47,
inference(avatar_split_clause,[],[f784,f1173]) ).
fof(f784,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).
fof(f1171,plain,
spl0_46,
inference(avatar_split_clause,[],[f783,f1168]) ).
fof(f1168,plain,
( spl0_46
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f783,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).
fof(f1166,plain,
spl0_45,
inference(avatar_split_clause,[],[f782,f1163]) ).
fof(f1163,plain,
( spl0_45
<=> class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f782,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).
fof(f1161,plain,
spl0_44,
inference(avatar_split_clause,[],[f781,f1158]) ).
fof(f781,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join) ).
fof(f1156,plain,
spl0_43,
inference(avatar_split_clause,[],[f780,f1153]) ).
fof(f1153,plain,
( spl0_43
<=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f780,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet) ).
fof(f1151,plain,
spl0_42,
inference(avatar_split_clause,[],[f779,f1148]) ).
fof(f1148,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f779,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f1146,plain,
spl0_41,
inference(avatar_split_clause,[],[f778,f1143]) ).
fof(f1143,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f778,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f1141,plain,
spl0_40,
inference(avatar_split_clause,[],[f777,f1138]) ).
fof(f1138,plain,
( spl0_40
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f777,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f1136,plain,
spl0_39,
inference(avatar_split_clause,[],[f776,f1133]) ).
fof(f1133,plain,
( spl0_39
<=> class_HOL_Oeq(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f776,axiom,
class_HOL_Oeq(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oeq) ).
fof(f1131,plain,
spl0_38,
inference(avatar_split_clause,[],[f775,f1128]) ).
fof(f775,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).
fof(f1126,plain,
spl0_37,
inference(avatar_split_clause,[],[f774,f1123]) ).
fof(f774,axiom,
class_Power_Opower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).
fof(f1121,plain,
spl0_36,
inference(avatar_split_clause,[],[f773,f1118]) ).
fof(f1118,plain,
( spl0_36
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f773,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f1116,plain,
spl0_35,
inference(avatar_split_clause,[],[f772,f1113]) ).
fof(f772,axiom,
class_Lattices_Olattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
fof(f1111,plain,
spl0_34,
inference(avatar_split_clause,[],[f771,f1108]) ).
fof(f1108,plain,
( spl0_34
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f771,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f1106,plain,
spl0_33,
inference(avatar_split_clause,[],[f770,f1103]) ).
fof(f1103,plain,
( spl0_33
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f770,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f1101,plain,
spl0_32,
inference(avatar_split_clause,[],[f769,f1098]) ).
fof(f769,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).
fof(f1096,plain,
spl0_31,
inference(avatar_split_clause,[],[f768,f1093]) ).
fof(f768,axiom,
class_Divides_Osemiring__div(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).
fof(f1091,plain,
spl0_30,
inference(avatar_split_clause,[],[f767,f1088]) ).
fof(f767,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f1086,plain,
spl0_29,
inference(avatar_split_clause,[],[f766,f1083]) ).
fof(f1083,plain,
( spl0_29
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f766,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f1081,plain,
spl0_28,
inference(avatar_split_clause,[],[f765,f1078]) ).
fof(f765,axiom,
class_Lattices_Odistrib__lattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
fof(f1076,plain,
spl0_27,
inference(avatar_split_clause,[],[f764,f1073]) ).
fof(f764,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).
fof(f1071,plain,
spl0_26,
inference(avatar_split_clause,[],[f763,f1068]) ).
fof(f763,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f1066,plain,
spl0_25,
inference(avatar_split_clause,[],[f762,f1063]) ).
fof(f762,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
fof(f1061,plain,
spl0_24,
inference(avatar_split_clause,[],[f761,f1058]) ).
fof(f1058,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f761,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f1056,plain,
spl0_23,
inference(avatar_split_clause,[],[f760,f1053]) ).
fof(f760,axiom,
class_Lattices_Olower__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
fof(f1051,plain,
spl0_22,
inference(avatar_split_clause,[],[f759,f1048]) ).
fof(f759,axiom,
class_Lattices_Oupper__semilattice(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
fof(f1046,plain,
spl0_21,
inference(avatar_split_clause,[],[f758,f1043]) ).
fof(f1043,plain,
( spl0_21
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f758,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f1041,plain,
spl0_20,
inference(avatar_split_clause,[],[f757,f1038]) ).
fof(f757,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f1036,plain,
spl0_19,
inference(avatar_split_clause,[],[f756,f1033]) ).
fof(f1033,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f756,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f1031,plain,
spl0_18,
inference(avatar_split_clause,[],[f755,f1028]) ).
fof(f1028,plain,
( spl0_18
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f755,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f1026,plain,
spl0_17,
inference(avatar_split_clause,[],[f754,f1023]) ).
fof(f1023,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f754,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).
fof(f1021,plain,
spl0_16,
inference(avatar_split_clause,[],[f753,f1018]) ).
fof(f753,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f1016,plain,
spl0_15,
inference(avatar_split_clause,[],[f752,f1013]) ).
fof(f752,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(f1011,plain,
spl0_14,
inference(avatar_split_clause,[],[f751,f1008]) ).
fof(f751,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(f1006,plain,
spl0_13,
inference(avatar_split_clause,[],[f750,f1003]) ).
fof(f750,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f1001,plain,
spl0_12,
inference(avatar_split_clause,[],[f749,f998]) ).
fof(f998,plain,
( spl0_12
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f749,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(f996,plain,
spl0_11,
inference(avatar_split_clause,[],[f748,f993]) ).
fof(f993,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f748,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f991,plain,
spl0_10,
inference(avatar_split_clause,[],[f747,f988]) ).
fof(f988,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f747,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f986,plain,
spl0_9,
inference(avatar_split_clause,[],[f746,f983]) ).
fof(f983,plain,
( spl0_9
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f746,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f981,plain,
spl0_8,
inference(avatar_split_clause,[],[f745,f978]) ).
fof(f978,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f745,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(f976,plain,
spl0_7,
inference(avatar_split_clause,[],[f744,f973]) ).
fof(f973,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f744,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(f971,plain,
spl0_6,
inference(avatar_split_clause,[],[f743,f968]) ).
fof(f968,plain,
( spl0_6
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f743,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(f966,plain,
spl0_5,
inference(avatar_split_clause,[],[f742,f963]) ).
fof(f963,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f742,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(f961,plain,
spl0_4,
inference(avatar_split_clause,[],[f741,f958]) ).
fof(f958,plain,
( spl0_4
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f741,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f956,plain,
spl0_3,
inference(avatar_split_clause,[],[f740,f953]) ).
fof(f953,plain,
( spl0_3
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f740,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).
fof(f951,plain,
spl0_2,
inference(avatar_split_clause,[],[f739,f948]) ).
fof(f948,plain,
( spl0_2
<=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f739,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(f946,plain,
spl0_1,
inference(avatar_split_clause,[],[f736,f943]) ).
fof(f736,axiom,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,v_x,tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG432-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 19:54:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (27526)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40 % (27529)WARNING: value z3 for option sas not known
% 0.22/0.40 % (27529)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)
% 0.22/0.41 % (27528)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.41 % (27527)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41 % (27530)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41 % (27531)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)
% 0.22/0.41 % (27532)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)
% 0.22/0.41 % (27533)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)
% 0.22/0.48 TRYING [1]
% 0.22/0.50 TRYING [2]
% 2.38/0.75 TRYING [3]
% 2.85/0.82 TRYING [1]
% 3.51/0.87 TRYING [2]
% 8.26/1.55 TRYING [1]
% 8.26/1.56 TRYING [2]
% 9.28/1.76 TRYING [3]
% 13.45/2.33 TRYING [3]
% 13.45/2.35 TRYING [4]
% 14.29/2.41 % (27531)First to succeed.
% 14.48/2.46 % (27531)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27526"
% 14.48/2.47 % (27531)Refutation found. Thanks to Tanya!
% 14.48/2.47 % SZS status Unsatisfiable for theBenchmark
% 14.48/2.47 % SZS output start Proof for theBenchmark
% See solution above
% 14.48/2.49 % (27531)------------------------------
% 14.48/2.49 % (27531)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 14.48/2.49 % (27531)Termination reason: Refutation
% 14.48/2.49
% 14.48/2.49 % (27531)Memory used [KB]: 32165
% 14.48/2.49 % (27531)Time elapsed: 2.055 s
% 14.48/2.49 % (27531)Instructions burned: 5725 (million)
% 14.48/2.49 % (27526)Success in time 2.114 s
%------------------------------------------------------------------------------