%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : ALG437-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n025.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 : Mon May 20 18:37:52 EDT 2024

% Result   : Unsatisfiable 21.61s 3.47s
% Output   : Refutation 21.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      : 2006
% Syntax   : Number of formulae    : 4837 ( 742 unt;   0 def)
%            Number of atoms       : 13356 (2907 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives : 15387 (6868   ~;7119   |;   0   &)
%                                         (1400 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    7 (   2 avg)
%            Number of predicates  : 1458 (1456 usr;1401 prp; 0-5 aty)
%            Number of functors    :   55 (  55 usr;   9 con; 0-5 aty)
%            Number of variables   : 8188 (8188   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f80697,plain,
    $false,
    inference(avatar_sat_refutation,[],[f690,f695,f700,f705,f710,f715,f720,f725,f730,f735,f740,f745,f750,f755,f760,f765,f770,f775,f780,f785,f790,f795,f800,f805,f810,f815,f820,f825,f830,f835,f840,f845,f850,f855,f860,f865,f870,f875,f880,f885,f890,f895,f900,f905,f910,f915,f920,f925,f930,f935,f940,f945,f950,f955,f960,f965,f970,f975,f980,f985,f990,f995,f1000,f1005,f1010,f1015,f1020,f1025,f1030,f1035,f1040,f1045,f1050,f1055,f1060,f1065,f1070,f1075,f1080,f1085,f1090,f1095,f1100,f1105,f1110,f1115,f1120,f1125,f1130,f1135,f1140,f1145,f1150,f1155,f1160,f1165,f1170,f1175,f1180,f1185,f1190,f1195,f1200,f1205,f1210,f1215,f1220,f1225,f1230,f1235,f1240,f1245,f1250,f1255,f1260,f1265,f1270,f1275,f1280,f1285,f1289,f1298,f1302,f1306,f1310,f1314,f1318,f1322,f1326,f1330,f1334,f1338,f1342,f1346,f1350,f1354,f1358,f1362,f1366,f1370,f1374,f1378,f1382,f1386,f1390,f1394,f1398,f1402,f1406,f1410,f1414,f1418,f1422,f1426,f1430,f1434,f1438,f1443,f1448,f1452,f1456,f1460,f1464,f1468,f1474,f1478,f1482,f1486,f1490,f1494,f1498,f1509,f1513,f1517,f1521,f1525,f1544,f1549,f1553,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1585,f1589,f1594,f1598,f1602,f1606,f1610,f1614,f1618,f1622,f1626,f1630,f1634,f1639,f1643,f1647,f1651,f1655,f1659,f1663,f1667,f1671,f1675,f1679,f1683,f1687,f1691,f1695,f1699,f1790,f1797,f1801,f1805,f1809,f1813,f1817,f1821,f1825,f1829,f1833,f1837,f1841,f1845,f1849,f1853,f1857,f1861,f1865,f1867,f1870,f1874,f1908,f1921,f1925,f1929,f1933,f1937,f1941,f1945,f1949,f1953,f1957,f1961,f1965,f1969,f1973,f1977,f1981,f1985,f1989,f1993,f1997,f2001,f2005,f2009,f2013,f2017,f2021,f2025,f2029,f2033,f2042,f2046,f2050,f2054,f2058,f2062,f2066,f2174,f2178,f2182,f2186,f2190,f2194,f2198,f2202,f2206,f2210,f2214,f2218,f2222,f2226,f2230,f2234,f2238,f2242,f2246,f2250,f2254,f2258,f2262,f2266,f2270,f2274,f2278,f2282,f2286,f2290,f2294,f2298,f2302,f2310,f2344,f2368,f2400,f2404,f2408,f2412,f2416,f2420,f2424,f2428,f2432,f2436,f2440,f2444,f2448,f2452,f2456,f2460,f2464,f2468,f2472,f2476,f2480,f2484,f2488,f2492,f2496,f2500,f2504,f2508,f2516,f2520,f2524,f2528,f2532,f2536,f2586,f2615,f2648,f2652,f2656,f2660,f2664,f2668,f2672,f2676,f2680,f2684,f2688,f2692,f2696,f2700,f2704,f2708,f2712,f2716,f2720,f2724,f2728,f2732,f2736,f2740,f2744,f2748,f2752,f2756,f2760,f2764,f2768,f2772,f2776,f2780,f2784,f2788,f2792,f2829,f2853,f2878,f2887,f2891,f2895,f2899,f2903,f2907,f2911,f2915,f2919,f2923,f2927,f2931,f2935,f2939,f2943,f2947,f2951,f2955,f2959,f2963,f2967,f2971,f2975,f2979,f2983,f2987,f2992,f2996,f3000,f3004,f3008,f3012,f3016,f3029,f3066,f3099,f3115,f3119,f3123,f3127,f3132,f3136,f3140,f3144,f3148,f3152,f3156,f3160,f3164,f3168,f3172,f3176,f3180,f3184,f3188,f3192,f3200,f3212,f3231,f3250,f3254,f3258,f3262,f3266,f3270,f3274,f3278,f3282,f3286,f3290,f3294,f3298,f3302,f3306,f3310,f3314,f3319,f3323,f3327,f3331,f3335,f3339,f3343,f3347,f3351,f3355,f3359,f3363,f3367,f3371,f3375,f3379,f3383,f3387,f3391,f3395,f3399,f3403,f3407,f3411,f3415,f3419,f3423,f3427,f3431,f3435,f3439,f3443,f3447,f3451,f3455,f3459,f3463,f3467,f3471,f3475,f3479,f3483,f3487,f3492,f3496,f3535,f3579,f3690,f3694,f3698,f3702,f3706,f3729,f3733,f3737,f3741,f3767,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3848,f3852,f3856,f3860,f3864,f3868,f3872,f3876,f3880,f3884,f3907,f3911,f3915,f3919,f3923,f3945,f4046,f4050,f4054,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4242,f4246,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4543,f4551,f4555,f4559,f4563,f4567,f4571,f4588,f4616,f4620,f4624,f4628,f4632,f4636,f4640,f4648,f4652,f4656,f4660,f4664,f4760,f4764,f4768,f4772,f4776,f4780,f4784,f4788,f4792,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4904,f4956,f4960,f4964,f4968,f4972,f4976,f4980,f4988,f4992,f4996,f5000,f5004,f5120,f5124,f5128,f5132,f5136,f5140,f5165,f5169,f5173,f5177,f5181,f5185,f5301,f5330,f5337,f5390,f5406,f5421,f5425,f5438,f5453,f5457,f5490,f5494,f5502,f5509,f5519,f5537,f5541,f5603,f5816,f5942,f5986,f5991,f5996,f6001,f6030,f6034,f6038,f6042,f6046,f6050,f6054,f6058,f6062,f6066,f6070,f6522,f6544,f6548,f6552,f6557,f6581,f6585,f6609,f6637,f6641,f6645,f6649,f6653,f6713,f6717,f6721,f6725,f6729,f6733,f6737,f6741,f6745,f6749,f6813,f6817,f6821,f6825,f6829,f6833,f6837,f6841,f6845,f6850,f6858,f6864,f6869,f6873,f6877,f6881,f6885,f6889,f6893,f6898,f6902,f6906,f6910,f6914,f6918,f6922,f6926,f6930,f6934,f6935,f6939,f6943,f6947,f6951,f6955,f7836,f8146,f8150,f8154,f8158,f8162,f8166,f8170,f8174,f8178,f8182,f8186,f8190,f8194,f8198,f8202,f8206,f8230,f8237,f8241,f8245,f8250,f8255,f8259,f8263,f8267,f8271,f8276,f8280,f8284,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8326,f8330,f8407,f8588,f8798,f8802,f8806,f8810,f8814,f8908,f8912,f8916,f8920,f8924,f8928,f8932,f8936,f8940,f8944,f8952,f8956,f8960,f8964,f8968,f8972,f8976,f8980,f8984,f8988,f8992,f8997,f9002,f9022,f9027,f9047,f9052,f9072,f9073,f9077,f9081,f9085,f9089,f9093,f9097,f9102,f9107,f9112,f9116,f9121,f9125,f9129,f9133,f9137,f9142,f9147,f9152,f9156,f9160,f9258,f9678,f10053,f10451,f10646,f10650,f10654,f10658,f10662,f10666,f10670,f10674,f10678,f10682,f10686,f10690,f10694,f10698,f10702,f10762,f10766,f10770,f10774,f10778,f10782,f10786,f10790,f10794,f10798,f10806,f10810,f10814,f10819,f10824,f10828,f11454,f11581,f11585,f11589,f11593,f11597,f11601,f11623,f11627,f11631,f11635,f11639,f11643,f11647,f11651,f11655,f11659,f11722,f11726,f11730,f11734,f11738,f11742,f11746,f11750,f11754,f11758,f11783,f11787,f11791,f11795,f11799,f11803,f11807,f11811,f11815,f11819,f11857,f11861,f11865,f11869,f11876,f11916,f11952,f11956,f12026,f12030,f12042,f12046,f12050,f12054,f12294,f12988,f13076,f13175,f13223,f13295,f13422,f13538,f13616,f13763,f13945,f14075,f14140,f14206,f14340,f14551,f14816,f15312,f15776,f16338,f17025,f17714,f17967,f18146,f18784,f19715,f20199,f20267,f20437,f21214,f21680,f21839,f21843,f21847,f21851,f21855,f21859,f21863,f21867,f21871,f21875,f21955,f21959,f21963,f21967,f21971,f21975,f21979,f21983,f21987,f21991,f22074,f22078,f22082,f22086,f22090,f22094,f22098,f22102,f22106,f22110,f22114,f22118,f22578,f23168,f23172,f23176,f23180,f23184,f23188,f23192,f23196,f23200,f23204,f23208,f23212,f23216,f23220,f23224,f23228,f23232,f23236,f23240,f23244,f23248,f23252,f23256,f23260,f23264,f23268,f23272,f23276,f23280,f23284,f23288,f23292,f23296,f23300,f23304,f23308,f23312,f23316,f23320,f23324,f23328,f23332,f23336,f23340,f23344,f23348,f23352,f23356,f23360,f23364,f23368,f23407,f23411,f23446,f23450,f23454,f23458,f23462,f23466,f23470,f23474,f23489,f23493,f23497,f23501,f23505,f23509,f23513,f23517,f23521,f23525,f23543,f23547,f23551,f23555,f23559,f23563,f23567,f23571,f23575,f23579,f23673,f23745,f23749,f23753,f23757,f24065,f25645,f26668,f28508,f28512,f28516,f28520,f28524,f28528,f28532,f28536,f28540,f28544,f28548,f28552,f28556,f28560,f28564,f28568,f28572,f28576,f28580,f28584,f28588,f28592,f28596,f28600,f28604,f28608,f28612,f29922,f29941,f29945,f29949,f29953,f29957,f29961,f29965,f29996,f30000,f30004,f30008,f30012,f30016,f30020,f30024,f30028,f30032,f30036,f30040,f30044,f30048,f30052,f30056,f30060,f30077,f30094,f30101,f30105,f30109,f30113,f30117,f30121,f30125,f30129,f30133,f30202,f30206,f30276,f30280,f30284,f30288,f30448,f30609,f30632,f30636,f30640,f30644,f30648,f30652,f31186,f31588,f32106,f33181,f33877,f33881,f33885,f33921,f33925,f33929,f33933,f33937,f33941,f33945,f33949,f33953,f33957,f33961,f33965,f33969,f33973,f33977,f33981,f33985,f33989,f33993,f33997,f34001,f34041,f34045,f34049,f34053,f34057,f34061,f34065,f34069,f34073,f34077,f34081,f34085,f34089,f34093,f34097,f34101,f34105,f34109,f34113,f34117,f34121,f34125,f34129,f34133,f34137,f34141,f34145,f37647,f37709,f37713,f37717,f37721,f37725,f37729,f37733,f37799,f37803,f37807,f37811,f37815,f37819,f37823,f37827,f37831,f37835,f37839,f37843,f37847,f37851,f37855,f37859,f37863,f37867,f37871,f37875,f37879,f37883,f38007,f38869,f38873,f38877,f38914,f38918,f38922,f38926,f38930,f38934,f38938,f38942,f38946,f38950,f38993,f38997,f39001,f39005,f39659,f39671,f39675,f39679,f39683,f39687,f39691,f39695,f39699,f39703,f39744,f39748,f39752,f39756,f39760,f39764,f39768,f39772,f39776,f39780,f39784,f39788,f39792,f39796,f39800,f39811,f39815,f39819,f39823,f39827,f39833,f39837,f39841,f39845,f39849,f39853,f39857,f39861,f39865,f39869,f39873,f39877,f39882,f39887,f39983,f40079,f40184,f40289,f40293,f40297,f40301,f40305,f40788,f40991,f42960,f42964,f43396,f43437,f43441,f43445,f43449,f43453,f43457,f43461,f43465,f43469,f43473,f43490,f43494,f43498,f43510,f43514,f43518,f43523,f43528,f43532,f43536,f43540,f43544,f43548,f43552,f43556,f43560,f43564,f43568,f43573,f43577,f43581,f44604,f44853,f45955,f46025,f46029,f46033,f46037,f46041,f46045,f46049,f46053,f46057,f46061,f46065,f46069,f46073,f47676,f47684,f47688,f47700,f47708,f47712,f47716,f55106,f58137,f58141,f59465,f59576,f59723,f60440,f64682,f65334,f65478,f66631,f67450,f67941,f73400,f73928,f74307,f74731,f75021,f76072,f77480,f77550,f80628,f80644,f80660,f80668,f80676,f80680,f80692,f80696]) ).

fof(f80696,plain,
    ~ spl0_1400,
    inference(avatar_contradiction_clause,[],[f80695]) ).

fof(f80695,plain,
    ( $false
    | ~ spl0_1400 ),
    inference(equality_resolution,[],[f80691]) ).

fof(f80691,plain,
    ( ! [X0] : v_p != X0
    | ~ spl0_1400 ),
    inference(avatar_component_clause,[],[f80690]) ).

fof(f80690,plain,
    ( spl0_1400
  <=> ! [X0] : v_p != X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).

fof(f80692,plain,
    ( spl0_1400
    | spl0_604
    | ~ spl0_930 ),
    inference(avatar_split_clause,[],[f46764,f12292,f4645,f80690]) ).

fof(f4645,plain,
    ( spl0_604
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).

fof(f12292,plain,
    ( spl0_930
  <=> ! [X0,X1] : X0 = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).

fof(f46764,plain,
    ( ! [X0] : v_p != X0
    | spl0_604
    | ~ spl0_930 ),
    inference(superposition,[],[f4646,f12293]) ).

fof(f12293,plain,
    ( ! [X0,X1] : X0 = X1
    | ~ spl0_930 ),
    inference(avatar_component_clause,[],[f12292]) ).

fof(f4646,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != v_p
    | spl0_604 ),
    inference(avatar_component_clause,[],[f4645]) ).

fof(f80680,plain,
    ( spl0_1399
    | ~ spl0_455
    | ~ spl0_1265 ),
    inference(avatar_split_clause,[],[f40378,f39669,f3276,f80678]) ).

fof(f80678,plain,
    ( spl0_1399
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).

fof(f3276,plain,
    ( spl0_455
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).

fof(f39669,plain,
    ( spl0_1265
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X0,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).

fof(f40378,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_455
    | ~ spl0_1265 ),
    inference(duplicate_literal_removal,[],[f40356]) ).

fof(f40356,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X2,X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_455
    | ~ spl0_1265 ),
    inference(resolution,[],[f39670,f3277]) ).

fof(f3277,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_455 ),
    inference(avatar_component_clause,[],[f3276]) ).

fof(f39670,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X0,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_1265 ),
    inference(avatar_component_clause,[],[f39669]) ).

fof(f80676,plain,
    ( spl0_1398
    | ~ spl0_455
    | ~ spl0_1167 ),
    inference(avatar_split_clause,[],[f34432,f33883,f3276,f80674]) ).

fof(f80674,plain,
    ( spl0_1398
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X4,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).

fof(f33883,plain,
    ( spl0_1167
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).

fof(f34432,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X4,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_455
    | ~ spl0_1167 ),
    inference(resolution,[],[f33884,f3277]) ).

fof(f33884,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2)) )
    | ~ spl0_1167 ),
    inference(avatar_component_clause,[],[f33883]) ).

fof(f80668,plain,
    ( spl0_1397
    | ~ spl0_922
    | ~ spl0_1272 ),
    inference(avatar_split_clause,[],[f40943,f39697,f11950,f80666]) ).

fof(f80666,plain,
    ( spl0_1397
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).

fof(f11950,plain,
    ( spl0_922
  <=> ! [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_922])]) ).

fof(f39697,plain,
    ( spl0_1272
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).

fof(f40943,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1),X1) )
    | ~ spl0_922
    | ~ spl0_1272 ),
    inference(duplicate_literal_removal,[],[f40888]) ).

fof(f40888,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X3,X2,X1),X1),X1) )
    | ~ spl0_922
    | ~ spl0_1272 ),
    inference(resolution,[],[f39698,f11951]) ).

fof(f11951,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X2),X1,X2)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,X2),X2) )
    | ~ spl0_922 ),
    inference(avatar_component_clause,[],[f11950]) ).

fof(f39698,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1) )
    | ~ spl0_1272 ),
    inference(avatar_component_clause,[],[f39697]) ).

fof(f80660,plain,
    ( spl0_1396
    | ~ spl0_285
    | ~ spl0_1272 ),
    inference(avatar_split_clause,[],[f40942,f39697,f2212,f80658]) ).

fof(f80658,plain,
    ( spl0_1396
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X3,X2,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).

fof(f2212,plain,
    ( spl0_285
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).

fof(f40942,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X3,X2,X1),X1) )
    | ~ spl0_285
    | ~ spl0_1272 ),
    inference(duplicate_literal_removal,[],[f40889]) ).

fof(f40889,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X2,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,X1),X1),X3,X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X3,X2,X1),X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
    | ~ spl0_285
    | ~ spl0_1272 ),
    inference(resolution,[],[f39698,f2213]) ).

fof(f2213,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_285 ),
    inference(avatar_component_clause,[],[f2212]) ).

fof(f80644,plain,
    ( spl0_1395
    | ~ spl0_396
    | ~ spl0_1265 ),
    inference(avatar_split_clause,[],[f40387,f39669,f2917,f80642]) ).

fof(f80642,plain,
    ( spl0_1395
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).

fof(f2917,plain,
    ( spl0_396
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).

fof(f40387,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_396
    | ~ spl0_1265 ),
    inference(duplicate_literal_removal,[],[f40319]) ).

fof(f40319,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_396
    | ~ spl0_1265 ),
    inference(resolution,[],[f39670,f2918]) ).

fof(f2918,plain,
    ( ! [X0,X7,X5,X12] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_396 ),
    inference(avatar_component_clause,[],[f2917]) ).

fof(f80628,plain,
    ( spl0_930
    | ~ spl0_1394 ),
    inference(avatar_split_clause,[],[f78209,f77478,f12292]) ).

fof(f77478,plain,
    ( spl0_1394
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).

fof(f78209,plain,
    ( ! [X0,X1] : X0 = X1
    | ~ spl0_1394 ),
    inference(superposition,[],[f77479,f77479]) ).

fof(f77479,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
    | ~ spl0_1394 ),
    inference(avatar_component_clause,[],[f77478]) ).

fof(f77550,plain,
    ( spl0_122
    | ~ spl0_604 ),
    inference(avatar_contradiction_clause,[],[f77549]) ).

fof(f77549,plain,
    ( $false
    | spl0_122
    | ~ spl0_604 ),
    inference(trivial_inequality_removal,[],[f77481]) ).

fof(f77481,plain,
    ( c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex)
    | spl0_122
    | ~ spl0_604 ),
    inference(superposition,[],[f1293,f4647]) ).

fof(f4647,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
    | ~ spl0_604 ),
    inference(avatar_component_clause,[],[f4645]) ).

fof(f1293,plain,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex)
    | spl0_122 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f1291,plain,
    ( spl0_122
  <=> c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).

fof(f77480,plain,
    ( spl0_604
    | spl0_1394
    | ~ spl0_594
    | ~ spl0_1393 ),
    inference(avatar_split_clause,[],[f76267,f76070,f4569,f77478,f4645]) ).

fof(f4569,plain,
    ( spl0_594
  <=> ! [X6,X5,X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,c_Polynomial_OpCons(X6,X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv2__1(X5,X6,X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).

fof(f76070,plain,
    ( spl0_1393
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).

fof(f76267,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p )
    | ~ spl0_594
    | ~ spl0_1393 ),
    inference(superposition,[],[f76071,f4570]) ).

fof(f4570,plain,
    ( ! [X6,X5,X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,c_Polynomial_OpCons(X6,X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv2__1(X5,X6,X12))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X12 )
    | ~ spl0_594 ),
    inference(avatar_component_clause,[],[f4569]) ).

fof(f76071,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1
    | ~ spl0_1393 ),
    inference(avatar_component_clause,[],[f76070]) ).

fof(f76072,plain,
    ( spl0_1393
    | ~ spl0_487
    | ~ spl0_1261
    | ~ spl0_1388 ),
    inference(avatar_split_clause,[],[f75598,f73398,f38995,f3405,f76070]) ).

fof(f3405,plain,
    ( spl0_487
  <=> ! [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_487])]) ).

fof(f38995,plain,
    ( spl0_1261
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).

fof(f73398,plain,
    ( spl0_1388
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).

fof(f75598,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1
    | ~ spl0_487
    | ~ spl0_1261
    | ~ spl0_1388 ),
    inference(forward_demodulation,[],[f75571,f3406]) ).

fof(f3406,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_487 ),
    inference(avatar_component_clause,[],[f3405]) ).

fof(f75571,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1261
    | ~ spl0_1388 ),
    inference(superposition,[],[f38996,f73399]) ).

fof(f73399,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1388 ),
    inference(avatar_component_clause,[],[f73398]) ).

fof(f38996,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_1261 ),
    inference(avatar_component_clause,[],[f38995]) ).

fof(f75021,plain,
    ( spl0_1392
    | ~ spl0_124
    | ~ spl0_487
    | ~ spl0_1350 ),
    inference(avatar_split_clause,[],[f45931,f43575,f3405,f1300,f75019]) ).

fof(f75019,plain,
    ( spl0_1392
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).

fof(f1300,plain,
    ( spl0_124
  <=> ! [X35] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X35) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).

fof(f43575,plain,
    ( spl0_1350
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).

fof(f45931,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_487
    | ~ spl0_1350 ),
    inference(forward_demodulation,[],[f45852,f3406]) ).

fof(f45852,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_124
    | ~ spl0_1350 ),
    inference(superposition,[],[f43576,f1301]) ).

fof(f1301,plain,
    ( ! [X35] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X35)
    | ~ spl0_124 ),
    inference(avatar_component_clause,[],[f1300]) ).

fof(f43576,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_1350 ),
    inference(avatar_component_clause,[],[f43575]) ).

fof(f74731,plain,
    ( spl0_1391
    | ~ spl0_124
    | ~ spl0_510
    | ~ spl0_1350 ),
    inference(avatar_split_clause,[],[f45913,f43575,f3533,f1300,f74729]) ).

fof(f74729,plain,
    ( spl0_1391
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).

fof(f3533,plain,
    ( spl0_510
  <=> ! [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_510])]) ).

fof(f45913,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_510
    | ~ spl0_1350 ),
    inference(forward_demodulation,[],[f45828,f3534]) ).

fof(f3534,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_510 ),
    inference(avatar_component_clause,[],[f3533]) ).

fof(f45828,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0),tc_Complex_Ocomplex)
    | ~ spl0_124
    | ~ spl0_1350 ),
    inference(superposition,[],[f43576,f1301]) ).

fof(f74307,plain,
    ( spl0_1390
    | ~ spl0_124
    | ~ spl0_454
    | ~ spl0_1345 ),
    inference(avatar_split_clause,[],[f45134,f43554,f3272,f1300,f74305]) ).

fof(f74305,plain,
    ( spl0_1390
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).

fof(f3272,plain,
    ( spl0_454
  <=> ! [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_454])]) ).

fof(f43554,plain,
    ( spl0_1345
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).

fof(f45134,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_454
    | ~ spl0_1345 ),
    inference(forward_demodulation,[],[f45080,f3273]) ).

fof(f3273,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_454 ),
    inference(avatar_component_clause,[],[f3272]) ).

fof(f45080,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_124
    | ~ spl0_1345 ),
    inference(superposition,[],[f43555,f1301]) ).

fof(f43555,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_1345 ),
    inference(avatar_component_clause,[],[f43554]) ).

fof(f73928,plain,
    ( spl0_1389
    | ~ spl0_124
    | ~ spl0_1212 ),
    inference(avatar_split_clause,[],[f37582,f34131,f1300,f73926]) ).

fof(f73926,plain,
    ( spl0_1389
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).

fof(f34131,plain,
    ( spl0_1212
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).

fof(f37582,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_1212 ),
    inference(superposition,[],[f34132,f1301]) ).

fof(f34132,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2))
    | ~ spl0_1212 ),
    inference(avatar_component_clause,[],[f34131]) ).

fof(f73400,plain,
    ( spl0_1388
    | ~ spl0_584
    | ~ spl0_679
    | ~ spl0_1150 ),
    inference(avatar_split_clause,[],[f32958,f30278,f6032,f4503,f73398]) ).

fof(f4503,plain,
    ( spl0_584
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).

fof(f6032,plain,
    ( spl0_679
  <=> ! [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_679])]) ).

fof(f30278,plain,
    ( spl0_1150
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).

fof(f32958,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_584
    | ~ spl0_679
    | ~ spl0_1150 ),
    inference(forward_demodulation,[],[f32859,f6033]) ).

fof(f6033,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_679 ),
    inference(avatar_component_clause,[],[f6032]) ).

fof(f32859,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_584
    | ~ spl0_1150 ),
    inference(superposition,[],[f30279,f4504]) ).

fof(f4504,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_584 ),
    inference(avatar_component_clause,[],[f4503]) ).

fof(f30279,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_1150 ),
    inference(avatar_component_clause,[],[f30278]) ).

fof(f67941,plain,
    ( spl0_1387
    | ~ spl0_1026
    | ~ spl0_1379 ),
    inference(avatar_split_clause,[],[f62379,f59574,f23290,f67939]) ).

fof(f67939,plain,
    ( spl0_1387
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).

fof(f23290,plain,
    ( spl0_1026
  <=> ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).

fof(f59574,plain,
    ( spl0_1379
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).

fof(f62379,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1026
    | ~ spl0_1379 ),
    inference(superposition,[],[f59575,f23291]) ).

fof(f23291,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_1026 ),
    inference(avatar_component_clause,[],[f23290]) ).

fof(f59575,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1379 ),
    inference(avatar_component_clause,[],[f59574]) ).

fof(f67450,plain,
    ( spl0_1386
    | ~ spl0_733
    | ~ spl0_1028
    | ~ spl0_1378 ),
    inference(avatar_split_clause,[],[f61360,f59463,f23298,f6896,f67448]) ).

fof(f67448,plain,
    ( spl0_1386
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).

fof(f6896,plain,
    ( spl0_733
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).

fof(f23298,plain,
    ( spl0_1028
  <=> ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).

fof(f59463,plain,
    ( spl0_1378
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).

fof(f61360,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_733
    | ~ spl0_1028
    | ~ spl0_1378 ),
    inference(forward_demodulation,[],[f61347,f23299]) ).

fof(f23299,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
    | ~ spl0_1028 ),
    inference(avatar_component_clause,[],[f23298]) ).

fof(f61347,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_733
    | ~ spl0_1378 ),
    inference(superposition,[],[f59464,f6897]) ).

fof(f6897,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_733 ),
    inference(avatar_component_clause,[],[f6896]) ).

fof(f59464,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1378 ),
    inference(avatar_component_clause,[],[f59463]) ).

fof(f66631,plain,
    ( spl0_1385
    | ~ spl0_733
    | ~ spl0_1378 ),
    inference(avatar_split_clause,[],[f61351,f59463,f6896,f66629]) ).

fof(f66629,plain,
    ( spl0_1385
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).

fof(f61351,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_733
    | ~ spl0_1378 ),
    inference(superposition,[],[f59464,f6897]) ).

fof(f65478,plain,
    ( spl0_1384
    | ~ spl0_1028
    | ~ spl0_1083 ),
    inference(avatar_split_clause,[],[f28379,f26666,f23298,f65476]) ).

fof(f65476,plain,
    ( spl0_1384
  <=> ! [X2,X0,X1,X3] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).

fof(f26666,plain,
    ( spl0_1083
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).

fof(f28379,plain,
    ( ! [X2,X3,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1028
    | ~ spl0_1083 ),
    inference(superposition,[],[f26667,f23299]) ).

fof(f26667,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1083 ),
    inference(avatar_component_clause,[],[f26666]) ).

fof(f65334,plain,
    ( spl0_1383
    | ~ spl0_1026
    | ~ spl0_1082 ),
    inference(avatar_split_clause,[],[f27913,f25643,f23290,f65332]) ).

fof(f65332,plain,
    ( spl0_1383
  <=> ! [X2,X0,X1,X3] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).

fof(f25643,plain,
    ( spl0_1082
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).

fof(f27913,plain,
    ( ! [X2,X3,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X3,c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1026
    | ~ spl0_1082 ),
    inference(superposition,[],[f25644,f23291]) ).

fof(f25644,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1082 ),
    inference(avatar_component_clause,[],[f25643]) ).

fof(f64682,plain,
    ( spl0_1382
    | ~ spl0_952
    | ~ spl0_1026 ),
    inference(avatar_split_clause,[],[f24328,f23290,f17965,f64680]) ).

fof(f64680,plain,
    ( spl0_1382
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).

fof(f17965,plain,
    ( spl0_952
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).

fof(f24328,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_952
    | ~ spl0_1026 ),
    inference(superposition,[],[f17966,f23291]) ).

fof(f17966,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_952 ),
    inference(avatar_component_clause,[],[f17965]) ).

fof(f60440,plain,
    ( spl0_1381
    | ~ spl0_1069
    | ~ spl0_1081 ),
    inference(avatar_split_clause,[],[f28075,f24063,f23553,f60438]) ).

fof(f60438,plain,
    ( spl0_1381
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).

fof(f23553,plain,
    ( spl0_1069
  <=> ! [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_1069])]) ).

fof(f24063,plain,
    ( spl0_1081
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).

fof(f28075,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1069
    | ~ spl0_1081 ),
    inference(superposition,[],[f24064,f23554]) ).

fof(f23554,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_1069 ),
    inference(avatar_component_clause,[],[f23553]) ).

fof(f24064,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1081 ),
    inference(avatar_component_clause,[],[f24063]) ).

fof(f59723,plain,
    ( spl0_1380
    | ~ spl0_951
    | ~ spl0_1028 ),
    inference(avatar_split_clause,[],[f24451,f23298,f17712,f59721]) ).

fof(f59721,plain,
    ( spl0_1380
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).

fof(f17712,plain,
    ( spl0_951
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).

fof(f24451,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_951
    | ~ spl0_1028 ),
    inference(superposition,[],[f17713,f23299]) ).

fof(f17713,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_951 ),
    inference(avatar_component_clause,[],[f17712]) ).

fof(f59576,plain,
    ( spl0_1379
    | ~ spl0_940
    | ~ spl0_1028 ),
    inference(avatar_split_clause,[],[f24450,f23298,f13943,f59574]) ).

fof(f13943,plain,
    ( spl0_940
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).

fof(f24450,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_940
    | ~ spl0_1028 ),
    inference(superposition,[],[f13944,f23299]) ).

fof(f13944,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_940 ),
    inference(avatar_component_clause,[],[f13943]) ).

fof(f59465,plain,
    ( spl0_1378
    | ~ spl0_938
    | ~ spl0_1026 ),
    inference(avatar_split_clause,[],[f24324,f23290,f13614,f59463]) ).

fof(f13614,plain,
    ( spl0_938
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).

fof(f24324,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_938
    | ~ spl0_1026 ),
    inference(superposition,[],[f13615,f23291]) ).

fof(f13615,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_938 ),
    inference(avatar_component_clause,[],[f13614]) ).

fof(f58141,plain,
    ( spl0_1377
    | ~ spl0_403
    | ~ spl0_905
    | ~ spl0_1047 ),
    inference(avatar_split_clause,[],[f47740,f23409,f11781,f2945,f58139]) ).

fof(f58139,plain,
    ( spl0_1377
  <=> ! [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(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).

fof(f2945,plain,
    ( spl0_403
  <=> ! [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_403])]) ).

fof(f11781,plain,
    ( spl0_905
  <=> ! [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_905])]) ).

fof(f23409,plain,
    ( spl0_1047
  <=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(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_1047])]) ).

fof(f47740,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(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_403
    | ~ spl0_905
    | ~ spl0_1047 ),
    inference(forward_demodulation,[],[f11782,f23413]) ).

fof(f23413,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_403
    | ~ spl0_1047 ),
    inference(superposition,[],[f23410,f2946]) ).

fof(f2946,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_403 ),
    inference(avatar_component_clause,[],[f2945]) ).

fof(f23410,plain,
    ( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_1047 ),
    inference(avatar_component_clause,[],[f23409]) ).

fof(f11782,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_905 ),
    inference(avatar_component_clause,[],[f11781]) ).

fof(f58137,plain,
    ( spl0_1376
    | ~ spl0_392
    | ~ spl0_904
    | ~ spl0_1045 ),
    inference(avatar_split_clause,[],[f47739,f23366,f11756,f2901,f58135]) ).

fof(f58135,plain,
    ( spl0_1376
  <=> ! [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(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).

fof(f2901,plain,
    ( spl0_392
  <=> ! [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_392])]) ).

fof(f11756,plain,
    ( spl0_904
  <=> ! [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_904])]) ).

fof(f23366,plain,
    ( spl0_1045
  <=> ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(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_1045])]) ).

fof(f47739,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(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_392
    | ~ spl0_904
    | ~ spl0_1045 ),
    inference(forward_demodulation,[],[f11757,f23370]) ).

fof(f23370,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_392
    | ~ spl0_1045 ),
    inference(superposition,[],[f23367,f2902]) ).

fof(f2902,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_392 ),
    inference(avatar_component_clause,[],[f2901]) ).

fof(f23367,plain,
    ( ! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_1045 ),
    inference(avatar_component_clause,[],[f23366]) ).

fof(f11757,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_904 ),
    inference(avatar_component_clause,[],[f11756]) ).

fof(f55106,plain,
    ( spl0_1375
    | ~ spl0_1127
    | ~ spl0_1316 ),
    inference(avatar_split_clause,[],[f43428,f40786,f30026,f55104]) ).

fof(f55104,plain,
    ( spl0_1375
  <=> ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).

fof(f30026,plain,
    ( spl0_1127
  <=> ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).

fof(f40786,plain,
    ( spl0_1316
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).

fof(f43428,plain,
    ( ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_1127
    | ~ spl0_1316 ),
    inference(forward_demodulation,[],[f43400,f40787]) ).

fof(f40787,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = X0
    | ~ spl0_1316 ),
    inference(avatar_component_clause,[],[f40786]) ).

fof(f43400,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)) )
    | ~ spl0_1127
    | ~ spl0_1316 ),
    inference(superposition,[],[f40787,f30027]) ).

fof(f30027,plain,
    ( ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_1127 ),
    inference(avatar_component_clause,[],[f30026]) ).

fof(f47716,plain,
    ( spl0_1374
    | ~ spl0_671
    | ~ spl0_930 ),
    inference(avatar_split_clause,[],[f46696,f12292,f5597,f47714]) ).

fof(f47714,plain,
    ( spl0_1374
  <=> ! [X0] : class_Ring__and__Field_Ocomm__semiring__1(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).

fof(f5597,plain,
    ( spl0_671
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).

fof(f46696,plain,
    ( ! [X0] : class_Ring__and__Field_Ocomm__semiring__1(X0)
    | ~ spl0_671
    | ~ spl0_930 ),
    inference(superposition,[],[f5598,f12293]) ).

fof(f5598,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_671 ),
    inference(avatar_component_clause,[],[f5597]) ).

fof(f47712,plain,
    ( spl0_1373
    | ~ spl0_284
    | ~ spl0_1265 ),
    inference(avatar_split_clause,[],[f40381,f39669,f2208,f47710]) ).

fof(f47710,plain,
    ( spl0_1373
  <=> ! [X2,X0,X1,X3] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X0),X2,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).

fof(f2208,plain,
    ( spl0_284
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).

fof(f40381,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X0),X2,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_284
    | ~ spl0_1265 ),
    inference(duplicate_literal_removal,[],[f40349]) ).

fof(f40349,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_284
    | ~ spl0_1265 ),
    inference(resolution,[],[f39670,f2209]) ).

fof(f2209,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_284 ),
    inference(avatar_component_clause,[],[f2208]) ).

fof(f47708,plain,
    ( spl0_1372
    | ~ spl0_284
    | ~ spl0_1167 ),
    inference(avatar_split_clause,[],[f34425,f33883,f2208,f47706]) ).

fof(f47706,plain,
    ( spl0_1372
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).

fof(f34425,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Ouminus__class_Ouminus(X3,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X1,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_284
    | ~ spl0_1167 ),
    inference(resolution,[],[f33884,f2209]) ).

fof(f47700,plain,
    ( spl0_1371
    | ~ spl0_396
    | ~ spl0_1167 ),
    inference(avatar_split_clause,[],[f34455,f33883,f2917,f47698]) ).

fof(f47698,plain,
    ( spl0_1371
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X0),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X4,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).

fof(f34455,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X0),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X4,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_396
    | ~ spl0_1167 ),
    inference(duplicate_literal_removal,[],[f34396]) ).

fof(f34396,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_Polynomial_Osmult(X3,X4,X0),X0),tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X1,X0),X4,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_396
    | ~ spl0_1167 ),
    inference(resolution,[],[f33884,f2918]) ).

fof(f47688,plain,
    ( spl0_1370
    | ~ spl0_286
    | ~ spl0_923 ),
    inference(avatar_split_clause,[],[f12020,f11954,f2216,f47686]) ).

fof(f47686,plain,
    ( spl0_1370
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).

fof(f2216,plain,
    ( spl0_286
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).

fof(f11954,plain,
    ( spl0_923
  <=> ! [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_923])]) ).

fof(f12020,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
    | ~ spl0_286
    | ~ spl0_923 ),
    inference(duplicate_literal_removal,[],[f12008]) ).

fof(f12008,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0),X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_286
    | ~ spl0_923 ),
    inference(resolution,[],[f11955,f2217]) ).

fof(f2217,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_286 ),
    inference(avatar_component_clause,[],[f2216]) ).

fof(f11955,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_923 ),
    inference(avatar_component_clause,[],[f11954]) ).

fof(f47684,plain,
    ( spl0_1369
    | ~ spl0_284
    | ~ spl0_922 ),
    inference(avatar_split_clause,[],[f11993,f11950,f2208,f47682]) ).

fof(f47682,plain,
    ( spl0_1369
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).

fof(f11993,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) )
    | ~ spl0_284
    | ~ spl0_922 ),
    inference(duplicate_literal_removal,[],[f11973]) ).

fof(f11973,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X2,X0),X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_284
    | ~ spl0_922 ),
    inference(resolution,[],[f11951,f2209]) ).

fof(f47676,plain,
    ( spl0_1368
    | ~ spl0_395
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f3526,f3276,f2913,f47674]) ).

fof(f47674,plain,
    ( spl0_1368
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X4,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2))
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).

fof(f2913,plain,
    ( spl0_395
  <=> ! [X5,X0,X12,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).

fof(f3526,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X4,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2))
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X3,X4,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_395
    | ~ spl0_455 ),
    inference(resolution,[],[f3277,f2914]) ).

fof(f2914,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_395 ),
    inference(avatar_component_clause,[],[f2913]) ).

fof(f46073,plain,
    ( ~ spl0_112
    | spl0_1367
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_638 ),
    inference(avatar_split_clause,[],[f5095,f4990,f2698,f2292,f1267,f46071,f1242]) ).

fof(f1242,plain,
    ( spl0_112
  <=> class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).

fof(f46071,plain,
    ( spl0_1367
  <=> ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).

fof(f1267,plain,
    ( spl0_117
  <=> class_HOL_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).

fof(f2292,plain,
    ( spl0_305
  <=> ! [X13,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = X13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).

fof(f2698,plain,
    ( spl0_361
  <=> ! [X5,X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_Polynomial_Omonom(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).

fof(f4990,plain,
    ( spl0_638
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Ouminus__class_Ouminus(X13,X0))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).

fof(f5095,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_638 ),
    inference(forward_demodulation,[],[f5094,f2837]) ).

fof(f2837,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_117
    | ~ spl0_361 ),
    inference(resolution,[],[f2699,f1269]) ).

fof(f1269,plain,
    ( class_HOL_Ozero(tc_Complex_Ocomplex)
    | ~ spl0_117 ),
    inference(avatar_component_clause,[],[f1267]) ).

fof(f2699,plain,
    ( ! [X0,X5] :
        ( ~ class_HOL_Ozero(X0)
        | c_Polynomial_Omonom(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_361 ),
    inference(avatar_component_clause,[],[f2698]) ).

fof(f5094,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,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),c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_638 ),
    inference(forward_demodulation,[],[f5082,f2837]) ).

fof(f5082,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X1,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),c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_305
    | ~ spl0_638 ),
    inference(superposition,[],[f4991,f2293]) ).

fof(f2293,plain,
    ( ! [X1,X13] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = X13
    | ~ spl0_305 ),
    inference(avatar_component_clause,[],[f2292]) ).

fof(f4991,plain,
    ( ! [X0,X12,X13] :
        ( c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Ouminus__class_Ouminus(X13,X0))
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_638 ),
    inference(avatar_component_clause,[],[f4990]) ).

fof(f46069,plain,
    ( spl0_919
    | spl0_1366
    | ~ spl0_508
    | ~ spl0_519 ),
    inference(avatar_split_clause,[],[f3788,f3735,f3490,f46067,f11871]) ).

fof(f11871,plain,
    ( spl0_919
  <=> ! [X2] : hBOOL(X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).

fof(f46067,plain,
    ( spl0_1366
  <=> ! [X0] :
        ( hBOOL(c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(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),tc_Complex_Ocomplex),X0))
        | ~ class_HOL_Ozero(X0)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).

fof(f3490,plain,
    ( spl0_508
  <=> ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).

fof(f3735,plain,
    ( spl0_519
  <=> ! [X0,X12,X31] :
        ( ~ class_HOL_Ozero(X0)
        | hBOOL(hAPP(X31,X12))
        | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
        | hBOOL(hAPP(X31,c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(X31,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).

fof(f3788,plain,
    ( ! [X0,X1] :
        ( hBOOL(c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(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),tc_Complex_Ocomplex),X0))
        | hBOOL(X1)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_508
    | ~ spl0_519 ),
    inference(forward_demodulation,[],[f3787,f3491]) ).

fof(f3491,plain,
    ( ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1
    | ~ spl0_508 ),
    inference(avatar_component_clause,[],[f3490]) ).

fof(f3787,plain,
    ( ! [X0,X1] :
        ( hBOOL(X1)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | ~ class_HOL_Ozero(X0)
        | hBOOL(hAPP(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),tc_Complex_Ocomplex),c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(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),tc_Complex_Ocomplex),X0))) )
    | ~ spl0_508
    | ~ spl0_519 ),
    inference(forward_demodulation,[],[f3778,f3491]) ).

fof(f3778,plain,
    ( ! [X0,X1] :
        ( ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))
        | hBOOL(hAPP(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),tc_Complex_Ocomplex),X1))
        | ~ class_HOL_Ozero(X0)
        | hBOOL(hAPP(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),tc_Complex_Ocomplex),c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(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),tc_Complex_Ocomplex),X0))) )
    | ~ spl0_508
    | ~ spl0_519 ),
    inference(superposition,[],[f3736,f3491]) ).

fof(f3736,plain,
    ( ! [X31,X0,X12] :
        ( ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
        | hBOOL(hAPP(X31,X12))
        | ~ class_HOL_Ozero(X0)
        | hBOOL(hAPP(X31,c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(X31,X0))) )
    | ~ spl0_519 ),
    inference(avatar_component_clause,[],[f3735]) ).

fof(f46065,plain,
    ( spl0_1365
    | ~ spl0_133
    | ~ spl0_517 ),
    inference(avatar_split_clause,[],[f3760,f3727,f1336,f46063]) ).

fof(f46063,plain,
    ( spl0_1365
  <=> ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).

fof(f1336,plain,
    ( spl0_133
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
        | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).

fof(f3727,plain,
    ( spl0_517
  <=> ! [X5,X0,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(X30,c_HOL_Otimes__class_Otimes(X5,X30,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).

fof(f3760,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
    | ~ spl0_133
    | ~ spl0_517 ),
    inference(resolution,[],[f3728,f1337]) ).

fof(f1337,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X48) )
    | ~ spl0_133 ),
    inference(avatar_component_clause,[],[f1336]) ).

fof(f3728,plain,
    ( ! [X0,X5,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(X30,c_HOL_Otimes__class_Otimes(X5,X30,X0),X0) )
    | ~ spl0_517 ),
    inference(avatar_component_clause,[],[f3727]) ).

fof(f46061,plain,
    ( spl0_1364
    | ~ spl0_124
    | ~ spl0_679
    | ~ spl0_1347 ),
    inference(avatar_split_clause,[],[f45496,f43562,f6032,f1300,f46059]) ).

fof(f46059,plain,
    ( spl0_1364
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).

fof(f43562,plain,
    ( spl0_1347
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).

fof(f45496,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_679
    | ~ spl0_1347 ),
    inference(forward_demodulation,[],[f45331,f6033]) ).

fof(f45331,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X1,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_124
    | ~ spl0_1347 ),
    inference(superposition,[],[f43563,f1301]) ).

fof(f43563,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_1347 ),
    inference(avatar_component_clause,[],[f43562]) ).

fof(f46057,plain,
    ( spl0_1363
    | ~ spl0_133
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f3756,f3704,f1336,f46055]) ).

fof(f46055,plain,
    ( spl0_1363
  <=> ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).

fof(f3704,plain,
    ( spl0_516
  <=> ! [X5,X0,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X30,X0),X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).

fof(f3756,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_133
    | ~ spl0_516 ),
    inference(resolution,[],[f3705,f1337]) ).

fof(f3705,plain,
    ( ! [X0,X5,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X30,X0),X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) )
    | ~ spl0_516 ),
    inference(avatar_component_clause,[],[f3704]) ).

fof(f46053,plain,
    ( spl0_1362
    | ~ spl0_134
    | ~ spl0_513 ),
    inference(avatar_split_clause,[],[f3745,f3692,f1340,f46051]) ).

fof(f46051,plain,
    ( spl0_1362
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).

fof(f1340,plain,
    ( spl0_134
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
        | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).

fof(f3692,plain,
    ( spl0_513
  <=> ! [X5,X0,X28] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X28,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).

fof(f3745,plain,
    ( ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) )
    | ~ spl0_134
    | ~ spl0_513 ),
    inference(resolution,[],[f3693,f1341]) ).

fof(f1341,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X48) )
    | ~ spl0_134 ),
    inference(avatar_component_clause,[],[f1340]) ).

fof(f3693,plain,
    ( ! [X28,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X28,X0) )
    | ~ spl0_513 ),
    inference(avatar_component_clause,[],[f3692]) ).

fof(f46049,plain,
    ( spl0_1361
    | ~ spl0_317
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3630,f3381,f2422,f46047]) ).

fof(f46047,plain,
    ( spl0_1361
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).

fof(f2422,plain,
    ( spl0_317
  <=> ! [X13,X0,X5,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).

fof(f3381,plain,
    ( spl0_481
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).

fof(f3630,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) )
    | ~ spl0_317
    | ~ spl0_481 ),
    inference(duplicate_literal_removal,[],[f3622]) ).

fof(f3622,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_317
    | ~ spl0_481 ),
    inference(resolution,[],[f3382,f2423]) ).

fof(f2423,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_317 ),
    inference(avatar_component_clause,[],[f2422]) ).

fof(f3382,plain,
    ( ! [X0,X6,X5,X13] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_481 ),
    inference(avatar_component_clause,[],[f3381]) ).

fof(f46045,plain,
    ( spl0_1360
    | ~ spl0_316
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3629,f3381,f2418,f46043]) ).

fof(f46043,plain,
    ( spl0_1360
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).

fof(f2418,plain,
    ( spl0_316
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).

fof(f3629,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2) )
    | ~ spl0_316
    | ~ spl0_481 ),
    inference(duplicate_literal_removal,[],[f3623]) ).

fof(f3623,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X3,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,X2),X4,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X3,X4,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_316
    | ~ spl0_481 ),
    inference(resolution,[],[f3382,f2419]) ).

fof(f2419,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_316 ),
    inference(avatar_component_clause,[],[f2418]) ).

fof(f46041,plain,
    ( spl0_1359
    | ~ spl0_285
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3624,f3381,f2212,f46039]) ).

fof(f46039,plain,
    ( spl0_1359
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).

fof(f3624,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Oplus__class_Oplus(X2,X3,X1),X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
    | ~ spl0_285
    | ~ spl0_481 ),
    inference(resolution,[],[f3382,f2213]) ).

fof(f46037,plain,
    ( spl0_1358
    | ~ spl0_354
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f3521,f3276,f2670,f46035]) ).

fof(f46035,plain,
    ( spl0_1358
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).

fof(f2670,plain,
    ( spl0_354
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).

fof(f3521,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Ominus__class_Ominus(X1,X3,X2),X2) )
    | ~ spl0_354
    | ~ spl0_455 ),
    inference(resolution,[],[f3277,f2671]) ).

fof(f2671,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0) )
    | ~ spl0_354 ),
    inference(avatar_component_clause,[],[f2670]) ).

fof(f46033,plain,
    ( spl0_1357
    | ~ spl0_314
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3245,f3190,f2410,f46031]) ).

fof(f46031,plain,
    ( spl0_1357
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).

fof(f2410,plain,
    ( spl0_314
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).

fof(f3190,plain,
    ( spl0_443
  <=> ! [X0,X12,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).

fof(f3245,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_314
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f2411]) ).

fof(f2411,plain,
    ( ! [X0,X6,X5,X13] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_314 ),
    inference(avatar_component_clause,[],[f2410]) ).

fof(f3191,plain,
    ( ! [X0,X7,X12] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X7,tc_Polynomial_Opoly(X0))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_443 ),
    inference(avatar_component_clause,[],[f3190]) ).

fof(f46029,plain,
    ( spl0_1356
    | ~ spl0_315
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3244,f3190,f2414,f46027]) ).

fof(f46027,plain,
    ( spl0_1356
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).

fof(f2414,plain,
    ( spl0_315
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).

fof(f3244,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_315
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f2415]) ).

fof(f2415,plain,
    ( ! [X0,X6,X5,X13] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_315 ),
    inference(avatar_component_clause,[],[f2414]) ).

fof(f46025,plain,
    ( spl0_1355
    | ~ spl0_354
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3043,f2917,f2670,f46023]) ).

fof(f46023,plain,
    ( spl0_1355
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X0,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2))
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X4,X1,X2),tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).

fof(f3043,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,X0,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2))
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_Polynomial_Osmult(X4,X1,X2),tc_Polynomial_Opoly(X2)) )
    | ~ spl0_354
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f2671]) ).

fof(f45955,plain,
    ( spl0_1354
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_743
    | ~ spl0_1150
    | ~ spl0_1347 ),
    inference(avatar_split_clause,[],[f45441,f43562,f30278,f6937,f1863,f1300,f45953]) ).

fof(f45953,plain,
    ( spl0_1354
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).

fof(f1863,plain,
    ( spl0_235
  <=> ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).

fof(f6937,plain,
    ( spl0_743
  <=> ! [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_743])]) ).

fof(f45441,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_235
    | ~ spl0_743
    | ~ spl0_1150
    | ~ spl0_1347 ),
    inference(forward_demodulation,[],[f45440,f1864]) ).

fof(f1864,plain,
    ( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1)
    | ~ spl0_235 ),
    inference(avatar_component_clause,[],[f1863]) ).

fof(f45440,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_743
    | ~ spl0_1150
    | ~ spl0_1347 ),
    inference(forward_demodulation,[],[f45439,f6938]) ).

fof(f6938,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_743 ),
    inference(avatar_component_clause,[],[f6937]) ).

fof(f45439,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_1150
    | ~ spl0_1347 ),
    inference(forward_demodulation,[],[f45307,f30279]) ).

fof(f45307,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(v_p,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0),tc_Complex_Ocomplex)
    | ~ spl0_124
    | ~ spl0_1347 ),
    inference(superposition,[],[f43563,f1301]) ).

fof(f44853,plain,
    ( spl0_1353
    | ~ spl0_1127
    | ~ spl0_1311 ),
    inference(avatar_split_clause,[],[f42740,f40287,f30026,f44851]) ).

fof(f44851,plain,
    ( spl0_1353
  <=> ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).

fof(f40287,plain,
    ( spl0_1311
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).

fof(f42740,plain,
    ( ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_1127
    | ~ spl0_1311 ),
    inference(forward_demodulation,[],[f42712,f40288]) ).

fof(f40288,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2
    | ~ spl0_1311 ),
    inference(avatar_component_clause,[],[f40287]) ).

fof(f42712,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )
    | ~ spl0_1127
    | ~ spl0_1311 ),
    inference(superposition,[],[f40288,f30027]) ).

fof(f44604,plain,
    ( spl0_1352
    | ~ spl0_1127
    | ~ spl0_1304 ),
    inference(avatar_split_clause,[],[f41544,f39871,f30026,f44602]) ).

fof(f44602,plain,
    ( spl0_1352
  <=> ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).

fof(f39871,plain,
    ( spl0_1304
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).

fof(f41544,plain,
    ( ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_1127
    | ~ spl0_1304 ),
    inference(forward_demodulation,[],[f41516,f39872]) ).

fof(f39872,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2
    | ~ spl0_1304 ),
    inference(avatar_component_clause,[],[f39871]) ).

fof(f41516,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )
    | ~ spl0_1127
    | ~ spl0_1304 ),
    inference(superposition,[],[f39872,f30027]) ).

fof(f43581,plain,
    ( spl0_1351
    | ~ spl0_45
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f4849,f4786,f907,f43579]) ).

fof(f43579,plain,
    ( spl0_1351
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).

fof(f907,plain,
    ( spl0_45
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).

fof(f4786,plain,
    ( spl0_616
  <=> ! [X0,X12,X1,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).

fof(f4849,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_616 ),
    inference(resolution,[],[f4787,f909]) ).

fof(f909,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal)
    | ~ spl0_45 ),
    inference(avatar_component_clause,[],[f907]) ).

fof(f4787,plain,
    ( ! [X0,X1,X7,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) )
    | ~ spl0_616 ),
    inference(avatar_component_clause,[],[f4786]) ).

fof(f43577,plain,
    ( spl0_1350
    | ~ spl0_89
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f4848,f4786,f1127,f43575]) ).

fof(f1127,plain,
    ( spl0_89
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).

fof(f4848,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_616 ),
    inference(resolution,[],[f4787,f1129]) ).

fof(f1129,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
    | ~ spl0_89 ),
    inference(avatar_component_clause,[],[f1127]) ).

fof(f43573,plain,
    ( spl0_1349
    | ~ spl0_8
    | ~ spl0_616 ),
    inference(avatar_split_clause,[],[f4847,f4786,f722,f43571]) ).

fof(f43571,plain,
    ( spl0_1349
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_nat),X2),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).

fof(f722,plain,
    ( spl0_8
  <=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f4847,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X0,tc_nat),X2),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat)
    | ~ spl0_8
    | ~ spl0_616 ),
    inference(resolution,[],[f4787,f724]) ).

fof(f724,plain,
    ( class_Ring__and__Field_Ocomm__semiring__0(tc_nat)
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f722]) ).

fof(f43568,plain,
    ( spl0_1348
    | ~ spl0_45
    | ~ spl0_615 ),
    inference(avatar_split_clause,[],[f4845,f4782,f907,f43566]) ).

fof(f43566,plain,
    ( spl0_1348
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).

fof(f4782,plain,
    ( spl0_615
  <=> ! [X0,X12,X1,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).

fof(f4845,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_615 ),
    inference(resolution,[],[f4783,f909]) ).

fof(f4783,plain,
    ( ! [X0,X1,X7,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) )
    | ~ spl0_615 ),
    inference(avatar_component_clause,[],[f4782]) ).

fof(f43564,plain,
    ( spl0_1347
    | ~ spl0_89
    | ~ spl0_615 ),
    inference(avatar_split_clause,[],[f4844,f4782,f1127,f43562]) ).

fof(f4844,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_615 ),
    inference(resolution,[],[f4783,f1129]) ).

fof(f43560,plain,
    ( spl0_1346
    | ~ spl0_8
    | ~ spl0_615 ),
    inference(avatar_split_clause,[],[f4843,f4782,f722,f43558]) ).

fof(f43558,plain,
    ( spl0_1346
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_nat),X2),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).

fof(f4843,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X0,tc_nat),X2),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat)
    | ~ spl0_8
    | ~ spl0_615 ),
    inference(resolution,[],[f4783,f724]) ).

fof(f43556,plain,
    ( spl0_1345
    | ~ spl0_102
    | ~ spl0_612 ),
    inference(avatar_split_clause,[],[f4814,f4770,f1192,f43554]) ).

fof(f1192,plain,
    ( spl0_102
  <=> class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).

fof(f4770,plain,
    ( spl0_612
  <=> ! [X0,X12,X1,X7] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).

fof(f4814,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_102
    | ~ spl0_612 ),
    inference(resolution,[],[f4771,f1194]) ).

fof(f1194,plain,
    ( class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex)
    | ~ spl0_102 ),
    inference(avatar_component_clause,[],[f1192]) ).

fof(f4771,plain,
    ( ! [X0,X1,X7,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) )
    | ~ spl0_612 ),
    inference(avatar_component_clause,[],[f4770]) ).

fof(f43552,plain,
    ( spl0_1344
    | ~ spl0_61
    | ~ spl0_612 ),
    inference(avatar_split_clause,[],[f4813,f4770,f987,f43550]) ).

fof(f43550,plain,
    ( spl0_1344
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).

fof(f987,plain,
    ( spl0_61
  <=> class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).

fof(f4813,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_61
    | ~ spl0_612 ),
    inference(resolution,[],[f4771,f989]) ).

fof(f989,plain,
    ( class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal)
    | ~ spl0_61 ),
    inference(avatar_component_clause,[],[f987]) ).

fof(f43548,plain,
    ( spl0_1343
    | ~ spl0_53
    | ~ spl0_611 ),
    inference(avatar_split_clause,[],[f4812,f4766,f947,f43546]) ).

fof(f43546,plain,
    ( spl0_1343
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).

fof(f947,plain,
    ( spl0_53
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).

fof(f4766,plain,
    ( spl0_611
  <=> ! [X0,X12,X15,X7] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).

fof(f4812,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_53
    | ~ spl0_611 ),
    inference(resolution,[],[f4767,f949]) ).

fof(f949,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
    | ~ spl0_53 ),
    inference(avatar_component_clause,[],[f947]) ).

fof(f4767,plain,
    ( ! [X0,X7,X15,X12] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) )
    | ~ spl0_611 ),
    inference(avatar_component_clause,[],[f4766]) ).

fof(f43544,plain,
    ( spl0_1342
    | ~ spl0_97
    | ~ spl0_611 ),
    inference(avatar_split_clause,[],[f4811,f4766,f1167,f43542]) ).

fof(f43542,plain,
    ( spl0_1342
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).

fof(f1167,plain,
    ( spl0_97
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).

fof(f4811,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_611 ),
    inference(resolution,[],[f4767,f1169]) ).

fof(f1169,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex)
    | ~ spl0_97 ),
    inference(avatar_component_clause,[],[f1167]) ).

fof(f43540,plain,
    ( spl0_1341
    | ~ spl0_13
    | ~ spl0_611 ),
    inference(avatar_split_clause,[],[f4810,f4766,f747,f43538]) ).

fof(f43538,plain,
    ( spl0_1341
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_nat),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).

fof(f747,plain,
    ( spl0_13
  <=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f4810,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_nat)),tc_nat),X2) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X0,tc_nat),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_nat),X2),tc_nat)
    | ~ spl0_13
    | ~ spl0_611 ),
    inference(resolution,[],[f4767,f749]) ).

fof(f749,plain,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_nat)
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f747]) ).

fof(f43536,plain,
    ( spl0_1340
    | ~ spl0_100
    | ~ spl0_609 ),
    inference(avatar_split_clause,[],[f4794,f4758,f1182,f43534]) ).

fof(f43534,plain,
    ( spl0_1340
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).

fof(f1182,plain,
    ( spl0_100
  <=> class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).

fof(f4758,plain,
    ( spl0_609
  <=> ! [X0,X12,X15,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).

fof(f4794,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_609 ),
    inference(resolution,[],[f4759,f1184]) ).

fof(f1184,plain,
    ( class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
    | ~ spl0_100 ),
    inference(avatar_component_clause,[],[f1182]) ).

fof(f4759,plain,
    ( ! [X0,X7,X15,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) )
    | ~ spl0_609 ),
    inference(avatar_component_clause,[],[f4758]) ).

fof(f43532,plain,
    ( spl0_1339
    | ~ spl0_59
    | ~ spl0_609 ),
    inference(avatar_split_clause,[],[f4793,f4758,f977,f43530]) ).

fof(f43530,plain,
    ( spl0_1339
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).

fof(f977,plain,
    ( spl0_59
  <=> class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).

fof(f4793,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X2) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X2),hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_609 ),
    inference(resolution,[],[f4759,f979]) ).

fof(f979,plain,
    ( class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal)
    | ~ spl0_59 ),
    inference(avatar_component_clause,[],[f977]) ).

fof(f43528,plain,
    ( spl0_1338
    | ~ spl0_1080
    | ~ spl0_1264 ),
    inference(avatar_split_clause,[],[f39705,f39657,f23755,f43526]) ).

fof(f43526,plain,
    ( spl0_1338
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X1,c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).

fof(f23755,plain,
    ( spl0_1080
  <=> ! [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) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).

fof(f39657,plain,
    ( spl0_1264
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).

fof(f39705,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X1,c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_1080
    | ~ spl0_1264 ),
    inference(superposition,[],[f39658,f23756]) ).

fof(f23756,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Complex_Ocomplex) )
    | ~ spl0_1080 ),
    inference(avatar_component_clause,[],[f23755]) ).

fof(f39658,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1
    | ~ spl0_1264 ),
    inference(avatar_component_clause,[],[f39657]) ).

fof(f43523,plain,
    ( ~ spl0_89
    | spl0_1337
    | ~ spl0_89
    | ~ spl0_97
    | ~ spl0_271
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_591 ),
    inference(avatar_split_clause,[],[f4584,f4557,f3739,f2252,f2052,f1167,f1127,f43521,f1127]) ).

fof(f43521,plain,
    ( spl0_1337
  <=> ! [X2,X0,X1] :
        ( X0 != X1
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).

fof(f2052,plain,
    ( spl0_271
  <=> ! [X0,X12] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).

fof(f2252,plain,
    ( spl0_295
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).

fof(f3739,plain,
    ( spl0_520
  <=> ! [X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X12))
        | c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).

fof(f4557,plain,
    ( spl0_591
  <=> ! [X13,X0,X12,X25,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(X12,X0),X13) = X25
        | c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).

fof(f4584,plain,
    ( ! [X2,X0,X1] :
        ( X0 != X1
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_89
    | ~ spl0_97
    | ~ spl0_271
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_591 ),
    inference(forward_demodulation,[],[f4583,f2158]) ).

fof(f2158,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_97
    | ~ spl0_271 ),
    inference(resolution,[],[f2053,f1169]) ).

fof(f2053,plain,
    ( ! [X0,X12] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 )
    | ~ spl0_271 ),
    inference(avatar_component_clause,[],[f2052]) ).

fof(f4583,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != X0
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_89
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_591 ),
    inference(forward_demodulation,[],[f4582,f2360]) ).

fof(f2360,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_89
    | ~ spl0_295 ),
    inference(resolution,[],[f2253,f1129]) ).

fof(f2253,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_295 ),
    inference(avatar_component_clause,[],[f2252]) ).

fof(f4582,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != X0
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_520
    | ~ spl0_591 ),
    inference(superposition,[],[f4558,f3740]) ).

fof(f3740,plain,
    ( ! [X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X12))
        | c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X12 )
    | ~ spl0_520 ),
    inference(avatar_component_clause,[],[f3739]) ).

fof(f4558,plain,
    ( ! [X0,X7,X12,X25,X13] :
        ( c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0)
        | hAPP(c_Polynomial_Opoly(X12,X0),X13) = X25
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
    | ~ spl0_591 ),
    inference(avatar_component_clause,[],[f4557]) ).

fof(f43518,plain,
    ( ~ spl0_89
    | spl0_1336
    | ~ spl0_89
    | ~ spl0_97
    | ~ spl0_271
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_586 ),
    inference(avatar_split_clause,[],[f4536,f4511,f3739,f2252,f2052,f1167,f1127,f43516,f1127]) ).

fof(f43516,plain,
    ( spl0_1336
  <=> ! [X2,X0,X1] :
        ( X0 != X1
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).

fof(f4511,plain,
    ( spl0_586
  <=> ! [X13,X0,X12,X25,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osynthetic__div(X12,X13,X0) = X7
        | c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).

fof(f4536,plain,
    ( ! [X2,X0,X1] :
        ( X0 != X1
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_89
    | ~ spl0_97
    | ~ spl0_271
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_586 ),
    inference(forward_demodulation,[],[f4535,f2158]) ).

fof(f4535,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != X0
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_89
    | ~ spl0_295
    | ~ spl0_520
    | ~ spl0_586 ),
    inference(forward_demodulation,[],[f4534,f2360]) ).

fof(f4534,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X1,c_Polynomial_Osmult(X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) != X0
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_520
    | ~ spl0_586 ),
    inference(superposition,[],[f4512,f3740]) ).

fof(f4512,plain,
    ( ! [X0,X7,X12,X25,X13] :
        ( c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0)
        | c_Polynomial_Osynthetic__div(X12,X13,X0) = X7
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
    | ~ spl0_586 ),
    inference(avatar_component_clause,[],[f4511]) ).

fof(f43514,plain,
    ( spl0_1335
    | ~ spl0_408
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f3975,f3858,f2965,f43512]) ).

fof(f43512,plain,
    ( spl0_1335
  <=> ! [X2,X4,X0,X3,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X4,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).

fof(f2965,plain,
    ( spl0_408
  <=> ! [X0,X29,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X29,X2,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).

fof(f3858,plain,
    ( spl0_532
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).

fof(f3975,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X4,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_408
    | ~ spl0_532 ),
    inference(duplicate_literal_removal,[],[f3970]) ).

fof(f3970,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X4,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_408
    | ~ spl0_532 ),
    inference(resolution,[],[f3859,f2966]) ).

fof(f2966,plain,
    ( ! [X2,X29,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X29,X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_408 ),
    inference(avatar_component_clause,[],[f2965]) ).

fof(f3859,plain,
    ( ! [X0,X7,X5,X12] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0))
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_532 ),
    inference(avatar_component_clause,[],[f3858]) ).

fof(f43510,plain,
    ( spl0_1334
    | ~ spl0_407
    | ~ spl0_532 ),
    inference(avatar_split_clause,[],[f3974,f3858,f2961,f43508]) ).

fof(f43508,plain,
    ( spl0_1334
  <=> ! [X2,X4,X0,X3,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).

fof(f2961,plain,
    ( spl0_407
  <=> ! [X0,X29,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X29,X1,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).

fof(f3974,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_407
    | ~ spl0_532 ),
    inference(duplicate_literal_removal,[],[f3971]) ).

fof(f3971,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Opoly__gcd(X3,X4,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_407
    | ~ spl0_532 ),
    inference(resolution,[],[f3859,f2962]) ).

fof(f2962,plain,
    ( ! [X2,X29,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X29,X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_407 ),
    inference(avatar_component_clause,[],[f2961]) ).

fof(f43498,plain,
    ( ~ spl0_117
    | spl0_1333
    | ~ spl0_350
    | ~ spl0_520 ),
    inference(avatar_split_clause,[],[f3801,f3739,f2654,f43496,f1267]) ).

fof(f43496,plain,
    ( spl0_1333
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex) != X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).

fof(f2654,plain,
    ( spl0_350
  <=> ! [X6,X0,X12,X5,X7] :
        ( ~ class_HOL_Ozero(X0)
        | X7 = X12
        | c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).

fof(f3801,plain,
    ( ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex) != X0
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X2
        | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_350
    | ~ spl0_520 ),
    inference(superposition,[],[f2655,f3740]) ).

fof(f2655,plain,
    ( ! [X0,X6,X7,X5,X12] :
        ( c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0)
        | X7 = X12
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_350 ),
    inference(avatar_component_clause,[],[f2654]) ).

fof(f43494,plain,
    ( spl0_1332
    | ~ spl0_145
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f3754,f3696,f1384,f43492]) ).

fof(f43492,plain,
    ( spl0_1332
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_Polynomial_Opoly(X1)),X2),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).

fof(f1384,plain,
    ( spl0_145
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X48)
        | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).

fof(f3696,plain,
    ( spl0_514
  <=> ! [X12,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).

fof(f3754,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_Polynomial_Opoly(X1)),X2),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) )
    | ~ spl0_145
    | ~ spl0_514 ),
    inference(resolution,[],[f3697,f1385]) ).

fof(f1385,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__ring(X48) )
    | ~ spl0_145 ),
    inference(avatar_component_clause,[],[f1384]) ).

fof(f3697,plain,
    ( ! [X0,X1,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) )
    | ~ spl0_514 ),
    inference(avatar_component_clause,[],[f3696]) ).

fof(f43490,plain,
    ( spl0_1331
    | ~ spl0_143
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f3744,f3688,f1376,f43488]) ).

fof(f43488,plain,
    ( spl0_1331
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_Polynomial_Opoly(X1)),X2),tc_Polynomial_Opoly(X1))
        | ~ class_OrderedGroup_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).

fof(f1376,plain,
    ( spl0_143
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Oab__group__add(X48)
        | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).

fof(f3688,plain,
    ( spl0_512
  <=> ! [X0,X12,X15] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).

fof(f3744,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),X2) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_Polynomial_Opoly(X1)),X2),tc_Polynomial_Opoly(X1))
        | ~ class_OrderedGroup_Oab__group__add(X1) )
    | ~ spl0_143
    | ~ spl0_512 ),
    inference(resolution,[],[f3689,f1377]) ).

fof(f1377,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X48))
        | ~ class_OrderedGroup_Oab__group__add(X48) )
    | ~ spl0_143 ),
    inference(avatar_component_clause,[],[f1376]) ).

fof(f3689,plain,
    ( ! [X0,X15,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) )
    | ~ spl0_512 ),
    inference(avatar_component_clause,[],[f3688]) ).

fof(f43473,plain,
    ( spl0_1330
    | ~ spl0_143
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f3681,f3473,f1376,f43471]) ).

fof(f43471,plain,
    ( spl0_1330
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),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_1330])]) ).

fof(f3473,plain,
    ( spl0_504
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).

fof(f3681,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) )
    | ~ spl0_143
    | ~ spl0_504 ),
    inference(resolution,[],[f3474,f1377]) ).

fof(f3474,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_504 ),
    inference(avatar_component_clause,[],[f3473]) ).

fof(f43469,plain,
    ( spl0_1329
    | ~ spl0_149
    | ~ spl0_503 ),
    inference(avatar_split_clause,[],[f3676,f3469,f1400,f43467]) ).

fof(f43467,plain,
    ( spl0_1329
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).

fof(f1400,plain,
    ( spl0_149
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Oab__group__add(X48)
        | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).

fof(f3469,plain,
    ( spl0_503
  <=> ! [X5,X0,X6] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).

fof(f3676,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) )
    | ~ spl0_149
    | ~ spl0_503 ),
    inference(resolution,[],[f3470,f1401]) ).

fof(f1401,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X48))
        | ~ class_OrderedGroup_Oab__group__add(X48) )
    | ~ spl0_149 ),
    inference(avatar_component_clause,[],[f1400]) ).

fof(f3470,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) )
    | ~ spl0_503 ),
    inference(avatar_component_clause,[],[f3469]) ).

fof(f43465,plain,
    ( spl0_1328
    | ~ spl0_141
    | ~ spl0_502 ),
    inference(avatar_split_clause,[],[f3673,f3465,f1368,f43463]) ).

fof(f43463,plain,
    ( spl0_1328
  <=> ! [X2,X0,X1] :
        ( c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X2)),c_HOL_Osgn__class_Osgn(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Oordered__idom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).

fof(f1368,plain,
    ( spl0_141
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oordered__idom(X48)
        | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).

fof(f3465,plain,
    ( spl0_502
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X5,X0),c_HOL_Osgn__class_Osgn(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).

fof(f3673,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X0,tc_Polynomial_Opoly(X2)),c_HOL_Osgn__class_Osgn(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Oordered__idom(X2) )
    | ~ spl0_141
    | ~ spl0_502 ),
    inference(resolution,[],[f3466,f1369]) ).

fof(f1369,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Oordered__idom(X48) )
    | ~ spl0_141 ),
    inference(avatar_component_clause,[],[f1368]) ).

fof(f3466,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X5,X0),c_HOL_Osgn__class_Osgn(X6,X0),X0) )
    | ~ spl0_502 ),
    inference(avatar_component_clause,[],[f3465]) ).

fof(f43461,plain,
    ( spl0_1327
    | ~ spl0_143
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f3665,f3453,f1376,f43459]) ).

fof(f43459,plain,
    ( spl0_1327
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),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_1327])]) ).

fof(f3453,plain,
    ( spl0_499
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).

fof(f3665,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) )
    | ~ spl0_143
    | ~ spl0_499 ),
    inference(resolution,[],[f3454,f1377]) ).

fof(f3454,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_499 ),
    inference(avatar_component_clause,[],[f3453]) ).

fof(f43457,plain,
    ( spl0_1326
    | ~ spl0_284
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3243,f3190,f2208,f43455]) ).

fof(f43455,plain,
    ( spl0_1326
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X2,X0),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).

fof(f3243,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X2,X0),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_284
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f2209]) ).

fof(f43453,plain,
    ( spl0_1325
    | ~ spl0_354
    | ~ spl0_438 ),
    inference(avatar_split_clause,[],[f3227,f3170,f2670,f43451]) ).

fof(f43451,plain,
    ( spl0_1325
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ class_Ring__and__Field_Oidom(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X0,X4,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).

fof(f3170,plain,
    ( spl0_438
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).

fof(f3227,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ class_Ring__and__Field_Oidom(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X0,X4,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X1,X4,X2),X2) )
    | ~ spl0_354
    | ~ spl0_438 ),
    inference(resolution,[],[f3171,f2671]) ).

fof(f3171,plain,
    ( ! [X0,X6,X5,X13] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_438 ),
    inference(avatar_component_clause,[],[f3170]) ).

fof(f43449,plain,
    ( spl0_1324
    | ~ spl0_354
    | ~ spl0_437 ),
    inference(avatar_split_clause,[],[f3224,f3166,f2670,f43447]) ).

fof(f43447,plain,
    ( spl0_1324
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ class_Ring__and__Field_Oidom(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X0,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).

fof(f3166,plain,
    ( spl0_437
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).

fof(f3224,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ class_Ring__and__Field_Oidom(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X0,X2),X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X3,c_HOL_Otimes__class_Otimes(X4,X1,X2),X2) )
    | ~ spl0_354
    | ~ spl0_437 ),
    inference(resolution,[],[f3167,f2671]) ).

fof(f3167,plain,
    ( ! [X0,X6,X5,X13] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_437 ),
    inference(avatar_component_clause,[],[f3166]) ).

fof(f43445,plain,
    ( spl0_1323
    | ~ spl0_316
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3045,f2917,f2418,f43443]) ).

fof(f43443,plain,
    ( spl0_1323
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).

fof(f3045,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_316
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f2419]) ).

fof(f43441,plain,
    ( spl0_1322
    | ~ spl0_317
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3044,f2917,f2422,f43439]) ).

fof(f43439,plain,
    ( spl0_1322
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).

fof(f3044,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_317
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f2423]) ).

fof(f43437,plain,
    ( spl0_1321
    | ~ spl0_314
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3042,f2913,f2410,f43435]) ).

fof(f43435,plain,
    ( spl0_1321
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X0,X3),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).

fof(f3042,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X0,X3),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) )
    | ~ spl0_314
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f2411]) ).

fof(f43396,plain,
    ( spl0_1320
    | ~ spl0_315
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3041,f2913,f2414,f43394]) ).

fof(f43394,plain,
    ( spl0_1320
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X0,X3),X1,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).

fof(f3041,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X4,X0,X3),X1,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) )
    | ~ spl0_315
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f2415]) ).

fof(f42964,plain,
    ( spl0_1319
    | ~ spl0_727
    | ~ spl0_810
    | ~ spl0_812
    | ~ spl0_814
    | ~ spl0_1033
    | ~ spl0_1306 ),
    inference(avatar_split_clause,[],[f39883,f39880,f23318,f8986,f8978,f8970,f6871,f42962]) ).

fof(f42962,plain,
    ( spl0_1319
  <=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).

fof(f6871,plain,
    ( spl0_727
  <=> ! [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_727])]) ).

fof(f8970,plain,
    ( spl0_810
  <=> ! [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_810])]) ).

fof(f8978,plain,
    ( spl0_812
  <=> ! [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_812])]) ).

fof(f8986,plain,
    ( spl0_814
  <=> ! [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_814])]) ).

fof(f23318,plain,
    ( spl0_1033
  <=> ! [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_1033])]) ).

fof(f39880,plain,
    ( spl0_1306
  <=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).

fof(f39883,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_727
    | ~ spl0_810
    | ~ spl0_812
    | ~ spl0_814
    | ~ spl0_1033
    | ~ spl0_1306 ),
    inference(forward_demodulation,[],[f39881,f25055]) ).

fof(f25055,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_727
    | ~ spl0_810
    | ~ spl0_812
    | ~ spl0_814
    | ~ spl0_1033 ),
    inference(forward_demodulation,[],[f25054,f9763]) ).

fof(f9763,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_812
    | ~ spl0_814 ),
    inference(superposition,[],[f8979,f8987]) ).

fof(f8987,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_814 ),
    inference(avatar_component_clause,[],[f8986]) ).

fof(f8979,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_812 ),
    inference(avatar_component_clause,[],[f8978]) ).

fof(f25054,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_727
    | ~ spl0_810
    | ~ spl0_1033 ),
    inference(forward_demodulation,[],[f24997,f9632]) ).

fof(f9632,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex)
    | ~ spl0_727
    | ~ spl0_810 ),
    inference(superposition,[],[f8971,f6872]) ).

fof(f6872,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_727 ),
    inference(avatar_component_clause,[],[f6871]) ).

fof(f8971,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_810 ),
    inference(avatar_component_clause,[],[f8970]) ).

fof(f24997,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_810
    | ~ spl0_1033 ),
    inference(superposition,[],[f23319,f8971]) ).

fof(f23319,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_1033 ),
    inference(avatar_component_clause,[],[f23318]) ).

fof(f39881,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_1306 ),
    inference(avatar_component_clause,[],[f39880]) ).

fof(f42960,plain,
    ( spl0_1318
    | ~ spl0_728
    | ~ spl0_809
    | ~ spl0_811
    | ~ spl0_813
    | ~ spl0_1034
    | ~ spl0_1305 ),
    inference(avatar_split_clause,[],[f39878,f39875,f23322,f8982,f8974,f8966,f6875,f42958]) ).

fof(f42958,plain,
    ( spl0_1318
  <=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).

fof(f6875,plain,
    ( spl0_728
  <=> ! [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_728])]) ).

fof(f8966,plain,
    ( spl0_809
  <=> ! [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_809])]) ).

fof(f8974,plain,
    ( spl0_811
  <=> ! [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_811])]) ).

fof(f8982,plain,
    ( spl0_813
  <=> ! [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_813])]) ).

fof(f23322,plain,
    ( spl0_1034
  <=> ! [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_1034])]) ).

fof(f39875,plain,
    ( spl0_1305
  <=> ! [X0,X3,X2,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).

fof(f39878,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_728
    | ~ spl0_809
    | ~ spl0_811
    | ~ spl0_813
    | ~ spl0_1034
    | ~ spl0_1305 ),
    inference(forward_demodulation,[],[f39876,f25159]) ).

fof(f25159,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_728
    | ~ spl0_809
    | ~ spl0_811
    | ~ spl0_813
    | ~ spl0_1034 ),
    inference(forward_demodulation,[],[f25158,f9733]) ).

fof(f9733,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X2,c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_811
    | ~ spl0_813 ),
    inference(superposition,[],[f8975,f8983]) ).

fof(f8983,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_813 ),
    inference(avatar_component_clause,[],[f8982]) ).

fof(f8975,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_811 ),
    inference(avatar_component_clause,[],[f8974]) ).

fof(f25158,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_728
    | ~ spl0_809
    | ~ spl0_1034 ),
    inference(forward_demodulation,[],[f25099,f9582]) ).

fof(f9582,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X0,tc_RealDef_Oreal)
    | ~ spl0_728
    | ~ spl0_809 ),
    inference(superposition,[],[f8967,f6876]) ).

fof(f6876,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
    | ~ spl0_728 ),
    inference(avatar_component_clause,[],[f6875]) ).

fof(f8967,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_809 ),
    inference(avatar_component_clause,[],[f8966]) ).

fof(f25099,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_809
    | ~ spl0_1034 ),
    inference(superposition,[],[f23323,f8967]) ).

fof(f23323,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_1034 ),
    inference(avatar_component_clause,[],[f23322]) ).

fof(f39876,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_1305 ),
    inference(avatar_component_clause,[],[f39875]) ).

fof(f40991,plain,
    ( spl0_1317
    | ~ spl0_1223
    | ~ spl0_1264 ),
    inference(avatar_split_clause,[],[f39709,f39657,f37731,f40989]) ).

fof(f40989,plain,
    ( spl0_1317
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).

fof(f37731,plain,
    ( spl0_1223
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(X0,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).

fof(f39709,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_1223
    | ~ spl0_1264 ),
    inference(superposition,[],[f39658,f37732]) ).

fof(f37732,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X0))
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) )
    | ~ spl0_1223 ),
    inference(avatar_component_clause,[],[f37731]) ).

fof(f40788,plain,
    ( spl0_1316
    | ~ spl0_1212
    | ~ spl0_1264 ),
    inference(avatar_split_clause,[],[f39706,f39657,f34131,f40786]) ).

fof(f39706,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = X0
    | ~ spl0_1212
    | ~ spl0_1264 ),
    inference(superposition,[],[f39658,f34132]) ).

fof(f40305,plain,
    ( spl0_1315
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(avatar_split_clause,[],[f4756,f4662,f2650,f40303]) ).

fof(f40303,plain,
    ( spl0_1315
  <=> ! [X6,X4,X3,X0,X7,X5,X2,X1] : hAPP(c_Fun_Ofcomp(c_Fun_Ofcomp(X0,X1,X6,X3,X4),X2,X6,X4,X5),X7) = hAPP(X2,hAPP(X1,hAPP(X0,X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).

fof(f2650,plain,
    ( spl0_349
  <=> ! [X10,X11,X0,X8,X9,X1] : hAPP(c_Fun_Ofcomp(X8,X9,X10,X11,X0),X1) = hAPP(X9,hAPP(X8,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).

fof(f4662,plain,
    ( spl0_608
  <=> ! [X28,X11,X9,X0,X8,X10,X39] : c_Fun_Ofcomp(c_Fun_Ofcomp(X8,X9,X0,X39,X11),X28,X0,X11,X10) = c_Fun_Ofcomp(X8,c_Fun_Ofcomp(X9,X28,X39,X11,X10),X0,X39,X10) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).

fof(f4756,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ofcomp(c_Fun_Ofcomp(X0,X1,X6,X3,X4),X2,X6,X4,X5),X7) = hAPP(X2,hAPP(X1,hAPP(X0,X7)))
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(forward_demodulation,[],[f4754,f2651]) ).

fof(f2651,plain,
    ( ! [X10,X0,X11,X1,X8,X9] : hAPP(c_Fun_Ofcomp(X8,X9,X10,X11,X0),X1) = hAPP(X9,hAPP(X8,X1))
    | ~ spl0_349 ),
    inference(avatar_component_clause,[],[f2650]) ).

fof(f4754,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ofcomp(X1,X2,X3,X4,X5),hAPP(X0,X7)) = hAPP(c_Fun_Ofcomp(c_Fun_Ofcomp(X0,X1,X6,X3,X4),X2,X6,X4,X5),X7)
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(superposition,[],[f2651,f4663]) ).

fof(f4663,plain,
    ( ! [X28,X39,X0,X11,X10,X8,X9] : c_Fun_Ofcomp(c_Fun_Ofcomp(X8,X9,X0,X39,X11),X28,X0,X11,X10) = c_Fun_Ofcomp(X8,c_Fun_Ofcomp(X9,X28,X39,X11,X10),X0,X39,X10)
    | ~ spl0_608 ),
    inference(avatar_component_clause,[],[f4662]) ).

fof(f40301,plain,
    ( spl0_1314
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(avatar_split_clause,[],[f4755,f4662,f2650,f40299]) ).

fof(f40299,plain,
    ( spl0_1314
  <=> ! [X2,X6,X4,X3,X0,X5,X1,X7] : hAPP(c_Fun_Ofcomp(X0,c_Fun_Ofcomp(X1,X5,X3,X4,X6),X2,X3,X6),X7) = hAPP(X5,hAPP(X1,hAPP(X0,X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).

fof(f4755,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ofcomp(X0,c_Fun_Ofcomp(X1,X5,X3,X4,X6),X2,X3,X6),X7) = hAPP(X5,hAPP(X1,hAPP(X0,X7)))
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(forward_demodulation,[],[f4752,f2651]) ).

fof(f4752,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X5,hAPP(c_Fun_Ofcomp(X0,X1,X2,X3,X4),X7)) = hAPP(c_Fun_Ofcomp(X0,c_Fun_Ofcomp(X1,X5,X3,X4,X6),X2,X3,X6),X7)
    | ~ spl0_349
    | ~ spl0_608 ),
    inference(superposition,[],[f2651,f4663]) ).

fof(f40297,plain,
    ( spl0_1313
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(avatar_split_clause,[],[f4738,f4658,f2730,f40295]) ).

fof(f40295,plain,
    ( spl0_1313
  <=> ! [X2,X6,X4,X3,X7,X0,X5,X1] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).

fof(f2730,plain,
    ( spl0_369
  <=> ! [X8,X9,X11,X0,X10,X1] : hAPP(X8,hAPP(X9,X1)) = hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).

fof(f4658,plain,
    ( spl0_607
  <=> ! [X11,X9,X0,X8,X10,X28,X39] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X28,X39,X11,X0),X11,X10,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X11,X10,X39),X28,X39,X10,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).

fof(f4738,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7) = hAPP(X0,hAPP(X1,hAPP(X5,X7)))
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(forward_demodulation,[],[f4734,f2731]) ).

fof(f2731,plain,
    ( ! [X10,X0,X11,X1,X8,X9] : hAPP(X8,hAPP(X9,X1)) = hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1)
    | ~ spl0_369 ),
    inference(avatar_component_clause,[],[f2730]) ).

fof(f4734,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(X0,X1,X2,X3,X4),hAPP(X5,X7)) = hAPP(c_Fun_Ocomp(X0,c_Fun_Ocomp(X1,X5,X4,X2,X6),X2,X3,X6),X7)
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(superposition,[],[f2731,f4659]) ).

fof(f4659,plain,
    ( ! [X28,X39,X0,X11,X10,X8,X9] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X28,X39,X11,X0),X11,X10,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X11,X10,X39),X28,X39,X10,X0)
    | ~ spl0_607 ),
    inference(avatar_component_clause,[],[f4658]) ).

fof(f40293,plain,
    ( spl0_1312
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(avatar_split_clause,[],[f4736,f4658,f2730,f40291]) ).

fof(f40291,plain,
    ( spl0_1312
  <=> ! [X6,X4,X3,X0,X7,X5,X2,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).

fof(f4736,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7) = hAPP(X0,hAPP(X1,hAPP(X2,X7)))
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(forward_demodulation,[],[f4728,f2731]) ).

fof(f4728,plain,
    ( ! [X2,X3,X0,X1,X6,X7,X4,X5] : hAPP(X0,hAPP(c_Fun_Ocomp(X1,X2,X3,X4,X5),X7)) = hAPP(c_Fun_Ocomp(c_Fun_Ocomp(X0,X1,X4,X6,X3),X2,X3,X6,X5),X7)
    | ~ spl0_369
    | ~ spl0_607 ),
    inference(superposition,[],[f2731,f4659]) ).

fof(f40289,plain,
    ( spl0_1311
    | ~ spl0_487
    | ~ spl0_1246
    | ~ spl0_1261 ),
    inference(avatar_split_clause,[],[f39526,f38995,f38005,f3405,f40287]) ).

fof(f38005,plain,
    ( spl0_1246
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).

fof(f39526,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2
    | ~ spl0_487
    | ~ spl0_1246
    | ~ spl0_1261 ),
    inference(forward_demodulation,[],[f39468,f3406]) ).

fof(f39468,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Opcompose(v_p,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1246
    | ~ spl0_1261 ),
    inference(superposition,[],[f38996,f38006]) ).

fof(f38006,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
    | ~ spl0_1246 ),
    inference(avatar_component_clause,[],[f38005]) ).

fof(f40184,plain,
    ( spl0_1310
    | ~ spl0_110
    | ~ spl0_87
    | ~ spl0_606 ),
    inference(avatar_split_clause,[],[f4714,f4654,f1117,f1232,f40182]) ).

fof(f40182,plain,
    ( spl0_1310
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(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_1310])]) ).

fof(f1232,plain,
    ( spl0_110
  <=> class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).

fof(f1117,plain,
    ( spl0_87
  <=> class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).

fof(f4654,plain,
    ( spl0_606
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).

fof(f4714,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_87
    | ~ spl0_606 ),
    inference(resolution,[],[f4655,f1119]) ).

fof(f1119,plain,
    ( class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
    | ~ spl0_87 ),
    inference(avatar_component_clause,[],[f1117]) ).

fof(f4655,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) )
    | ~ spl0_606 ),
    inference(avatar_component_clause,[],[f4654]) ).

fof(f40079,plain,
    ( spl0_1309
    | ~ spl0_71
    | ~ spl0_43
    | ~ spl0_606 ),
    inference(avatar_split_clause,[],[f4713,f4654,f897,f1037,f40077]) ).

fof(f40077,plain,
    ( spl0_1309
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(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_1309])]) ).

fof(f1037,plain,
    ( spl0_71
  <=> class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).

fof(f897,plain,
    ( spl0_43
  <=> class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).

fof(f4713,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
        | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ spl0_43
    | ~ spl0_606 ),
    inference(resolution,[],[f4655,f899]) ).

fof(f899,plain,
    ( class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal)
    | ~ spl0_43 ),
    inference(avatar_component_clause,[],[f897]) ).

fof(f39983,plain,
    ( spl0_1308
    | ~ spl0_110
    | ~ spl0_87
    | ~ spl0_605 ),
    inference(avatar_split_clause,[],[f4712,f4650,f1117,f1232,f39981]) ).

fof(f39981,plain,
    ( spl0_1308
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).

fof(f4650,plain,
    ( spl0_605
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).

fof(f4712,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_87
    | ~ spl0_605 ),
    inference(resolution,[],[f4651,f1119]) ).

fof(f4651,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) )
    | ~ spl0_605 ),
    inference(avatar_component_clause,[],[f4650]) ).

fof(f39887,plain,
    ( spl0_1307
    | ~ spl0_71
    | ~ spl0_43
    | ~ spl0_605 ),
    inference(avatar_split_clause,[],[f4711,f4650,f897,f1037,f39885]) ).

fof(f39885,plain,
    ( spl0_1307
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).

fof(f4711,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
        | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_HOL_Oinverse__class_Odivide(X1,X2,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ spl0_43
    | ~ spl0_605 ),
    inference(resolution,[],[f4651,f899]) ).

fof(f39882,plain,
    ( spl0_1306
    | ~ spl0_100
    | ~ spl0_601 ),
    inference(avatar_split_clause,[],[f4703,f4634,f1182,f39880]) ).

fof(f4634,plain,
    ( spl0_601
  <=> ! [X5,X6,X13,X0,X27] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),c_HOL_Ominus__class_Ominus(X13,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).

fof(f4703,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_601 ),
    inference(resolution,[],[f4635,f1184]) ).

fof(f4635,plain,
    ( ! [X0,X6,X27,X5,X13] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),c_HOL_Ominus__class_Ominus(X13,X27,X0),X0) )
    | ~ spl0_601 ),
    inference(avatar_component_clause,[],[f4634]) ).

fof(f39877,plain,
    ( spl0_1305
    | ~ spl0_59
    | ~ spl0_601 ),
    inference(avatar_split_clause,[],[f4702,f4634,f977,f39875]) ).

fof(f4702,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X2,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_601 ),
    inference(resolution,[],[f4635,f979]) ).

fof(f39873,plain,
    ( spl0_1304
    | ~ spl0_487
    | ~ spl0_1178
    | ~ spl0_1261 ),
    inference(avatar_split_clause,[],[f39525,f38995,f33959,f3405,f39871]) ).

fof(f33959,plain,
    ( spl0_1178
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).

fof(f39525,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X2
    | ~ spl0_487
    | ~ spl0_1178
    | ~ spl0_1261 ),
    inference(forward_demodulation,[],[f39467,f3406]) ).

fof(f39467,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(X2,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X2,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1178
    | ~ spl0_1261 ),
    inference(superposition,[],[f38996,f33960]) ).

fof(f33960,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2)
    | ~ spl0_1178 ),
    inference(avatar_component_clause,[],[f33959]) ).

fof(f39869,plain,
    ( spl0_1303
    | ~ spl0_44
    | ~ spl0_53
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(avatar_split_clause,[],[f4701,f4630,f3296,f947,f902,f39867]) ).

fof(f39867,plain,
    ( spl0_1303
  <=> ! [X0,X3,X2,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).

fof(f902,plain,
    ( spl0_44
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).

fof(f3296,plain,
    ( spl0_460
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).

fof(f4630,plain,
    ( spl0_600
  <=> ! [X5,X0,X13,X6,X27] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).

fof(f4701,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_53
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(forward_demodulation,[],[f4698,f3545]) ).

fof(f3545,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_53
    | ~ spl0_460 ),
    inference(resolution,[],[f3297,f949]) ).

fof(f3297,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) )
    | ~ spl0_460 ),
    inference(avatar_component_clause,[],[f3296]) ).

fof(f4698,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_600 ),
    inference(resolution,[],[f4631,f904]) ).

fof(f904,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal)
    | ~ spl0_44 ),
    inference(avatar_component_clause,[],[f902]) ).

fof(f4631,plain,
    ( ! [X0,X6,X27,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) )
    | ~ spl0_600 ),
    inference(avatar_component_clause,[],[f4630]) ).

fof(f39865,plain,
    ( spl0_1302
    | ~ spl0_88
    | ~ spl0_97
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(avatar_split_clause,[],[f4700,f4630,f3296,f1167,f1122,f39863]) ).

fof(f39863,plain,
    ( spl0_1302
  <=> ! [X0,X3,X2,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).

fof(f1122,plain,
    ( spl0_88
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).

fof(f4700,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_97
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(forward_demodulation,[],[f4697,f3544]) ).

fof(f3544,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_97
    | ~ spl0_460 ),
    inference(resolution,[],[f3297,f1169]) ).

fof(f4697,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_600 ),
    inference(resolution,[],[f4631,f1124]) ).

fof(f1124,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_88 ),
    inference(avatar_component_clause,[],[f1122]) ).

fof(f39861,plain,
    ( spl0_1301
    | ~ spl0_7
    | ~ spl0_13
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(avatar_split_clause,[],[f4699,f4630,f3296,f747,f717,f39859]) ).

fof(f39859,plain,
    ( spl0_1301
  <=> ! [X0,X3,X2,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).

fof(f717,plain,
    ( spl0_7
  <=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f4699,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat),tc_nat)
    | ~ spl0_7
    | ~ spl0_13
    | ~ spl0_460
    | ~ spl0_600 ),
    inference(forward_demodulation,[],[f4696,f3543]) ).

fof(f3543,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_13
    | ~ spl0_460 ),
    inference(resolution,[],[f3297,f749]) ).

fof(f4696,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_HOL_Oplus__class_Oplus(X2,X3,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X3,tc_nat),tc_nat)
    | ~ spl0_7
    | ~ spl0_600 ),
    inference(resolution,[],[f4631,f719]) ).

fof(f719,plain,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_nat)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f717]) ).

fof(f39857,plain,
    ( spl0_1300
    | ~ spl0_110
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f4694,f4626,f1232,f39855]) ).

fof(f39855,plain,
    ( spl0_1300
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).

fof(f4626,plain,
    ( spl0_599
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).

fof(f4694,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )
    | ~ spl0_110
    | ~ spl0_599 ),
    inference(resolution,[],[f4627,f1234]) ).

fof(f1234,plain,
    ( class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
    | ~ spl0_110 ),
    inference(avatar_component_clause,[],[f1232]) ).

fof(f4627,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) )
    | ~ spl0_599 ),
    inference(avatar_component_clause,[],[f4626]) ).

fof(f39853,plain,
    ( spl0_1299
    | ~ spl0_71
    | ~ spl0_599 ),
    inference(avatar_split_clause,[],[f4693,f4626,f1037,f39851]) ).

fof(f39851,plain,
    ( spl0_1299
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
        | c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).

fof(f4693,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
        | c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)) )
    | ~ spl0_71
    | ~ spl0_599 ),
    inference(resolution,[],[f4627,f1039]) ).

fof(f1039,plain,
    ( class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
    | ~ spl0_71 ),
    inference(avatar_component_clause,[],[f1037]) ).

fof(f39849,plain,
    ( spl0_1298
    | ~ spl0_110
    | ~ spl0_598 ),
    inference(avatar_split_clause,[],[f4692,f4622,f1232,f39847]) ).

fof(f39847,plain,
    ( spl0_1298
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).

fof(f4622,plain,
    ( spl0_598
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
        | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).

fof(f4692,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) )
    | ~ spl0_110
    | ~ spl0_598 ),
    inference(resolution,[],[f4623,f1234]) ).

fof(f4623,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
        | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) )
    | ~ spl0_598 ),
    inference(avatar_component_clause,[],[f4622]) ).

fof(f39845,plain,
    ( spl0_1297
    | ~ spl0_71
    | ~ spl0_598 ),
    inference(avatar_split_clause,[],[f4691,f4622,f1037,f39843]) ).

fof(f39843,plain,
    ( spl0_1297
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
        | c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).

fof(f4691,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
        | c_HOL_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal)) )
    | ~ spl0_71
    | ~ spl0_598 ),
    inference(resolution,[],[f4623,f1039]) ).

fof(f39841,plain,
    ( spl0_1296
    | ~ spl0_44
    | ~ spl0_47
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f4671,f4614,f3345,f917,f902,f39839]) ).

fof(f39839,plain,
    ( spl0_1296
  <=> ! [X0,X3,X2,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).

fof(f917,plain,
    ( spl0_47
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).

fof(f3345,plain,
    ( spl0_472
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).

fof(f4614,plain,
    ( spl0_596
  <=> ! [X0,X21,X23,X22,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).

fof(f4671,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_47
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(forward_demodulation,[],[f4668,f3593]) ).

fof(f3593,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_47
    | ~ spl0_472 ),
    inference(resolution,[],[f3346,f919]) ).

fof(f919,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal)
    | ~ spl0_47 ),
    inference(avatar_component_clause,[],[f917]) ).

fof(f3346,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) )
    | ~ spl0_472 ),
    inference(avatar_component_clause,[],[f3345]) ).

fof(f4668,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X2,X3,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(X1,X3,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_596 ),
    inference(resolution,[],[f4615,f904]) ).

fof(f4615,plain,
    ( ! [X21,X0,X22,X23,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) )
    | ~ spl0_596 ),
    inference(avatar_component_clause,[],[f4614]) ).

fof(f39837,plain,
    ( spl0_1295
    | ~ spl0_88
    | ~ spl0_91
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f4670,f4614,f3345,f1137,f1122,f39835]) ).

fof(f39835,plain,
    ( spl0_1295
  <=> ! [X0,X3,X2,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).

fof(f1137,plain,
    ( spl0_91
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).

fof(f4670,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_91
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(forward_demodulation,[],[f4667,f3592]) ).

fof(f3592,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_91
    | ~ spl0_472 ),
    inference(resolution,[],[f3346,f1139]) ).

fof(f1139,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex)
    | ~ spl0_91 ),
    inference(avatar_component_clause,[],[f1137]) ).

fof(f4667,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X2,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(X1,X3,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_596 ),
    inference(resolution,[],[f4615,f1124]) ).

fof(f39833,plain,
    ( spl0_1294
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(avatar_split_clause,[],[f4669,f4614,f3345,f727,f717,f39831]) ).

fof(f39831,plain,
    ( spl0_1294
  <=> ! [X0,X3,X2,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).

fof(f727,plain,
    ( spl0_9
  <=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f4669,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X2,c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat),tc_nat)
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_472
    | ~ spl0_596 ),
    inference(forward_demodulation,[],[f4666,f3591]) ).

fof(f3591,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_9
    | ~ spl0_472 ),
    inference(resolution,[],[f3346,f729]) ).

fof(f729,plain,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_nat)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f727]) ).

fof(f4666,plain,
    ( ! [X2,X3,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X3,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X3,tc_nat),tc_nat)
    | ~ spl0_7
    | ~ spl0_596 ),
    inference(resolution,[],[f4615,f719]) ).

fof(f39827,plain,
    ( spl0_1293
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_520
    | ~ spl0_580 ),
    inference(avatar_split_clause,[],[f4489,f4244,f3739,f2698,f1267,f39825]) ).

fof(f39825,plain,
    ( spl0_1293
  <=> ! [X0] :
        ( c_Polynomial_Omonom(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).

fof(f4244,plain,
    ( spl0_580
  <=> ! [X12,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).

fof(f4489,plain,
    ( ! [X0] :
        ( c_Polynomial_Omonom(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_520
    | ~ spl0_580 ),
    inference(forward_demodulation,[],[f4485,f2837]) ).

fof(f4485,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X0 )
    | ~ spl0_520
    | ~ spl0_580 ),
    inference(trivial_inequality_removal,[],[f4484]) ).

fof(f4484,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X0 )
    | ~ spl0_520
    | ~ spl0_580 ),
    inference(superposition,[],[f4245,f3740]) ).

fof(f4245,plain,
    ( ! [X1,X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) )
    | ~ spl0_580 ),
    inference(avatar_component_clause,[],[f4244]) ).

fof(f39823,plain,
    ( spl0_1292
    | ~ spl0_186
    | ~ spl0_533 ),
    inference(avatar_split_clause,[],[f3985,f3862,f1575,f39821]) ).

fof(f39821,plain,
    ( spl0_1292
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).

fof(f1575,plain,
    ( spl0_186
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).

fof(f3862,plain,
    ( spl0_533
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).

fof(f3985,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_186
    | ~ spl0_533 ),
    inference(resolution,[],[f3863,f1576]) ).

fof(f1576,plain,
    ( ! [X0,X6,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_186 ),
    inference(avatar_component_clause,[],[f1575]) ).

fof(f3863,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0))
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_533 ),
    inference(avatar_component_clause,[],[f3862]) ).

fof(f39819,plain,
    ( spl0_1291
    | ~ spl0_187
    | ~ spl0_533 ),
    inference(avatar_split_clause,[],[f3984,f3862,f1579,f39817]) ).

fof(f39817,plain,
    ( spl0_1291
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).

fof(f1579,plain,
    ( spl0_187
  <=> ! [X29,X0,X6] :
        ( ~ class_Ring__and__Field_Odvd(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Otimes__class_Otimes(X6,X29,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).

fof(f3984,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X2,X0),X3,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_187
    | ~ spl0_533 ),
    inference(resolution,[],[f3863,f1580]) ).

fof(f1580,plain,
    ( ! [X29,X0,X6] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Otimes__class_Otimes(X6,X29,X0),X0)
        | ~ class_Ring__and__Field_Odvd(X0) )
    | ~ spl0_187 ),
    inference(avatar_component_clause,[],[f1579]) ).

fof(f39815,plain,
    ( spl0_1290
    | ~ spl0_185
    | ~ spl0_533 ),
    inference(avatar_split_clause,[],[f3983,f3862,f1571,f39813]) ).

fof(f39813,plain,
    ( spl0_1290
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Osmult(X1,X2,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).

fof(f1571,plain,
    ( spl0_185
  <=> ! [X5,X0,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).

fof(f3983,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_HOL_Otimes__class_Otimes(X3,c_Polynomial_Osmult(X1,X2,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_185
    | ~ spl0_533 ),
    inference(resolution,[],[f3863,f1572]) ).

fof(f1572,plain,
    ( ! [X0,X6,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_185 ),
    inference(avatar_component_clause,[],[f1571]) ).

fof(f39811,plain,
    ( spl0_1289
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_520 ),
    inference(avatar_split_clause,[],[f3809,f3739,f2698,f2292,f1267,f39809]) ).

fof(f39809,plain,
    ( spl0_1289
  <=> ! [X0] :
        ( c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).

fof(f3809,plain,
    ( ! [X0] :
        ( c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_520 ),
    inference(forward_demodulation,[],[f3796,f2837]) ).

fof(f3796,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) )
    | ~ spl0_305
    | ~ spl0_520 ),
    inference(superposition,[],[f3740,f2293]) ).

fof(f39800,plain,
    ( ~ spl0_117
    | spl0_1288
    | ~ spl0_351
    | ~ spl0_520 ),
    inference(avatar_split_clause,[],[f3803,f3739,f2658,f39798,f1267]) ).

fof(f39798,plain,
    ( spl0_1288
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex) != X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0))
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).

fof(f2658,plain,
    ( spl0_351
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_HOL_Ozero(X0)
        | X5 = X6
        | c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).

fof(f3803,plain,
    ( ! [X2,X0,X1] :
        ( c_Polynomial_OpCons(X1,X2,tc_Complex_Ocomplex) != X0
        | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = X1
        | ~ class_HOL_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_351
    | ~ spl0_520 ),
    inference(superposition,[],[f2659,f3740]) ).

fof(f2659,plain,
    ( ! [X0,X6,X7,X5,X12] :
        ( c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0)
        | X5 = X6
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_351 ),
    inference(avatar_component_clause,[],[f2658]) ).

fof(f39796,plain,
    ( spl0_1287
    | ~ spl0_145
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f3652,f3433,f1384,f39794]) ).

fof(f39794,plain,
    ( spl0_1287
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).

fof(f3433,plain,
    ( spl0_494
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).

fof(f3652,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) )
    | ~ spl0_145
    | ~ spl0_494 ),
    inference(resolution,[],[f3434,f1385]) ).

fof(f3434,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_494 ),
    inference(avatar_component_clause,[],[f3433]) ).

fof(f39792,plain,
    ( spl0_1286
    | ~ spl0_134
    | ~ spl0_490 ),
    inference(avatar_split_clause,[],[f3644,f3417,f1340,f39790]) ).

fof(f39790,plain,
    ( spl0_1286
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).

fof(f3417,plain,
    ( spl0_490
  <=> ! [X5,X0,X12,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,X12,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X5,X6,X0),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).

fof(f3644,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X3) )
    | ~ spl0_134
    | ~ spl0_490 ),
    inference(resolution,[],[f3418,f1341]) ).

fof(f3418,plain,
    ( ! [X0,X6,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,X12,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X5,X6,X0),X12,X0) )
    | ~ spl0_490 ),
    inference(avatar_component_clause,[],[f3417]) ).

fof(f39788,plain,
    ( spl0_1285
    | ~ spl0_354
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3631,f3381,f2670,f39786]) ).

fof(f39786,plain,
    ( spl0_1285
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).

fof(f3631,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_354
    | ~ spl0_481 ),
    inference(duplicate_literal_removal,[],[f3621]) ).

fof(f3621,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X1,X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,X3,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X4,X0,X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X4,c_HOL_Oplus__class_Oplus(X1,X3,X2),X2) )
    | ~ spl0_354
    | ~ spl0_481 ),
    inference(resolution,[],[f3382,f2671]) ).

fof(f39784,plain,
    ( spl0_1284
    | ~ spl0_1127
    | ~ spl0_1264 ),
    inference(avatar_split_clause,[],[f39735,f39657,f30026,f39782]) ).

fof(f39782,plain,
    ( spl0_1284
  <=> ! [X0] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).

fof(f39735,plain,
    ( ! [X0] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex)) = X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_1127
    | ~ spl0_1264 ),
    inference(forward_demodulation,[],[f39707,f39658]) ).

fof(f39707,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(c_Polynomial_OpCons(X0,v_p,tc_Complex_Ocomplex)) )
    | ~ spl0_1127
    | ~ spl0_1264 ),
    inference(superposition,[],[f39658,f30027]) ).

fof(f39780,plain,
    ( spl0_1283
    | ~ spl0_134
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3613,f3369,f1340,f39778]) ).

fof(f39778,plain,
    ( spl0_1283
  <=> ! [X0,X3,X2,X1] :
        ( c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).

fof(f3369,plain,
    ( spl0_478
  <=> ! [X5,X0,X6,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_Omonom(X6,X15,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X5,X6,X0),X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).

fof(f3613,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Polynomial_Osmult(X0,c_Polynomial_Omonom(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X3) )
    | ~ spl0_134
    | ~ spl0_478 ),
    inference(resolution,[],[f3370,f1341]) ).

fof(f3370,plain,
    ( ! [X0,X6,X15,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_Omonom(X6,X15,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X5,X6,X0),X15,X0) )
    | ~ spl0_478 ),
    inference(avatar_component_clause,[],[f3369]) ).

fof(f39776,plain,
    ( spl0_1282
    | ~ spl0_133
    | ~ spl0_475 ),
    inference(avatar_split_clause,[],[f3605,f3357,f1336,f39774]) ).

fof(f39774,plain,
    ( spl0_1282
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).

fof(f3357,plain,
    ( spl0_475
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).

fof(f3605,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_133
    | ~ spl0_475 ),
    inference(resolution,[],[f3358,f1337]) ).

fof(f3358,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) )
    | ~ spl0_475 ),
    inference(avatar_component_clause,[],[f3357]) ).

fof(f39772,plain,
    ( spl0_1281
    | ~ spl0_133
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3601,f3353,f1336,f39770]) ).

fof(f39770,plain,
    ( spl0_1281
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).

fof(f3353,plain,
    ( spl0_474
  <=> ! [X20,X0,X23,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).

fof(f3601,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_133
    | ~ spl0_474 ),
    inference(resolution,[],[f3354,f1337]) ).

fof(f3354,plain,
    ( ! [X0,X22,X23,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) )
    | ~ spl0_474 ),
    inference(avatar_component_clause,[],[f3353]) ).

fof(f39768,plain,
    ( spl0_1280
    | ~ spl0_133
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f3594,f3349,f1336,f39766]) ).

fof(f39766,plain,
    ( spl0_1280
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X3,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).

fof(f3349,plain,
    ( spl0_473
  <=> ! [X21,X20,X0,X22] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).

fof(f3594,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X3,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_133
    | ~ spl0_473 ),
    inference(resolution,[],[f3350,f1337]) ).

fof(f3350,plain,
    ( ! [X21,X0,X22,X20] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) )
    | ~ spl0_473 ),
    inference(avatar_component_clause,[],[f3349]) ).

fof(f39764,plain,
    ( spl0_1279
    | ~ spl0_135
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f3590,f3345,f1344,f39762]) ).

fof(f39762,plain,
    ( spl0_1279
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).

fof(f1344,plain,
    ( spl0_135
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
        | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).

fof(f3590,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X2) )
    | ~ spl0_135
    | ~ spl0_472 ),
    inference(resolution,[],[f3346,f1345]) ).

fof(f1345,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X48) )
    | ~ spl0_135 ),
    inference(avatar_component_clause,[],[f1344]) ).

fof(f39760,plain,
    ( spl0_1278
    | ~ spl0_133
    | ~ spl0_466 ),
    inference(avatar_split_clause,[],[f3564,f3321,f1336,f39758]) ).

fof(f39758,plain,
    ( spl0_1278
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).

fof(f3321,plain,
    ( spl0_466
  <=> ! [X0,X13,X5,X27] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X5,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).

fof(f3564,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_133
    | ~ spl0_466 ),
    inference(resolution,[],[f3322,f1337]) ).

fof(f3322,plain,
    ( ! [X0,X27,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X5,X27,X0),X0) )
    | ~ spl0_466 ),
    inference(avatar_component_clause,[],[f3321]) ).

fof(f39756,plain,
    ( spl0_1277
    | ~ spl0_133
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f3557,f3312,f1336,f39754]) ).

fof(f39754,plain,
    ( spl0_1277
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X3,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).

fof(f3312,plain,
    ( spl0_464
  <=> ! [X5,X0,X13,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).

fof(f3557,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)),X3,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X3,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_133
    | ~ spl0_464 ),
    inference(resolution,[],[f3313,f1337]) ).

fof(f3313,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X6,X0) )
    | ~ spl0_464 ),
    inference(avatar_component_clause,[],[f3312]) ).

fof(f39752,plain,
    ( spl0_1276
    | ~ spl0_133
    | ~ spl0_463 ),
    inference(avatar_split_clause,[],[f3553,f3308,f1336,f39750]) ).

fof(f39750,plain,
    ( spl0_1276
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).

fof(f3308,plain,
    ( spl0_463
  <=> ! [X5,X13,X0,X27] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X27,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).

fof(f3553,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_133
    | ~ spl0_463 ),
    inference(resolution,[],[f3309,f1337]) ).

fof(f3309,plain,
    ( ! [X0,X27,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X27,X0) )
    | ~ spl0_463 ),
    inference(avatar_component_clause,[],[f3308]) ).

fof(f39748,plain,
    ( spl0_1275
    | ~ spl0_143
    | ~ spl0_461 ),
    inference(avatar_split_clause,[],[f3548,f3300,f1376,f39746]) ).

fof(f39746,plain,
    ( spl0_1275
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Oab__group__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).

fof(f3300,plain,
    ( spl0_461
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).

fof(f3548,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Oab__group__add(X3) )
    | ~ spl0_143
    | ~ spl0_461 ),
    inference(resolution,[],[f3301,f1377]) ).

fof(f3301,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) )
    | ~ spl0_461 ),
    inference(avatar_component_clause,[],[f3300]) ).

fof(f39744,plain,
    ( spl0_1274
    | ~ spl0_139
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f3542,f3296,f1360,f39742]) ).

fof(f39742,plain,
    ( spl0_1274
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).

fof(f1360,plain,
    ( spl0_139
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
        | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).

fof(f3542,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X3)),X2,tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X3) )
    | ~ spl0_139
    | ~ spl0_460 ),
    inference(resolution,[],[f3297,f1361]) ).

fof(f1361,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X48))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X48) )
    | ~ spl0_139 ),
    inference(avatar_component_clause,[],[f1360]) ).

fof(f39703,plain,
    ( spl0_1273
    | ~ spl0_139
    | ~ spl0_459 ),
    inference(avatar_split_clause,[],[f3538,f3292,f1360,f39701]) ).

fof(f39701,plain,
    ( spl0_1273
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).

fof(f3292,plain,
    ( spl0_459
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).

fof(f3538,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3)) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_OrderedGroup_Ocomm__monoid__add(X3) )
    | ~ spl0_139
    | ~ spl0_459 ),
    inference(resolution,[],[f3293,f1361]) ).

fof(f3293,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) )
    | ~ spl0_459 ),
    inference(avatar_component_clause,[],[f3292]) ).

fof(f39699,plain,
    ( spl0_1272
    | ~ spl0_285
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f3528,f3276,f2212,f39697]) ).

fof(f3528,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X2,X3,X1),X1) )
    | ~ spl0_285
    | ~ spl0_455 ),
    inference(duplicate_literal_removal,[],[f3524]) ).

fof(f3524,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X2,X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,X1),X3,X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ominus__class_Ominus(X2,X3,X1),X1)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
    | ~ spl0_285
    | ~ spl0_455 ),
    inference(resolution,[],[f3277,f2213]) ).

fof(f39695,plain,
    ( spl0_1271
    | ~ spl0_255
    | ~ spl0_455 ),
    inference(avatar_split_clause,[],[f3525,f3276,f1987,f39693]) ).

fof(f39693,plain,
    ( spl0_1271
  <=> ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).

fof(f1987,plain,
    ( spl0_255
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).

fof(f3525,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_255
    | ~ spl0_455 ),
    inference(resolution,[],[f3277,f1988]) ).

fof(f1988,plain,
    ( ! [X0,X5] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_255 ),
    inference(avatar_component_clause,[],[f1987]) ).

fof(f39691,plain,
    ( spl0_1270
    | ~ spl0_396
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3237,f3190,f2917,f39689]) ).

fof(f39689,plain,
    ( spl0_1270
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,X2,X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).

fof(f3237,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X1,X2,X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_396
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f2918]) ).

fof(f39687,plain,
    ( spl0_1269
    | ~ spl0_133
    | ~ spl0_440 ),
    inference(avatar_split_clause,[],[f3232,f3178,f1336,f39685]) ).

fof(f39685,plain,
    ( spl0_1269
  <=> ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).

fof(f3178,plain,
    ( spl0_440
  <=> ! [X0,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X30,X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X30,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).

fof(f3232,plain,
    ( ! [X0,X1] :
        ( c_HOL_Oplus__class_Oplus(X0,X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)),X0,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1) )
    | ~ spl0_133
    | ~ spl0_440 ),
    inference(resolution,[],[f3179,f1337]) ).

fof(f3179,plain,
    ( ! [X0,X30] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X30,X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X30,X0) )
    | ~ spl0_440 ),
    inference(avatar_component_clause,[],[f3178]) ).

fof(f39683,plain,
    ( spl0_1268
    | ~ spl0_286
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f3077,f2965,f2216,f39681]) ).

fof(f39681,plain,
    ( spl0_1268
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Opoly__gcd(X3,X2,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).

fof(f3077,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Opoly__gcd(X3,X2,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) )
    | ~ spl0_286
    | ~ spl0_408 ),
    inference(resolution,[],[f2966,f2217]) ).

fof(f39679,plain,
    ( spl0_1267
    | ~ spl0_286
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f3070,f2961,f2216,f39677]) ).

fof(f39677,plain,
    ( spl0_1267
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Opoly__gcd(X2,X3,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).

fof(f3070,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Opoly__gcd(X2,X3,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) )
    | ~ spl0_286
    | ~ spl0_407 ),
    inference(resolution,[],[f2962,f2217]) ).

fof(f39675,plain,
    ( spl0_1266
    | ~ spl0_285
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3046,f2917,f2212,f39673]) ).

fof(f39673,plain,
    ( spl0_1266
  <=> ! [X0,X3,X2,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X3,X2,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).

fof(f3046,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X3,X2,X1),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1)) )
    | ~ spl0_285
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f2213]) ).

fof(f39671,plain,
    ( spl0_1265
    | ~ spl0_284
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3040,f2913,f2208,f39669]) ).

fof(f3040,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X3,X0,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_284
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f2209]) ).

fof(f39659,plain,
    ( spl0_1264
    | ~ spl0_487
    | ~ spl0_1164
    | ~ spl0_1261 ),
    inference(avatar_split_clause,[],[f39523,f38995,f33179,f3405,f39657]) ).

fof(f33179,plain,
    ( spl0_1164
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).

fof(f39523,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) = X1
    | ~ spl0_487
    | ~ spl0_1164
    | ~ spl0_1261 ),
    inference(forward_demodulation,[],[f39464,f3406]) ).

fof(f39464,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1164
    | ~ spl0_1261 ),
    inference(superposition,[],[f38996,f33180]) ).

fof(f33180,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_1164 ),
    inference(avatar_component_clause,[],[f33179]) ).

fof(f39005,plain,
    ( spl0_1263
    | ~ spl0_207
    | ~ spl0_610 ),
    inference(avatar_split_clause,[],[f4798,f4762,f1661,f39003]) ).

fof(f39003,plain,
    ( spl0_1263
  <=> ! [X3,X4,X0,X6,X5,X2,X1] :
        ( c_Fun_Ocomp(X3,X4,X5,X0,X2) != X1
        | hAPP(X3,hAPP(X4,X6)) = hAPP(c_Fun_Oid(X0),hAPP(X1,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).

fof(f1661,plain,
    ( spl0_207
  <=> ! [X9,X0,X10] : c_Fun_Ocomp(c_Fun_Oid(X10),X9,X10,X10,X0) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).

fof(f4762,plain,
    ( spl0_610
  <=> ! [X41,X10,X0,X11,X39,X6,X27,X5,X13] :
        ( hAPP(X5,hAPP(X6,X41)) = hAPP(X13,hAPP(X27,X41))
        | c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(X13,X27,X39,X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).

fof(f4798,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( c_Fun_Ocomp(X3,X4,X5,X0,X2) != X1
        | hAPP(X3,hAPP(X4,X6)) = hAPP(c_Fun_Oid(X0),hAPP(X1,X6)) )
    | ~ spl0_207
    | ~ spl0_610 ),
    inference(superposition,[],[f4763,f1662]) ).

fof(f1662,plain,
    ( ! [X10,X0,X9] : c_Fun_Ocomp(c_Fun_Oid(X10),X9,X10,X10,X0) = X9
    | ~ spl0_207 ),
    inference(avatar_component_clause,[],[f1661]) ).

fof(f4763,plain,
    ( ! [X41,X10,X0,X11,X39,X6,X27,X5,X13] :
        ( c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(X13,X27,X39,X10,X0)
        | hAPP(X5,hAPP(X6,X41)) = hAPP(X13,hAPP(X27,X41)) )
    | ~ spl0_610 ),
    inference(avatar_component_clause,[],[f4762]) ).

fof(f39001,plain,
    ( spl0_1262
    | ~ spl0_45
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f4595,f4561,f3882,f907,f38999]) ).

fof(f38999,plain,
    ( spl0_1262
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).

fof(f3882,plain,
    ( spl0_538
  <=> ! [X0,X12,X5,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X5,X12,X0),X0),X1) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).

fof(f4561,plain,
    ( spl0_592
  <=> ! [X0,X12,X5,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,X12,X0),X0),X1) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).

fof(f4595,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(forward_demodulation,[],[f4592,f4029]) ).

fof(f4029,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_538 ),
    inference(resolution,[],[f3883,f909]) ).

fof(f3883,plain,
    ( ! [X0,X1,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X5,X12,X0),X0),X1) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) )
    | ~ spl0_538 ),
    inference(avatar_component_clause,[],[f3882]) ).

fof(f4592,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_592 ),
    inference(resolution,[],[f4562,f909]) ).

fof(f4562,plain,
    ( ! [X0,X1,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,X12,X0),X0),X1) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0),X0) )
    | ~ spl0_592 ),
    inference(avatar_component_clause,[],[f4561]) ).

fof(f38997,plain,
    ( spl0_1261
    | ~ spl0_89
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f4594,f4561,f3882,f1127,f38995]) ).

fof(f4594,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(forward_demodulation,[],[f4591,f4028]) ).

fof(f4028,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_538 ),
    inference(resolution,[],[f3883,f1129]) ).

fof(f4591,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_592 ),
    inference(resolution,[],[f4562,f1129]) ).

fof(f38993,plain,
    ( spl0_1260
    | ~ spl0_8
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(avatar_split_clause,[],[f4593,f4561,f3882,f722,f38991]) ).

fof(f38991,plain,
    ( spl0_1260
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_nat),tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).

fof(f4593,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Oplus__class_Oplus(X0,hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,X1,tc_nat),tc_nat),X2),tc_nat)
    | ~ spl0_8
    | ~ spl0_538
    | ~ spl0_592 ),
    inference(forward_demodulation,[],[f4590,f4027]) ).

fof(f4027,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat)
    | ~ spl0_8
    | ~ spl0_538 ),
    inference(resolution,[],[f3883,f724]) ).

fof(f4590,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X2,hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat),tc_nat)
    | ~ spl0_8
    | ~ spl0_592 ),
    inference(resolution,[],[f4562,f724]) ).

fof(f38950,plain,
    ( spl0_1259
    | ~ spl0_102
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f4579,f4553,f1192,f38948]) ).

fof(f38948,plain,
    ( spl0_1259
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).

fof(f4553,plain,
    ( spl0_590
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).

fof(f4579,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_102
    | ~ spl0_590 ),
    inference(resolution,[],[f4554,f1194]) ).

fof(f4554,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_590 ),
    inference(avatar_component_clause,[],[f4553]) ).

fof(f38946,plain,
    ( spl0_1258
    | ~ spl0_61
    | ~ spl0_590 ),
    inference(avatar_split_clause,[],[f4578,f4553,f987,f38944]) ).

fof(f38944,plain,
    ( spl0_1258
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).

fof(f4578,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_61
    | ~ spl0_590 ),
    inference(resolution,[],[f4554,f989]) ).

fof(f38942,plain,
    ( spl0_1257
    | ~ spl0_45
    | ~ spl0_589 ),
    inference(avatar_split_clause,[],[f4577,f4549,f907,f38940]) ).

fof(f38940,plain,
    ( spl0_1257
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).

fof(f4549,plain,
    ( spl0_589
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).

fof(f4577,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_589 ),
    inference(resolution,[],[f4550,f909]) ).

fof(f4550,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_589 ),
    inference(avatar_component_clause,[],[f4549]) ).

fof(f38938,plain,
    ( spl0_1256
    | ~ spl0_89
    | ~ spl0_589 ),
    inference(avatar_split_clause,[],[f4576,f4549,f1127,f38936]) ).

fof(f38936,plain,
    ( spl0_1256
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).

fof(f4576,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_589 ),
    inference(resolution,[],[f4550,f1129]) ).

fof(f38934,plain,
    ( spl0_1255
    | ~ spl0_8
    | ~ spl0_589 ),
    inference(avatar_split_clause,[],[f4575,f4549,f722,f38932]) ).

fof(f38932,plain,
    ( spl0_1255
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_nat),c_Polynomial_Osmult(X0,X2,tc_nat),tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).

fof(f4575,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X1,tc_nat),c_Polynomial_Osmult(X0,X2,tc_nat),tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_8
    | ~ spl0_589 ),
    inference(resolution,[],[f4550,f724]) ).

fof(f38930,plain,
    ( spl0_1254
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_580 ),
    inference(avatar_split_clause,[],[f4488,f4244,f2698,f2292,f1267,f38928]) ).

fof(f38928,plain,
    ( spl0_1254
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).

fof(f4488,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0 )
    | ~ spl0_117
    | ~ spl0_305
    | ~ spl0_361
    | ~ spl0_580 ),
    inference(forward_demodulation,[],[f4483,f2837]) ).

fof(f4483,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) )
    | ~ spl0_305
    | ~ spl0_580 ),
    inference(superposition,[],[f4245,f2293]) ).

fof(f38926,plain,
    ( spl0_1253
    | ~ spl0_152
    | ~ spl0_506 ),
    inference(avatar_split_clause,[],[f3686,f3481,f1412,f38924]) ).

fof(f38924,plain,
    ( spl0_1253
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Polynomial_Opoly(X2))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = hAPP(c_Polynomial_Opoly(X1,tc_Polynomial_Opoly(X2)),X0)
        | ~ class_Ring__and__Field_Oidom(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).

fof(f1412,plain,
    ( spl0_152
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oidom(X48)
        | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).

fof(f3481,plain,
    ( spl0_506
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X5,X12,X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).

fof(f3686,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X0,X1,tc_Polynomial_Opoly(X2))
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = hAPP(c_Polynomial_Opoly(X1,tc_Polynomial_Opoly(X2)),X0)
        | ~ class_Ring__and__Field_Oidom(X2) )
    | ~ spl0_152
    | ~ spl0_506 ),
    inference(resolution,[],[f3482,f1413]) ).

fof(f1413,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Oidom(X48) )
    | ~ spl0_152 ),
    inference(avatar_component_clause,[],[f1412]) ).

fof(f3482,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X5,X12,X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),X5) )
    | ~ spl0_506 ),
    inference(avatar_component_clause,[],[f3481]) ).

fof(f38922,plain,
    ( spl0_1252
    | ~ spl0_145
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f3221,f3162,f1384,f38920]) ).

fof(f38920,plain,
    ( spl0_1252
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1)))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).

fof(f3162,plain,
    ( spl0_436
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X5,X0),X12,X0) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).

fof(f3221,plain,
    ( ! [X2,X0,X1] :
        ( c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1)))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) )
    | ~ spl0_145
    | ~ spl0_436 ),
    inference(resolution,[],[f3163,f1385]) ).

fof(f3163,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X5,X0),X12,X0) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_436 ),
    inference(avatar_component_clause,[],[f3162]) ).

fof(f38918,plain,
    ( spl0_1251
    | ~ spl0_143
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f3216,f3150,f1376,f38916]) ).

fof(f38916,plain,
    ( spl0_1251
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).

fof(f3150,plain,
    ( spl0_433
  <=> ! [X5,X0,X15] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X5,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X5,X0),X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).

fof(f3216,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X2))) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_OrderedGroup_Oab__group__add(X2) )
    | ~ spl0_143
    | ~ spl0_433 ),
    inference(resolution,[],[f3151,f1377]) ).

fof(f3151,plain,
    ( ! [X0,X15,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X5,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X5,X0),X15,X0) )
    | ~ spl0_433 ),
    inference(avatar_component_clause,[],[f3150]) ).

fof(f38914,plain,
    ( spl0_1250
    | ~ spl0_152
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f3208,f3125,f1412,f38912]) ).

fof(f38912,plain,
    ( spl0_1250
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_Polynomial_Odegree(X2,tc_Polynomial_Opoly(X0)) = c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).

fof(f3125,plain,
    ( spl0_427
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).

fof(f3208,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_Polynomial_Odegree(X2,tc_Polynomial_Opoly(X0)) = c_Polynomial_Odegree(c_Polynomial_Osmult(X1,X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_152
    | ~ spl0_427 ),
    inference(resolution,[],[f3126,f1413]) ).

fof(f3126,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X12,X0),X0) )
    | ~ spl0_427 ),
    inference(avatar_component_clause,[],[f3125]) ).

fof(f38877,plain,
    ( spl0_1249
    | ~ spl0_255
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3047,f2917,f1987,f38875]) ).

fof(f38875,plain,
    ( spl0_1249
  <=> ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X2,X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).

fof(f3047,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X2,X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_255
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f1988]) ).

fof(f38873,plain,
    ( spl0_1248
    | ~ spl0_165
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f2868,f2750,f1466,f38871]) ).

fof(f38871,plain,
    ( spl0_1248
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).

fof(f1466,plain,
    ( spl0_165
  <=> ! [X48,X49] :
        ( ~ class_Lattices_Olattice(X48)
        | class_Lattices_Olattice(tc_fun(X49,X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).

fof(f2750,plain,
    ( spl0_374
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).

fof(f2868,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_165
    | ~ spl0_374 ),
    inference(resolution,[],[f2751,f1467]) ).

fof(f1467,plain,
    ( ! [X48,X49] :
        ( class_Lattices_Olattice(tc_fun(X49,X48))
        | ~ class_Lattices_Olattice(X48) )
    | ~ spl0_165 ),
    inference(avatar_component_clause,[],[f1466]) ).

fof(f2751,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) )
    | ~ spl0_374 ),
    inference(avatar_component_clause,[],[f2750]) ).

fof(f38869,plain,
    ( spl0_1247
    | ~ spl0_161
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f2847,f2718,f1450,f38867]) ).

fof(f38867,plain,
    ( spl0_1247
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).

fof(f1450,plain,
    ( spl0_161
  <=> ! [X48,X49] :
        ( ~ class_Lattices_Olattice(X48)
        | class_Lattices_Oupper__semilattice(tc_fun(X49,X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).

fof(f2718,plain,
    ( spl0_366
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).

fof(f2847,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_161
    | ~ spl0_366 ),
    inference(resolution,[],[f2719,f1451]) ).

fof(f1451,plain,
    ( ! [X48,X49] :
        ( class_Lattices_Oupper__semilattice(tc_fun(X49,X48))
        | ~ class_Lattices_Olattice(X48) )
    | ~ spl0_161 ),
    inference(avatar_component_clause,[],[f1450]) ).

fof(f2719,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) )
    | ~ spl0_366 ),
    inference(avatar_component_clause,[],[f2718]) ).

fof(f38007,plain,
    ( spl0_1246
    | ~ spl0_679
    | ~ spl0_1150
    | ~ spl0_1216 ),
    inference(avatar_split_clause,[],[f37761,f37645,f30278,f6032,f38005]) ).

fof(f37645,plain,
    ( spl0_1216
  <=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).

fof(f37761,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
    | ~ spl0_679
    | ~ spl0_1150
    | ~ spl0_1216 ),
    inference(forward_demodulation,[],[f37737,f6033]) ).

fof(f37737,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X2,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X2,c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
    | ~ spl0_1150
    | ~ spl0_1216 ),
    inference(superposition,[],[f30279,f37646]) ).

fof(f37646,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
    | ~ spl0_1216 ),
    inference(avatar_component_clause,[],[f37645]) ).

fof(f37883,plain,
    ( spl0_1245
    | ~ spl0_207
    | ~ spl0_602 ),
    inference(avatar_split_clause,[],[f4706,f4638,f1661,f37881]) ).

fof(f37881,plain,
    ( spl0_1245
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Fun_Ocomp(c_Fun_Oid(X0),X3,X0,X0,X2) != X1
        | hAPP(X3,X4) = hAPP(c_Fun_Oid(X0),hAPP(X1,X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).

fof(f4638,plain,
    ( spl0_602
  <=> ! [X41,X10,X11,X13,X0,X6,X5] :
        ( hAPP(X5,hAPP(X6,X41)) = hAPP(X13,X41)
        | c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(c_Fun_Oid(X10),X13,X10,X10,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).

fof(f4706,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Fun_Ocomp(c_Fun_Oid(X0),X3,X0,X0,X2) != X1
        | hAPP(X3,X4) = hAPP(c_Fun_Oid(X0),hAPP(X1,X4)) )
    | ~ spl0_207
    | ~ spl0_602 ),
    inference(superposition,[],[f4639,f1662]) ).

fof(f4639,plain,
    ( ! [X41,X10,X0,X11,X6,X5,X13] :
        ( c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(c_Fun_Oid(X10),X13,X10,X10,X0)
        | hAPP(X5,hAPP(X6,X41)) = hAPP(X13,X41) )
    | ~ spl0_602 ),
    inference(avatar_component_clause,[],[f4638]) ).

fof(f37879,plain,
    ( spl0_1244
    | ~ spl0_1212
    | ~ spl0_1216 ),
    inference(avatar_split_clause,[],[f37735,f37645,f34131,f37877]) ).

fof(f37877,plain,
    ( spl0_1244
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).

fof(f37735,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2)
    | ~ spl0_1212
    | ~ spl0_1216 ),
    inference(superposition,[],[f37646,f34132]) ).

fof(f37875,plain,
    ( spl0_1243
    | ~ spl0_343
    | ~ spl0_597 ),
    inference(avatar_split_clause,[],[f4683,f4618,f2526,f37873]) ).

fof(f37873,plain,
    ( spl0_1243
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_Polynomial_Osmult(X4,X0,X1) = c_Polynomial_Osmult(X4,X3,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).

fof(f2526,plain,
    ( spl0_343
  <=> ! [X0,X7,X25,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X1 = X25
        | ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).

fof(f4618,plain,
    ( spl0_597
  <=> ! [X2,X1,X0,X5,X25,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X5,X1,X0),X2,c_Polynomial_Osmult(X5,X7,X0),c_Polynomial_Osmult(X5,X25,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).

fof(f4683,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_Polynomial_Osmult(X4,X0,X1) = c_Polynomial_Osmult(X4,X3,X1) )
    | ~ spl0_343
    | ~ spl0_597 ),
    inference(duplicate_literal_removal,[],[f4673]) ).

fof(f4673,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_Polynomial_Osmult(X4,X0,X1) = c_Polynomial_Osmult(X4,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1) )
    | ~ spl0_343
    | ~ spl0_597 ),
    inference(resolution,[],[f4619,f2527]) ).

fof(f2527,plain,
    ( ! [X0,X1,X7,X25] :
        ( ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0)
        | X1 = X25
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_343 ),
    inference(avatar_component_clause,[],[f2526]) ).

fof(f4619,plain,
    ( ! [X2,X0,X1,X7,X5,X25] :
        ( c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X5,X1,X0),X2,c_Polynomial_Osmult(X5,X7,X0),c_Polynomial_Osmult(X5,X25,X0),X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_597 ),
    inference(avatar_component_clause,[],[f4618]) ).

fof(f37871,plain,
    ( spl0_1242
    | ~ spl0_100
    | ~ spl0_587 ),
    inference(avatar_split_clause,[],[f4538,f4515,f1182,f37869]) ).

fof(f37869,plain,
    ( spl0_1242
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).

fof(f4515,plain,
    ( spl0_587
  <=> ! [X5,X0,X6,X15] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X5,X6,X0),X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).

fof(f4538,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_587 ),
    inference(resolution,[],[f4516,f1184]) ).

fof(f4516,plain,
    ( ! [X0,X6,X15,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X5,X6,X0),X15,X0) )
    | ~ spl0_587 ),
    inference(avatar_component_clause,[],[f4515]) ).

fof(f37867,plain,
    ( spl0_1241
    | ~ spl0_59
    | ~ spl0_587 ),
    inference(avatar_split_clause,[],[f4537,f4515,f977,f37865]) ).

fof(f37865,plain,
    ( spl0_1241
  <=> ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).

fof(f4537,plain,
    ( ! [X2,X0,X1] : c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_587 ),
    inference(resolution,[],[f4516,f979]) ).

fof(f37863,plain,
    ( spl0_1240
    | ~ spl0_102
    | ~ spl0_585 ),
    inference(avatar_split_clause,[],[f4531,f4507,f1192,f37861]) ).

fof(f37861,plain,
    ( spl0_1240
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).

fof(f4507,plain,
    ( spl0_585
  <=> ! [X5,X0,X12,X6] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X5,X6,X0),X12,X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).

fof(f4531,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_102
    | ~ spl0_585 ),
    inference(resolution,[],[f4508,f1194]) ).

fof(f4508,plain,
    ( ! [X0,X6,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X5,X6,X0),X12,X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_585 ),
    inference(avatar_component_clause,[],[f4507]) ).

fof(f37859,plain,
    ( spl0_1239
    | ~ spl0_61
    | ~ spl0_585 ),
    inference(avatar_split_clause,[],[f4530,f4507,f987,f37857]) ).

fof(f37857,plain,
    ( spl0_1239
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).

fof(f4530,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_61
    | ~ spl0_585 ),
    inference(resolution,[],[f4508,f989]) ).

fof(f37855,plain,
    ( spl0_1238
    | ~ spl0_53
    | ~ spl0_583 ),
    inference(avatar_split_clause,[],[f4529,f4499,f947,f37853]) ).

fof(f37853,plain,
    ( spl0_1238
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).

fof(f4499,plain,
    ( spl0_583
  <=> ! [X5,X0,X6,X15] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X5,X6,X0),X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).

fof(f4529,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ spl0_53
    | ~ spl0_583 ),
    inference(resolution,[],[f4500,f949]) ).

fof(f4500,plain,
    ( ! [X0,X6,X15,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X5,X6,X0),X15,X0) )
    | ~ spl0_583 ),
    inference(avatar_component_clause,[],[f4499]) ).

fof(f37851,plain,
    ( spl0_1237
    | ~ spl0_97
    | ~ spl0_583 ),
    inference(avatar_split_clause,[],[f4528,f4499,f1167,f37849]) ).

fof(f37849,plain,
    ( spl0_1237
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).

fof(f4528,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_97
    | ~ spl0_583 ),
    inference(resolution,[],[f4500,f1169]) ).

fof(f37847,plain,
    ( spl0_1236
    | ~ spl0_13
    | ~ spl0_583 ),
    inference(avatar_split_clause,[],[f4527,f4499,f747,f37845]) ).

fof(f37845,plain,
    ( spl0_1236
  <=> ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_nat),c_Polynomial_Omonom(X2,X1,tc_nat),tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).

fof(f4527,plain,
    ( ! [X2,X0,X1] : c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X0,X1,tc_nat),c_Polynomial_Omonom(X2,X1,tc_nat),tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)
    | ~ spl0_13
    | ~ spl0_583 ),
    inference(resolution,[],[f4500,f749]) ).

fof(f37843,plain,
    ( spl0_1235
    | ~ spl0_45
    | ~ spl0_582 ),
    inference(avatar_split_clause,[],[f4525,f4495,f907,f37841]) ).

fof(f37841,plain,
    ( spl0_1235
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).

fof(f4495,plain,
    ( spl0_582
  <=> ! [X5,X0,X12,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X5,X6,X0),X12,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).

fof(f4525,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_RealDef_Oreal),c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_582 ),
    inference(resolution,[],[f4496,f909]) ).

fof(f4496,plain,
    ( ! [X0,X6,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X5,X6,X0),X12,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_582 ),
    inference(avatar_component_clause,[],[f4495]) ).

fof(f37839,plain,
    ( spl0_1234
    | ~ spl0_89
    | ~ spl0_582 ),
    inference(avatar_split_clause,[],[f4524,f4495,f1127,f37837]) ).

fof(f37837,plain,
    ( spl0_1234
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).

fof(f4524,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_Complex_Ocomplex),c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_582 ),
    inference(resolution,[],[f4496,f1129]) ).

fof(f37835,plain,
    ( spl0_1233
    | ~ spl0_1164
    | ~ spl0_1212 ),
    inference(avatar_split_clause,[],[f37605,f34131,f33179,f37833]) ).

fof(f37833,plain,
    ( spl0_1233
  <=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).

fof(f37605,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(c_Polynomial_Osmult(X0,v_p,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2)
    | ~ spl0_1164
    | ~ spl0_1212 ),
    inference(superposition,[],[f34132,f33180]) ).

fof(f37831,plain,
    ( spl0_1232
    | ~ spl0_8
    | ~ spl0_582 ),
    inference(avatar_split_clause,[],[f4523,f4495,f722,f37829]) ).

fof(f37829,plain,
    ( spl0_1232
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_nat),c_Polynomial_Osmult(X1,X2,tc_nat),tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).

fof(f4523,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X0,X2,tc_nat),c_Polynomial_Osmult(X1,X2,tc_nat),tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_8
    | ~ spl0_582 ),
    inference(resolution,[],[f4496,f724]) ).

fof(f37827,plain,
    ( spl0_1231
    | ~ spl0_45
    | ~ spl0_581 ),
    inference(avatar_split_clause,[],[f4521,f4491,f907,f37825]) ).

fof(f37825,plain,
    ( spl0_1231
  <=> ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).

fof(f4491,plain,
    ( spl0_581
  <=> ! [X13,X0,X12,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X5,X12,X0),X13,X0) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_Polynomial_Osynthetic__div(X12,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).

fof(f4521,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_581 ),
    inference(resolution,[],[f4492,f909]) ).

fof(f4492,plain,
    ( ! [X0,X5,X12,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X5,X12,X0),X13,X0) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_Polynomial_Osynthetic__div(X12,X13,X0),X0) )
    | ~ spl0_581 ),
    inference(avatar_component_clause,[],[f4491]) ).

fof(f37823,plain,
    ( spl0_1230
    | ~ spl0_89
    | ~ spl0_581 ),
    inference(avatar_split_clause,[],[f4520,f4491,f1127,f37821]) ).

fof(f37821,plain,
    ( spl0_1230
  <=> ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).

fof(f4520,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_581 ),
    inference(resolution,[],[f4492,f1129]) ).

fof(f37819,plain,
    ( spl0_1229
    | ~ spl0_8
    | ~ spl0_581 ),
    inference(avatar_split_clause,[],[f4519,f4491,f722,f37817]) ).

fof(f37817,plain,
    ( spl0_1229
  <=> ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_nat),X2,tc_nat) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).

fof(f4519,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X0,X1,tc_nat),X2,tc_nat) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),c_Polynomial_Osynthetic__div(X1,X2,tc_nat),tc_nat)
    | ~ spl0_8
    | ~ spl0_581 ),
    inference(resolution,[],[f4492,f724]) ).

fof(f37815,plain,
    ( spl0_1228
    | ~ spl0_315
    | ~ spl0_573 ),
    inference(avatar_split_clause,[],[f4401,f4189,f2414,f37813]) ).

fof(f37813,plain,
    ( spl0_1228
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).

fof(f4189,plain,
    ( spl0_573
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).

fof(f4401,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X1,X2,X0),X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_315
    | ~ spl0_573 ),
    inference(resolution,[],[f4190,f2415]) ).

fof(f4190,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_573 ),
    inference(avatar_component_clause,[],[f4189]) ).

fof(f37811,plain,
    ( spl0_1227
    | ~ spl0_314
    | ~ spl0_572 ),
    inference(avatar_split_clause,[],[f4369,f4185,f2410,f37809]) ).

fof(f37809,plain,
    ( spl0_1227
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X0),X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).

fof(f4185,plain,
    ( spl0_572
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).

fof(f4369,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,X3,X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X2,X1,X0),X1,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_314
    | ~ spl0_572 ),
    inference(resolution,[],[f4186,f2411]) ).

fof(f4186,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_572 ),
    inference(avatar_component_clause,[],[f4185]) ).

fof(f37807,plain,
    ( spl0_1226
    | ~ spl0_378
    | ~ spl0_524 ),
    inference(avatar_split_clause,[],[f3934,f3820,f2766,f37805]) ).

fof(f37805,plain,
    ( spl0_1226
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).

fof(f2766,plain,
    ( spl0_378
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).

fof(f3820,plain,
    ( spl0_524
  <=> ! [X2,X1,X0,X25,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X2,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).

fof(f3934,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_378
    | ~ spl0_524 ),
    inference(duplicate_literal_removal,[],[f3933]) ).

fof(f3933,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_378
    | ~ spl0_524 ),
    inference(resolution,[],[f3821,f2767]) ).

fof(f2767,plain,
    ( ! [X2,X0] :
        ( c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0)
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_378 ),
    inference(avatar_component_clause,[],[f2766]) ).

fof(f3821,plain,
    ( ! [X2,X0,X1,X7,X25] :
        ( ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X2,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)) = X1 )
    | ~ spl0_524 ),
    inference(avatar_component_clause,[],[f3820]) ).

fof(f37803,plain,
    ( spl0_1225
    | ~ spl0_255
    | ~ spl0_481 ),
    inference(avatar_split_clause,[],[f3628,f3381,f1987,f37801]) ).

fof(f37801,plain,
    ( spl0_1225
  <=> ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).

fof(f3628,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0) )
    | ~ spl0_255
    | ~ spl0_481 ),
    inference(duplicate_literal_removal,[],[f3625]) ).

fof(f3625,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_255
    | ~ spl0_481 ),
    inference(resolution,[],[f3382,f1988]) ).

fof(f37799,plain,
    ( spl0_1224
    | ~ spl0_156
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f3202,f3121,f1428,f37797]) ).

fof(f37797,plain,
    ( spl0_1224
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X0)
        | ~ class_HOL_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).

fof(f1428,plain,
    ( spl0_156
  <=> ! [X48] :
        ( ~ class_HOL_Ozero(X48)
        | class_HOL_Ozero(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).

fof(f3121,plain,
    ( spl0_426
  <=> ! [X0,X5,X15,X30] :
        ( ~ class_HOL_Ozero(X0)
        | X15 = X30
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X30,X0),X0),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).

fof(f3202,plain,
    ( ! [X2,X3,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X2)) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X3,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X0)
        | ~ class_HOL_Ozero(X2) )
    | ~ spl0_156
    | ~ spl0_426 ),
    inference(resolution,[],[f3122,f1429]) ).

fof(f1429,plain,
    ( ! [X48] :
        ( class_HOL_Ozero(tc_Polynomial_Opoly(X48))
        | ~ class_HOL_Ozero(X48) )
    | ~ spl0_156 ),
    inference(avatar_component_clause,[],[f1428]) ).

fof(f3122,plain,
    ( ! [X0,X15,X5,X30] :
        ( ~ class_HOL_Ozero(X0)
        | X15 = X30
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X30,X0),X0),X15) )
    | ~ spl0_426 ),
    inference(avatar_component_clause,[],[f3121]) ).

fof(f37733,plain,
    ( spl0_1223
    | ~ spl0_114
    | ~ spl0_112
    | ~ spl0_420
    | ~ spl0_425 ),
    inference(avatar_split_clause,[],[f3201,f3117,f3014,f1242,f1252,f37731]) ).

fof(f1252,plain,
    ( spl0_114
  <=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).

fof(f3014,plain,
    ( spl0_420
  <=> ! [X12] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).

fof(f3117,plain,
    ( spl0_425
  <=> ! [X0,X12] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,X0),X0,X0)
        | c_Polynomial_Odegree(X12,X0) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).

fof(f3201,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | ~ class_Int_Oring__char__0(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(X0,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X0)) )
    | ~ spl0_420
    | ~ spl0_425 ),
    inference(resolution,[],[f3118,f3015]) ).

fof(f3015,plain,
    ( ! [X12] :
        ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X12)) )
    | ~ spl0_420 ),
    inference(avatar_component_clause,[],[f3014]) ).

fof(f3118,plain,
    ( ! [X0,X12] :
        ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,X0),X0,X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | ~ class_Int_Oring__char__0(X0)
        | c_Polynomial_Odegree(X12,X0) = c_HOL_Ozero__class_Ozero(tc_nat) )
    | ~ spl0_425 ),
    inference(avatar_component_clause,[],[f3117]) ).

fof(f37729,plain,
    ( spl0_1222
    | ~ spl0_151
    | ~ spl0_411 ),
    inference(avatar_split_clause,[],[f3092,f2977,f1408,f37727]) ).

fof(f37727,plain,
    ( spl0_1222
  <=> ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).

fof(f1408,plain,
    ( spl0_151
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X48)
        | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).

fof(f2977,plain,
    ( spl0_411
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).

fof(f3092,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring(X1) )
    | ~ spl0_151
    | ~ spl0_411 ),
    inference(resolution,[],[f2978,f1409]) ).

fof(f1409,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__ring(X48) )
    | ~ spl0_151 ),
    inference(avatar_component_clause,[],[f1408]) ).

fof(f2978,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_411 ),
    inference(avatar_component_clause,[],[f2977]) ).

fof(f37725,plain,
    ( spl0_1221
    | ~ spl0_151
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f3061,f2941,f1408,f37723]) ).

fof(f37723,plain,
    ( spl0_1221
  <=> ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).

fof(f2941,plain,
    ( spl0_402
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).

fof(f3061,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) )
    | ~ spl0_151
    | ~ spl0_402 ),
    inference(resolution,[],[f2942,f1409]) ).

fof(f2942,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_402 ),
    inference(avatar_component_clause,[],[f2941]) ).

fof(f37721,plain,
    ( spl0_1220
    | ~ spl0_152
    | ~ spl0_401 ),
    inference(avatar_split_clause,[],[f3058,f2937,f1412,f37719]) ).

fof(f37719,plain,
    ( spl0_1220
  <=> ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Oidom(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).

fof(f2937,plain,
    ( spl0_401
  <=> ! [X6,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Otimes__class_Otimes(X6,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).

fof(f3058,plain,
    ( ! [X0,X1] :
        ( c_HOL_Otimes__class_Otimes(X0,X0,tc_Polynomial_Opoly(X1)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Oidom(X1) )
    | ~ spl0_152
    | ~ spl0_401 ),
    inference(resolution,[],[f2938,f1413]) ).

fof(f2938,plain,
    ( ! [X0,X6] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Otimes__class_Otimes(X6,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_401 ),
    inference(avatar_component_clause,[],[f2937]) ).

fof(f37717,plain,
    ( spl0_1219
    | ~ spl0_151
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3022,f2889,f1408,f37715]) ).

fof(f37715,plain,
    ( spl0_1219
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).

fof(f2889,plain,
    ( spl0_389
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).

fof(f3022,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) )
    | ~ spl0_151
    | ~ spl0_389 ),
    inference(resolution,[],[f2890,f1409]) ).

fof(f2890,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_389 ),
    inference(avatar_component_clause,[],[f2889]) ).

fof(f37713,plain,
    ( spl0_1218
    | ~ spl0_151
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f3019,f2885,f1408,f37711]) ).

fof(f37711,plain,
    ( spl0_1218
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).

fof(f2885,plain,
    ( spl0_388
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).

fof(f3019,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X2)),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring(X2) )
    | ~ spl0_151
    | ~ spl0_388 ),
    inference(resolution,[],[f2886,f1409]) ).

fof(f2886,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) )
    | ~ spl0_388 ),
    inference(avatar_component_clause,[],[f2885]) ).

fof(f37709,plain,
    ( spl0_1217
    | ~ spl0_164
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f2579,f2430,f1462,f37707]) ).

fof(f37707,plain,
    ( spl0_1217
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Oboolean__algebra(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).

fof(f1462,plain,
    ( spl0_164
  <=> ! [X48,X49] :
        ( ~ class_Lattices_Oboolean__algebra(X48)
        | class_Lattices_Oboolean__algebra(tc_fun(X49,X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).

fof(f2430,plain,
    ( spl0_319
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).

fof(f2579,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_fun(X2,X3)),tc_fun(X2,X3))
        | ~ class_Lattices_Oboolean__algebra(X3) )
    | ~ spl0_164
    | ~ spl0_319 ),
    inference(resolution,[],[f2431,f1463]) ).

fof(f1463,plain,
    ( ! [X48,X49] :
        ( class_Lattices_Oboolean__algebra(tc_fun(X49,X48))
        | ~ class_Lattices_Oboolean__algebra(X48) )
    | ~ spl0_164 ),
    inference(avatar_component_clause,[],[f1462]) ).

fof(f2431,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
    | ~ spl0_319 ),
    inference(avatar_component_clause,[],[f2430]) ).

fof(f37647,plain,
    ( spl0_1216
    | ~ spl0_124
    | ~ spl0_1212 ),
    inference(avatar_split_clause,[],[f37597,f34131,f1300,f37645]) ).

fof(f37597,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(v_p,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1)
    | ~ spl0_124
    | ~ spl0_1212 ),
    inference(superposition,[],[f34132,f1301]) ).

fof(f34145,plain,
    ( spl0_1215
    | ~ spl0_332
    | ~ spl0_607 ),
    inference(avatar_split_clause,[],[f4729,f4658,f2482,f34143]) ).

fof(f34143,plain,
    ( spl0_1215
  <=> ! [X2,X3,X4,X0,X5,X1] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).

fof(f2482,plain,
    ( spl0_332
  <=> ! [X11,X13,X10,X8] : hAPP(c_Fun_Ocomp(c_COMBK(X13,X10,X11),X8,X11,X10,t_a),v_x) = X13 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).

fof(f4729,plain,
    ( ! [X2,X3,X0,X1,X4,X5] : hAPP(c_Fun_Ocomp(c_Fun_Ocomp(c_COMBK(X0,X1,X2),X3,X2,X1,X5),X4,X5,X1,t_a),v_x) = X0
    | ~ spl0_332
    | ~ spl0_607 ),
    inference(superposition,[],[f2483,f4659]) ).

fof(f2483,plain,
    ( ! [X10,X11,X8,X13] : hAPP(c_Fun_Ocomp(c_COMBK(X13,X10,X11),X8,X11,X10,t_a),v_x) = X13
    | ~ spl0_332 ),
    inference(avatar_component_clause,[],[f2482]) ).

fof(f34141,plain,
    ( spl0_1214
    | ~ spl0_419
    | ~ spl0_597 ),
    inference(avatar_split_clause,[],[f4684,f4618,f3010,f34139]) ).

fof(f34139,plain,
    ( spl0_1214
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X4,X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).

fof(f3010,plain,
    ( spl0_419
  <=> ! [X25,X0,X1,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
        | ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).

fof(f4684,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X4,X2,X1) )
    | ~ spl0_419
    | ~ spl0_597 ),
    inference(duplicate_literal_removal,[],[f4672]) ).

fof(f4672,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Polynomial_Opdivmod__rel(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),X2,X3,X1)
        | ~ class_Ring__and__Field_Ofield(X1)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = c_Polynomial_Osmult(X4,X2,X1)
        | ~ class_Ring__and__Field_Ofield(X1) )
    | ~ spl0_419
    | ~ spl0_597 ),
    inference(resolution,[],[f4619,f3011]) ).

fof(f3011,plain,
    ( ! [X0,X1,X7,X25] :
        ( ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_419 ),
    inference(avatar_component_clause,[],[f3010]) ).

fof(f34137,plain,
    ( spl0_1213
    | ~ spl0_45
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4479,f4240,f907,f34135]) ).

fof(f34135,plain,
    ( spl0_1213
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).

fof(f4240,plain,
    ( spl0_579
  <=> ! [X0,X12,X1,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X12,X7,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),hAPP(c_Polynomial_Opoly(X7,X0),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).

fof(f4479,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2))
    | ~ spl0_45
    | ~ spl0_579 ),
    inference(resolution,[],[f4241,f909]) ).

fof(f4241,plain,
    ( ! [X0,X1,X7,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X12,X7,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),hAPP(c_Polynomial_Opoly(X7,X0),X1)) )
    | ~ spl0_579 ),
    inference(avatar_component_clause,[],[f4240]) ).

fof(f34133,plain,
    ( spl0_1212
    | ~ spl0_89
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4478,f4240,f1127,f34131]) ).

fof(f4478,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X2))
    | ~ spl0_89
    | ~ spl0_579 ),
    inference(resolution,[],[f4241,f1129]) ).

fof(f34129,plain,
    ( spl0_1211
    | ~ spl0_8
    | ~ spl0_579 ),
    inference(avatar_split_clause,[],[f4477,f4240,f722,f34127]) ).

fof(f34127,plain,
    ( spl0_1211
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_nat),tc_nat),X2) = hAPP(c_Polynomial_Opoly(X0,tc_nat),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).

fof(f4477,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X0,X1,tc_nat),tc_nat),X2) = hAPP(c_Polynomial_Opoly(X0,tc_nat),hAPP(c_Polynomial_Opoly(X1,tc_nat),X2))
    | ~ spl0_8
    | ~ spl0_579 ),
    inference(resolution,[],[f4241,f724]) ).

fof(f34125,plain,
    ( spl0_1210
    | ~ spl0_983
    | ~ spl0_1111 ),
    inference(avatar_split_clause,[],[f29985,f29920,f22076,f34123]) ).

fof(f34123,plain,
    ( spl0_1210
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).

fof(f22076,plain,
    ( spl0_983
  <=> ! [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_983])]) ).

fof(f29920,plain,
    ( spl0_1111
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).

fof(f29985,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X0,X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_983
    | ~ spl0_1111 ),
    inference(superposition,[],[f29921,f22077]) ).

fof(f22077,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_983 ),
    inference(avatar_component_clause,[],[f22076]) ).

fof(f29921,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1111 ),
    inference(avatar_component_clause,[],[f29920]) ).

fof(f34121,plain,
    ( spl0_1209
    | ~ spl0_110
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f4438,f4193,f1232,f34119]) ).

fof(f34119,plain,
    ( spl0_1209
  <=> ! [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_1209])]) ).

fof(f4193,plain,
    ( spl0_574
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).

fof(f4438,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_110
    | ~ spl0_574 ),
    inference(resolution,[],[f4194,f1234]) ).

fof(f4194,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) )
    | ~ spl0_574 ),
    inference(avatar_component_clause,[],[f4193]) ).

fof(f34117,plain,
    ( spl0_1208
    | ~ spl0_71
    | ~ spl0_574 ),
    inference(avatar_split_clause,[],[f4437,f4193,f1037,f34115]) ).

fof(f34115,plain,
    ( spl0_1208
  <=> ! [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_1208])]) ).

fof(f4437,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_71
    | ~ spl0_574 ),
    inference(resolution,[],[f4194,f1039]) ).

fof(f34113,plain,
    ( spl0_1207
    | ~ spl0_107
    | ~ spl0_570 ),
    inference(avatar_split_clause,[],[f4358,f4177,f1217,f34111]) ).

fof(f34111,plain,
    ( spl0_1207
  <=> ! [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_1207])]) ).

fof(f1217,plain,
    ( spl0_107
  <=> class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).

fof(f4177,plain,
    ( spl0_570
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).

fof(f4358,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_107
    | ~ spl0_570 ),
    inference(resolution,[],[f4178,f1219]) ).

fof(f1219,plain,
    ( class_RealVector_Oreal__vector(tc_Complex_Ocomplex)
    | ~ spl0_107 ),
    inference(avatar_component_clause,[],[f1217]) ).

fof(f4178,plain,
    ( ! [X2,X0,X1,X5] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) )
    | ~ spl0_570 ),
    inference(avatar_component_clause,[],[f4177]) ).

fof(f34109,plain,
    ( spl0_1206
    | ~ spl0_67
    | ~ spl0_570 ),
    inference(avatar_split_clause,[],[f4357,f4177,f1017,f34107]) ).

fof(f34107,plain,
    ( spl0_1206
  <=> ! [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_1206])]) ).

fof(f1017,plain,
    ( spl0_67
  <=> class_RealVector_Oreal__vector(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).

fof(f4357,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_67
    | ~ spl0_570 ),
    inference(resolution,[],[f4178,f1019]) ).

fof(f1019,plain,
    ( class_RealVector_Oreal__vector(tc_RealDef_Oreal)
    | ~ spl0_67 ),
    inference(avatar_component_clause,[],[f1017]) ).

fof(f34105,plain,
    ( spl0_1205
    | ~ spl0_90
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4356,f4173,f1132,f34103]) ).

fof(f34103,plain,
    ( spl0_1205
  <=> ! [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_1205])]) ).

fof(f1132,plain,
    ( spl0_90
  <=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).

fof(f4173,plain,
    ( spl0_569
  <=> ! [X5,X36,X0,X6] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X36,X0),X6,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X36,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).

fof(f4356,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_90
    | ~ spl0_569 ),
    inference(resolution,[],[f4174,f1134]) ).

fof(f1134,plain,
    ( class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex)
    | ~ spl0_90 ),
    inference(avatar_component_clause,[],[f1132]) ).

fof(f4174,plain,
    ( ! [X0,X36,X6,X5] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X36,X0),X6,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X36,X6,X0),X0) )
    | ~ spl0_569 ),
    inference(avatar_component_clause,[],[f4173]) ).

fof(f34101,plain,
    ( spl0_1204
    | ~ spl0_46
    | ~ spl0_569 ),
    inference(avatar_split_clause,[],[f4355,f4173,f912,f34099]) ).

fof(f34099,plain,
    ( spl0_1204
  <=> ! [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_1204])]) ).

fof(f912,plain,
    ( spl0_46
  <=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).

fof(f4355,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_46
    | ~ spl0_569 ),
    inference(resolution,[],[f4174,f914]) ).

fof(f914,plain,
    ( class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal)
    | ~ spl0_46 ),
    inference(avatar_component_clause,[],[f912]) ).

fof(f34097,plain,
    ( spl0_1203
    | ~ spl0_90
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f4354,f4163,f1132,f34095]) ).

fof(f34095,plain,
    ( spl0_1203
  <=> ! [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_1203])]) ).

fof(f4163,plain,
    ( spl0_568
  <=> ! [X35,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(X35,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).

fof(f4354,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_90
    | ~ spl0_568 ),
    inference(resolution,[],[f4164,f1134]) ).

fof(f4164,plain,
    ( ! [X2,X0,X1,X35] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(X35,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) )
    | ~ spl0_568 ),
    inference(avatar_component_clause,[],[f4163]) ).

fof(f34093,plain,
    ( spl0_1202
    | ~ spl0_46
    | ~ spl0_568 ),
    inference(avatar_split_clause,[],[f4353,f4163,f912,f34091]) ).

fof(f34091,plain,
    ( spl0_1202
  <=> ! [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_1202])]) ).

fof(f4353,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_46
    | ~ spl0_568 ),
    inference(resolution,[],[f4164,f914]) ).

fof(f34089,plain,
    ( spl0_1201
    | ~ spl0_38
    | ~ spl0_565 ),
    inference(avatar_split_clause,[],[f4350,f4151,f872,f34087]) ).

fof(f34087,plain,
    ( spl0_1201
  <=> ! [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_1201])]) ).

fof(f872,plain,
    ( spl0_38
  <=> class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f4151,plain,
    ( spl0_565
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X13,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).

fof(f4350,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_38
    | ~ spl0_565 ),
    inference(resolution,[],[f4152,f874]) ).

fof(f874,plain,
    ( class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal)
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f872]) ).

fof(f4152,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X13,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) )
    | ~ spl0_565 ),
    inference(avatar_component_clause,[],[f4151]) ).

fof(f34085,plain,
    ( spl0_1200
    | ~ spl0_38
    | ~ spl0_564 ),
    inference(avatar_split_clause,[],[f4349,f4147,f872,f34083]) ).

fof(f34083,plain,
    ( spl0_1200
  <=> ! [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_1200])]) ).

fof(f4147,plain,
    ( spl0_564
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X13,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).

fof(f4349,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_38
    | ~ spl0_564 ),
    inference(resolution,[],[f4148,f874]) ).

fof(f4148,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X13,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) )
    | ~ spl0_564 ),
    inference(avatar_component_clause,[],[f4147]) ).

fof(f34081,plain,
    ( spl0_1199
    | ~ spl0_705
    | ~ spl0_1111 ),
    inference(avatar_split_clause,[],[f29968,f29920,f6719,f34079]) ).

fof(f34079,plain,
    ( spl0_1199
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).

fof(f6719,plain,
    ( spl0_705
  <=> ! [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_705])]) ).

fof(f29968,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_705
    | ~ spl0_1111 ),
    inference(superposition,[],[f29921,f6720]) ).

fof(f6720,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_705 ),
    inference(avatar_component_clause,[],[f6719]) ).

fof(f34077,plain,
    ( spl0_1198
    | ~ spl0_7
    | ~ spl0_562 ),
    inference(avatar_split_clause,[],[f4315,f4139,f717,f34075]) ).

fof(f34075,plain,
    ( spl0_1198
  <=> ! [X2,X0,X1] : 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) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).

fof(f4139,plain,
    ( spl0_562
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).

fof(f4315,plain,
    ( ! [X2,X0,X1] : 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) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
    | ~ spl0_7
    | ~ spl0_562 ),
    inference(resolution,[],[f4140,f719]) ).

fof(f4140,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) )
    | ~ spl0_562 ),
    inference(avatar_component_clause,[],[f4139]) ).

fof(f34073,plain,
    ( spl0_1197
    | ~ spl0_90
    | ~ spl0_560 ),
    inference(avatar_split_clause,[],[f4311,f4131,f1132,f34071]) ).

fof(f34071,plain,
    ( spl0_1197
  <=> ! [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_1197])]) ).

fof(f4131,plain,
    ( spl0_560
  <=> ! [X35,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(X35,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).

fof(f4311,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_90
    | ~ spl0_560 ),
    inference(resolution,[],[f4132,f1134]) ).

fof(f4132,plain,
    ( ! [X2,X0,X1,X35] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(X35,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) )
    | ~ spl0_560 ),
    inference(avatar_component_clause,[],[f4131]) ).

fof(f34069,plain,
    ( spl0_1196
    | ~ spl0_46
    | ~ spl0_560 ),
    inference(avatar_split_clause,[],[f4310,f4131,f912,f34067]) ).

fof(f34067,plain,
    ( spl0_1196
  <=> ! [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_1196])]) ).

fof(f4310,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_46
    | ~ spl0_560 ),
    inference(resolution,[],[f4132,f914]) ).

fof(f34065,plain,
    ( spl0_1195
    | ~ spl0_44
    | ~ spl0_559 ),
    inference(avatar_split_clause,[],[f4309,f4127,f902,f34063]) ).

fof(f34063,plain,
    ( spl0_1195
  <=> ! [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_1195])]) ).

fof(f4127,plain,
    ( spl0_559
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).

fof(f4309,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_44
    | ~ spl0_559 ),
    inference(resolution,[],[f4128,f904]) ).

fof(f4128,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) )
    | ~ spl0_559 ),
    inference(avatar_component_clause,[],[f4127]) ).

fof(f34061,plain,
    ( spl0_1194
    | ~ spl0_88
    | ~ spl0_559 ),
    inference(avatar_split_clause,[],[f4308,f4127,f1122,f34059]) ).

fof(f34059,plain,
    ( spl0_1194
  <=> ! [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_1194])]) ).

fof(f4308,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_88
    | ~ spl0_559 ),
    inference(resolution,[],[f4128,f1124]) ).

fof(f34057,plain,
    ( spl0_1193
    | ~ spl0_7
    | ~ spl0_559 ),
    inference(avatar_split_clause,[],[f4307,f4127,f717,f34055]) ).

fof(f34055,plain,
    ( spl0_1193
  <=> ! [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_1193])]) ).

fof(f4307,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_7
    | ~ spl0_559 ),
    inference(resolution,[],[f4128,f719]) ).

fof(f34053,plain,
    ( spl0_1192
    | ~ spl0_45
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4305,f4119,f907,f34051]) ).

fof(f34051,plain,
    ( spl0_1192
  <=> ! [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_1192])]) ).

fof(f4119,plain,
    ( spl0_557
  <=> ! [X6,X0,X12,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_OpCons(X6,X12,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_Polynomial_Osmult(X5,X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).

fof(f4305,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_45
    | ~ spl0_557 ),
    inference(resolution,[],[f4120,f909]) ).

fof(f4120,plain,
    ( ! [X0,X6,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_Polynomial_OpCons(X6,X12,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_Polynomial_Osmult(X5,X12,X0),X0) )
    | ~ spl0_557 ),
    inference(avatar_component_clause,[],[f4119]) ).

fof(f34049,plain,
    ( spl0_1191
    | ~ spl0_89
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4304,f4119,f1127,f34047]) ).

fof(f34047,plain,
    ( spl0_1191
  <=> ! [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_1191])]) ).

fof(f4304,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_89
    | ~ spl0_557 ),
    inference(resolution,[],[f4120,f1129]) ).

fof(f34045,plain,
    ( spl0_1190
    | ~ spl0_8
    | ~ spl0_557 ),
    inference(avatar_split_clause,[],[f4303,f4119,f722,f34043]) ).

fof(f34043,plain,
    ( spl0_1190
  <=> ! [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_1190])]) ).

fof(f4303,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_8
    | ~ spl0_557 ),
    inference(resolution,[],[f4120,f724]) ).

fof(f34041,plain,
    ( spl0_1189
    | ~ spl0_33
    | ~ spl0_554 ),
    inference(avatar_split_clause,[],[f4299,f4107,f847,f34039]) ).

fof(f34039,plain,
    ( spl0_1189
  <=> ! [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_1189])]) ).

fof(f847,plain,
    ( spl0_33
  <=> class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f4107,plain,
    ( spl0_554
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X13,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).

fof(f4299,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_33
    | ~ spl0_554 ),
    inference(resolution,[],[f4108,f849]) ).

fof(f849,plain,
    ( class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal)
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f847]) ).

fof(f4108,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X13,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) )
    | ~ spl0_554 ),
    inference(avatar_component_clause,[],[f4107]) ).

fof(f34001,plain,
    ( spl0_1188
    | ~ spl0_33
    | ~ spl0_553 ),
    inference(avatar_split_clause,[],[f4298,f4103,f847,f33999]) ).

fof(f33999,plain,
    ( spl0_1188
  <=> ! [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_1188])]) ).

fof(f4103,plain,
    ( spl0_553
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X13,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).

fof(f4298,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_33
    | ~ spl0_553 ),
    inference(resolution,[],[f4104,f849]) ).

fof(f4104,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X13,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) )
    | ~ spl0_553 ),
    inference(avatar_component_clause,[],[f4103]) ).

fof(f33997,plain,
    ( spl0_1187
    | ~ spl0_28
    | ~ spl0_552 ),
    inference(avatar_split_clause,[],[f4270,f4099,f822,f33995]) ).

fof(f33995,plain,
    ( spl0_1187
  <=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).

fof(f822,plain,
    ( spl0_28
  <=> class_Lattices_Odistrib__lattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f4099,plain,
    ( spl0_552
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).

fof(f4270,plain,
    ( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool)
    | ~ spl0_28
    | ~ spl0_552 ),
    inference(resolution,[],[f4100,f824]) ).

fof(f824,plain,
    ( class_Lattices_Odistrib__lattice(tc_bool)
    | ~ spl0_28 ),
    inference(avatar_component_clause,[],[f822]) ).

fof(f4100,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) )
    | ~ spl0_552 ),
    inference(avatar_component_clause,[],[f4099]) ).

fof(f33993,plain,
    ( spl0_1186
    | ~ spl0_63
    | ~ spl0_552 ),
    inference(avatar_split_clause,[],[f4268,f4099,f997,f33991]) ).

fof(f33991,plain,
    ( spl0_1186
  <=> ! [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_1186])]) ).

fof(f997,plain,
    ( spl0_63
  <=> class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).

fof(f4268,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_63
    | ~ spl0_552 ),
    inference(resolution,[],[f4100,f999]) ).

fof(f999,plain,
    ( class_Lattices_Odistrib__lattice(tc_RealDef_Oreal)
    | ~ spl0_63 ),
    inference(avatar_component_clause,[],[f997]) ).

fof(f33989,plain,
    ( spl0_1185
    | ~ spl0_19
    | ~ spl0_552 ),
    inference(avatar_split_clause,[],[f4267,f4099,f777,f33987]) ).

fof(f33987,plain,
    ( spl0_1185
  <=> ! [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_1185])]) ).

fof(f777,plain,
    ( spl0_19
  <=> class_Lattices_Odistrib__lattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f4267,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_19
    | ~ spl0_552 ),
    inference(resolution,[],[f4100,f779]) ).

fof(f779,plain,
    ( class_Lattices_Odistrib__lattice(tc_nat)
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f777]) ).

fof(f33985,plain,
    ( spl0_1184
    | ~ spl0_28
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f4266,f4095,f822,f33983]) ).

fof(f33983,plain,
    ( spl0_1184
  <=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).

fof(f4095,plain,
    ( spl0_551
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).

fof(f4266,plain,
    ( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool)
    | ~ spl0_28
    | ~ spl0_551 ),
    inference(resolution,[],[f4096,f824]) ).

fof(f4096,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X0),X0) )
    | ~ spl0_551 ),
    inference(avatar_component_clause,[],[f4095]) ).

fof(f33981,plain,
    ( spl0_1183
    | ~ spl0_63
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f4264,f4095,f997,f33979]) ).

fof(f33979,plain,
    ( spl0_1183
  <=> ! [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_1183])]) ).

fof(f4264,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_63
    | ~ spl0_551 ),
    inference(resolution,[],[f4096,f999]) ).

fof(f33977,plain,
    ( spl0_1182
    | ~ spl0_19
    | ~ spl0_551 ),
    inference(avatar_split_clause,[],[f4263,f4095,f777,f33975]) ).

fof(f33975,plain,
    ( spl0_1182
  <=> ! [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_1182])]) ).

fof(f4263,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_19
    | ~ spl0_551 ),
    inference(resolution,[],[f4096,f779]) ).

fof(f33973,plain,
    ( spl0_1181
    | ~ spl0_110
    | ~ spl0_549 ),
    inference(avatar_split_clause,[],[f4260,f4087,f1232,f33971]) ).

fof(f33971,plain,
    ( spl0_1181
  <=> ! [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_1181])]) ).

fof(f4087,plain,
    ( spl0_549
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X6,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).

fof(f4260,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_110
    | ~ spl0_549 ),
    inference(resolution,[],[f4088,f1234]) ).

fof(f4088,plain,
    ( ! [X0,X6,X5,X13] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X6,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) )
    | ~ spl0_549 ),
    inference(avatar_component_clause,[],[f4087]) ).

fof(f33969,plain,
    ( spl0_1180
    | ~ spl0_71
    | ~ spl0_549 ),
    inference(avatar_split_clause,[],[f4259,f4087,f1037,f33967]) ).

fof(f33967,plain,
    ( spl0_1180
  <=> ! [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_1180])]) ).

fof(f4259,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_71
    | ~ spl0_549 ),
    inference(resolution,[],[f4088,f1039]) ).

fof(f33965,plain,
    ( spl0_1179
    | ~ spl0_107
    | ~ spl0_547 ),
    inference(avatar_split_clause,[],[f4256,f4052,f1217,f33963]) ).

fof(f33963,plain,
    ( spl0_1179
  <=> ! [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_1179])]) ).

fof(f4052,plain,
    ( spl0_547
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).

fof(f4256,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_107
    | ~ spl0_547 ),
    inference(resolution,[],[f4053,f1219]) ).

fof(f4053,plain,
    ( ! [X2,X0,X1,X5] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) )
    | ~ spl0_547 ),
    inference(avatar_component_clause,[],[f4052]) ).

fof(f33961,plain,
    ( spl0_1178
    | ~ spl0_1069
    | ~ spl0_1164 ),
    inference(avatar_split_clause,[],[f33888,f33179,f23553,f33959]) ).

fof(f33888,plain,
    ( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2)
    | ~ spl0_1069
    | ~ spl0_1164 ),
    inference(superposition,[],[f33180,f23554]) ).

fof(f33957,plain,
    ( spl0_1177
    | ~ spl0_67
    | ~ spl0_547 ),
    inference(avatar_split_clause,[],[f4255,f4052,f1017,f33955]) ).

fof(f33955,plain,
    ( spl0_1177
  <=> ! [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_1177])]) ).

fof(f4255,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_67
    | ~ spl0_547 ),
    inference(resolution,[],[f4053,f1019]) ).

fof(f33953,plain,
    ( spl0_1176
    | ~ spl0_28
    | ~ spl0_546 ),
    inference(avatar_split_clause,[],[f4254,f4048,f822,f33951]) ).

fof(f33951,plain,
    ( spl0_1176
  <=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).

fof(f4048,plain,
    ( spl0_546
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).

fof(f4254,plain,
    ( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool)
    | ~ spl0_28
    | ~ spl0_546 ),
    inference(resolution,[],[f4049,f824]) ).

fof(f4049,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X0) )
    | ~ spl0_546 ),
    inference(avatar_component_clause,[],[f4048]) ).

fof(f33949,plain,
    ( spl0_1175
    | ~ spl0_63
    | ~ spl0_546 ),
    inference(avatar_split_clause,[],[f4252,f4048,f997,f33947]) ).

fof(f33947,plain,
    ( spl0_1175
  <=> ! [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_1175])]) ).

fof(f4252,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_63
    | ~ spl0_546 ),
    inference(resolution,[],[f4049,f999]) ).

fof(f33945,plain,
    ( spl0_1174
    | ~ spl0_19
    | ~ spl0_546 ),
    inference(avatar_split_clause,[],[f4251,f4048,f777,f33943]) ).

fof(f33943,plain,
    ( spl0_1174
  <=> ! [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_1174])]) ).

fof(f4251,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_19
    | ~ spl0_546 ),
    inference(resolution,[],[f4049,f779]) ).

fof(f33941,plain,
    ( spl0_1173
    | ~ spl0_28
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f4250,f4044,f822,f33939]) ).

fof(f33939,plain,
    ( spl0_1173
  <=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).

fof(f4044,plain,
    ( spl0_545
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).

fof(f4250,plain,
    ( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
    | ~ spl0_28
    | ~ spl0_545 ),
    inference(resolution,[],[f4045,f824]) ).

fof(f4045,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Odistrib__lattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) )
    | ~ spl0_545 ),
    inference(avatar_component_clause,[],[f4044]) ).

fof(f33937,plain,
    ( spl0_1172
    | ~ spl0_63
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f4248,f4044,f997,f33935]) ).

fof(f33935,plain,
    ( spl0_1172
  <=> ! [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_1172])]) ).

fof(f4248,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_63
    | ~ spl0_545 ),
    inference(resolution,[],[f4045,f999]) ).

fof(f33933,plain,
    ( spl0_1171
    | ~ spl0_19
    | ~ spl0_545 ),
    inference(avatar_split_clause,[],[f4247,f4044,f777,f33931]) ).

fof(f33931,plain,
    ( spl0_1171
  <=> ! [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_1171])]) ).

fof(f4247,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_19
    | ~ spl0_545 ),
    inference(resolution,[],[f4045,f779]) ).

fof(f33929,plain,
    ( spl0_1170
    | ~ spl0_186
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3242,f3190,f1575,f33927]) ).

fof(f33927,plain,
    ( spl0_1170
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).

fof(f3242,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_186
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f1576]) ).

fof(f33925,plain,
    ( spl0_1169
    | ~ spl0_187
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3241,f3190,f1579,f33923]) ).

fof(f33923,plain,
    ( spl0_1169
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).

fof(f3241,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_187
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f1580]) ).

fof(f33921,plain,
    ( spl0_1168
    | ~ spl0_185
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3240,f3190,f1571,f33919]) ).

fof(f33919,plain,
    ( spl0_1168
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X2,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).

fof(f3240,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X2,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_185
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f1572]) ).

fof(f33885,plain,
    ( spl0_1167
    | ~ spl0_395
    | ~ spl0_396 ),
    inference(avatar_split_clause,[],[f3049,f2917,f2913,f33883]) ).

fof(f3049,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2)) )
    | ~ spl0_395
    | ~ spl0_396 ),
    inference(duplicate_literal_removal,[],[f3048]) ).

fof(f3048,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,X2),X3,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X4,X3,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2) )
    | ~ spl0_395
    | ~ spl0_396 ),
    inference(resolution,[],[f2918,f2914]) ).

fof(f33881,plain,
    ( spl0_1166
    | ~ spl0_286
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f2811,f2670,f2216,f33879]) ).

fof(f33879,plain,
    ( spl0_1166
  <=> ! [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_1166])]) ).

fof(f2811,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_286
    | ~ spl0_354 ),
    inference(resolution,[],[f2671,f2217]) ).

fof(f33877,plain,
    ( spl0_1165
    | ~ spl0_284
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f2806,f2670,f2208,f33875]) ).

fof(f33875,plain,
    ( spl0_1165
  <=> ! [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_1165])]) ).

fof(f2806,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_284
    | ~ spl0_354 ),
    inference(resolution,[],[f2671,f2209]) ).

fof(f33181,plain,
    ( spl0_1164
    | ~ spl0_124
    | ~ spl0_679
    | ~ spl0_1150 ),
    inference(avatar_split_clause,[],[f32955,f30278,f6032,f1300,f33179]) ).

fof(f32955,plain,
    ( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_679
    | ~ spl0_1150 ),
    inference(forward_demodulation,[],[f32857,f6033]) ).

fof(f32857,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X1,v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_1150 ),
    inference(superposition,[],[f30279,f1301]) ).

fof(f32106,plain,
    ( spl0_1163
    | ~ spl0_936
    | ~ spl0_1069 ),
    inference(avatar_split_clause,[],[f28069,f23553,f13420,f32104]) ).

fof(f32104,plain,
    ( spl0_1163
  <=> ! [X0,X3,X2,X1] : c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).

fof(f13420,plain,
    ( spl0_936
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).

fof(f28069,plain,
    ( ! [X2,X3,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X3,c_Polynomial_Osmult(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_936
    | ~ spl0_1069 ),
    inference(superposition,[],[f13421,f23554]) ).

fof(f13421,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_936 ),
    inference(avatar_component_clause,[],[f13420]) ).

fof(f31588,plain,
    ( spl0_1162
    | ~ spl0_937
    | ~ spl0_1028 ),
    inference(avatar_split_clause,[],[f24447,f23298,f13536,f31586]) ).

fof(f31586,plain,
    ( spl0_1162
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).

fof(f13536,plain,
    ( spl0_937
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).

fof(f24447,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_937
    | ~ spl0_1028 ),
    inference(superposition,[],[f13537,f23299]) ).

fof(f13537,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_937 ),
    inference(avatar_component_clause,[],[f13536]) ).

fof(f31186,plain,
    ( spl0_1161
    | ~ spl0_939
    | ~ spl0_1026 ),
    inference(avatar_split_clause,[],[f24325,f23290,f13761,f31184]) ).

fof(f31184,plain,
    ( spl0_1161
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).

fof(f13761,plain,
    ( spl0_939
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).

fof(f24325,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_939
    | ~ spl0_1026 ),
    inference(superposition,[],[f13762,f23291]) ).

fof(f13762,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_939 ),
    inference(avatar_component_clause,[],[f13761]) ).

fof(f30652,plain,
    ( spl0_1160
    | ~ spl0_207
    | ~ spl0_602 ),
    inference(avatar_split_clause,[],[f4707,f4638,f1661,f30650]) ).

fof(f30650,plain,
    ( spl0_1160
  <=> ! [X3,X4,X0,X6,X5,X2,X1] :
        ( c_Fun_Ocomp(X3,X4,X5,X0,X2) != X1
        | hAPP(X1,X6) = hAPP(X3,hAPP(X4,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).

fof(f4707,plain,
    ( ! [X2,X3,X0,X1,X6,X4,X5] :
        ( c_Fun_Ocomp(X3,X4,X5,X0,X2) != X1
        | hAPP(X1,X6) = hAPP(X3,hAPP(X4,X6)) )
    | ~ spl0_207
    | ~ spl0_602 ),
    inference(superposition,[],[f4639,f1662]) ).

fof(f30648,plain,
    ( spl0_1159
    | ~ spl0_45
    | ~ spl0_541 ),
    inference(avatar_split_clause,[],[f4039,f3913,f907,f30646]) ).

fof(f30646,plain,
    ( spl0_1159
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).

fof(f3913,plain,
    ( spl0_541
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).

fof(f4039,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),X2,tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_541 ),
    inference(resolution,[],[f3914,f909]) ).

fof(f3914,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_541 ),
    inference(avatar_component_clause,[],[f3913]) ).

fof(f30644,plain,
    ( spl0_1158
    | ~ spl0_89
    | ~ spl0_541 ),
    inference(avatar_split_clause,[],[f4038,f3913,f1127,f30642]) ).

fof(f30642,plain,
    ( spl0_1158
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).

fof(f4038,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_541 ),
    inference(resolution,[],[f3914,f1129]) ).

fof(f30640,plain,
    ( spl0_1157
    | ~ spl0_8
    | ~ spl0_541 ),
    inference(avatar_split_clause,[],[f4037,f3913,f722,f30638]) ).

fof(f30638,plain,
    ( spl0_1157
  <=> ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_nat),X2,tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).

fof(f4037,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Osmult(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X0,X1,tc_nat),X2,tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_8
    | ~ spl0_541 ),
    inference(resolution,[],[f3914,f724]) ).

fof(f30636,plain,
    ( spl0_1156
    | ~ spl0_45
    | ~ spl0_540 ),
    inference(avatar_split_clause,[],[f4035,f3909,f907,f30634]) ).

fof(f30634,plain,
    ( spl0_1156
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).

fof(f3909,plain,
    ( spl0_540
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Otimes__class_Otimes(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).

fof(f4035,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_540 ),
    inference(resolution,[],[f3910,f909]) ).

fof(f3910,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Otimes__class_Otimes(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_540 ),
    inference(avatar_component_clause,[],[f3909]) ).

fof(f30632,plain,
    ( spl0_1155
    | ~ spl0_89
    | ~ spl0_540 ),
    inference(avatar_split_clause,[],[f4034,f3909,f1127,f30630]) ).

fof(f30630,plain,
    ( spl0_1155
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).

fof(f4034,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_540 ),
    inference(resolution,[],[f3910,f1129]) ).

fof(f30609,plain,
    ( spl0_1154
    | ~ spl0_8
    | ~ spl0_540 ),
    inference(avatar_split_clause,[],[f4033,f3909,f722,f30607]) ).

fof(f30607,plain,
    ( spl0_1154
  <=> ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_nat),tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).

fof(f4033,plain,
    ( ! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Polynomial_Osmult(X1,X2,tc_nat),tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_Osmult(X1,c_HOL_Otimes__class_Otimes(X0,X2,tc_Polynomial_Opoly(tc_nat)),tc_nat)
    | ~ spl0_8
    | ~ spl0_540 ),
    inference(resolution,[],[f3910,f724]) ).

fof(f30448,plain,
    ( spl0_1153
    | ~ spl0_110
    | ~ spl0_87
    | ~ spl0_539 ),
    inference(avatar_split_clause,[],[f4031,f3905,f1117,f1232,f30446]) ).

fof(f30446,plain,
    ( spl0_1153
  <=> ! [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_1153])]) ).

fof(f3905,plain,
    ( spl0_539
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).

fof(f4031,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(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_87
    | ~ spl0_539 ),
    inference(resolution,[],[f3906,f1119]) ).

fof(f3906,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) )
    | ~ spl0_539 ),
    inference(avatar_component_clause,[],[f3905]) ).

fof(f30288,plain,
    ( spl0_1152
    | ~ spl0_71
    | ~ spl0_43
    | ~ spl0_539 ),
    inference(avatar_split_clause,[],[f4030,f3905,f897,f1037,f30286]) ).

fof(f30286,plain,
    ( spl0_1152
  <=> ! [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_1152])]) ).

fof(f4030,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(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_43
    | ~ spl0_539 ),
    inference(resolution,[],[f3906,f899]) ).

fof(f30284,plain,
    ( spl0_1151
    | ~ spl0_45
    | ~ spl0_538 ),
    inference(avatar_split_clause,[],[f4029,f3882,f907,f30282]) ).

fof(f30282,plain,
    ( spl0_1151
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).

fof(f30280,plain,
    ( spl0_1150
    | ~ spl0_89
    | ~ spl0_538 ),
    inference(avatar_split_clause,[],[f4028,f3882,f1127,f30278]) ).

fof(f30276,plain,
    ( spl0_1149
    | ~ spl0_8
    | ~ spl0_538 ),
    inference(avatar_split_clause,[],[f4027,f3882,f722,f30274]) ).

fof(f30274,plain,
    ( spl0_1149
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Opoly(X1,tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).

fof(f30206,plain,
    ( spl0_1148
    | ~ spl0_96
    | ~ spl0_116
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f4025,f3878,f1262,f1162,f30204]) ).

fof(f30204,plain,
    ( spl0_1148
  <=> ! [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_1148])]) ).

fof(f1162,plain,
    ( spl0_96
  <=> class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).

fof(f1262,plain,
    ( spl0_116
  <=> class_SEQ_Obanach(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).

fof(f3878,plain,
    ( spl0_537
  <=> ! [X2,X0,X1] :
        ( ~ class_SEQ_Obanach(X0)
        | ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).

fof(f4025,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_116
    | ~ spl0_537 ),
    inference(resolution,[],[f3879,f1264]) ).

fof(f1264,plain,
    ( class_SEQ_Obanach(tc_Complex_Ocomplex)
    | ~ spl0_116 ),
    inference(avatar_component_clause,[],[f1262]) ).

fof(f3879,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_SEQ_Obanach(X0)
        | ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) )
    | ~ spl0_537 ),
    inference(avatar_component_clause,[],[f3878]) ).

fof(f30202,plain,
    ( spl0_1147
    | ~ spl0_859
    | ~ spl0_939 ),
    inference(avatar_split_clause,[],[f19867,f13761,f10692,f30200]) ).

fof(f30200,plain,
    ( spl0_1147
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).

fof(f10692,plain,
    ( spl0_859
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).

fof(f19867,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_859
    | ~ spl0_939 ),
    inference(superposition,[],[f13762,f10693]) ).

fof(f10693,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Complex_Ocomplex)
    | ~ spl0_859 ),
    inference(avatar_component_clause,[],[f10692]) ).

fof(f30133,plain,
    ( spl0_1146
    | ~ spl0_52
    | ~ spl0_78
    | ~ spl0_537 ),
    inference(avatar_split_clause,[],[f4024,f3878,f1072,f942,f30131]) ).

fof(f30131,plain,
    ( spl0_1146
  <=> ! [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_1146])]) ).

fof(f942,plain,
    ( spl0_52
  <=> class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).

fof(f1072,plain,
    ( spl0_78
  <=> class_SEQ_Obanach(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).

fof(f4024,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_78
    | ~ spl0_537 ),
    inference(resolution,[],[f3879,f1074]) ).

fof(f1074,plain,
    ( class_SEQ_Obanach(tc_RealDef_Oreal)
    | ~ spl0_78 ),
    inference(avatar_component_clause,[],[f1072]) ).

fof(f30129,plain,
    ( spl0_1145
    | ~ spl0_228
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f4013,f3870,f1835,f30127]) ).

fof(f30127,plain,
    ( spl0_1145
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,c_Polynomial_Osmult(X1,X3,X0),X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).

fof(f1835,plain,
    ( spl0_228
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X2,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).

fof(f3870,plain,
    ( spl0_535
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).

fof(f4013,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,c_Polynomial_Osmult(X1,X3,X0),X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_228
    | ~ spl0_535 ),
    inference(duplicate_literal_removal,[],[f4010]) ).

fof(f4010,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X2,c_Polynomial_Osmult(X1,X3,X0),X0),X3,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_228
    | ~ spl0_535 ),
    inference(resolution,[],[f3871,f1836]) ).

fof(f1836,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_228 ),
    inference(avatar_component_clause,[],[f1835]) ).

fof(f3871,plain,
    ( ! [X0,X7,X5,X12] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0))
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_535 ),
    inference(avatar_component_clause,[],[f3870]) ).

fof(f30125,plain,
    ( spl0_1144
    | ~ spl0_229
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f4012,f3870,f1839,f30123]) ).

fof(f30123,plain,
    ( spl0_1144
  <=> ! [X0,X3,X2,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Osmult(X1,X2,X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).

fof(f1839,plain,
    ( spl0_229
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X1,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).

fof(f4012,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Osmult(X1,X2,X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_229
    | ~ spl0_535 ),
    inference(duplicate_literal_removal,[],[f4011]) ).

fof(f4011,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Osmult(X1,X2,X0),X3,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_229
    | ~ spl0_535 ),
    inference(resolution,[],[f3871,f1840]) ).

fof(f1840,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X1,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_229 ),
    inference(avatar_component_clause,[],[f1839]) ).

fof(f30121,plain,
    ( spl0_1143
    | ~ spl0_157
    | ~ spl0_535 ),
    inference(avatar_split_clause,[],[f4006,f3870,f1432,f30119]) ).

fof(f30119,plain,
    ( spl0_1143
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).

fof(f1432,plain,
    ( spl0_157
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).

fof(f4006,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X1,X2,X0),X2,tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_157
    | ~ spl0_535 ),
    inference(resolution,[],[f3871,f1433]) ).

fof(f1433,plain,
    ( ! [X0,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_157 ),
    inference(avatar_component_clause,[],[f1432]) ).

fof(f30117,plain,
    ( spl0_1142
    | ~ spl0_157
    | ~ spl0_533 ),
    inference(avatar_split_clause,[],[f3981,f3862,f1432,f30115]) ).

fof(f30115,plain,
    ( spl0_1142
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X1,X2,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).

fof(f3981,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(X0) = X1
        | c_Ring__and__Field_Odvd__class_Odvd(X2,c_Polynomial_Osmult(X1,X2,X0),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_157
    | ~ spl0_533 ),
    inference(resolution,[],[f3863,f1433]) ).

fof(f30113,plain,
    ( spl0_1141
    | ~ spl0_45
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f3951,f3836,f907,f30111]) ).

fof(f30111,plain,
    ( spl0_1141
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).

fof(f3836,plain,
    ( spl0_528
  <=> ! [X0,X12,X5,X15] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X5,X12,X0),X0),X15) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).

fof(f3951,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_RealDef_Oreal),X2),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_528 ),
    inference(resolution,[],[f3837,f909]) ).

fof(f3837,plain,
    ( ! [X0,X15,X5,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X5,X12,X0),X0),X15) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) )
    | ~ spl0_528 ),
    inference(avatar_component_clause,[],[f3836]) ).

fof(f30109,plain,
    ( spl0_1140
    | ~ spl0_89
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f3950,f3836,f1127,f30107]) ).

fof(f30107,plain,
    ( spl0_1140
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).

fof(f3950,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_Complex_Ocomplex),X2),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_528 ),
    inference(resolution,[],[f3837,f1129]) ).

fof(f30105,plain,
    ( spl0_1139
    | ~ spl0_8
    | ~ spl0_528 ),
    inference(avatar_split_clause,[],[f3949,f3836,f722,f30103]) ).

fof(f30103,plain,
    ( spl0_1139
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_nat),X2),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).

fof(f3949,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X0,X1,tc_nat),tc_nat),X2) = c_HOL_Otimes__class_Otimes(X0,hAPP(c_Polynomial_Ocoeff(X1,tc_nat),X2),tc_nat)
    | ~ spl0_8
    | ~ spl0_528 ),
    inference(resolution,[],[f3837,f724]) ).

fof(f30101,plain,
    ( spl0_1138
    | ~ spl0_110
    | ~ spl0_527 ),
    inference(avatar_split_clause,[],[f3947,f3832,f1232,f30099]) ).

fof(f30099,plain,
    ( spl0_1138
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).

fof(f3832,plain,
    ( spl0_527
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).

fof(f3947,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | 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_110
    | ~ spl0_527 ),
    inference(resolution,[],[f3833,f1234]) ).

fof(f3833,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_527 ),
    inference(avatar_component_clause,[],[f3832]) ).

fof(f30094,plain,
    ( spl0_1137
    | ~ spl0_71
    | ~ spl0_527 ),
    inference(avatar_split_clause,[],[f3946,f3832,f1037,f30092]) ).

fof(f30092,plain,
    ( spl0_1137
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | 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) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).

fof(f3946,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | 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_71
    | ~ spl0_527 ),
    inference(resolution,[],[f3833,f1039]) ).

fof(f30077,plain,
    ( spl0_1136
    | ~ spl0_96
    | ~ spl0_116
    | ~ spl0_526 ),
    inference(avatar_split_clause,[],[f3941,f3828,f1262,f1162,f30075]) ).

fof(f30075,plain,
    ( spl0_1136
  <=> ! [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_1136])]) ).

fof(f3828,plain,
    ( spl0_526
  <=> ! [X2,X0,X1] :
        ( ~ class_SEQ_Obanach(X0)
        | ~ class_RealVector_Oreal__normed__field(X0)
        | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).

fof(f3941,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_116
    | ~ spl0_526 ),
    inference(resolution,[],[f3829,f1264]) ).

fof(f3829,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_SEQ_Obanach(X0)
        | ~ class_RealVector_Oreal__normed__field(X0)
        | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) )
    | ~ spl0_526 ),
    inference(avatar_component_clause,[],[f3828]) ).

fof(f30060,plain,
    ( spl0_1135
    | ~ spl0_52
    | ~ spl0_78
    | ~ spl0_526 ),
    inference(avatar_split_clause,[],[f3940,f3828,f1072,f942,f30058]) ).

fof(f30058,plain,
    ( spl0_1135
  <=> ! [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_1135])]) ).

fof(f3940,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_78
    | ~ spl0_526 ),
    inference(resolution,[],[f3829,f1074]) ).

fof(f30056,plain,
    ( spl0_1134
    | ~ spl0_45
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f3939,f3824,f907,f30054]) ).

fof(f30054,plain,
    ( spl0_1134
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).

fof(f3824,plain,
    ( spl0_525
  <=> ! [X28,X0,X12,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Oplus__class_Oplus(X28,X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).

fof(f3939,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X2) = hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(X1,X2,tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_525 ),
    inference(resolution,[],[f3825,f909]) ).

fof(f3825,plain,
    ( ! [X28,X0,X1,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Oplus__class_Oplus(X28,X1,X0)) )
    | ~ spl0_525 ),
    inference(avatar_component_clause,[],[f3824]) ).

fof(f30052,plain,
    ( spl0_1133
    | ~ spl0_89
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f3938,f3824,f1127,f30050]) ).

fof(f30050,plain,
    ( spl0_1133
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).

fof(f3938,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(X1,X2,tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_525 ),
    inference(resolution,[],[f3825,f1129]) ).

fof(f30048,plain,
    ( spl0_1132
    | ~ spl0_8
    | ~ spl0_525 ),
    inference(avatar_split_clause,[],[f3937,f3824,f722,f30046]) ).

fof(f30046,plain,
    ( spl0_1132
  <=> ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat),X2) = hAPP(c_Polynomial_Opoly(X0,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).

fof(f3937,plain,
    ( ! [X2,X0,X1] : hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat),X2) = hAPP(c_Polynomial_Opoly(X0,tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
    | ~ spl0_8
    | ~ spl0_525 ),
    inference(resolution,[],[f3825,f724]) ).

fof(f30044,plain,
    ( spl0_1131
    | ~ spl0_301
    | ~ spl0_524 ),
    inference(avatar_split_clause,[],[f3935,f3820,f2276,f30042]) ).

fof(f30042,plain,
    ( spl0_1131
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).

fof(f2276,plain,
    ( spl0_301
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).

fof(f3935,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1 )
    | ~ spl0_301
    | ~ spl0_524 ),
    inference(duplicate_literal_removal,[],[f3932]) ).

fof(f3932,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_301
    | ~ spl0_524 ),
    inference(resolution,[],[f3821,f2277]) ).

fof(f2277,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0)
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_301 ),
    inference(avatar_component_clause,[],[f2276]) ).

fof(f30040,plain,
    ( spl0_1130
    | ~ spl0_100
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f3930,f3816,f1182,f30038]) ).

fof(f30038,plain,
    ( spl0_1130
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).

fof(f3816,plain,
    ( spl0_523
  <=> ! [X5,X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).

fof(f3930,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_523 ),
    inference(resolution,[],[f3817,f1184]) ).

fof(f3817,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_523 ),
    inference(avatar_component_clause,[],[f3816]) ).

fof(f30036,plain,
    ( spl0_1129
    | ~ spl0_311
    | ~ spl0_1111 ),
    inference(avatar_split_clause,[],[f29975,f29920,f2398,f30034]) ).

fof(f30034,plain,
    ( spl0_1129
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).

fof(f2398,plain,
    ( spl0_311
  <=> ! [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_311])]) ).

fof(f29975,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_311
    | ~ spl0_1111 ),
    inference(superposition,[],[f29921,f2399]) ).

fof(f2399,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_311 ),
    inference(avatar_component_clause,[],[f2398]) ).

fof(f30032,plain,
    ( spl0_1128
    | ~ spl0_59
    | ~ spl0_523 ),
    inference(avatar_split_clause,[],[f3929,f3816,f977,f30030]) ).

fof(f30030,plain,
    ( spl0_1128
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).

fof(f3929,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_523 ),
    inference(resolution,[],[f3817,f979]) ).

fof(f30028,plain,
    ( spl0_1127
    | ~ spl0_305
    | ~ spl0_520 ),
    inference(avatar_split_clause,[],[f3799,f3739,f2292,f30026]) ).

fof(f3799,plain,
    ( ! [X0,X1] :
        ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X0) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X1)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X0)) )
    | ~ spl0_305
    | ~ spl0_520 ),
    inference(superposition,[],[f2293,f3740]) ).

fof(f30024,plain,
    ( spl0_1126
    | ~ spl0_186
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3039,f2913,f1575,f30022]) ).

fof(f30022,plain,
    ( spl0_1126
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X0,X2),X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).

fof(f3039,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X0,X2),X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_186
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f1576]) ).

fof(f30020,plain,
    ( spl0_1125
    | ~ spl0_187
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3038,f2913,f1579,f30018]) ).

fof(f30018,plain,
    ( spl0_1125
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X0,X2),X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).

fof(f3038,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X1,X0,X2),X3,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_187
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f1580]) ).

fof(f30016,plain,
    ( spl0_1124
    | ~ spl0_185
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3037,f2913,f1571,f30014]) ).

fof(f30014,plain,
    ( spl0_1124
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X0,X3),tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).

fof(f3037,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X0,X3),tc_Polynomial_Opoly(X3)),tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X3)) )
    | ~ spl0_185
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f1572]) ).

fof(f30012,plain,
    ( spl0_1123
    | ~ spl0_156
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f2862,f2746,f1428,f30010]) ).

fof(f30010,plain,
    ( spl0_1123
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X2
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).

fof(f2746,plain,
    ( spl0_373
  <=> ! [X5,X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X5,X15,X0),X0) = X15 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).

fof(f2862,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X1,X2,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X2
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_156
    | ~ spl0_373 ),
    inference(resolution,[],[f2747,f1429]) ).

fof(f2747,plain,
    ( ! [X0,X15,X5] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X5,X15,X0),X0) = X15 )
    | ~ spl0_373 ),
    inference(avatar_component_clause,[],[f2746]) ).

fof(f30008,plain,
    ( spl0_1122
    | ~ spl0_143
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f2841,f2702,f1376,f30006]) ).

fof(f30006,plain,
    ( spl0_1122
  <=> ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_OrderedGroup_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).

fof(f2702,plain,
    ( spl0_362
  <=> ! [X0,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).

fof(f2841,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_OrderedGroup_Oab__group__add(X0) )
    | ~ spl0_143
    | ~ spl0_362 ),
    inference(resolution,[],[f2703,f1377]) ).

fof(f2703,plain,
    ( ! [X0,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_362 ),
    inference(avatar_component_clause,[],[f2702]) ).

fof(f30004,plain,
    ( spl0_1121
    | ~ spl0_156
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f2835,f2698,f1428,f30002]) ).

fof(f30002,plain,
    ( spl0_1121
  <=> ! [X0,X1] :
        ( c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X1))
        | ~ class_HOL_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).

fof(f2835,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(X1))
        | ~ class_HOL_Ozero(X1) )
    | ~ spl0_156
    | ~ spl0_361 ),
    inference(resolution,[],[f2699,f1429]) ).

fof(f30000,plain,
    ( spl0_1120
    | ~ spl0_315
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f2818,f2670,f2414,f29998]) ).

fof(f29998,plain,
    ( spl0_1120
  <=> ! [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_1120])]) ).

fof(f2818,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_315
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f2807]) ).

fof(f2807,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_315
    | ~ spl0_354 ),
    inference(resolution,[],[f2671,f2415]) ).

fof(f29996,plain,
    ( spl0_1119
    | ~ spl0_314
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f2817,f2670,f2410,f29994]) ).

fof(f29994,plain,
    ( spl0_1119
  <=> ! [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_1119])]) ).

fof(f2817,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_314
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f2808]) ).

fof(f2808,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_314
    | ~ spl0_354 ),
    inference(resolution,[],[f2671,f2411]) ).

fof(f29965,plain,
    ( spl0_1118
    | ~ spl0_156
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f2641,f2534,f1428,f29963]) ).

fof(f29963,plain,
    ( spl0_1118
  <=> ! [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_1118])]) ).

fof(f2534,plain,
    ( spl0_345
  <=> ! [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_345])]) ).

fof(f2641,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_156
    | ~ spl0_345 ),
    inference(resolution,[],[f2535,f1429]) ).

fof(f2535,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_345 ),
    inference(avatar_component_clause,[],[f2534]) ).

fof(f29961,plain,
    ( spl0_1117
    | ~ spl0_156
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f2627,f2502,f1428,f29959]) ).

fof(f29959,plain,
    ( spl0_1117
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0),tc_nat),tc_Polynomial_Opoly(X0))
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).

fof(f2502,plain,
    ( spl0_337
  <=> ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(X0),X0,tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).

fof(f2627,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0),tc_nat),tc_Polynomial_Opoly(X0))
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_156
    | ~ spl0_337 ),
    inference(resolution,[],[f2503,f1429]) ).

fof(f2503,plain,
    ( ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(X0),X0,tc_nat),X0) )
    | ~ spl0_337 ),
    inference(avatar_component_clause,[],[f2502]) ).

fof(f29957,plain,
    ( spl0_1116
    | ~ spl0_155
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f2582,f2434,f1424,f29955]) ).

fof(f29955,plain,
    ( spl0_1116
  <=> ! [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_1116])]) ).

fof(f1424,plain,
    ( spl0_155
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X48)
        | class_Int_Onumber__ring(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).

fof(f2434,plain,
    ( spl0_320
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).

fof(f2582,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_155
    | ~ spl0_320 ),
    inference(resolution,[],[f2435,f1425]) ).

fof(f1425,plain,
    ( ! [X48] :
        ( class_Int_Onumber__ring(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X48) )
    | ~ spl0_155 ),
    inference(avatar_component_clause,[],[f1424]) ).

fof(f2435,plain,
    ( ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) )
    | ~ spl0_320 ),
    inference(avatar_component_clause,[],[f2434]) ).

fof(f29953,plain,
    ( spl0_1115
    | ~ spl0_284
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f2567,f2422,f2208,f29951]) ).

fof(f29951,plain,
    ( spl0_1115
  <=> ! [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_1115])]) ).

fof(f2567,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_284
    | ~ spl0_317 ),
    inference(resolution,[],[f2423,f2209]) ).

fof(f29949,plain,
    ( spl0_1114
    | ~ spl0_284
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f2553,f2418,f2208,f29947]) ).

fof(f29947,plain,
    ( spl0_1114
  <=> ! [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_1114])]) ).

fof(f2553,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_284
    | ~ spl0_316 ),
    inference(resolution,[],[f2419,f2209]) ).

fof(f29945,plain,
    ( spl0_1113
    | ~ spl0_285
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f2546,f2414,f2212,f29943]) ).

fof(f29943,plain,
    ( spl0_1113
  <=> ! [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_1113])]) ).

fof(f2546,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_285
    | ~ spl0_315 ),
    inference(resolution,[],[f2415,f2213]) ).

fof(f29941,plain,
    ( spl0_1112
    | ~ spl0_285
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f2543,f2410,f2212,f29939]) ).

fof(f29939,plain,
    ( spl0_1112
  <=> ! [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_1112])]) ).

fof(f2543,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_285
    | ~ spl0_314 ),
    inference(resolution,[],[f2411,f2213]) ).

fof(f29922,plain,
    ( spl0_1111
    | ~ spl0_755
    | ~ spl0_1058 ),
    inference(avatar_split_clause,[],[f27233,f23495,f8168,f29920]) ).

fof(f8168,plain,
    ( spl0_755
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).

fof(f23495,plain,
    ( spl0_1058
  <=> ! [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_1058])]) ).

fof(f27233,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X1,X2,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_755
    | ~ spl0_1058 ),
    inference(superposition,[],[f8169,f23496]) ).

fof(f23496,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_1058 ),
    inference(avatar_component_clause,[],[f23495]) ).

fof(f8169,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_755 ),
    inference(avatar_component_clause,[],[f8168]) ).

fof(f28612,plain,
    ( spl0_1110
    | ~ spl0_158
    | ~ spl0_206
    | ~ spl0_602 ),
    inference(avatar_split_clause,[],[f4710,f4638,f1657,f1436,f28610]) ).

fof(f28610,plain,
    ( spl0_1110
  <=> ! [X2,X4,X0,X3,X1] :
        ( hAPP(X3,X4) = hAPP(X0,X4)
        | c_Fun_Ocomp(c_Fun_Oid(X2),X3,X2,X2,X1) != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).

fof(f1436,plain,
    ( spl0_158
  <=> ! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).

fof(f1657,plain,
    ( spl0_206
  <=> ! [X0,X8,X10] : c_Fun_Ocomp(X8,c_Fun_Oid(X0),X0,X10,X0) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).

fof(f4710,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( hAPP(X3,X4) = hAPP(X0,X4)
        | c_Fun_Ocomp(c_Fun_Oid(X2),X3,X2,X2,X1) != X0 )
    | ~ spl0_158
    | ~ spl0_206
    | ~ spl0_602 ),
    inference(forward_demodulation,[],[f4705,f1437]) ).

fof(f1437,plain,
    ( ! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1
    | ~ spl0_158 ),
    inference(avatar_component_clause,[],[f1436]) ).

fof(f4705,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Fun_Ocomp(c_Fun_Oid(X2),X3,X2,X2,X1) != X0
        | hAPP(X0,hAPP(c_Fun_Oid(X1),X4)) = hAPP(X3,X4) )
    | ~ spl0_206
    | ~ spl0_602 ),
    inference(superposition,[],[f4639,f1658]) ).

fof(f1658,plain,
    ( ! [X10,X0,X8] : c_Fun_Ocomp(X8,c_Fun_Oid(X0),X0,X10,X0) = X8
    | ~ spl0_206 ),
    inference(avatar_component_clause,[],[f1657]) ).

fof(f28608,plain,
    ( spl0_1109
    | ~ spl0_45
    | ~ spl0_518 ),
    inference(avatar_split_clause,[],[f3771,f3731,f907,f28606]) ).

fof(f28606,plain,
    ( spl0_1109
  <=> ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).

fof(f3731,plain,
    ( spl0_518
  <=> ! [X13,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X13,X0) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(X0),tc_Polynomial_Opoly(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).

fof(f3771,plain,
    ( ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_518 ),
    inference(resolution,[],[f3732,f909]) ).

fof(f3732,plain,
    ( ! [X0,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X13,X0) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(X0),tc_Polynomial_Opoly(X0),X0) )
    | ~ spl0_518 ),
    inference(avatar_component_clause,[],[f3731]) ).

fof(f28604,plain,
    ( spl0_1108
    | ~ spl0_89
    | ~ spl0_518 ),
    inference(avatar_split_clause,[],[f3770,f3731,f1127,f28602]) ).

fof(f28602,plain,
    ( spl0_1108
  <=> ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).

fof(f3770,plain,
    ( ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_518 ),
    inference(resolution,[],[f3732,f1129]) ).

fof(f28600,plain,
    ( spl0_1107
    | ~ spl0_8
    | ~ spl0_518 ),
    inference(avatar_split_clause,[],[f3769,f3731,f722,f28598]) ).

fof(f28598,plain,
    ( spl0_1107
  <=> ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).

fof(f3769,plain,
    ( ! [X0] : c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_Polynomial_Opoly(tc_nat),tc_nat)
    | ~ spl0_8
    | ~ spl0_518 ),
    inference(resolution,[],[f3732,f724]) ).

fof(f28596,plain,
    ( spl0_1106
    | ~ spl0_44
    | ~ spl0_517 ),
    inference(avatar_split_clause,[],[f3763,f3727,f902,f28594]) ).

fof(f28594,plain,
    ( spl0_1106
  <=> ! [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_1106])]) ).

fof(f3763,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_44
    | ~ spl0_517 ),
    inference(resolution,[],[f3728,f904]) ).

fof(f28592,plain,
    ( spl0_1105
    | ~ spl0_88
    | ~ spl0_517 ),
    inference(avatar_split_clause,[],[f3762,f3727,f1122,f28590]) ).

fof(f28590,plain,
    ( spl0_1105
  <=> ! [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_1105])]) ).

fof(f3762,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_88
    | ~ spl0_517 ),
    inference(resolution,[],[f3728,f1124]) ).

fof(f28588,plain,
    ( spl0_1104
    | ~ spl0_7
    | ~ spl0_517 ),
    inference(avatar_split_clause,[],[f3761,f3727,f717,f28586]) ).

fof(f28586,plain,
    ( spl0_1104
  <=> ! [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_1104])]) ).

fof(f3761,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_7
    | ~ spl0_517 ),
    inference(resolution,[],[f3728,f719]) ).

fof(f28584,plain,
    ( spl0_1103
    | ~ spl0_44
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f3759,f3704,f902,f28582]) ).

fof(f28582,plain,
    ( spl0_1103
  <=> ! [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_1103])]) ).

fof(f3759,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_44
    | ~ spl0_516 ),
    inference(resolution,[],[f3705,f904]) ).

fof(f28580,plain,
    ( spl0_1102
    | ~ spl0_943
    | ~ spl0_1028 ),
    inference(avatar_split_clause,[],[f24456,f23298,f14204,f28578]) ).

fof(f28578,plain,
    ( spl0_1102
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).

fof(f14204,plain,
    ( spl0_943
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).

fof(f24456,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_943
    | ~ spl0_1028 ),
    inference(superposition,[],[f14205,f23299]) ).

fof(f14205,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_943 ),
    inference(avatar_component_clause,[],[f14204]) ).

fof(f28576,plain,
    ( spl0_1101
    | ~ spl0_88
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f3758,f3704,f1122,f28574]) ).

fof(f28574,plain,
    ( spl0_1101
  <=> ! [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_1101])]) ).

fof(f3758,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_88
    | ~ spl0_516 ),
    inference(resolution,[],[f3705,f1124]) ).

fof(f28572,plain,
    ( spl0_1100
    | ~ spl0_7
    | ~ spl0_516 ),
    inference(avatar_split_clause,[],[f3757,f3704,f717,f28570]) ).

fof(f28570,plain,
    ( spl0_1100
  <=> ! [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_1100])]) ).

fof(f3757,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_7
    | ~ spl0_516 ),
    inference(resolution,[],[f3705,f719]) ).

fof(f28568,plain,
    ( spl0_1099
    | ~ spl0_102
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f3753,f3696,f1192,f28566]) ).

fof(f28566,plain,
    ( spl0_1099
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).

fof(f3753,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex)
    | ~ spl0_102
    | ~ spl0_514 ),
    inference(resolution,[],[f3697,f1194]) ).

fof(f28564,plain,
    ( spl0_1098
    | ~ spl0_61
    | ~ spl0_514 ),
    inference(avatar_split_clause,[],[f3752,f3696,f987,f28562]) ).

fof(f28562,plain,
    ( spl0_1098
  <=> ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X1),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).

fof(f3752,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X0,tc_RealDef_Oreal),X1),tc_RealDef_Oreal)
    | ~ spl0_61
    | ~ spl0_514 ),
    inference(resolution,[],[f3697,f989]) ).

fof(f28560,plain,
    ( spl0_1097
    | ~ spl0_100
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f3743,f3688,f1182,f28558]) ).

fof(f28558,plain,
    ( spl0_1097
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).

fof(f3743,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),X1),tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_512 ),
    inference(resolution,[],[f3689,f1184]) ).

fof(f28556,plain,
    ( spl0_1096
    | ~ spl0_59
    | ~ spl0_512 ),
    inference(avatar_split_clause,[],[f3742,f3688,f977,f28554]) ).

fof(f28554,plain,
    ( spl0_1096
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X1),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).

fof(f3742,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),X1),tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_512 ),
    inference(resolution,[],[f3689,f979]) ).

fof(f28552,plain,
    ( spl0_1095
    | ~ spl0_134
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f2635,f2522,f1340,f28550]) ).

fof(f28550,plain,
    ( spl0_1095
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).

fof(f2522,plain,
    ( spl0_342
  <=> ! [X0,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).

fof(f2635,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
    | ~ spl0_134
    | ~ spl0_342 ),
    inference(resolution,[],[f2523,f1341]) ).

fof(f2523,plain,
    ( ! [X0,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) )
    | ~ spl0_342 ),
    inference(avatar_component_clause,[],[f2522]) ).

fof(f28548,plain,
    ( spl0_1094
    | ~ spl0_134
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f2631,f2518,f1340,f28546]) ).

fof(f28546,plain,
    ( spl0_1094
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).

fof(f2518,plain,
    ( spl0_341
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).

fof(f2631,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
    | ~ spl0_134
    | ~ spl0_341 ),
    inference(resolution,[],[f2519,f1341]) ).

fof(f2519,plain,
    ( ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_341 ),
    inference(avatar_component_clause,[],[f2518]) ).

fof(f28544,plain,
    ( spl0_1093
    | ~ spl0_149
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f2622,f2494,f1400,f28542]) ).

fof(f28542,plain,
    ( spl0_1093
  <=> ! [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_1093])]) ).

fof(f2494,plain,
    ( spl0_335
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).

fof(f2622,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_149
    | ~ spl0_335 ),
    inference(resolution,[],[f2495,f1401]) ).

fof(f2495,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = X6 )
    | ~ spl0_335 ),
    inference(avatar_component_clause,[],[f2494]) ).

fof(f28540,plain,
    ( spl0_1092
    | ~ spl0_143
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f2619,f2490,f1376,f28538]) ).

fof(f28538,plain,
    ( spl0_1092
  <=> ! [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_1092])]) ).

fof(f2490,plain,
    ( spl0_334
  <=> ! [X2,X0,X3] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).

fof(f2619,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_143
    | ~ spl0_334 ),
    inference(resolution,[],[f2491,f1377]) ).

fof(f2491,plain,
    ( ! [X2,X3,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = X2 )
    | ~ spl0_334 ),
    inference(avatar_component_clause,[],[f2490]) ).

fof(f28536,plain,
    ( spl0_1091
    | ~ spl0_944
    | ~ spl0_1026 ),
    inference(avatar_split_clause,[],[f24330,f23290,f14338,f28534]) ).

fof(f28534,plain,
    ( spl0_1091
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).

fof(f14338,plain,
    ( spl0_944
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).

fof(f24330,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_944
    | ~ spl0_1026 ),
    inference(superposition,[],[f14339,f23291]) ).

fof(f14339,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_944 ),
    inference(avatar_component_clause,[],[f14338]) ).

fof(f28532,plain,
    ( spl0_1090
    | ~ spl0_156
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f2608,f2478,f1428,f28530]) ).

fof(f28530,plain,
    ( spl0_1090
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_HOL_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).

fof(f2478,plain,
    ( spl0_331
  <=> ! [X5,X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).

fof(f2608,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_HOL_Ozero(X1) )
    | ~ spl0_156
    | ~ spl0_331 ),
    inference(resolution,[],[f2479,f1429]) ).

fof(f2479,plain,
    ( ! [X0,X5] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) )
    | ~ spl0_331 ),
    inference(avatar_component_clause,[],[f2478]) ).

fof(f28528,plain,
    ( spl0_1089
    | ~ spl0_143
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f2602,f2462,f1376,f28526]) ).

fof(f28526,plain,
    ( spl0_1089
  <=> ! [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_1089])]) ).

fof(f2462,plain,
    ( spl0_327
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X6,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).

fof(f2602,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_143
    | ~ spl0_327 ),
    inference(resolution,[],[f2463,f1377]) ).

fof(f2463,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X6,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) )
    | ~ spl0_327 ),
    inference(avatar_component_clause,[],[f2462]) ).

fof(f28524,plain,
    ( spl0_1088
    | ~ spl0_149
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f2599,f2458,f1400,f28522]) ).

fof(f28522,plain,
    ( spl0_1088
  <=> ! [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_1088])]) ).

fof(f2458,plain,
    ( spl0_326
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).

fof(f2599,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_149
    | ~ spl0_326 ),
    inference(resolution,[],[f2459,f1401]) ).

fof(f2459,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_326 ),
    inference(avatar_component_clause,[],[f2458]) ).

fof(f28520,plain,
    ( spl0_1087
    | ~ spl0_149
    | ~ spl0_324 ),
    inference(avatar_split_clause,[],[f2593,f2450,f1400,f28518]) ).

fof(f28518,plain,
    ( spl0_1087
  <=> ! [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_1087])]) ).

fof(f2450,plain,
    ( spl0_324
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).

fof(f2593,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_149
    | ~ spl0_324 ),
    inference(resolution,[],[f2451,f1401]) ).

fof(f2451,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_324 ),
    inference(avatar_component_clause,[],[f2450]) ).

fof(f28516,plain,
    ( spl0_1086
    | ~ spl0_155
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f2590,f2446,f1424,f28514]) ).

fof(f28514,plain,
    ( spl0_1086
  <=> ! [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_1086])]) ).

fof(f2446,plain,
    ( spl0_323
  <=> ! [X2,X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).

fof(f2590,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_155
    | ~ spl0_323 ),
    inference(resolution,[],[f2447,f1425]) ).

fof(f2447,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
    | ~ spl0_323 ),
    inference(avatar_component_clause,[],[f2446]) ).

fof(f28512,plain,
    ( spl0_1085
    | ~ spl0_149
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f2541,f2406,f1400,f28510]) ).

fof(f28510,plain,
    ( spl0_1085
  <=> ! [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_1085])]) ).

fof(f2406,plain,
    ( spl0_313
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0),X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).

fof(f2541,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_149
    | ~ spl0_313 ),
    inference(resolution,[],[f2407,f1401]) ).

fof(f2407,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0),X0) = X6 )
    | ~ spl0_313 ),
    inference(avatar_component_clause,[],[f2406]) ).

fof(f28508,plain,
    ( spl0_1084
    | ~ spl0_171
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2067,f1919,f1492,f28506]) ).

fof(f28506,plain,
    ( spl0_1084
  <=> ! [X0] :
        ( ~ class_HOL_Ozero(tc_Polynomial_Opoly(X0))
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_fequal(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_HOL_Oeq(X0)
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).

fof(f1492,plain,
    ( spl0_171
  <=> ! [X48] :
        ( ~ class_HOL_Ozero(X48)
        | ~ class_HOL_Oeq(X48)
        | class_HOL_Oeq(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).

fof(f1919,plain,
    ( spl0_238
  <=> ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)) = c_fequal(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).

fof(f2067,plain,
    ( ! [X0] :
        ( ~ class_HOL_Ozero(tc_Polynomial_Opoly(X0))
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_fequal(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_HOL_Oeq(X0)
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_171
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f1493]) ).

fof(f1493,plain,
    ( ! [X48] :
        ( class_HOL_Oeq(tc_Polynomial_Opoly(X48))
        | ~ class_HOL_Oeq(X48)
        | ~ class_HOL_Ozero(X48) )
    | ~ spl0_171 ),
    inference(avatar_component_clause,[],[f1492]) ).

fof(f1920,plain,
    ( ! [X0] :
        ( ~ class_HOL_Oeq(X0)
        | ~ class_HOL_Ozero(X0)
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)) = c_fequal(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_238 ),
    inference(avatar_component_clause,[],[f1919]) ).

fof(f26668,plain,
    ( spl0_1083
    | ~ spl0_938
    | ~ spl0_1028 ),
    inference(avatar_split_clause,[],[f24448,f23298,f13614,f26666]) ).

fof(f24448,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X2,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_938
    | ~ spl0_1028 ),
    inference(superposition,[],[f13615,f23299]) ).

fof(f25645,plain,
    ( spl0_1082
    | ~ spl0_940
    | ~ spl0_1026 ),
    inference(avatar_split_clause,[],[f24326,f23290,f13943,f25643]) ).

fof(f24326,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_940
    | ~ spl0_1026 ),
    inference(superposition,[],[f13944,f23291]) ).

fof(f24065,plain,
    ( spl0_1081
    | ~ spl0_403
    | ~ spl0_1046 ),
    inference(avatar_split_clause,[],[f23903,f23405,f2945,f24063]) ).

fof(f23405,plain,
    ( spl0_1046
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).

fof(f23903,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_403
    | ~ spl0_1046 ),
    inference(superposition,[],[f23406,f2946]) ).

fof(f23406,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_1046 ),
    inference(avatar_component_clause,[],[f23405]) ).

fof(f23757,plain,
    ( spl0_1080
    | ~ spl0_112
    | ~ spl0_506 ),
    inference(avatar_split_clause,[],[f3685,f3481,f1242,f23755]) ).

fof(f3685,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) = hAPP(c_Polynomial_Opoly(X1,tc_Complex_Ocomplex),X0) )
    | ~ spl0_112
    | ~ spl0_506 ),
    inference(resolution,[],[f3482,f1244]) ).

fof(f1244,plain,
    ( class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
    | ~ spl0_112 ),
    inference(avatar_component_clause,[],[f1242]) ).

fof(f23753,plain,
    ( spl0_1079
    | ~ spl0_73
    | ~ spl0_506 ),
    inference(avatar_split_clause,[],[f3684,f3481,f1047,f23751]) ).

fof(f23751,plain,
    ( spl0_1079
  <=> ! [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) = hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).

fof(f1047,plain,
    ( spl0_73
  <=> class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).

fof(f3684,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) = hAPP(c_Polynomial_Opoly(X1,tc_RealDef_Oreal),X0) )
    | ~ spl0_73
    | ~ spl0_506 ),
    inference(resolution,[],[f3482,f1049]) ).

fof(f1049,plain,
    ( class_Ring__and__Field_Oidom(tc_RealDef_Oreal)
    | ~ spl0_73 ),
    inference(avatar_component_clause,[],[f1047]) ).

fof(f23749,plain,
    ( spl0_1078
    | ~ spl0_83
    | ~ spl0_501 ),
    inference(avatar_split_clause,[],[f3671,f3461,f1097,f23747]) ).

fof(f23747,plain,
    ( spl0_1078
  <=> ! [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_1078])]) ).

fof(f1097,plain,
    ( spl0_83
  <=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).

fof(f3461,plain,
    ( spl0_501
  <=> ! [X2,X0,X1] :
        ( ~ class_RealVector_Oreal__normed__div__algebra(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_501])]) ).

fof(f3671,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_83
    | ~ spl0_501 ),
    inference(resolution,[],[f3462,f1099]) ).

fof(f1099,plain,
    ( class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
    | ~ spl0_83 ),
    inference(avatar_component_clause,[],[f1097]) ).

fof(f3462,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_RealVector_Oreal__normed__div__algebra(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) )
    | ~ spl0_501 ),
    inference(avatar_component_clause,[],[f3461]) ).

fof(f23745,plain,
    ( spl0_1077
    | ~ spl0_37
    | ~ spl0_501 ),
    inference(avatar_split_clause,[],[f3670,f3461,f867,f23743]) ).

fof(f23743,plain,
    ( spl0_1077
  <=> ! [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_1077])]) ).

fof(f867,plain,
    ( spl0_37
  <=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f3670,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_37
    | ~ spl0_501 ),
    inference(resolution,[],[f3462,f869]) ).

fof(f869,plain,
    ( class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal)
    | ~ spl0_37 ),
    inference(avatar_component_clause,[],[f867]) ).

fof(f23673,plain,
    ( ~ spl0_110
    | spl0_1076
    | ~ spl0_87
    | ~ spl0_88
    | ~ spl0_242
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f3662,f3445,f1935,f1122,f1117,f23671,f1232]) ).

fof(f23671,plain,
    ( spl0_1076
  <=> ! [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_1076])]) ).

fof(f1935,plain,
    ( spl0_242
  <=> ! [X5,X0,X6] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).

fof(f3445,plain,
    ( spl0_497
  <=> ! [X13,X0,X6] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,X13,X0),X13,X0) = X6 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).

fof(f3662,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_Ofield(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_87
    | ~ spl0_88
    | ~ spl0_242
    | ~ spl0_497 ),
    inference(forward_demodulation,[],[f3660,f2082]) ).

fof(f2082,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_242 ),
    inference(resolution,[],[f1936,f1124]) ).

fof(f1936,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) )
    | ~ spl0_242 ),
    inference(avatar_component_clause,[],[f1935]) ).

fof(f3660,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(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_87
    | ~ spl0_497 ),
    inference(resolution,[],[f3446,f1119]) ).

fof(f3446,plain,
    ( ! [X0,X6,X13] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,X13,X0),X13,X0) = X6 )
    | ~ spl0_497 ),
    inference(avatar_component_clause,[],[f3445]) ).

fof(f23579,plain,
    ( ~ spl0_71
    | spl0_1075
    | ~ spl0_43
    | ~ spl0_44
    | ~ spl0_242
    | ~ spl0_497 ),
    inference(avatar_split_clause,[],[f3661,f3445,f1935,f902,f897,f23577,f1037]) ).

fof(f23577,plain,
    ( spl0_1075
  <=> ! [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_1075])]) ).

fof(f3661,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_Ofield(tc_RealDef_Oreal)
        | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0 )
    | ~ spl0_43
    | ~ spl0_44
    | ~ spl0_242
    | ~ spl0_497 ),
    inference(forward_demodulation,[],[f3659,f2083]) ).

fof(f2083,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(X1,X0,tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_242 ),
    inference(resolution,[],[f1936,f904]) ).

fof(f3659,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(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_43
    | ~ spl0_497 ),
    inference(resolution,[],[f3446,f899]) ).

fof(f23575,plain,
    ( spl0_1074
    | ~ spl0_92
    | ~ spl0_495 ),
    inference(avatar_split_clause,[],[f3656,f3437,f1142,f23573]) ).

fof(f23573,plain,
    ( spl0_1074
  <=> ! [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_1074])]) ).

fof(f1142,plain,
    ( spl0_92
  <=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).

fof(f3437,plain,
    ( spl0_495
  <=> ! [X5,X0,X6,X25] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).

fof(f3656,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_92
    | ~ spl0_495 ),
    inference(resolution,[],[f3438,f1144]) ).

fof(f1144,plain,
    ( class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
    | ~ spl0_92 ),
    inference(avatar_component_clause,[],[f1142]) ).

fof(f3438,plain,
    ( ! [X0,X6,X5,X25] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),X0) )
    | ~ spl0_495 ),
    inference(avatar_component_clause,[],[f3437]) ).

fof(f23571,plain,
    ( spl0_1073
    | ~ spl0_48
    | ~ spl0_495 ),
    inference(avatar_split_clause,[],[f3655,f3437,f922,f23569]) ).

fof(f23569,plain,
    ( spl0_1073
  <=> ! [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_1073])]) ).

fof(f922,plain,
    ( spl0_48
  <=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).

fof(f3655,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_48
    | ~ spl0_495 ),
    inference(resolution,[],[f3438,f924]) ).

fof(f924,plain,
    ( class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal)
    | ~ spl0_48 ),
    inference(avatar_component_clause,[],[f922]) ).

fof(f23567,plain,
    ( spl0_1072
    | ~ spl0_96
    | ~ spl0_493 ),
    inference(avatar_split_clause,[],[f3649,f3429,f1162,f23565]) ).

fof(f23565,plain,
    ( spl0_1072
  <=> ! [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_1072])]) ).

fof(f3429,plain,
    ( spl0_493
  <=> ! [X0,X25,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X25,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).

fof(f3649,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_96
    | ~ spl0_493 ),
    inference(resolution,[],[f3430,f1164]) ).

fof(f1164,plain,
    ( class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex)
    | ~ spl0_96 ),
    inference(avatar_component_clause,[],[f1162]) ).

fof(f3430,plain,
    ( ! [X2,X0,X1,X25] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X25,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) )
    | ~ spl0_493 ),
    inference(avatar_component_clause,[],[f3429]) ).

fof(f23563,plain,
    ( spl0_1071
    | ~ spl0_52
    | ~ spl0_493 ),
    inference(avatar_split_clause,[],[f3648,f3429,f942,f23561]) ).

fof(f23561,plain,
    ( spl0_1071
  <=> ! [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_1071])]) ).

fof(f3648,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_52
    | ~ spl0_493 ),
    inference(resolution,[],[f3430,f944]) ).

fof(f944,plain,
    ( class_RealVector_Oreal__normed__field(tc_RealDef_Oreal)
    | ~ spl0_52 ),
    inference(avatar_component_clause,[],[f942]) ).

fof(f23559,plain,
    ( spl0_1070
    | ~ spl0_45
    | ~ spl0_490 ),
    inference(avatar_split_clause,[],[f3647,f3417,f907,f23557]) ).

fof(f23557,plain,
    ( spl0_1070
  <=> ! [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_1070])]) ).

fof(f3647,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_45
    | ~ spl0_490 ),
    inference(resolution,[],[f3418,f909]) ).

fof(f23555,plain,
    ( spl0_1069
    | ~ spl0_89
    | ~ spl0_490 ),
    inference(avatar_split_clause,[],[f3646,f3417,f1127,f23553]) ).

fof(f3646,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_89
    | ~ spl0_490 ),
    inference(resolution,[],[f3418,f1129]) ).

fof(f23551,plain,
    ( spl0_1068
    | ~ spl0_8
    | ~ spl0_490 ),
    inference(avatar_split_clause,[],[f3645,f3417,f722,f23549]) ).

fof(f23549,plain,
    ( spl0_1068
  <=> ! [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_1068])]) ).

fof(f3645,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_8
    | ~ spl0_490 ),
    inference(resolution,[],[f3418,f724]) ).

fof(f23547,plain,
    ( spl0_1067
    | ~ spl0_29
    | ~ spl0_489 ),
    inference(avatar_split_clause,[],[f3642,f3413,f827,f23545]) ).

fof(f23545,plain,
    ( spl0_1067
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).

fof(f827,plain,
    ( spl0_29
  <=> class_Lattices_Oboolean__algebra(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f3413,plain,
    ( spl0_489
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).

fof(f3642,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool)
    | ~ spl0_29
    | ~ spl0_489 ),
    inference(resolution,[],[f3414,f829]) ).

fof(f829,plain,
    ( class_Lattices_Oboolean__algebra(tc_bool)
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f827]) ).

fof(f3414,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) )
    | ~ spl0_489 ),
    inference(avatar_component_clause,[],[f3413]) ).

fof(f23543,plain,
    ( spl0_1066
    | ~ spl0_38
    | ~ spl0_488 ),
    inference(avatar_split_clause,[],[f3641,f3409,f872,f23541]) ).

fof(f23541,plain,
    ( spl0_1066
  <=> ! [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_1066])]) ).

fof(f3409,plain,
    ( spl0_488
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).

fof(f3641,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_38
    | ~ spl0_488 ),
    inference(resolution,[],[f3410,f874]) ).

fof(f3410,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) )
    | ~ spl0_488 ),
    inference(avatar_component_clause,[],[f3409]) ).

fof(f23525,plain,
    ( spl0_1065
    | ~ spl0_38
    | ~ spl0_486 ),
    inference(avatar_split_clause,[],[f3640,f3401,f872,f23523]) ).

fof(f23523,plain,
    ( spl0_1065
  <=> ! [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_1065])]) ).

fof(f3401,plain,
    ( spl0_486
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).

fof(f3640,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_38
    | ~ spl0_486 ),
    inference(resolution,[],[f3402,f874]) ).

fof(f3402,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0),X0) )
    | ~ spl0_486 ),
    inference(avatar_component_clause,[],[f3401]) ).

fof(f23521,plain,
    ( spl0_1064
    | ~ spl0_90
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3635,f3389,f1132,f23519]) ).

fof(f23519,plain,
    ( spl0_1064
  <=> ! [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_1064])]) ).

fof(f3389,plain,
    ( spl0_483
  <=> ! [X5,X0,X6,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).

fof(f3635,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_90
    | ~ spl0_483 ),
    inference(resolution,[],[f3390,f1134]) ).

fof(f3390,plain,
    ( ! [X0,X6,X5,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) )
    | ~ spl0_483 ),
    inference(avatar_component_clause,[],[f3389]) ).

fof(f23517,plain,
    ( spl0_1063
    | ~ spl0_46
    | ~ spl0_483 ),
    inference(avatar_split_clause,[],[f3634,f3389,f912,f23515]) ).

fof(f23515,plain,
    ( spl0_1063
  <=> ! [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_1063])]) ).

fof(f3634,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_46
    | ~ spl0_483 ),
    inference(resolution,[],[f3390,f914]) ).

fof(f23513,plain,
    ( spl0_1062
    | ~ spl0_90
    | ~ spl0_482 ),
    inference(avatar_split_clause,[],[f3633,f3385,f1132,f23511]) ).

fof(f23511,plain,
    ( spl0_1062
  <=> ! [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_1062])]) ).

fof(f3385,plain,
    ( spl0_482
  <=> ! [X5,X0,X6,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X25,X5,X0),X6,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).

fof(f3633,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_90
    | ~ spl0_482 ),
    inference(resolution,[],[f3386,f1134]) ).

fof(f3386,plain,
    ( ! [X0,X6,X5,X25] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X25,X5,X0),X6,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) )
    | ~ spl0_482 ),
    inference(avatar_component_clause,[],[f3385]) ).

fof(f23509,plain,
    ( spl0_1061
    | ~ spl0_46
    | ~ spl0_482 ),
    inference(avatar_split_clause,[],[f3632,f3385,f912,f23507]) ).

fof(f23507,plain,
    ( spl0_1061
  <=> ! [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_1061])]) ).

fof(f3632,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_46
    | ~ spl0_482 ),
    inference(resolution,[],[f3386,f914]) ).

fof(f23505,plain,
    ( spl0_1060
    | ~ spl0_38
    | ~ spl0_480 ),
    inference(avatar_split_clause,[],[f3620,f3377,f872,f23503]) ).

fof(f23503,plain,
    ( spl0_1060
  <=> ! [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_1060])]) ).

fof(f3377,plain,
    ( spl0_480
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).

fof(f3620,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_38
    | ~ spl0_480 ),
    inference(resolution,[],[f3378,f874]) ).

fof(f3378,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_480 ),
    inference(avatar_component_clause,[],[f3377]) ).

fof(f23501,plain,
    ( spl0_1059
    | ~ spl0_45
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3616,f3369,f907,f23499]) ).

fof(f23499,plain,
    ( spl0_1059
  <=> ! [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_1059])]) ).

fof(f3616,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_45
    | ~ spl0_478 ),
    inference(resolution,[],[f3370,f909]) ).

fof(f23497,plain,
    ( spl0_1058
    | ~ spl0_89
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3615,f3369,f1127,f23495]) ).

fof(f3615,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_89
    | ~ spl0_478 ),
    inference(resolution,[],[f3370,f1129]) ).

fof(f23493,plain,
    ( spl0_1057
    | ~ spl0_8
    | ~ spl0_478 ),
    inference(avatar_split_clause,[],[f3614,f3369,f722,f23491]) ).

fof(f23491,plain,
    ( spl0_1057
  <=> ! [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_1057])]) ).

fof(f3614,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_8
    | ~ spl0_478 ),
    inference(resolution,[],[f3370,f724]) ).

fof(f23489,plain,
    ( spl0_1056
    | ~ spl0_44
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3604,f3353,f902,f23487]) ).

fof(f23487,plain,
    ( spl0_1056
  <=> ! [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_1056])]) ).

fof(f3604,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_44
    | ~ spl0_474 ),
    inference(resolution,[],[f3354,f904]) ).

fof(f23474,plain,
    ( spl0_1055
    | ~ spl0_88
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3603,f3353,f1122,f23472]) ).

fof(f23472,plain,
    ( spl0_1055
  <=> ! [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_1055])]) ).

fof(f3603,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_88
    | ~ spl0_474 ),
    inference(resolution,[],[f3354,f1124]) ).

fof(f23470,plain,
    ( spl0_1054
    | ~ spl0_7
    | ~ spl0_474 ),
    inference(avatar_split_clause,[],[f3602,f3353,f717,f23468]) ).

fof(f23468,plain,
    ( spl0_1054
  <=> ! [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_1054])]) ).

fof(f3602,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_7
    | ~ spl0_474 ),
    inference(resolution,[],[f3354,f719]) ).

fof(f23466,plain,
    ( spl0_1053
    | ~ spl0_44
    | ~ spl0_47
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f3600,f3349,f3345,f917,f902,f23464]) ).

fof(f23464,plain,
    ( spl0_1053
  <=> ! [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_1053])]) ).

fof(f3600,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_44
    | ~ spl0_47
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(forward_demodulation,[],[f3597,f3593]) ).

fof(f3597,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_44
    | ~ spl0_473 ),
    inference(resolution,[],[f3350,f904]) ).

fof(f23462,plain,
    ( spl0_1052
    | ~ spl0_88
    | ~ spl0_91
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f3599,f3349,f3345,f1137,f1122,f23460]) ).

fof(f23460,plain,
    ( spl0_1052
  <=> ! [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_1052])]) ).

fof(f3599,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_88
    | ~ spl0_91
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(forward_demodulation,[],[f3596,f3592]) ).

fof(f3596,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_88
    | ~ spl0_473 ),
    inference(resolution,[],[f3350,f1124]) ).

fof(f23458,plain,
    ( spl0_1051
    | ~ spl0_7
    | ~ spl0_9
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(avatar_split_clause,[],[f3598,f3349,f3345,f727,f717,f23456]) ).

fof(f23456,plain,
    ( spl0_1051
  <=> ! [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_1051])]) ).

fof(f3598,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_7
    | ~ spl0_9
    | ~ spl0_472
    | ~ spl0_473 ),
    inference(forward_demodulation,[],[f3595,f3591]) ).

fof(f3595,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_7
    | ~ spl0_473 ),
    inference(resolution,[],[f3350,f719]) ).

fof(f23454,plain,
    ( spl0_1050
    | ~ spl0_47
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f3593,f3345,f917,f23452]) ).

fof(f23452,plain,
    ( spl0_1050
  <=> ! [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_1050])]) ).

fof(f23450,plain,
    ( spl0_1049
    | ~ spl0_91
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f3592,f3345,f1137,f23448]) ).

fof(f23448,plain,
    ( spl0_1049
  <=> ! [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_1049])]) ).

fof(f23446,plain,
    ( spl0_1048
    | ~ spl0_9
    | ~ spl0_472 ),
    inference(avatar_split_clause,[],[f3591,f3345,f727,f23444]) ).

fof(f23444,plain,
    ( spl0_1048
  <=> ! [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_1048])]) ).

fof(f23411,plain,
    ( spl0_1047
    | ~ spl0_110
    | ~ spl0_87
    | ~ spl0_471 ),
    inference(avatar_split_clause,[],[f3589,f3341,f1117,f1232,f23409]) ).

fof(f3341,plain,
    ( spl0_471
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).

fof(f3589,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
        | c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_87
    | ~ spl0_471 ),
    inference(resolution,[],[f3342,f1119]) ).

fof(f3342,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) )
    | ~ spl0_471 ),
    inference(avatar_component_clause,[],[f3341]) ).

fof(f23407,plain,
    ( spl0_1046
    | ~ spl0_755
    | ~ spl0_987 ),
    inference(avatar_split_clause,[],[f23068,f22092,f8168,f23405]) ).

fof(f22092,plain,
    ( spl0_987
  <=> ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).

fof(f23068,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_755
    | ~ spl0_987 ),
    inference(superposition,[],[f8169,f22093]) ).

fof(f22093,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_987 ),
    inference(avatar_component_clause,[],[f22092]) ).

fof(f23368,plain,
    ( spl0_1045
    | ~ spl0_71
    | ~ spl0_43
    | ~ spl0_471 ),
    inference(avatar_split_clause,[],[f3588,f3341,f897,f1037,f23366]) ).

fof(f3588,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(tc_RealDef_Oreal)
        | c_HOL_Oinverse__class_Odivide(X0,X1,tc_RealDef_Oreal) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ spl0_43
    | ~ spl0_471 ),
    inference(resolution,[],[f3342,f899]) ).

fof(f23364,plain,
    ( spl0_1044
    | ~ spl0_26
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3575,f3329,f812,f23362]) ).

fof(f23362,plain,
    ( spl0_1044
  <=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).

fof(f812,plain,
    ( spl0_26
  <=> class_Lattices_Oupper__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f3329,plain,
    ( spl0_468
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).

fof(f3575,plain,
    ( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),X2,tc_bool)
    | ~ spl0_26
    | ~ spl0_468 ),
    inference(resolution,[],[f3330,f814]) ).

fof(f814,plain,
    ( class_Lattices_Oupper__semilattice(tc_bool)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f812]) ).

fof(f3330,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) )
    | ~ spl0_468 ),
    inference(avatar_component_clause,[],[f3329]) ).

fof(f23360,plain,
    ( spl0_1043
    | ~ spl0_57
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3573,f3329,f967,f23358]) ).

fof(f23358,plain,
    ( spl0_1043
  <=> ! [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_1043])]) ).

fof(f967,plain,
    ( spl0_57
  <=> class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).

fof(f3573,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_57
    | ~ spl0_468 ),
    inference(resolution,[],[f3330,f969]) ).

fof(f969,plain,
    ( class_Lattices_Oupper__semilattice(tc_RealDef_Oreal)
    | ~ spl0_57 ),
    inference(avatar_component_clause,[],[f967]) ).

fof(f23356,plain,
    ( spl0_1042
    | ~ spl0_15
    | ~ spl0_468 ),
    inference(avatar_split_clause,[],[f3572,f3329,f757,f23354]) ).

fof(f23354,plain,
    ( spl0_1042
  <=> ! [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_1042])]) ).

fof(f757,plain,
    ( spl0_15
  <=> class_Lattices_Oupper__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f3572,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_15
    | ~ spl0_468 ),
    inference(resolution,[],[f3330,f759]) ).

fof(f759,plain,
    ( class_Lattices_Oupper__semilattice(tc_nat)
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f757]) ).

fof(f23352,plain,
    ( spl0_1041
    | ~ spl0_26
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f3571,f3325,f812,f23350]) ).

fof(f23350,plain,
    ( spl0_1041
  <=> ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).

fof(f3325,plain,
    ( spl0_467
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).

fof(f3571,plain,
    ( ! [X2,X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,tc_bool),tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X0,X2,tc_bool),tc_bool)
    | ~ spl0_26
    | ~ spl0_467 ),
    inference(resolution,[],[f3326,f814]) ).

fof(f3326,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) )
    | ~ spl0_467 ),
    inference(avatar_component_clause,[],[f3325]) ).

fof(f23348,plain,
    ( spl0_1040
    | ~ spl0_57
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f3569,f3325,f967,f23346]) ).

fof(f23346,plain,
    ( spl0_1040
  <=> ! [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_1040])]) ).

fof(f3569,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_57
    | ~ spl0_467 ),
    inference(resolution,[],[f3326,f969]) ).

fof(f23344,plain,
    ( spl0_1039
    | ~ spl0_15
    | ~ spl0_467 ),
    inference(avatar_split_clause,[],[f3568,f3325,f757,f23342]) ).

fof(f23342,plain,
    ( spl0_1039
  <=> ! [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_1039])]) ).

fof(f3568,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_15
    | ~ spl0_467 ),
    inference(resolution,[],[f3326,f759]) ).

fof(f23340,plain,
    ( spl0_1038
    | ~ spl0_44
    | ~ spl0_53
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f3563,f3312,f3296,f947,f902,f23338]) ).

fof(f23338,plain,
    ( spl0_1038
  <=> ! [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_1038])]) ).

fof(f3563,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_44
    | ~ spl0_53
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(forward_demodulation,[],[f3560,f3545]) ).

fof(f3560,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_44
    | ~ spl0_464 ),
    inference(resolution,[],[f3313,f904]) ).

fof(f23336,plain,
    ( spl0_1037
    | ~ spl0_88
    | ~ spl0_97
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f3562,f3312,f3296,f1167,f1122,f23334]) ).

fof(f23334,plain,
    ( spl0_1037
  <=> ! [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_1037])]) ).

fof(f3562,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_88
    | ~ spl0_97
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(forward_demodulation,[],[f3559,f3544]) ).

fof(f3559,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_88
    | ~ spl0_464 ),
    inference(resolution,[],[f3313,f1124]) ).

fof(f23332,plain,
    ( spl0_1036
    | ~ spl0_921
    | ~ spl0_981 ),
    inference(avatar_split_clause,[],[f22586,f21989,f11914,f23330]) ).

fof(f23330,plain,
    ( spl0_1036
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).

fof(f11914,plain,
    ( spl0_921
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).

fof(f21989,plain,
    ( spl0_981
  <=> ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).

fof(f22586,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_921
    | ~ spl0_981 ),
    inference(superposition,[],[f11915,f21990]) ).

fof(f21990,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_981 ),
    inference(avatar_component_clause,[],[f21989]) ).

fof(f11915,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_921 ),
    inference(avatar_component_clause,[],[f11914]) ).

fof(f23328,plain,
    ( spl0_1035
    | ~ spl0_7
    | ~ spl0_13
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(avatar_split_clause,[],[f3561,f3312,f3296,f747,f717,f23326]) ).

fof(f23326,plain,
    ( spl0_1035
  <=> ! [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_1035])]) ).

fof(f3561,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_7
    | ~ spl0_13
    | ~ spl0_460
    | ~ spl0_464 ),
    inference(forward_demodulation,[],[f3558,f3543]) ).

fof(f3558,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_7
    | ~ spl0_464 ),
    inference(resolution,[],[f3313,f719]) ).

fof(f23324,plain,
    ( spl0_1034
    | ~ spl0_53
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f3545,f3296,f947,f23322]) ).

fof(f23320,plain,
    ( spl0_1033
    | ~ spl0_97
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f3544,f3296,f1167,f23318]) ).

fof(f23316,plain,
    ( spl0_1032
    | ~ spl0_13
    | ~ spl0_460 ),
    inference(avatar_split_clause,[],[f3543,f3296,f747,f23314]) ).

fof(f23314,plain,
    ( spl0_1032
  <=> ! [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_1032])]) ).

fof(f23312,plain,
    ( spl0_1031
    | ~ spl0_53
    | ~ spl0_459 ),
    inference(avatar_split_clause,[],[f3541,f3292,f947,f23310]) ).

fof(f23310,plain,
    ( spl0_1031
  <=> ! [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_1031])]) ).

fof(f3541,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_53
    | ~ spl0_459 ),
    inference(resolution,[],[f3293,f949]) ).

fof(f23308,plain,
    ( spl0_1030
    | ~ spl0_97
    | ~ spl0_459 ),
    inference(avatar_split_clause,[],[f3540,f3292,f1167,f23306]) ).

fof(f23306,plain,
    ( spl0_1030
  <=> ! [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_1030])]) ).

fof(f3540,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_97
    | ~ spl0_459 ),
    inference(resolution,[],[f3293,f1169]) ).

fof(f23304,plain,
    ( spl0_1029
    | ~ spl0_13
    | ~ spl0_459 ),
    inference(avatar_split_clause,[],[f3539,f3292,f747,f23302]) ).

fof(f23302,plain,
    ( spl0_1029
  <=> ! [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_1029])]) ).

fof(f3539,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_13
    | ~ spl0_459 ),
    inference(resolution,[],[f3293,f749]) ).

fof(f23300,plain,
    ( spl0_1028
    | ~ spl0_110
    | ~ spl0_458 ),
    inference(avatar_split_clause,[],[f3537,f3288,f1232,f23298]) ).

fof(f3288,plain,
    ( spl0_458
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).

fof(f3537,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X2,tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_458 ),
    inference(resolution,[],[f3289,f1234]) ).

fof(f3289,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X0),X3,X0) )
    | ~ spl0_458 ),
    inference(avatar_component_clause,[],[f3288]) ).

fof(f23296,plain,
    ( spl0_1027
    | ~ spl0_71
    | ~ spl0_458 ),
    inference(avatar_split_clause,[],[f3536,f3288,f1037,f23294]) ).

fof(f23294,plain,
    ( spl0_1027
  <=> ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).

fof(f3536,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal),X2,tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_458 ),
    inference(resolution,[],[f3289,f1039]) ).

fof(f23292,plain,
    ( spl0_1026
    | ~ spl0_110
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f3531,f3284,f1232,f23290]) ).

fof(f3284,plain,
    ( spl0_457
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).

fof(f3531,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_457 ),
    inference(resolution,[],[f3285,f1234]) ).

fof(f3285,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X0),X0) )
    | ~ spl0_457 ),
    inference(avatar_component_clause,[],[f3284]) ).

fof(f23288,plain,
    ( spl0_1025
    | ~ spl0_805
    | ~ spl0_981 ),
    inference(avatar_split_clause,[],[f22583,f21989,f8950,f23286]) ).

fof(f23286,plain,
    ( spl0_1025
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).

fof(f8950,plain,
    ( spl0_805
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).

fof(f22583,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_805
    | ~ spl0_981 ),
    inference(superposition,[],[f8951,f21990]) ).

fof(f8951,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_805 ),
    inference(avatar_component_clause,[],[f8950]) ).

fof(f23284,plain,
    ( spl0_1024
    | ~ spl0_71
    | ~ spl0_457 ),
    inference(avatar_split_clause,[],[f3530,f3284,f1037,f23282]) ).

fof(f23282,plain,
    ( spl0_1024
  <=> ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).

fof(f3530,plain,
    ( ! [X2,X0,X1] : c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X0,X2,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_457 ),
    inference(resolution,[],[f3285,f1039]) ).

fof(f23280,plain,
    ( spl0_1023
    | ~ spl0_38
    | ~ spl0_456 ),
    inference(avatar_split_clause,[],[f3529,f3280,f872,f23278]) ).

fof(f23278,plain,
    ( spl0_1023
  <=> ! [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_1023])]) ).

fof(f3280,plain,
    ( spl0_456
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).

fof(f3529,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_38
    | ~ spl0_456 ),
    inference(resolution,[],[f3281,f874]) ).

fof(f3281,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) )
    | ~ spl0_456 ),
    inference(avatar_component_clause,[],[f3280]) ).

fof(f23276,plain,
    ( spl0_1022
    | ~ spl0_27
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f3512,f3260,f817,f23274]) ).

fof(f23274,plain,
    ( spl0_1022
  <=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).

fof(f817,plain,
    ( spl0_27
  <=> class_Lattices_Olower__semilattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f3260,plain,
    ( spl0_451
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).

fof(f3512,plain,
    ( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),X2,tc_bool)
    | ~ spl0_27
    | ~ spl0_451 ),
    inference(resolution,[],[f3261,f819]) ).

fof(f819,plain,
    ( class_Lattices_Olower__semilattice(tc_bool)
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f817]) ).

fof(f3261,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) )
    | ~ spl0_451 ),
    inference(avatar_component_clause,[],[f3260]) ).

fof(f23272,plain,
    ( spl0_1021
    | ~ spl0_58
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f3510,f3260,f972,f23270]) ).

fof(f23270,plain,
    ( spl0_1021
  <=> ! [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_1021])]) ).

fof(f972,plain,
    ( spl0_58
  <=> class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).

fof(f3510,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_58
    | ~ spl0_451 ),
    inference(resolution,[],[f3261,f974]) ).

fof(f974,plain,
    ( class_Lattices_Olower__semilattice(tc_RealDef_Oreal)
    | ~ spl0_58 ),
    inference(avatar_component_clause,[],[f972]) ).

fof(f23268,plain,
    ( spl0_1020
    | ~ spl0_16
    | ~ spl0_451 ),
    inference(avatar_split_clause,[],[f3509,f3260,f762,f23266]) ).

fof(f23266,plain,
    ( spl0_1020
  <=> ! [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_1020])]) ).

fof(f762,plain,
    ( spl0_16
  <=> class_Lattices_Olower__semilattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f3509,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_16
    | ~ spl0_451 ),
    inference(resolution,[],[f3261,f764]) ).

fof(f764,plain,
    ( class_Lattices_Olower__semilattice(tc_nat)
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f762]) ).

fof(f23264,plain,
    ( spl0_1019
    | ~ spl0_27
    | ~ spl0_450 ),
    inference(avatar_split_clause,[],[f3508,f3256,f817,f23262]) ).

fof(f23262,plain,
    ( spl0_1019
  <=> ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).

fof(f3256,plain,
    ( spl0_450
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).

fof(f3508,plain,
    ( ! [X2,X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X0,X2,tc_bool),tc_bool)
    | ~ spl0_27
    | ~ spl0_450 ),
    inference(resolution,[],[f3257,f819]) ).

fof(f3257,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) )
    | ~ spl0_450 ),
    inference(avatar_component_clause,[],[f3256]) ).

fof(f23260,plain,
    ( spl0_1018
    | ~ spl0_58
    | ~ spl0_450 ),
    inference(avatar_split_clause,[],[f3506,f3256,f972,f23258]) ).

fof(f23258,plain,
    ( spl0_1018
  <=> ! [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_1018])]) ).

fof(f3506,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_58
    | ~ spl0_450 ),
    inference(resolution,[],[f3257,f974]) ).

fof(f23256,plain,
    ( spl0_1017
    | ~ spl0_16
    | ~ spl0_450 ),
    inference(avatar_split_clause,[],[f3505,f3256,f762,f23254]) ).

fof(f23254,plain,
    ( spl0_1017
  <=> ! [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_1017])]) ).

fof(f3505,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_16
    | ~ spl0_450 ),
    inference(resolution,[],[f3257,f764]) ).

fof(f23252,plain,
    ( spl0_1016
    | ~ spl0_156
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f2623,f2498,f1428,f23250]) ).

fof(f23250,plain,
    ( spl0_1016
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
        | ~ class_HOL_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).

fof(f2498,plain,
    ( spl0_336
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X12,X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).

fof(f2623,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
        | ~ class_HOL_Ozero(X2) )
    | ~ spl0_156
    | ~ spl0_336 ),
    inference(resolution,[],[f2499,f1429]) ).

fof(f2499,plain,
    ( ! [X0,X5,X12] :
        ( ~ class_HOL_Ozero(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X12,X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 )
    | ~ spl0_336 ),
    inference(avatar_component_clause,[],[f2498]) ).

fof(f23248,plain,
    ( spl0_1015
    | ~ spl0_152
    | ~ spl0_307 ),
    inference(avatar_split_clause,[],[f2396,f2300,f1412,f23246]) ).

fof(f23246,plain,
    ( spl0_1015
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_Ring__and__Field_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).

fof(f2300,plain,
    ( spl0_307
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).

fof(f2396,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_152
    | ~ spl0_307 ),
    inference(resolution,[],[f2301,f1413]) ).

fof(f2301,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X5) )
    | ~ spl0_307 ),
    inference(avatar_component_clause,[],[f2300]) ).

fof(f23244,plain,
    ( spl0_1014
    | ~ spl0_921
    | ~ spl0_979 ),
    inference(avatar_split_clause,[],[f22504,f21981,f11914,f23242]) ).

fof(f23242,plain,
    ( spl0_1014
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).

fof(f21981,plain,
    ( spl0_979
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).

fof(f22504,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_921
    | ~ spl0_979 ),
    inference(superposition,[],[f11915,f21982]) ).

fof(f21982,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_979 ),
    inference(avatar_component_clause,[],[f21981]) ).

fof(f23240,plain,
    ( spl0_1013
    | ~ spl0_134
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f2390,f2296,f1340,f23238]) ).

fof(f23238,plain,
    ( spl0_1013
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).

fof(f2296,plain,
    ( spl0_306
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).

fof(f2390,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X0) )
    | ~ spl0_134
    | ~ spl0_306 ),
    inference(resolution,[],[f2297,f1341]) ).

fof(f2297,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X1) )
    | ~ spl0_306 ),
    inference(avatar_component_clause,[],[f2296]) ).

fof(f23236,plain,
    ( spl0_1012
    | ~ spl0_156
    | ~ spl0_304 ),
    inference(avatar_split_clause,[],[f2386,f2288,f1428,f23234]) ).

fof(f23234,plain,
    ( spl0_1012
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).

fof(f2288,plain,
    ( spl0_304
  <=> ! [X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X15) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).

fof(f2386,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0)),X1)
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_156
    | ~ spl0_304 ),
    inference(resolution,[],[f2289,f1429]) ).

fof(f2289,plain,
    ( ! [X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X15) )
    | ~ spl0_304 ),
    inference(avatar_component_clause,[],[f2288]) ).

fof(f23232,plain,
    ( spl0_1011
    | ~ spl0_134
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f2382,f2284,f1340,f23230]) ).

fof(f23230,plain,
    ( spl0_1011
  <=> ! [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_1011])]) ).

fof(f2284,plain,
    ( spl0_303
  <=> ! [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_303])]) ).

fof(f2382,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_134
    | ~ spl0_303 ),
    inference(resolution,[],[f2285,f1341]) ).

fof(f2285,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_303 ),
    inference(avatar_component_clause,[],[f2284]) ).

fof(f23228,plain,
    ( spl0_1010
    | ~ spl0_134
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f2378,f2280,f1340,f23226]) ).

fof(f23226,plain,
    ( spl0_1010
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(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_1010])]) ).

fof(f2280,plain,
    ( spl0_302
  <=> ! [X0,X28] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).

fof(f2378,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(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_134
    | ~ spl0_302 ),
    inference(resolution,[],[f2281,f1341]) ).

fof(f2281,plain,
    ( ! [X28,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) )
    | ~ spl0_302 ),
    inference(avatar_component_clause,[],[f2280]) ).

fof(f23224,plain,
    ( spl0_1009
    | ~ spl0_141
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f2377,f2272,f1368,f23222]) ).

fof(f23222,plain,
    ( spl0_1009
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).

fof(f2272,plain,
    ( spl0_300
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(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)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).

fof(f2377,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_Ring__and__Field_Oordered__idom(X0) )
    | ~ spl0_141
    | ~ spl0_300 ),
    inference(resolution,[],[f2273,f1369]) ).

fof(f2273,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(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)) )
    | ~ spl0_300 ),
    inference(avatar_component_clause,[],[f2272]) ).

fof(f23220,plain,
    ( spl0_1008
    | ~ spl0_134
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f2372,f2264,f1340,f23218]) ).

fof(f23218,plain,
    ( spl0_1008
  <=> ! [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_1008])]) ).

fof(f2264,plain,
    ( spl0_298
  <=> ! [X13,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)),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).

fof(f2372,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_134
    | ~ spl0_298 ),
    inference(resolution,[],[f2265,f1341]) ).

fof(f2265,plain,
    ( ! [X0,X13] :
        ( ~ 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)),X13,X0) )
    | ~ spl0_298 ),
    inference(avatar_component_clause,[],[f2264]) ).

fof(f23216,plain,
    ( spl0_1007
    | ~ spl0_143
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2371,f2260,f1376,f23214]) ).

fof(f23214,plain,
    ( spl0_1007
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_OrderedGroup_Oab__group__add(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).

fof(f2260,plain,
    ( spl0_297
  <=> ! [X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).

fof(f2371,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0)))
        | ~ class_OrderedGroup_Oab__group__add(X0) )
    | ~ spl0_143
    | ~ spl0_297 ),
    inference(resolution,[],[f2261,f1377]) ).

fof(f2261,plain,
    ( ! [X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) )
    | ~ spl0_297 ),
    inference(avatar_component_clause,[],[f2260]) ).

fof(f23212,plain,
    ( spl0_1006
    | ~ spl0_152
    | ~ spl0_296 ),
    inference(avatar_split_clause,[],[f2364,f2256,f1412,f23210]) ).

fof(f23210,plain,
    ( spl0_1006
  <=> ! [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_1006])]) ).

fof(f2256,plain,
    ( spl0_296
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).

fof(f2364,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_152
    | ~ spl0_296 ),
    inference(resolution,[],[f2257,f1413]) ).

fof(f2257,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_296 ),
    inference(avatar_component_clause,[],[f2256]) ).

fof(f23208,plain,
    ( spl0_1005
    | ~ spl0_134
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f2358,f2252,f1340,f23206]) ).

fof(f23206,plain,
    ( spl0_1005
  <=> ! [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_1005])]) ).

fof(f2358,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_134
    | ~ spl0_295 ),
    inference(resolution,[],[f2253,f1341]) ).

fof(f23204,plain,
    ( spl0_1004
    | ~ spl0_255
    | ~ spl0_284 ),
    inference(avatar_split_clause,[],[f2327,f2208,f1987,f23202]) ).

fof(f23202,plain,
    ( spl0_1004
  <=> ! [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_1004])]) ).

fof(f2327,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_255
    | ~ spl0_284 ),
    inference(resolution,[],[f2209,f1988]) ).

fof(f23200,plain,
    ( spl0_1003
    | ~ spl0_805
    | ~ spl0_979 ),
    inference(avatar_split_clause,[],[f22501,f21981,f8950,f23198]) ).

fof(f23198,plain,
    ( spl0_1003
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).

fof(f22501,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex),c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_805
    | ~ spl0_979 ),
    inference(superposition,[],[f8951,f21982]) ).

fof(f23196,plain,
    ( spl0_1002
    | ~ spl0_134
    | ~ spl0_279 ),
    inference(avatar_split_clause,[],[f2317,f2188,f1340,f23194]) ).

fof(f23194,plain,
    ( spl0_1002
  <=> ! [X2,X0,X1] :
        ( c_Polynomial_Odegree(X0,tc_Polynomial_Opoly(X1)) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).

fof(f2188,plain,
    ( spl0_279
  <=> ! [X12,X0,X28] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).

fof(f2317,plain,
    ( ! [X2,X0,X1] :
        ( c_Polynomial_Odegree(X0,tc_Polynomial_Opoly(X1)) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X2,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__0(X1) )
    | ~ spl0_134
    | ~ spl0_279 ),
    inference(resolution,[],[f2189,f1341]) ).

fof(f2189,plain,
    ( ! [X28,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0) )
    | ~ spl0_279 ),
    inference(avatar_component_clause,[],[f2188]) ).

fof(f23192,plain,
    ( spl0_1001
    | ~ spl0_152
    | ~ spl0_278 ),
    inference(avatar_split_clause,[],[f2314,f2184,f1412,f23190]) ).

fof(f23190,plain,
    ( spl0_1001
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Oidom(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).

fof(f2184,plain,
    ( spl0_278
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X0) = c_HOL_Ozero__class_Ozero(tc_nat) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).

fof(f2314,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_152
    | ~ spl0_278 ),
    inference(resolution,[],[f2185,f1413]) ).

fof(f2185,plain,
    ( ! [X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X0) = c_HOL_Ozero__class_Ozero(tc_nat) )
    | ~ spl0_278 ),
    inference(avatar_component_clause,[],[f2184]) ).

fof(f23188,plain,
    ( spl0_1000
    | ~ spl0_143
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2305,f2172,f1376,f23186]) ).

fof(f23186,plain,
    ( spl0_1000
  <=> ! [X0,X1] :
        ( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Polynomial_Odegree(X0,tc_Polynomial_Opoly(X1))
        | ~ class_OrderedGroup_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).

fof(f2172,plain,
    ( spl0_275
  <=> ! [X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) = c_Polynomial_Odegree(X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).

fof(f2305,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(X1)) = c_Polynomial_Odegree(X0,tc_Polynomial_Opoly(X1))
        | ~ class_OrderedGroup_Oab__group__add(X1) )
    | ~ spl0_143
    | ~ spl0_275 ),
    inference(resolution,[],[f2173,f1377]) ).

fof(f2173,plain,
    ( ! [X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) = c_Polynomial_Odegree(X12,X0) )
    | ~ spl0_275 ),
    inference(avatar_component_clause,[],[f2172]) ).

fof(f23184,plain,
    ( spl0_999
    | ~ spl0_165
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2142,f2019,f1466,f23182]) ).

fof(f23182,plain,
    ( spl0_999
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).

fof(f2019,plain,
    ( spl0_263
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).

fof(f2142,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_165
    | ~ spl0_263 ),
    inference(resolution,[],[f2020,f1467]) ).

fof(f2020,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 )
    | ~ spl0_263 ),
    inference(avatar_component_clause,[],[f2019]) ).

fof(f23180,plain,
    ( spl0_998
    | ~ spl0_161
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2108,f1975,f1450,f23178]) ).

fof(f23178,plain,
    ( spl0_998
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).

fof(f1975,plain,
    ( spl0_252
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).

fof(f2108,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_161
    | ~ spl0_252 ),
    inference(resolution,[],[f1976,f1451]) ).

fof(f1976,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) )
    | ~ spl0_252 ),
    inference(avatar_component_clause,[],[f1975]) ).

fof(f23176,plain,
    ( spl0_997
    | ~ spl0_162
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2091,f1947,f1454,f23174]) ).

fof(f23174,plain,
    ( spl0_997
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).

fof(f1454,plain,
    ( spl0_162
  <=> ! [X48,X49] :
        ( ~ class_Lattices_Olattice(X48)
        | class_Lattices_Olower__semilattice(tc_fun(X49,X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).

fof(f1947,plain,
    ( spl0_245
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).

fof(f2091,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_fun(X2,X3)) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_fun(X2,X3))
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_162
    | ~ spl0_245 ),
    inference(resolution,[],[f1948,f1455]) ).

fof(f1455,plain,
    ( ! [X48,X49] :
        ( class_Lattices_Olower__semilattice(tc_fun(X49,X48))
        | ~ class_Lattices_Olattice(X48) )
    | ~ spl0_162 ),
    inference(avatar_component_clause,[],[f1454]) ).

fof(f1948,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) )
    | ~ spl0_245 ),
    inference(avatar_component_clause,[],[f1947]) ).

fof(f23172,plain,
    ( spl0_996
    | ~ spl0_165
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f2075,f1927,f1466,f23170]) ).

fof(f23170,plain,
    ( spl0_996
  <=> ! [X0,X3,X2,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
        | ~ class_Lattices_Olattice(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).

fof(f1927,plain,
    ( spl0_240
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).

fof(f2075,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_fun(X2,X3)),tc_fun(X2,X3)) = X0
        | ~ class_Lattices_Olattice(X3) )
    | ~ spl0_165
    | ~ spl0_240 ),
    inference(resolution,[],[f1928,f1467]) ).

fof(f1928,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 )
    | ~ spl0_240 ),
    inference(avatar_component_clause,[],[f1927]) ).

fof(f23168,plain,
    ( spl0_995
    | ~ spl0_121
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2071,f1919,f1287,f23166]) ).

fof(f23166,plain,
    ( spl0_995
  <=> ! [X0,X1] :
        ( ~ class_HOL_Ozero(tc_prod(X0,X1))
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_prod(X0,X1))) = c_fequal(tc_Polynomial_Opoly(tc_prod(X0,X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).

fof(f1287,plain,
    ( spl0_121
  <=> ! [X48,X49] : class_HOL_Oeq(tc_prod(X49,X48)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).

fof(f2071,plain,
    ( ! [X0,X1] :
        ( ~ class_HOL_Ozero(tc_prod(X0,X1))
        | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_prod(X0,X1))) = c_fequal(tc_Polynomial_Opoly(tc_prod(X0,X1))) )
    | ~ spl0_121
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f1288]) ).

fof(f1288,plain,
    ( ! [X48,X49] : class_HOL_Oeq(tc_prod(X49,X48))
    | ~ spl0_121 ),
    inference(avatar_component_clause,[],[f1287]) ).

fof(f22578,plain,
    ( ~ spl0_872
    | spl0_994
    | ~ spl0_187
    | ~ spl0_992 ),
    inference(avatar_split_clause,[],[f22160,f22112,f1579,f22576,f10800]) ).

fof(f10800,plain,
    ( spl0_872
  <=> class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).

fof(f22576,plain,
    ( spl0_994
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).

fof(f22112,plain,
    ( spl0_992
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).

fof(f22160,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
    | ~ spl0_187
    | ~ spl0_992 ),
    inference(superposition,[],[f1580,f22113]) ).

fof(f22113,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_992 ),
    inference(avatar_component_clause,[],[f22112]) ).

fof(f22118,plain,
    ( spl0_993
    | ~ spl0_654 ),
    inference(avatar_split_clause,[],[f5314,f5299,f22116]) ).

fof(f22116,plain,
    ( spl0_993
  <=> ! [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_993])]) ).

fof(f5299,plain,
    ( spl0_654
  <=> ! [X5,X6,X13,X0,X27,X26] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X26,X0),X13,X0) = X27
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),X27,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).

fof(f5314,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_654 ),
    inference(equality_resolution,[],[f5300]) ).

fof(f5300,plain,
    ( ! [X0,X6,X26,X27,X5,X13] :
        ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),X27,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),X13,X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X26,X0),X13,X0) = X27
        | ~ class_Ring__and__Field_Oring(X0) )
    | ~ spl0_654 ),
    inference(avatar_component_clause,[],[f5299]) ).

fof(f22114,plain,
    ( spl0_992
    | ~ spl0_671
    | ~ spl0_883 ),
    inference(avatar_split_clause,[],[f20269,f11595,f5597,f22112]) ).

fof(f11595,plain,
    ( spl0_883
  <=> ! [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_883])]) ).

fof(f20269,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_671
    | ~ spl0_883 ),
    inference(resolution,[],[f11596,f5598]) ).

fof(f11596,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | 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)) )
    | ~ spl0_883 ),
    inference(avatar_component_clause,[],[f11595]) ).

fof(f22110,plain,
    ( spl0_991
    | ~ spl0_437
    | ~ spl0_572 ),
    inference(avatar_split_clause,[],[f4386,f4185,f3166,f22108]) ).

fof(f22108,plain,
    ( spl0_991
  <=> ! [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_991])]) ).

fof(f4386,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_437
    | ~ spl0_572 ),
    inference(duplicate_literal_removal,[],[f4363]) ).

fof(f4363,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_437
    | ~ spl0_572 ),
    inference(resolution,[],[f4186,f3167]) ).

fof(f22106,plain,
    ( spl0_990
    | ~ spl0_45
    | ~ spl0_79
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(avatar_split_clause,[],[f3751,f3692,f2698,f1077,f907,f22104]) ).

fof(f22104,plain,
    ( spl0_990
  <=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).

fof(f1077,plain,
    ( spl0_79
  <=> class_HOL_Ozero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).

fof(f3751,plain,
    ( ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_79
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(forward_demodulation,[],[f3748,f2838]) ).

fof(f2838,plain,
    ( ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal)
    | ~ spl0_79
    | ~ spl0_361 ),
    inference(resolution,[],[f2699,f1079]) ).

fof(f1079,plain,
    ( class_HOL_Ozero(tc_RealDef_Oreal)
    | ~ spl0_79 ),
    inference(avatar_component_clause,[],[f1077]) ).

fof(f3748,plain,
    ( ! [X0,X1] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_513 ),
    inference(resolution,[],[f3693,f909]) ).

fof(f22102,plain,
    ( spl0_989
    | ~ spl0_89
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(avatar_split_clause,[],[f3750,f3692,f2698,f1267,f1127,f22100]) ).

fof(f22100,plain,
    ( spl0_989
  <=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).

fof(f3750,plain,
    ( ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(forward_demodulation,[],[f3747,f2837]) ).

fof(f3747,plain,
    ( ! [X0,X1] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_513 ),
    inference(resolution,[],[f3693,f1129]) ).

fof(f22098,plain,
    ( spl0_988
    | ~ spl0_8
    | ~ spl0_24
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(avatar_split_clause,[],[f3749,f3692,f2698,f802,f722,f22096]) ).

fof(f22096,plain,
    ( spl0_988
  <=> ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).

fof(f802,plain,
    ( spl0_24
  <=> class_HOL_Ozero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f3749,plain,
    ( ! [X0,X1] : c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),X1,tc_nat)
    | ~ spl0_8
    | ~ spl0_24
    | ~ spl0_361
    | ~ spl0_513 ),
    inference(forward_demodulation,[],[f3746,f2836]) ).

fof(f2836,plain,
    ( ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_361 ),
    inference(resolution,[],[f2699,f804]) ).

fof(f804,plain,
    ( class_HOL_Ozero(tc_nat)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f802]) ).

fof(f3746,plain,
    ( ! [X0,X1] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),X1,tc_nat)
    | ~ spl0_8
    | ~ spl0_513 ),
    inference(resolution,[],[f3693,f724]) ).

fof(f22094,plain,
    ( spl0_987
    | ~ spl0_102
    | ~ spl0_436
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f3654,f3433,f3162,f1192,f22092]) ).

fof(f3654,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_102
    | ~ spl0_436
    | ~ spl0_494 ),
    inference(forward_demodulation,[],[f3651,f3220]) ).

fof(f3220,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_102
    | ~ spl0_436 ),
    inference(resolution,[],[f3163,f1194]) ).

fof(f3651,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_102
    | ~ spl0_494 ),
    inference(resolution,[],[f3434,f1194]) ).

fof(f22090,plain,
    ( spl0_986
    | ~ spl0_61
    | ~ spl0_436
    | ~ spl0_494 ),
    inference(avatar_split_clause,[],[f3653,f3433,f3162,f987,f22088]) ).

fof(f22088,plain,
    ( spl0_986
  <=> ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).

fof(f3653,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_61
    | ~ spl0_436
    | ~ spl0_494 ),
    inference(forward_demodulation,[],[f3650,f3219]) ).

fof(f3219,plain,
    ( ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_61
    | ~ spl0_436 ),
    inference(resolution,[],[f3163,f989]) ).

fof(f3650,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Osmult(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_61
    | ~ spl0_494 ),
    inference(resolution,[],[f3434,f989]) ).

fof(f22086,plain,
    ( spl0_985
    | ~ spl0_157
    | ~ spl0_443 ),
    inference(avatar_split_clause,[],[f3238,f3190,f1432,f22084]) ).

fof(f22084,plain,
    ( spl0_985
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).

fof(f3238,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X1,X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) )
    | ~ spl0_157
    | ~ spl0_443 ),
    inference(resolution,[],[f3191,f1433]) ).

fof(f22082,plain,
    ( spl0_984
    | ~ spl0_44
    | ~ spl0_440 ),
    inference(avatar_split_clause,[],[f3235,f3178,f902,f22080]) ).

fof(f22080,plain,
    ( spl0_984
  <=> ! [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_984])]) ).

fof(f3235,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_44
    | ~ spl0_440 ),
    inference(resolution,[],[f3179,f904]) ).

fof(f22078,plain,
    ( spl0_983
    | ~ spl0_88
    | ~ spl0_440 ),
    inference(avatar_split_clause,[],[f3234,f3178,f1122,f22076]) ).

fof(f3234,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_88
    | ~ spl0_440 ),
    inference(resolution,[],[f3179,f1124]) ).

fof(f22074,plain,
    ( spl0_982
    | ~ spl0_7
    | ~ spl0_440 ),
    inference(avatar_split_clause,[],[f3233,f3178,f717,f22072]) ).

fof(f22072,plain,
    ( spl0_982
  <=> ! [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_982])]) ).

fof(f3233,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_7
    | ~ spl0_440 ),
    inference(resolution,[],[f3179,f719]) ).

fof(f21991,plain,
    ( spl0_981
    | ~ spl0_102
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f3220,f3162,f1192,f21989]) ).

fof(f21987,plain,
    ( spl0_980
    | ~ spl0_61
    | ~ spl0_436 ),
    inference(avatar_split_clause,[],[f3219,f3162,f987,f21985]) ).

fof(f21985,plain,
    ( spl0_980
  <=> ! [X0,X1] : c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).

fof(f21983,plain,
    ( spl0_979
    | ~ spl0_100
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f3215,f3150,f1182,f21981]) ).

fof(f3215,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_433 ),
    inference(resolution,[],[f3151,f1184]) ).

fof(f21979,plain,
    ( spl0_978
    | ~ spl0_59
    | ~ spl0_433 ),
    inference(avatar_split_clause,[],[f3214,f3150,f977,f21977]) ).

fof(f21977,plain,
    ( spl0_978
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).

fof(f3214,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),X1,tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_433 ),
    inference(resolution,[],[f3151,f979]) ).

fof(f21975,plain,
    ( spl0_977
    | ~ spl0_112
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f3207,f3125,f1242,f21973]) ).

fof(f21973,plain,
    ( spl0_977
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).

fof(f3207,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Polynomial_Odegree(X1,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) )
    | ~ spl0_112
    | ~ spl0_427 ),
    inference(resolution,[],[f3126,f1244]) ).

fof(f21971,plain,
    ( spl0_976
    | ~ spl0_73
    | ~ spl0_427 ),
    inference(avatar_split_clause,[],[f3206,f3125,f1047,f21969]) ).

fof(f21969,plain,
    ( spl0_976
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Polynomial_Odegree(X1,tc_RealDef_Oreal) = c_Polynomial_Odegree(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).

fof(f3206,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Polynomial_Odegree(X1,tc_RealDef_Oreal) = c_Polynomial_Odegree(c_Polynomial_Osmult(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) )
    | ~ spl0_73
    | ~ spl0_427 ),
    inference(resolution,[],[f3126,f1049]) ).

fof(f21967,plain,
    ( spl0_975
    | ~ spl0_79
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f3205,f3121,f1077,f21965]) ).

fof(f21965,plain,
    ( spl0_975
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).

fof(f3205,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X0) )
    | ~ spl0_79
    | ~ spl0_426 ),
    inference(resolution,[],[f3122,f1079]) ).

fof(f21963,plain,
    ( spl0_974
    | ~ spl0_117
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f3204,f3121,f1267,f21961]) ).

fof(f21961,plain,
    ( spl0_974
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).

fof(f3204,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) )
    | ~ spl0_117
    | ~ spl0_426 ),
    inference(resolution,[],[f3122,f1269]) ).

fof(f21959,plain,
    ( spl0_973
    | ~ spl0_24
    | ~ spl0_426 ),
    inference(avatar_split_clause,[],[f3203,f3121,f802,f21957]) ).

fof(f21957,plain,
    ( spl0_973
  <=> ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_nat),tc_nat),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).

fof(f3203,plain,
    ( ! [X2,X0,X1] :
        ( X0 = X1
        | c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X2,X1,tc_nat),tc_nat),X0) )
    | ~ spl0_24
    | ~ spl0_426 ),
    inference(resolution,[],[f3122,f804]) ).

fof(f21955,plain,
    ( spl0_972
    | ~ spl0_255
    | ~ spl0_315 ),
    inference(avatar_split_clause,[],[f2547,f2414,f1987,f21953]) ).

fof(f21953,plain,
    ( spl0_972
  <=> ! [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_972])]) ).

fof(f2547,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_255
    | ~ spl0_315 ),
    inference(duplicate_literal_removal,[],[f2545]) ).

fof(f2545,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_255
    | ~ spl0_315 ),
    inference(resolution,[],[f2415,f1988]) ).

fof(f21875,plain,
    ( spl0_971
    | ~ spl0_255
    | ~ spl0_314 ),
    inference(avatar_split_clause,[],[f2544,f2410,f1987,f21873]) ).

fof(f21873,plain,
    ( spl0_971
  <=> ! [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_971])]) ).

fof(f2544,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_255
    | ~ spl0_314 ),
    inference(duplicate_literal_removal,[],[f2542]) ).

fof(f2542,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_255
    | ~ spl0_314 ),
    inference(resolution,[],[f2411,f1988]) ).

fof(f21871,plain,
    ( spl0_970
    | ~ spl0_156
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2345,f2220,f1428,f21869]) ).

fof(f21869,plain,
    ( spl0_970
  <=> ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X1) = X0
        | ~ class_HOL_Ozero(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).

fof(f2220,plain,
    ( spl0_287
  <=> ! [X5,X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X1,X0),X0),X1) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).

fof(f2345,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_Polynomial_Opoly(X2)),tc_Polynomial_Opoly(X2)),X1) = X0
        | ~ class_HOL_Ozero(X2) )
    | ~ spl0_156
    | ~ spl0_287 ),
    inference(resolution,[],[f2221,f1429]) ).

fof(f2221,plain,
    ( ! [X0,X1,X5] :
        ( ~ class_HOL_Ozero(X0)
        | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X1,X0),X0),X1) = X5 )
    | ~ spl0_287 ),
    inference(avatar_component_clause,[],[f2220]) ).

fof(f21867,plain,
    ( spl0_969
    | ~ spl0_156
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2167,f2064,f1428,f21865]) ).

fof(f21865,plain,
    ( spl0_969
  <=> ! [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_969])]) ).

fof(f2064,plain,
    ( spl0_274
  <=> ! [X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).

fof(f2167,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_156
    | ~ spl0_274 ),
    inference(resolution,[],[f2065,f1429]) ).

fof(f2065,plain,
    ( ! [X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X15,X0) )
    | ~ spl0_274 ),
    inference(avatar_component_clause,[],[f2064]) ).

fof(f21863,plain,
    ( spl0_968
    | ~ spl0_152
    | ~ spl0_273 ),
    inference(avatar_split_clause,[],[f2166,f2060,f1412,f21861]) ).

fof(f21861,plain,
    ( spl0_968
  <=> ! [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_968])]) ).

fof(f2060,plain,
    ( spl0_273
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).

fof(f2166,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_152
    | ~ spl0_273 ),
    inference(resolution,[],[f2061,f1413]) ).

fof(f2061,plain,
    ( ! [X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0) )
    | ~ spl0_273 ),
    inference(avatar_component_clause,[],[f2060]) ).

fof(f21859,plain,
    ( spl0_967
    | ~ spl0_134
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2160,f2056,f1340,f21857]) ).

fof(f21857,plain,
    ( spl0_967
  <=> ! [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_967])]) ).

fof(f2056,plain,
    ( spl0_272
  <=> ! [X0,X12] :
        ( ~ 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),X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).

fof(f2160,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_134
    | ~ spl0_272 ),
    inference(resolution,[],[f2057,f1341]) ).

fof(f2057,plain,
    ( ! [X0,X12] :
        ( ~ 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),X12,X0) )
    | ~ spl0_272 ),
    inference(avatar_component_clause,[],[f2056]) ).

fof(f21855,plain,
    ( spl0_966
    | ~ spl0_155
    | ~ spl0_266 ),
    inference(avatar_split_clause,[],[f2148,f2031,f1424,f21853]) ).

fof(f21853,plain,
    ( spl0_966
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(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_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).

fof(f2031,plain,
    ( spl0_266
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).

fof(f2148,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(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_Ocomm__ring__1(X0) )
    | ~ spl0_155
    | ~ spl0_266 ),
    inference(resolution,[],[f2032,f1425]) ).

fof(f2032,plain,
    ( ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 )
    | ~ spl0_266 ),
    inference(avatar_component_clause,[],[f2031]) ).

fof(f21851,plain,
    ( spl0_965
    | ~ spl0_155
    | ~ spl0_257 ),
    inference(avatar_split_clause,[],[f2128,f1995,f1424,f21849]) ).

fof(f21849,plain,
    ( spl0_965
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(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_Ocomm__ring__1(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).

fof(f1995,plain,
    ( spl0_257
  <=> ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).

fof(f2128,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Oidom(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_Ocomm__ring__1(X0) )
    | ~ spl0_155
    | ~ spl0_257 ),
    inference(resolution,[],[f1996,f1425]) ).

fof(f1996,plain,
    ( ! [X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
    | ~ spl0_257 ),
    inference(avatar_component_clause,[],[f1995]) ).

fof(f21847,plain,
    ( spl0_964
    | ~ spl0_149
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2102,f1959,f1400,f21845]) ).

fof(f21845,plain,
    ( spl0_964
  <=> ! [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_964])]) ).

fof(f1959,plain,
    ( spl0_248
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).

fof(f2102,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_149
    | ~ spl0_248 ),
    inference(resolution,[],[f1960,f1401]) ).

fof(f1960,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) )
    | ~ spl0_248 ),
    inference(avatar_component_clause,[],[f1959]) ).

fof(f21843,plain,
    ( spl0_963
    | ~ spl0_143
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2099,f1955,f1376,f21841]) ).

fof(f21841,plain,
    ( spl0_963
  <=> ! [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_963])]) ).

fof(f1955,plain,
    ( spl0_247
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).

fof(f2099,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_143
    | ~ spl0_247 ),
    inference(resolution,[],[f1956,f1377]) ).

fof(f1956,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) )
    | ~ spl0_247 ),
    inference(avatar_component_clause,[],[f1955]) ).

fof(f21839,plain,
    ( spl0_962
    | ~ spl0_141
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f2085,f1939,f1368,f21837]) ).

fof(f21837,plain,
    ( spl0_962
  <=> ! [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_962])]) ).

fof(f1939,plain,
    ( spl0_243
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Osgn__class_Osgn(X5,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).

fof(f2085,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_141
    | ~ spl0_243 ),
    inference(resolution,[],[f1940,f1369]) ).

fof(f1940,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Osgn__class_Osgn(X5,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X5,X0),X0) )
    | ~ spl0_243 ),
    inference(avatar_component_clause,[],[f1939]) ).

fof(f21680,plain,
    ( spl0_961
    | ~ spl0_29
    | ~ spl0_479
    | ~ spl0_712
    | ~ spl0_803 ),
    inference(avatar_split_clause,[],[f13531,f8942,f6747,f3373,f827,f21678]) ).

fof(f21678,plain,
    ( spl0_961
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_bool),X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).

fof(f3373,plain,
    ( spl0_479
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(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_479])]) ).

fof(f6747,plain,
    ( spl0_712
  <=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).

fof(f8942,plain,
    ( spl0_803
  <=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).

fof(f13531,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X1,tc_bool),X0,tc_bool)
    | ~ spl0_29
    | ~ spl0_479
    | ~ spl0_712
    | ~ spl0_803 ),
    inference(forward_demodulation,[],[f13529,f9377]) ).

fof(f9377,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X1,tc_bool),X0,tc_bool)
    | ~ spl0_712
    | ~ spl0_803 ),
    inference(superposition,[],[f8943,f6748]) ).

fof(f6748,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
    | ~ spl0_712 ),
    inference(avatar_component_clause,[],[f6747]) ).

fof(f8943,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool)
    | ~ spl0_803 ),
    inference(avatar_component_clause,[],[f8942]) ).

fof(f13529,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool)
    | ~ spl0_29
    | ~ spl0_479 ),
    inference(resolution,[],[f3374,f829]) ).

fof(f3374,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(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_479 ),
    inference(avatar_component_clause,[],[f3373]) ).

fof(f21214,plain,
    ( spl0_960
    | ~ spl0_671
    | ~ spl0_887 ),
    inference(avatar_split_clause,[],[f20285,f11629,f5597,f21212]) ).

fof(f21212,plain,
    ( spl0_960
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).

fof(f11629,plain,
    ( spl0_887
  <=> ! [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_887])]) ).

fof(f20285,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_671
    | ~ spl0_887 ),
    inference(resolution,[],[f11630,f5598]) ).

fof(f11630,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(X2)) )
    | ~ spl0_887 ),
    inference(avatar_component_clause,[],[f11629]) ).

fof(f20437,plain,
    ( spl0_959
    | ~ spl0_671
    | ~ spl0_885 ),
    inference(avatar_split_clause,[],[f20277,f11621,f5597,f20435]) ).

fof(f20435,plain,
    ( spl0_959
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).

fof(f11621,plain,
    ( spl0_885
  <=> ! [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_885])]) ).

fof(f20277,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_671
    | ~ spl0_885 ),
    inference(resolution,[],[f11622,f5598]) ).

fof(f11622,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(X2)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(X2)) )
    | ~ spl0_885 ),
    inference(avatar_component_clause,[],[f11621]) ).

fof(f20267,plain,
    ( spl0_958
    | ~ spl0_671
    | ~ spl0_882 ),
    inference(avatar_split_clause,[],[f20260,f11591,f5597,f20265]) ).

fof(f20265,plain,
    ( spl0_958
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).

fof(f11591,plain,
    ( spl0_882
  <=> ! [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_882])]) ).

fof(f20260,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_671
    | ~ spl0_882 ),
    inference(resolution,[],[f11592,f5598]) ).

fof(f11592,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | 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)) )
    | ~ spl0_882 ),
    inference(avatar_component_clause,[],[f11591]) ).

fof(f20199,plain,
    ( spl0_957
    | ~ spl0_857
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f19812,f13536,f10684,f20197]) ).

fof(f20197,plain,
    ( spl0_957
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).

fof(f10684,plain,
    ( spl0_857
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).

fof(f19812,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_857
    | ~ spl0_937 ),
    inference(superposition,[],[f13537,f10685]) ).

fof(f10685,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_857 ),
    inference(avatar_component_clause,[],[f10684]) ).

fof(f19715,plain,
    ( spl0_956
    | ~ spl0_787
    | ~ spl0_955 ),
    inference(avatar_split_clause,[],[f19149,f18782,f8405,f19713]) ).

fof(f19713,plain,
    ( spl0_956
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).

fof(f8405,plain,
    ( spl0_787
  <=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).

fof(f18782,plain,
    ( spl0_955
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).

fof(f19149,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_787
    | ~ spl0_955 ),
    inference(superposition,[],[f18783,f8406]) ).

fof(f8406,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_787 ),
    inference(avatar_component_clause,[],[f8405]) ).

fof(f18783,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_955 ),
    inference(avatar_component_clause,[],[f18782]) ).

fof(f18784,plain,
    ( ~ spl0_804
    | spl0_955
    | ~ spl0_285
    | ~ spl0_931 ),
    inference(avatar_split_clause,[],[f13024,f12986,f2212,f18782,f8946]) ).

fof(f8946,plain,
    ( spl0_804
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).

fof(f12986,plain,
    ( spl0_931
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).

fof(f13024,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_285
    | ~ spl0_931 ),
    inference(resolution,[],[f12987,f2213]) ).

fof(f12987,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_931 ),
    inference(avatar_component_clause,[],[f12986]) ).

fof(f18146,plain,
    ( ~ spl0_953
    | spl0_954
    | ~ spl0_443
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f11619,f10804,f3190,f18144,f18140]) ).

fof(f18140,plain,
    ( spl0_953
  <=> class_Ring__and__Field_Ofield(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).

fof(f18144,plain,
    ( spl0_954
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).

fof(f10804,plain,
    ( spl0_873
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).

fof(f11619,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ofield(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_443
    | ~ spl0_873 ),
    inference(resolution,[],[f10805,f3191]) ).

fof(f10805,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | ~ spl0_873 ),
    inference(avatar_component_clause,[],[f10804]) ).

fof(f17967,plain,
    ( spl0_952
    | ~ spl0_733
    | ~ spl0_951 ),
    inference(avatar_split_clause,[],[f17771,f17712,f6896,f17965]) ).

fof(f17771,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_733
    | ~ spl0_951 ),
    inference(superposition,[],[f17713,f6897]) ).

fof(f17714,plain,
    ( spl0_951
    | ~ spl0_804
    | ~ spl0_922
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f13567,f13536,f11950,f8946,f17712]) ).

fof(f13567,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_922
    | ~ spl0_937 ),
    inference(resolution,[],[f13537,f11951]) ).

fof(f17025,plain,
    ( spl0_950
    | ~ spl0_787
    | ~ spl0_949 ),
    inference(avatar_split_clause,[],[f16855,f16336,f8405,f17023]) ).

fof(f17023,plain,
    ( spl0_950
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).

fof(f16336,plain,
    ( spl0_949
  <=> ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).

fof(f16855,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_787
    | ~ spl0_949 ),
    inference(superposition,[],[f16337,f8406]) ).

fof(f16337,plain,
    ( ! [X2,X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_949 ),
    inference(avatar_component_clause,[],[f16336]) ).

fof(f16338,plain,
    ( ~ spl0_88
    | spl0_949
    | ~ spl0_89
    | ~ spl0_395
    | ~ spl0_540
    | ~ spl0_931 ),
    inference(avatar_split_clause,[],[f13031,f12986,f3909,f2913,f1127,f16336,f1122]) ).

fof(f13031,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X2,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
    | ~ spl0_89
    | ~ spl0_395
    | ~ spl0_540
    | ~ spl0_931 ),
    inference(forward_demodulation,[],[f13026,f4034]) ).

fof(f13026,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Osmult(X2,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
    | ~ spl0_395
    | ~ spl0_931 ),
    inference(resolution,[],[f12987,f2914]) ).

fof(f15776,plain,
    ( ~ spl0_946
    | spl0_948
    | ~ spl0_285
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f11613,f10804,f2212,f15774,f14810]) ).

fof(f14810,plain,
    ( spl0_946
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).

fof(f15774,plain,
    ( spl0_948
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).

fof(f11613,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
    | ~ spl0_285
    | ~ spl0_873 ),
    inference(resolution,[],[f10805,f2213]) ).

fof(f15312,plain,
    ( ~ spl0_804
    | ~ spl0_142
    | spl0_946 ),
    inference(avatar_split_clause,[],[f14844,f14810,f1372,f8946]) ).

fof(f1372,plain,
    ( spl0_142
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X48)
        | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).

fof(f14844,plain,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_142
    | spl0_946 ),
    inference(resolution,[],[f14812,f1373]) ).

fof(f1373,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__ring__1(X48) )
    | ~ spl0_142 ),
    inference(avatar_component_clause,[],[f1372]) ).

fof(f14812,plain,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | spl0_946 ),
    inference(avatar_component_clause,[],[f14810]) ).

fof(f14816,plain,
    ( ~ spl0_946
    | spl0_947
    | ~ spl0_283
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f11606,f10804,f2204,f14814,f14810]) ).

fof(f14814,plain,
    ( spl0_947
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).

fof(f2204,plain,
    ( spl0_283
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).

fof(f11606,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
    | ~ spl0_283
    | ~ spl0_873 ),
    inference(resolution,[],[f10805,f2205]) ).

fof(f2205,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
        | ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
    | ~ spl0_283 ),
    inference(avatar_component_clause,[],[f2204]) ).

fof(f14551,plain,
    ( ~ spl0_110
    | spl0_945
    | ~ spl0_535
    | ~ spl0_724 ),
    inference(avatar_split_clause,[],[f7366,f6856,f3870,f14549,f1232]) ).

fof(f14549,plain,
    ( spl0_945
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).

fof(f6856,plain,
    ( spl0_724
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).

fof(f7366,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X0,X1,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) )
    | ~ spl0_535
    | ~ spl0_724 ),
    inference(resolution,[],[f6857,f3871]) ).

fof(f6857,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_724 ),
    inference(avatar_component_clause,[],[f6856]) ).

fof(f14340,plain,
    ( spl0_944
    | ~ spl0_671
    | ~ spl0_841
    | ~ spl0_940 ),
    inference(avatar_split_clause,[],[f13975,f13943,f9154,f5597,f14338]) ).

fof(f9154,plain,
    ( spl0_841
  <=> ! [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_841])]) ).

fof(f13975,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_841
    | ~ spl0_940 ),
    inference(resolution,[],[f13944,f9155]) ).

fof(f9155,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_841 ),
    inference(avatar_component_clause,[],[f9154]) ).

fof(f14206,plain,
    ( spl0_943
    | ~ spl0_671
    | ~ spl0_841
    | ~ spl0_938 ),
    inference(avatar_split_clause,[],[f13675,f13614,f9154,f5597,f14204]) ).

fof(f13675,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_841
    | ~ spl0_938 ),
    inference(resolution,[],[f13615,f9155]) ).

fof(f14140,plain,
    ( spl0_942
    | ~ spl0_804
    | ~ spl0_774
    | ~ spl0_922 ),
    inference(avatar_split_clause,[],[f11988,f11950,f8269,f8946,f14138]) ).

fof(f14138,plain,
    ( spl0_942
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).

fof(f8269,plain,
    ( spl0_774
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).

fof(f11988,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_774
    | ~ spl0_922 ),
    inference(resolution,[],[f11951,f8270]) ).

fof(f8270,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_774 ),
    inference(avatar_component_clause,[],[f8269]) ).

fof(f14075,plain,
    ( ~ spl0_88
    | spl0_941
    | ~ spl0_395
    | ~ spl0_921 ),
    inference(avatar_split_clause,[],[f12038,f11914,f2913,f14073,f1122]) ).

fof(f14073,plain,
    ( spl0_941
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).

fof(f12038,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
    | ~ spl0_395
    | ~ spl0_921 ),
    inference(resolution,[],[f11915,f2914]) ).

fof(f13945,plain,
    ( ~ spl0_804
    | spl0_940
    | ~ spl0_285
    | ~ spl0_939 ),
    inference(avatar_split_clause,[],[f13899,f13761,f2212,f13943,f8946]) ).

fof(f13899,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_285
    | ~ spl0_939 ),
    inference(resolution,[],[f13762,f2213]) ).

fof(f13763,plain,
    ( ~ spl0_110
    | spl0_939
    | ~ spl0_407
    | ~ spl0_805 ),
    inference(avatar_split_clause,[],[f9163,f8950,f2961,f13761,f1232]) ).

fof(f9163,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) )
    | ~ spl0_407
    | ~ spl0_805 ),
    inference(resolution,[],[f8951,f2962]) ).

fof(f13616,plain,
    ( ~ spl0_804
    | spl0_938
    | ~ spl0_285
    | ~ spl0_937 ),
    inference(avatar_split_clause,[],[f13568,f13536,f2212,f13614,f8946]) ).

fof(f13568,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_285
    | ~ spl0_937 ),
    inference(resolution,[],[f13537,f2213]) ).

fof(f13538,plain,
    ( ~ spl0_110
    | spl0_937
    | ~ spl0_408
    | ~ spl0_805 ),
    inference(avatar_split_clause,[],[f9162,f8950,f2965,f13536,f1232]) ).

fof(f9162,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) )
    | ~ spl0_408
    | ~ spl0_805 ),
    inference(resolution,[],[f8951,f2966]) ).

fof(f13422,plain,
    ( ~ spl0_88
    | spl0_936
    | ~ spl0_395
    | ~ spl0_755 ),
    inference(avatar_split_clause,[],[f8219,f8168,f2913,f13420,f1122]) ).

fof(f8219,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,c_Polynomial_Osmult(X2,X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
    | ~ spl0_395
    | ~ spl0_755 ),
    inference(resolution,[],[f8169,f2914]) ).

fof(f13295,plain,
    ( spl0_935
    | ~ spl0_804
    | ~ spl0_748
    | ~ spl0_923 ),
    inference(avatar_split_clause,[],[f12012,f11954,f7834,f8946,f13293]) ).

fof(f13293,plain,
    ( spl0_935
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).

fof(f7834,plain,
    ( spl0_748
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).

fof(f12012,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_748
    | ~ spl0_923 ),
    inference(resolution,[],[f11955,f7835]) ).

fof(f7835,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_748 ),
    inference(avatar_component_clause,[],[f7834]) ).

fof(f13223,plain,
    ( ~ spl0_671
    | spl0_934
    | ~ spl0_395
    | ~ spl0_873 ),
    inference(avatar_split_clause,[],[f11618,f10804,f2913,f13221,f5597]) ).

fof(f13221,plain,
    ( spl0_934
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).

fof(f11618,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_395
    | ~ spl0_873 ),
    inference(resolution,[],[f10805,f2914]) ).

fof(f13175,plain,
    ( ~ spl0_872
    | spl0_933
    | ~ spl0_187
    | ~ spl0_844 ),
    inference(avatar_split_clause,[],[f11670,f9676,f1579,f13173,f10800]) ).

fof(f13173,plain,
    ( spl0_933
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).

fof(f9676,plain,
    ( spl0_844
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).

fof(f11670,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
    | ~ spl0_187
    | ~ spl0_844 ),
    inference(superposition,[],[f1580,f9677]) ).

fof(f9677,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_844 ),
    inference(avatar_component_clause,[],[f9676]) ).

fof(f13076,plain,
    ( spl0_932
    | ~ spl0_787
    | ~ spl0_931 ),
    inference(avatar_split_clause,[],[f13029,f12986,f8405,f13074]) ).

fof(f13074,plain,
    ( spl0_932
  <=> ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).

fof(f13029,plain,
    ( ! [X0,X1] : c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_787
    | ~ spl0_931 ),
    inference(superposition,[],[f12987,f8406]) ).

fof(f12988,plain,
    ( ~ spl0_723
    | spl0_931
    | ~ spl0_187
    | ~ spl0_787 ),
    inference(avatar_split_clause,[],[f8608,f8405,f1579,f12986,f6852]) ).

fof(f6852,plain,
    ( spl0_723
  <=> class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).

fof(f8608,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_187
    | ~ spl0_787 ),
    inference(superposition,[],[f1580,f8406]) ).

fof(f12294,plain,
    ( spl0_930
    | ~ spl0_236
    | ~ spl0_919 ),
    inference(avatar_split_clause,[],[f11877,f11871,f1872,f12292]) ).

fof(f1872,plain,
    ( spl0_236
  <=> ! [X50,X0,X51] :
        ( X50 = X51
        | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X50),X51)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).

fof(f11877,plain,
    ( ! [X0,X1] : X0 = X1
    | ~ spl0_236
    | ~ spl0_919 ),
    inference(resolution,[],[f11872,f1873]) ).

fof(f1873,plain,
    ( ! [X50,X51,X0] :
        ( ~ hBOOL(hAPP(hAPP(c_fequal(X0),X50),X51))
        | X50 = X51 )
    | ~ spl0_236 ),
    inference(avatar_component_clause,[],[f1872]) ).

fof(f11872,plain,
    ( ! [X2] : hBOOL(X2)
    | ~ spl0_919 ),
    inference(avatar_component_clause,[],[f11871]) ).

fof(f12054,plain,
    ( spl0_929
    | ~ spl0_315
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f2571,f2422,f2414,f12052]) ).

fof(f12052,plain,
    ( spl0_929
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).

fof(f2571,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X1,X3) )
    | ~ spl0_315
    | ~ spl0_317 ),
    inference(duplicate_literal_removal,[],[f2568]) ).

fof(f2568,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X1,X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_315
    | ~ spl0_317 ),
    inference(resolution,[],[f2423,f2415]) ).

fof(f12050,plain,
    ( spl0_928
    | ~ spl0_314
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f2570,f2422,f2410,f12048]) ).

fof(f12048,plain,
    ( spl0_928
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).

fof(f2570,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X2,X3) )
    | ~ spl0_314
    | ~ spl0_317 ),
    inference(duplicate_literal_removal,[],[f2569]) ).

fof(f2569,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X4,X0,X3),X2,X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_314
    | ~ spl0_317 ),
    inference(resolution,[],[f2423,f2411]) ).

fof(f12046,plain,
    ( spl0_927
    | ~ spl0_315
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f2557,f2418,f2414,f12044]) ).

fof(f12044,plain,
    ( spl0_927
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).

fof(f2557,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X1,X3) )
    | ~ spl0_315
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f2554]) ).

fof(f2554,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X1,X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_315
    | ~ spl0_316 ),
    inference(resolution,[],[f2419,f2415]) ).

fof(f12042,plain,
    ( spl0_926
    | ~ spl0_314
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f2556,f2418,f2410,f12040]) ).

fof(f12040,plain,
    ( spl0_926
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).

fof(f2556,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X2,X3) )
    | ~ spl0_314
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f2555]) ).

fof(f2555,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Otimes__class_Otimes(X1,X2,X3),X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X0,X4,X3),X2,X3)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X3) )
    | ~ spl0_314
    | ~ spl0_316 ),
    inference(resolution,[],[f2419,f2411]) ).

fof(f12030,plain,
    ( spl0_925
    | ~ spl0_229
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2326,f2204,f1839,f12028]) ).

fof(f12028,plain,
    ( spl0_925
  <=> ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,X1),X0,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).

fof(f2326,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(X1)),X2,X1),X0,tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ofield(X1) )
    | ~ spl0_229
    | ~ spl0_283 ),
    inference(resolution,[],[f2205,f1840]) ).

fof(f12026,plain,
    ( spl0_924
    | ~ spl0_228
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2325,f2204,f1835,f12024]) ).

fof(f12024,plain,
    ( spl0_924
  <=> ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).

fof(f2325,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X2)),X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) )
    | ~ spl0_228
    | ~ spl0_283 ),
    inference(resolution,[],[f2205,f1836]) ).

fof(f11956,plain,
    ( spl0_923
    | ~ spl0_283
    | ~ spl0_286 ),
    inference(avatar_split_clause,[],[f2339,f2216,f2204,f11954]) ).

fof(f2339,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_283
    | ~ spl0_286 ),
    inference(duplicate_literal_removal,[],[f2338]) ).

fof(f2338,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_283
    | ~ spl0_286 ),
    inference(resolution,[],[f2217,f2205]) ).

fof(f11952,plain,
    ( spl0_922
    | ~ spl0_284
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2336,f2212,f2208,f11950]) ).

fof(f2336,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_284
    | ~ spl0_285 ),
    inference(duplicate_literal_removal,[],[f2335]) ).

fof(f2335,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_284
    | ~ spl0_285 ),
    inference(resolution,[],[f2213,f2209]) ).

fof(f11916,plain,
    ( ~ spl0_804
    | spl0_921
    | ~ spl0_285
    | ~ spl0_724 ),
    inference(avatar_split_clause,[],[f7374,f6856,f2212,f11914,f8946]) ).

fof(f7374,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_285
    | ~ spl0_724 ),
    inference(resolution,[],[f6857,f2213]) ).

fof(f11876,plain,
    ( spl0_919
    | spl0_920
    | ~ spl0_158
    | ~ spl0_519 ),
    inference(avatar_split_clause,[],[f3794,f3735,f1436,f11874,f11871]) ).

fof(f11874,plain,
    ( spl0_920
  <=> ! [X0,X1] :
        ( hBOOL(c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(c_Fun_Oid(X0),X1))
        | ~ class_HOL_Ozero(X1)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).

fof(f3794,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(c_Fun_Oid(X0),X1))
        | hBOOL(X2)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_HOL_Ozero(X1) )
    | ~ spl0_158
    | ~ spl0_519 ),
    inference(forward_demodulation,[],[f3793,f1437]) ).

fof(f3793,plain,
    ( ! [X2,X0,X1] :
        ( hBOOL(X2)
        | ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | ~ class_HOL_Ozero(X1)
        | hBOOL(hAPP(c_Fun_Oid(X0),c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(c_Fun_Oid(X0),X1))) )
    | ~ spl0_158
    | ~ spl0_519 ),
    inference(forward_demodulation,[],[f3782,f1437]) ).

fof(f3782,plain,
    ( ! [X2,X0,X1] :
        ( ~ hBOOL(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)))
        | hBOOL(hAPP(c_Fun_Oid(X0),X2))
        | ~ class_HOL_Ozero(X1)
        | hBOOL(hAPP(c_Fun_Oid(X0),c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(c_Fun_Oid(X0),X1))) )
    | ~ spl0_158
    | ~ spl0_519 ),
    inference(superposition,[],[f3736,f1437]) ).

fof(f11869,plain,
    ( spl0_918
    | ~ spl0_100
    | ~ spl0_115
    | ~ spl0_323
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f3683,f3473,f2446,f1257,f1182,f11867]) ).

fof(f11867,plain,
    ( spl0_918
  <=> ! [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_918])]) ).

fof(f1257,plain,
    ( spl0_115
  <=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).

fof(f3683,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_100
    | ~ spl0_115
    | ~ spl0_323
    | ~ spl0_504 ),
    inference(forward_demodulation,[],[f3680,f2589]) ).

fof(f2589,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_115
    | ~ spl0_323 ),
    inference(resolution,[],[f2447,f1259]) ).

fof(f1259,plain,
    ( class_Int_Onumber__ring(tc_Complex_Ocomplex)
    | ~ spl0_115 ),
    inference(avatar_component_clause,[],[f1257]) ).

fof(f3680,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_100
    | ~ spl0_504 ),
    inference(resolution,[],[f3474,f1184]) ).

fof(f11865,plain,
    ( spl0_917
    | ~ spl0_59
    | ~ spl0_77
    | ~ spl0_323
    | ~ spl0_504 ),
    inference(avatar_split_clause,[],[f3682,f3473,f2446,f1067,f977,f11863]) ).

fof(f11863,plain,
    ( spl0_917
  <=> ! [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_917])]) ).

fof(f1067,plain,
    ( spl0_77
  <=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).

fof(f3682,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_59
    | ~ spl0_77
    | ~ spl0_323
    | ~ spl0_504 ),
    inference(forward_demodulation,[],[f3679,f2588]) ).

fof(f2588,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_77
    | ~ spl0_323 ),
    inference(resolution,[],[f2447,f1069]) ).

fof(f1069,plain,
    ( class_Int_Onumber__ring(tc_RealDef_Oreal)
    | ~ spl0_77 ),
    inference(avatar_component_clause,[],[f1067]) ).

fof(f3679,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_59
    | ~ spl0_504 ),
    inference(resolution,[],[f3474,f979]) ).

fof(f11861,plain,
    ( spl0_916
    | ~ spl0_108
    | ~ spl0_115
    | ~ spl0_323
    | ~ spl0_503 ),
    inference(avatar_split_clause,[],[f3678,f3469,f2446,f1257,f1222,f11859]) ).

fof(f11859,plain,
    ( spl0_916
  <=> ! [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_916])]) ).

fof(f1222,plain,
    ( spl0_108
  <=> class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).

fof(f3678,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_108
    | ~ spl0_115
    | ~ spl0_323
    | ~ spl0_503 ),
    inference(forward_demodulation,[],[f3675,f2589]) ).

fof(f3675,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_108
    | ~ spl0_503 ),
    inference(resolution,[],[f3470,f1224]) ).

fof(f1224,plain,
    ( class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
    | ~ spl0_108 ),
    inference(avatar_component_clause,[],[f1222]) ).

fof(f11857,plain,
    ( spl0_915
    | ~ spl0_68
    | ~ spl0_77
    | ~ spl0_323
    | ~ spl0_503 ),
    inference(avatar_split_clause,[],[f3677,f3469,f2446,f1067,f1022,f11855]) ).

fof(f11855,plain,
    ( spl0_915
  <=> ! [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_915])]) ).

fof(f1022,plain,
    ( spl0_68
  <=> class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).

fof(f3677,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_68
    | ~ spl0_77
    | ~ spl0_323
    | ~ spl0_503 ),
    inference(forward_demodulation,[],[f3674,f2588]) ).

fof(f3674,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_68
    | ~ spl0_503 ),
    inference(resolution,[],[f3470,f1024]) ).

fof(f1024,plain,
    ( class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal)
    | ~ spl0_68 ),
    inference(avatar_component_clause,[],[f1022]) ).

fof(f11819,plain,
    ( spl0_914
    | ~ spl0_100
    | ~ spl0_327
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f3667,f3453,f2462,f1182,f11817]) ).

fof(f11817,plain,
    ( spl0_914
  <=> ! [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_914])]) ).

fof(f3667,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_100
    | ~ spl0_327
    | ~ spl0_499 ),
    inference(forward_demodulation,[],[f3664,f2601]) ).

fof(f2601,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_100
    | ~ spl0_327 ),
    inference(resolution,[],[f2463,f1184]) ).

fof(f3664,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_100
    | ~ spl0_499 ),
    inference(resolution,[],[f3454,f1184]) ).

fof(f11815,plain,
    ( spl0_913
    | ~ spl0_59
    | ~ spl0_327
    | ~ spl0_499 ),
    inference(avatar_split_clause,[],[f3666,f3453,f2462,f977,f11813]) ).

fof(f11813,plain,
    ( spl0_913
  <=> ! [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_913])]) ).

fof(f3666,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_59
    | ~ spl0_327
    | ~ spl0_499 ),
    inference(forward_demodulation,[],[f3663,f2600]) ).

fof(f2600,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_59
    | ~ spl0_327 ),
    inference(resolution,[],[f2463,f979]) ).

fof(f3663,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_59
    | ~ spl0_499 ),
    inference(resolution,[],[f3454,f979]) ).

fof(f11811,plain,
    ( spl0_912
    | ~ spl0_29
    | ~ spl0_319
    | ~ spl0_479 ),
    inference(avatar_split_clause,[],[f3619,f3373,f2430,f827,f11809]) ).

fof(f11809,plain,
    ( spl0_912
  <=> ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),X1,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).

fof(f3619,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),X1,tc_bool)
    | ~ spl0_29
    | ~ spl0_319
    | ~ spl0_479 ),
    inference(forward_demodulation,[],[f3617,f2578]) ).

fof(f2578,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool)
    | ~ spl0_29
    | ~ spl0_319 ),
    inference(resolution,[],[f2431,f829]) ).

fof(f3617,plain,
    ( ! [X0,X1] : c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),c_HOL_Ouminus__class_Ouminus(X1,tc_bool),tc_bool)
    | ~ spl0_29
    | ~ spl0_479 ),
    inference(resolution,[],[f3374,f829]) ).

fof(f11807,plain,
    ( spl0_911
    | ~ spl0_228
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f3082,f2965,f1835,f11805]) ).

fof(f11805,plain,
    ( spl0_911
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).

fof(f3082,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3) )
    | ~ spl0_228
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f3079]) ).

fof(f3079,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X2,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3)
        | ~ class_Ring__and__Field_Ofield(X3) )
    | ~ spl0_228
    | ~ spl0_408 ),
    inference(resolution,[],[f2966,f1836]) ).

fof(f11803,plain,
    ( spl0_910
    | ~ spl0_229
    | ~ spl0_408 ),
    inference(avatar_split_clause,[],[f3081,f2965,f1839,f11801]) ).

fof(f11801,plain,
    ( spl0_910
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).

fof(f3081,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) )
    | ~ spl0_229
    | ~ spl0_408 ),
    inference(duplicate_literal_removal,[],[f3080]) ).

fof(f3080,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X1,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2)
        | ~ class_Ring__and__Field_Ofield(X2) )
    | ~ spl0_229
    | ~ spl0_408 ),
    inference(resolution,[],[f2966,f1840]) ).

fof(f11799,plain,
    ( spl0_909
    | ~ spl0_228
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f3075,f2961,f1835,f11797]) ).

fof(f11797,plain,
    ( spl0_909
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X1,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).

fof(f3075,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X1,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3) )
    | ~ spl0_228
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f3072]) ).

fof(f3072,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X0,c_Polynomial_Opoly__gcd(X1,X2,X3),X3),X1,tc_Polynomial_Opoly(X3))
        | ~ class_Ring__and__Field_Ofield(X3)
        | ~ class_Ring__and__Field_Ofield(X3) )
    | ~ spl0_228
    | ~ spl0_407 ),
    inference(resolution,[],[f2962,f1836]) ).

fof(f11795,plain,
    ( spl0_908
    | ~ spl0_229
    | ~ spl0_407 ),
    inference(avatar_split_clause,[],[f3074,f2961,f1839,f11793]) ).

fof(f11793,plain,
    ( spl0_908
  <=> ! [X0,X3,X2,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X0,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).

fof(f3074,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X0,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2) )
    | ~ spl0_229
    | ~ spl0_407 ),
    inference(duplicate_literal_removal,[],[f3073]) ).

fof(f3073,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X0,X1,X2),X3,X2),X0,tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ofield(X2)
        | ~ class_Ring__and__Field_Ofield(X2) )
    | ~ spl0_229
    | ~ spl0_407 ),
    inference(resolution,[],[f2962,f1840]) ).

fof(f11791,plain,
    ( spl0_907
    | ~ spl0_111
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f3060,f2941,f1237,f11789]) ).

fof(f11789,plain,
    ( spl0_907
  <=> ! [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_907])]) ).

fof(f1237,plain,
    ( spl0_111
  <=> class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).

fof(f3060,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_111
    | ~ spl0_402 ),
    inference(resolution,[],[f2942,f1239]) ).

fof(f1239,plain,
    ( class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
    | ~ spl0_111 ),
    inference(avatar_component_clause,[],[f1237]) ).

fof(f11787,plain,
    ( spl0_906
    | ~ spl0_72
    | ~ spl0_402 ),
    inference(avatar_split_clause,[],[f3059,f2941,f1042,f11785]) ).

fof(f11785,plain,
    ( spl0_906
  <=> ! [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_906])]) ).

fof(f1042,plain,
    ( spl0_72
  <=> class_Ring__and__Field_Oring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).

fof(f3059,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_72
    | ~ spl0_402 ),
    inference(resolution,[],[f2942,f1044]) ).

fof(f1044,plain,
    ( class_Ring__and__Field_Oring(tc_RealDef_Oreal)
    | ~ spl0_72 ),
    inference(avatar_component_clause,[],[f1042]) ).

fof(f11783,plain,
    ( spl0_905
    | ~ spl0_110
    | ~ spl0_398 ),
    inference(avatar_split_clause,[],[f3051,f2925,f1232,f11781]) ).

fof(f2925,plain,
    ( spl0_398
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).

fof(f3051,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_110
    | ~ spl0_398 ),
    inference(resolution,[],[f2926,f1234]) ).

fof(f2926,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) )
    | ~ spl0_398 ),
    inference(avatar_component_clause,[],[f2925]) ).

fof(f11758,plain,
    ( spl0_904
    | ~ spl0_71
    | ~ spl0_398 ),
    inference(avatar_split_clause,[],[f3050,f2925,f1037,f11756]) ).

fof(f3050,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_71
    | ~ spl0_398 ),
    inference(resolution,[],[f2926,f1039]) ).

fof(f11754,plain,
    ( spl0_903
    | ~ spl0_157
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3035,f2913,f1432,f11752]) ).

fof(f11752,plain,
    ( spl0_903
  <=> ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).

fof(f3035,plain,
    ( ! [X2,X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,X2),tc_Polynomial_Opoly(X2))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X2)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X2)) )
    | ~ spl0_157
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f1433]) ).

fof(f11750,plain,
    ( spl0_902
    | ~ spl0_107
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f3031,f2905,f1217,f11748]) ).

fof(f11748,plain,
    ( spl0_902
  <=> ! [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_902])]) ).

fof(f2905,plain,
    ( spl0_393
  <=> ! [X5,X0,X1] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).

fof(f3031,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_107
    | ~ spl0_393 ),
    inference(resolution,[],[f2906,f1219]) ).

fof(f2906,plain,
    ( ! [X0,X1,X5] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X0) )
    | ~ spl0_393 ),
    inference(avatar_component_clause,[],[f2905]) ).

fof(f11746,plain,
    ( spl0_901
    | ~ spl0_67
    | ~ spl0_393 ),
    inference(avatar_split_clause,[],[f3030,f2905,f1017,f11744]) ).

fof(f11744,plain,
    ( spl0_901
  <=> ! [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_901])]) ).

fof(f3030,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_67
    | ~ spl0_393 ),
    inference(resolution,[],[f2906,f1019]) ).

fof(f11742,plain,
    ( spl0_900
    | ~ spl0_110
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f3024,f2893,f1232,f11740]) ).

fof(f11740,plain,
    ( spl0_900
  <=> ! [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_900])]) ).

fof(f2893,plain,
    ( spl0_390
  <=> ! [X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),X13,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).

fof(f3024,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_110
    | ~ spl0_390 ),
    inference(resolution,[],[f2894,f1234]) ).

fof(f2894,plain,
    ( ! [X0,X5,X13] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X13
        | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),X13,X0) = X5 )
    | ~ spl0_390 ),
    inference(avatar_component_clause,[],[f2893]) ).

fof(f11738,plain,
    ( spl0_899
    | ~ spl0_71
    | ~ spl0_390 ),
    inference(avatar_split_clause,[],[f3023,f2893,f1037,f11736]) ).

fof(f11736,plain,
    ( spl0_899
  <=> ! [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_899])]) ).

fof(f3023,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_71
    | ~ spl0_390 ),
    inference(resolution,[],[f2894,f1039]) ).

fof(f11734,plain,
    ( spl0_898
    | ~ spl0_111
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3021,f2889,f1237,f11732]) ).

fof(f11732,plain,
    ( spl0_898
  <=> ! [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_898])]) ).

fof(f3021,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_111
    | ~ spl0_389 ),
    inference(resolution,[],[f2890,f1239]) ).

fof(f11730,plain,
    ( spl0_897
    | ~ spl0_72
    | ~ spl0_389 ),
    inference(avatar_split_clause,[],[f3020,f2889,f1042,f11728]) ).

fof(f11728,plain,
    ( spl0_897
  <=> ! [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_897])]) ).

fof(f3020,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_72
    | ~ spl0_389 ),
    inference(resolution,[],[f2890,f1044]) ).

fof(f11726,plain,
    ( spl0_896
    | ~ spl0_111
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f3018,f2885,f1237,f11724]) ).

fof(f11724,plain,
    ( spl0_896
  <=> ! [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_896])]) ).

fof(f3018,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_111
    | ~ spl0_388 ),
    inference(resolution,[],[f2886,f1239]) ).

fof(f11722,plain,
    ( spl0_895
    | ~ spl0_72
    | ~ spl0_388 ),
    inference(avatar_split_clause,[],[f3017,f2885,f1042,f11720]) ).

fof(f11720,plain,
    ( spl0_895
  <=> ! [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_895])]) ).

fof(f3017,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_72
    | ~ spl0_388 ),
    inference(resolution,[],[f2886,f1044]) ).

fof(f11659,plain,
    ( spl0_894
    | ~ spl0_186
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2334,f2212,f1575,f11657]) ).

fof(f11657,plain,
    ( spl0_894
  <=> ! [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_894])]) ).

fof(f2334,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_186
    | ~ spl0_285 ),
    inference(resolution,[],[f2213,f1576]) ).

fof(f11655,plain,
    ( spl0_893
    | ~ spl0_187
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2333,f2212,f1579,f11653]) ).

fof(f11653,plain,
    ( spl0_893
  <=> ! [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_893])]) ).

fof(f2333,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_187
    | ~ spl0_285 ),
    inference(resolution,[],[f2213,f1580]) ).

fof(f11651,plain,
    ( spl0_892
    | ~ spl0_185
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2332,f2212,f1571,f11649]) ).

fof(f11649,plain,
    ( spl0_892
  <=> ! [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_892])]) ).

fof(f2332,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_185
    | ~ spl0_285 ),
    inference(resolution,[],[f2213,f1572]) ).

fof(f11647,plain,
    ( spl0_891
    | ~ spl0_139
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2156,f2052,f1360,f11645]) ).

fof(f11645,plain,
    ( spl0_891
  <=> ! [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_891])]) ).

fof(f2156,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_139
    | ~ spl0_271 ),
    inference(resolution,[],[f2053,f1361]) ).

fof(f11643,plain,
    ( spl0_890
    | ~ spl0_139
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2152,f2048,f1360,f11641]) ).

fof(f11641,plain,
    ( spl0_890
  <=> ! [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_890])]) ).

fof(f2048,plain,
    ( spl0_270
  <=> ! [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_270])]) ).

fof(f2152,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_139
    | ~ spl0_270 ),
    inference(resolution,[],[f2049,f1361]) ).

fof(f2049,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_270 ),
    inference(avatar_component_clause,[],[f2048]) ).

fof(f11639,plain,
    ( spl0_889
    | ~ spl0_143
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2151,f2044,f1376,f11637]) ).

fof(f11637,plain,
    ( spl0_889
  <=> ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))) = X0
        | ~ class_OrderedGroup_Oab__group__add(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).

fof(f2044,plain,
    ( spl0_269
  <=> ! [X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).

fof(f2151,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(X1))) = X0
        | ~ class_OrderedGroup_Oab__group__add(X1) )
    | ~ spl0_143
    | ~ spl0_269 ),
    inference(resolution,[],[f2045,f1377]) ).

fof(f2045,plain,
    ( ! [X0,X12] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 )
    | ~ spl0_269 ),
    inference(avatar_component_clause,[],[f2044]) ).

fof(f11635,plain,
    ( spl0_888
    | ~ spl0_139
    | ~ spl0_262 ),
    inference(avatar_split_clause,[],[f2136,f2015,f1360,f11633]) ).

fof(f11633,plain,
    ( spl0_888
  <=> ! [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_888])]) ).

fof(f2015,plain,
    ( spl0_262
  <=> ! [X5,X0,X6] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).

fof(f2136,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_139
    | ~ spl0_262 ),
    inference(resolution,[],[f2016,f1361]) ).

fof(f2016,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) )
    | ~ spl0_262 ),
    inference(avatar_component_clause,[],[f2015]) ).

fof(f11631,plain,
    ( spl0_887
    | ~ spl0_133
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f2132,f2007,f1336,f11629]) ).

fof(f2007,plain,
    ( spl0_260
  <=> ! [X5,X0,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,X13,X0) = c_HOL_Oplus__class_Oplus(X13,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).

fof(f2132,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_133
    | ~ spl0_260 ),
    inference(resolution,[],[f2008,f1337]) ).

fof(f2008,plain,
    ( ! [X0,X5,X13] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,X13,X0) = c_HOL_Oplus__class_Oplus(X13,X5,X0) )
    | ~ spl0_260 ),
    inference(avatar_component_clause,[],[f2007]) ).

fof(f11627,plain,
    ( spl0_886
    | ~ spl0_149
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f2116,f1983,f1400,f11625]) ).

fof(f11625,plain,
    ( spl0_886
  <=> ! [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_886])]) ).

fof(f1983,plain,
    ( spl0_254
  <=> ! [X5,X0,X6] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X6,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).

fof(f2116,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_149
    | ~ spl0_254 ),
    inference(resolution,[],[f1984,f1401]) ).

fof(f1984,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X6,X0) = X5 )
    | ~ spl0_254 ),
    inference(avatar_component_clause,[],[f1983]) ).

fof(f11623,plain,
    ( spl0_885
    | ~ spl0_133
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2080,f1935,f1336,f11621]) ).

fof(f2080,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_133
    | ~ spl0_242 ),
    inference(resolution,[],[f1936,f1337]) ).

fof(f11601,plain,
    ( spl0_884
    | ~ spl0_149
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f2079,f1931,f1400,f11599]) ).

fof(f11599,plain,
    ( spl0_884
  <=> ! [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_884])]) ).

fof(f1931,plain,
    ( spl0_241
  <=> ! [X5,X0,X6] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X6,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).

fof(f2079,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_149
    | ~ spl0_241 ),
    inference(resolution,[],[f1932,f1401]) ).

fof(f1932,plain,
    ( ! [X0,X6,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X6,X0) = X5 )
    | ~ spl0_241 ),
    inference(avatar_component_clause,[],[f1931]) ).

fof(f11597,plain,
    ( spl0_883
    | ~ spl0_133
    | ~ spl0_226 ),
    inference(avatar_split_clause,[],[f1901,f1827,f1336,f11595]) ).

fof(f1827,plain,
    ( spl0_226
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).

fof(f1901,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_133
    | ~ spl0_226 ),
    inference(resolution,[],[f1828,f1337]) ).

fof(f1828,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_226 ),
    inference(avatar_component_clause,[],[f1827]) ).

fof(f11593,plain,
    ( spl0_882
    | ~ spl0_133
    | ~ spl0_223 ),
    inference(avatar_split_clause,[],[f1893,f1815,f1336,f11591]) ).

fof(f1815,plain,
    ( spl0_223
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).

fof(f1893,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_133
    | ~ spl0_223 ),
    inference(resolution,[],[f1816,f1337]) ).

fof(f1816,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) )
    | ~ spl0_223 ),
    inference(avatar_component_clause,[],[f1815]) ).

fof(f11589,plain,
    ( spl0_881
    | ~ spl0_127
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f1884,f1803,f1312,f11587]) ).

fof(f11587,plain,
    ( spl0_881
  <=> ! [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_881])]) ).

fof(f1312,plain,
    ( spl0_127
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oidom(X48)
        | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).

fof(f1803,plain,
    ( spl0_220
  <=> ! [X6,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),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).

fof(f1884,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_127
    | ~ spl0_220 ),
    inference(resolution,[],[f1804,f1313]) ).

fof(f1313,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Oidom(X48) )
    | ~ spl0_127 ),
    inference(avatar_component_clause,[],[f1312]) ).

fof(f1804,plain,
    ( ! [X0,X6] :
        ( ~ 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),X6,X0) )
    | ~ spl0_220 ),
    inference(avatar_component_clause,[],[f1803]) ).

fof(f11585,plain,
    ( spl0_880
    | ~ spl0_127
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f1881,f1799,f1312,f11583]) ).

fof(f11583,plain,
    ( spl0_880
  <=> ! [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_880])]) ).

fof(f1799,plain,
    ( spl0_219
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).

fof(f1881,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_127
    | ~ spl0_219 ),
    inference(resolution,[],[f1800,f1313]) ).

fof(f1800,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_219 ),
    inference(avatar_component_clause,[],[f1799]) ).

fof(f11581,plain,
    ( spl0_879
    | ~ spl0_164
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1735,f1604,f1462,f11579]) ).

fof(f11579,plain,
    ( spl0_879
  <=> ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Oboolean__algebra(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).

fof(f1604,plain,
    ( spl0_193
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).

fof(f1735,plain,
    ( ! [X2,X0,X1] :
        ( c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_fun(X1,X2)),tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Oboolean__algebra(X2) )
    | ~ spl0_164
    | ~ spl0_193 ),
    inference(resolution,[],[f1605,f1463]) ).

fof(f1605,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 )
    | ~ spl0_193 ),
    inference(avatar_component_clause,[],[f1604]) ).

fof(f11454,plain,
    ( ~ spl0_671
    | ~ spl0_153
    | spl0_872 ),
    inference(avatar_split_clause,[],[f11055,f10800,f1416,f5597]) ).

fof(f1416,plain,
    ( spl0_153
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
        | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).

fof(f11055,plain,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_153
    | spl0_872 ),
    inference(resolution,[],[f10802,f1417]) ).

fof(f1417,plain,
    ( ! [X48] :
        ( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X48) )
    | ~ spl0_153 ),
    inference(avatar_component_clause,[],[f1416]) ).

fof(f10802,plain,
    ( ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
    | spl0_872 ),
    inference(avatar_component_clause,[],[f10800]) ).

fof(f10828,plain,
    ( spl0_878
    | ~ spl0_353
    | ~ spl0_572 ),
    inference(avatar_split_clause,[],[f4387,f4185,f2666,f10826]) ).

fof(f10826,plain,
    ( spl0_878
  <=> ! [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_878])]) ).

fof(f2666,plain,
    ( spl0_353
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).

fof(f4387,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_353
    | ~ spl0_572 ),
    inference(duplicate_literal_removal,[],[f4362]) ).

fof(f4362,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_353
    | ~ spl0_572 ),
    inference(resolution,[],[f4186,f2667]) ).

fof(f2667,plain,
    ( ! [X0,X6,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0),X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_353 ),
    inference(avatar_component_clause,[],[f2666]) ).

fof(f10824,plain,
    ( spl0_877
    | ~ spl0_110
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f2882,f2770,f1232,f10821]) ).

fof(f10821,plain,
    ( spl0_877
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).

fof(f2770,plain,
    ( spl0_379
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).

fof(f2882,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_379 ),
    inference(resolution,[],[f2771,f1234]) ).

fof(f2771,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_379 ),
    inference(avatar_component_clause,[],[f2770]) ).

fof(f10819,plain,
    ( spl0_876
    | ~ spl0_71
    | ~ spl0_379 ),
    inference(avatar_split_clause,[],[f2881,f2770,f1037,f10816]) ).

fof(f10816,plain,
    ( spl0_876
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).

fof(f2881,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_379 ),
    inference(resolution,[],[f2771,f1039]) ).

fof(f10814,plain,
    ( spl0_875
    | ~ spl0_30
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f2869,f2750,f832,f10812]) ).

fof(f10812,plain,
    ( spl0_875
  <=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).

fof(f832,plain,
    ( spl0_30
  <=> class_Lattices_Olattice(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f2869,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool)
    | ~ spl0_30
    | ~ spl0_374 ),
    inference(resolution,[],[f2751,f834]) ).

fof(f834,plain,
    ( class_Lattices_Olattice(tc_bool)
    | ~ spl0_30 ),
    inference(avatar_component_clause,[],[f832]) ).

fof(f10810,plain,
    ( spl0_874
    | ~ spl0_75
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f2867,f2750,f1057,f10808]) ).

fof(f10808,plain,
    ( spl0_874
  <=> ! [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_874])]) ).

fof(f1057,plain,
    ( spl0_75
  <=> class_Lattices_Olattice(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).

fof(f2867,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_75
    | ~ spl0_374 ),
    inference(resolution,[],[f2751,f1059]) ).

fof(f1059,plain,
    ( class_Lattices_Olattice(tc_RealDef_Oreal)
    | ~ spl0_75 ),
    inference(avatar_component_clause,[],[f1057]) ).

fof(f10806,plain,
    ( ~ spl0_872
    | spl0_873
    | ~ spl0_187
    | ~ spl0_843 ),
    inference(avatar_split_clause,[],[f10713,f9256,f1579,f10804,f10800]) ).

fof(f9256,plain,
    ( spl0_843
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).

fof(f10713,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) )
    | ~ spl0_187
    | ~ spl0_843 ),
    inference(superposition,[],[f1580,f9257]) ).

fof(f9257,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_843 ),
    inference(avatar_component_clause,[],[f9256]) ).

fof(f10798,plain,
    ( spl0_871
    | ~ spl0_23
    | ~ spl0_374 ),
    inference(avatar_split_clause,[],[f2866,f2750,f797,f10796]) ).

fof(f10796,plain,
    ( spl0_871
  <=> ! [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_871])]) ).

fof(f797,plain,
    ( spl0_23
  <=> class_Lattices_Olattice(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f2866,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_23
    | ~ spl0_374 ),
    inference(resolution,[],[f2751,f799]) ).

fof(f799,plain,
    ( class_Lattices_Olattice(tc_nat)
    | ~ spl0_23 ),
    inference(avatar_component_clause,[],[f797]) ).

fof(f10794,plain,
    ( spl0_870
    | ~ spl0_79
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f2865,f2746,f1077,f10792]) ).

fof(f10792,plain,
    ( spl0_870
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).

fof(f2865,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = X1 )
    | ~ spl0_79
    | ~ spl0_373 ),
    inference(resolution,[],[f2747,f1079]) ).

fof(f10790,plain,
    ( spl0_869
    | ~ spl0_117
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f2864,f2746,f1267,f10788]) ).

fof(f10788,plain,
    ( spl0_869
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).

fof(f2864,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X1 )
    | ~ spl0_117
    | ~ spl0_373 ),
    inference(resolution,[],[f2747,f1269]) ).

fof(f10786,plain,
    ( spl0_868
    | ~ spl0_24
    | ~ spl0_373 ),
    inference(avatar_split_clause,[],[f2863,f2746,f802,f10784]) ).

fof(f10784,plain,
    ( spl0_868
  <=> ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).

fof(f2863,plain,
    ( ! [X0,X1] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = X0
        | c_Polynomial_Odegree(c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat) = X1 )
    | ~ spl0_24
    | ~ spl0_373 ),
    inference(resolution,[],[f2747,f804]) ).

fof(f10782,plain,
    ( spl0_867
    | ~ spl0_26
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f2848,f2718,f812,f10780]) ).

fof(f10780,plain,
    ( spl0_867
  <=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).

fof(f2848,plain,
    ( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool)
    | ~ spl0_26
    | ~ spl0_366 ),
    inference(resolution,[],[f2719,f814]) ).

fof(f10778,plain,
    ( spl0_866
    | ~ spl0_57
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f2846,f2718,f967,f10776]) ).

fof(f10776,plain,
    ( spl0_866
  <=> ! [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_866])]) ).

fof(f2846,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_57
    | ~ spl0_366 ),
    inference(resolution,[],[f2719,f969]) ).

fof(f10774,plain,
    ( spl0_865
    | ~ spl0_15
    | ~ spl0_366 ),
    inference(avatar_split_clause,[],[f2845,f2718,f757,f10772]) ).

fof(f10772,plain,
    ( spl0_865
  <=> ! [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_865])]) ).

fof(f2845,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_15
    | ~ spl0_366 ),
    inference(resolution,[],[f2719,f759]) ).

fof(f10770,plain,
    ( spl0_864
    | ~ spl0_100
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f2840,f2702,f1182,f10768]) ).

fof(f10768,plain,
    ( spl0_864
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).

fof(f2840,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_100
    | ~ spl0_362 ),
    inference(resolution,[],[f2703,f1184]) ).

fof(f10766,plain,
    ( spl0_863
    | ~ spl0_59
    | ~ spl0_362 ),
    inference(avatar_split_clause,[],[f2839,f2702,f977,f10764]) ).

fof(f10764,plain,
    ( spl0_863
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).

fof(f2839,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_59
    | ~ spl0_362 ),
    inference(resolution,[],[f2703,f979]) ).

fof(f10762,plain,
    ( spl0_862
    | ~ spl0_79
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f2838,f2698,f1077,f10760]) ).

fof(f10760,plain,
    ( spl0_862
  <=> ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).

fof(f10702,plain,
    ( spl0_861
    | ~ spl0_117
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f2837,f2698,f1267,f10700]) ).

fof(f10700,plain,
    ( spl0_861
  <=> ! [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_861])]) ).

fof(f10698,plain,
    ( spl0_860
    | ~ spl0_24
    | ~ spl0_361 ),
    inference(avatar_split_clause,[],[f2836,f2698,f802,f10696]) ).

fof(f10696,plain,
    ( spl0_860
  <=> ! [X0] : c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) = c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).

fof(f10694,plain,
    ( spl0_859
    | ~ spl0_110
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f2831,f2678,f1232,f10692]) ).

fof(f2678,plain,
    ( spl0_356
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).

fof(f2831,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X1,tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_356 ),
    inference(resolution,[],[f2679,f1234]) ).

fof(f2679,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X2,X0) )
    | ~ spl0_356 ),
    inference(avatar_component_clause,[],[f2678]) ).

fof(f10690,plain,
    ( spl0_858
    | ~ spl0_71
    | ~ spl0_356 ),
    inference(avatar_split_clause,[],[f2830,f2678,f1037,f10688]) ).

fof(f10688,plain,
    ( spl0_858
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),X1,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).

fof(f2830,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),X1,tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_356 ),
    inference(resolution,[],[f2679,f1039]) ).

fof(f10686,plain,
    ( spl0_857
    | ~ spl0_110
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f2824,f2674,f1232,f10684]) ).

fof(f2674,plain,
    ( spl0_355
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).

fof(f2824,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_355 ),
    inference(resolution,[],[f2675,f1234]) ).

fof(f2675,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_355 ),
    inference(avatar_component_clause,[],[f2674]) ).

fof(f10682,plain,
    ( spl0_856
    | ~ spl0_71
    | ~ spl0_355 ),
    inference(avatar_split_clause,[],[f2823,f2674,f1037,f10680]) ).

fof(f10680,plain,
    ( spl0_856
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).

fof(f2823,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_355 ),
    inference(resolution,[],[f2675,f1039]) ).

fof(f10678,plain,
    ( spl0_855
    | ~ spl0_317
    | ~ spl0_353 ),
    inference(avatar_split_clause,[],[f2799,f2666,f2422,f10676]) ).

fof(f10676,plain,
    ( spl0_855
  <=> ! [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_855])]) ).

fof(f2799,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_317
    | ~ spl0_353 ),
    inference(resolution,[],[f2667,f2423]) ).

fof(f10674,plain,
    ( spl0_854
    | ~ spl0_316
    | ~ spl0_352 ),
    inference(avatar_split_clause,[],[f2798,f2662,f2418,f10672]) ).

fof(f10672,plain,
    ( spl0_854
  <=> ! [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_854])]) ).

fof(f2662,plain,
    ( spl0_352
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).

fof(f2798,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_316
    | ~ spl0_352 ),
    inference(resolution,[],[f2663,f2419]) ).

fof(f2663,plain,
    ( ! [X0,X6,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X0),X0),X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_352 ),
    inference(avatar_component_clause,[],[f2662]) ).

fof(f10670,plain,
    ( spl0_853
    | ~ spl0_185
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f2573,f2422,f1571,f10668]) ).

fof(f10668,plain,
    ( spl0_853
  <=> ! [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_853])]) ).

fof(f2573,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_185
    | ~ spl0_317 ),
    inference(duplicate_literal_removal,[],[f2564]) ).

fof(f2564,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_185
    | ~ spl0_317 ),
    inference(resolution,[],[f2423,f1572]) ).

fof(f10666,plain,
    ( spl0_852
    | ~ spl0_186
    | ~ spl0_317 ),
    inference(avatar_split_clause,[],[f2572,f2422,f1575,f10664]) ).

fof(f10664,plain,
    ( spl0_852
  <=> ! [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_852])]) ).

fof(f2572,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_186
    | ~ spl0_317 ),
    inference(duplicate_literal_removal,[],[f2566]) ).

fof(f2566,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_186
    | ~ spl0_317 ),
    inference(resolution,[],[f2423,f1576]) ).

fof(f10662,plain,
    ( spl0_851
    | ~ spl0_671
    | ~ spl0_796 ),
    inference(avatar_split_clause,[],[f9201,f8914,f5597,f10660]) ).

fof(f10660,plain,
    ( spl0_851
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).

fof(f8914,plain,
    ( spl0_796
  <=> ! [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_796])]) ).

fof(f9201,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_671
    | ~ spl0_796 ),
    inference(resolution,[],[f8915,f5598]) ).

fof(f8915,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0 )
    | ~ spl0_796 ),
    inference(avatar_component_clause,[],[f8914]) ).

fof(f10658,plain,
    ( spl0_850
    | ~ spl0_185
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f2559,f2418,f1571,f10656]) ).

fof(f10656,plain,
    ( spl0_850
  <=> ! [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_850])]) ).

fof(f2559,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_185
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f2550]) ).

fof(f2550,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_185
    | ~ spl0_316 ),
    inference(resolution,[],[f2419,f1572]) ).

fof(f10654,plain,
    ( spl0_849
    | ~ spl0_186
    | ~ spl0_316 ),
    inference(avatar_split_clause,[],[f2558,f2418,f1575,f10652]) ).

fof(f10652,plain,
    ( spl0_849
  <=> ! [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_849])]) ).

fof(f2558,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_186
    | ~ spl0_316 ),
    inference(duplicate_literal_removal,[],[f2552]) ).

fof(f2552,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_186
    | ~ spl0_316 ),
    inference(resolution,[],[f2419,f1576]) ).

fof(f10650,plain,
    ( spl0_848
    | ~ spl0_156
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f1875,f1795,f1428,f10648]) ).

fof(f10648,plain,
    ( spl0_848
  <=> ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).

fof(f1795,plain,
    ( spl0_218
  <=> ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).

fof(f1875,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(X0))),tc_Polynomial_Opoly(X0))
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_156
    | ~ spl0_218 ),
    inference(resolution,[],[f1796,f1429]) ).

fof(f1796,plain,
    ( ! [X0] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) )
    | ~ spl0_218 ),
    inference(avatar_component_clause,[],[f1795]) ).

fof(f10646,plain,
    ( spl0_847
    | ~ spl0_130
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1741,f1612,f1324,f10644]) ).

fof(f10644,plain,
    ( spl0_847
  <=> ! [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_847])]) ).

fof(f1324,plain,
    ( spl0_130
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oordered__idom(X48)
        | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).

fof(f1612,plain,
    ( spl0_195
  <=> ! [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_195])]) ).

fof(f1741,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_130
    | ~ spl0_195 ),
    inference(resolution,[],[f1613,f1325]) ).

fof(f1325,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Oordered__idom(X48) )
    | ~ spl0_130 ),
    inference(avatar_component_clause,[],[f1324]) ).

fof(f1613,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_195 ),
    inference(avatar_component_clause,[],[f1612]) ).

fof(f10451,plain,
    ( spl0_846
    | ~ spl0_671
    | ~ spl0_795 ),
    inference(avatar_split_clause,[],[f9196,f8910,f5597,f10449]) ).

fof(f10449,plain,
    ( spl0_846
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).

fof(f8910,plain,
    ( spl0_795
  <=> ! [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_795])]) ).

fof(f9196,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_671
    | ~ spl0_795 ),
    inference(resolution,[],[f8911,f5598]) ).

fof(f8911,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1 )
    | ~ spl0_795 ),
    inference(avatar_component_clause,[],[f8910]) ).

fof(f10053,plain,
    ( spl0_845
    | ~ spl0_671
    | ~ spl0_792 ),
    inference(avatar_split_clause,[],[f9185,f8808,f5597,f10051]) ).

fof(f10051,plain,
    ( spl0_845
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).

fof(f8808,plain,
    ( spl0_792
  <=> ! [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_792])]) ).

fof(f9185,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_671
    | ~ spl0_792 ),
    inference(resolution,[],[f8809,f5598]) ).

fof(f8809,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1 )
    | ~ spl0_792 ),
    inference(avatar_component_clause,[],[f8808]) ).

fof(f9678,plain,
    ( spl0_844
    | ~ spl0_671
    | ~ spl0_791 ),
    inference(avatar_split_clause,[],[f9180,f8804,f5597,f9676]) ).

fof(f8804,plain,
    ( spl0_791
  <=> ! [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_791])]) ).

fof(f9180,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),X0,tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_671
    | ~ spl0_791 ),
    inference(resolution,[],[f8805,f5598]) ).

fof(f8805,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X0)),X1,tc_Polynomial_Opoly(X0)) = X1 )
    | ~ spl0_791 ),
    inference(avatar_component_clause,[],[f8804]) ).

fof(f9258,plain,
    ( spl0_843
    | ~ spl0_671
    | ~ spl0_790 ),
    inference(avatar_split_clause,[],[f9175,f8800,f5597,f9256]) ).

fof(f8800,plain,
    ( spl0_790
  <=> ! [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_790])]) ).

fof(f9175,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))),tc_Polynomial_Opoly(tc_Polynomial_Opoly(tc_Complex_Ocomplex))) = X0
    | ~ spl0_671
    | ~ spl0_790 ),
    inference(resolution,[],[f8801,f5598]) ).

fof(f8801,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0 )
    | ~ spl0_790 ),
    inference(avatar_component_clause,[],[f8800]) ).

fof(f9160,plain,
    ( spl0_842
    | ~ spl0_338
    | ~ spl0_395 ),
    inference(avatar_split_clause,[],[f3034,f2913,f2506,f9158]) ).

fof(f9158,plain,
    ( spl0_842
  <=> ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | ~ class_Ring__and__Field_Ofield(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).

fof(f2506,plain,
    ( spl0_338
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).

fof(f3034,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X1)
        | ~ class_Ring__and__Field_Ofield(X1) )
    | ~ spl0_338
    | ~ spl0_395 ),
    inference(resolution,[],[f2914,f2507]) ).

fof(f2507,plain,
    ( ! [X0,X12] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | ~ class_Ring__and__Field_Ofield(X0) )
    | ~ spl0_338 ),
    inference(avatar_component_clause,[],[f2506]) ).

fof(f9156,plain,
    ( spl0_841
    | ~ spl0_166
    | ~ spl0_354 ),
    inference(avatar_split_clause,[],[f2816,f2670,f1472,f9154]) ).

fof(f1472,plain,
    ( spl0_166
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).

fof(f2816,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_166
    | ~ spl0_354 ),
    inference(duplicate_literal_removal,[],[f2812]) ).

fof(f2812,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_166
    | ~ spl0_354 ),
    inference(resolution,[],[f2671,f1473]) ).

fof(f1473,plain,
    ( ! [X0,X5] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0)
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X0) )
    | ~ spl0_166 ),
    inference(avatar_component_clause,[],[f1472]) ).

fof(f9152,plain,
    ( spl0_840
    | ~ spl0_79
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f2644,f2534,f1077,f9149]) ).

fof(f9149,plain,
    ( spl0_840
  <=> 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_840])]) ).

fof(f2644,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_79
    | ~ spl0_345 ),
    inference(resolution,[],[f2535,f1079]) ).

fof(f9147,plain,
    ( spl0_839
    | ~ spl0_117
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f2643,f2534,f1267,f9144]) ).

fof(f9144,plain,
    ( spl0_839
  <=> 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_839])]) ).

fof(f2643,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_117
    | ~ spl0_345 ),
    inference(resolution,[],[f2535,f1269]) ).

fof(f9142,plain,
    ( spl0_838
    | ~ spl0_24
    | ~ spl0_345 ),
    inference(avatar_split_clause,[],[f2642,f2534,f802,f9139]) ).

fof(f9139,plain,
    ( spl0_838
  <=> 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_838])]) ).

fof(f2642,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_24
    | ~ spl0_345 ),
    inference(resolution,[],[f2535,f804]) ).

fof(f9137,plain,
    ( spl0_837
    | ~ spl0_45
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f2638,f2522,f907,f9135]) ).

fof(f9135,plain,
    ( spl0_837
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).

fof(f2638,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_342 ),
    inference(resolution,[],[f2523,f909]) ).

fof(f9133,plain,
    ( spl0_836
    | ~ spl0_89
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f2637,f2522,f1127,f9131]) ).

fof(f9131,plain,
    ( spl0_836
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).

fof(f2637,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_342 ),
    inference(resolution,[],[f2523,f1129]) ).

fof(f9129,plain,
    ( spl0_835
    | ~ spl0_8
    | ~ spl0_342 ),
    inference(avatar_split_clause,[],[f2636,f2522,f722,f9127]) ).

fof(f9127,plain,
    ( spl0_835
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).

fof(f2636,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_8
    | ~ spl0_342 ),
    inference(resolution,[],[f2523,f724]) ).

fof(f9125,plain,
    ( spl0_834
    | ~ spl0_45
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f2634,f2518,f907,f9123]) ).

fof(f9123,plain,
    ( spl0_834
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).

fof(f2634,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_45
    | ~ spl0_341 ),
    inference(resolution,[],[f2519,f909]) ).

fof(f9121,plain,
    ( spl0_833
    | ~ spl0_89
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f2633,f2518,f1127,f9119]) ).

fof(f9119,plain,
    ( spl0_833
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).

fof(f2633,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_89
    | ~ spl0_341 ),
    inference(resolution,[],[f2519,f1129]) ).

fof(f9116,plain,
    ( spl0_832
    | ~ spl0_8
    | ~ spl0_341 ),
    inference(avatar_split_clause,[],[f2632,f2518,f722,f9114]) ).

fof(f9114,plain,
    ( spl0_832
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).

fof(f2632,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_8
    | ~ spl0_341 ),
    inference(resolution,[],[f2519,f724]) ).

fof(f9112,plain,
    ( spl0_831
    | ~ spl0_79
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f2630,f2502,f1077,f9109]) ).

fof(f9109,plain,
    ( spl0_831
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).

fof(f2630,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal,tc_nat),tc_RealDef_Oreal)
    | ~ spl0_79
    | ~ spl0_337 ),
    inference(resolution,[],[f2503,f1079]) ).

fof(f9107,plain,
    ( spl0_830
    | ~ spl0_117
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f2629,f2502,f1267,f9104]) ).

fof(f9104,plain,
    ( spl0_830
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).

fof(f2629,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_nat),tc_Complex_Ocomplex)
    | ~ spl0_117
    | ~ spl0_337 ),
    inference(resolution,[],[f2503,f1269]) ).

fof(f9102,plain,
    ( spl0_829
    | ~ spl0_24
    | ~ spl0_337 ),
    inference(avatar_split_clause,[],[f2628,f2502,f802,f9099]) ).

fof(f9099,plain,
    ( spl0_829
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).

fof(f2628,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat,tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_337 ),
    inference(resolution,[],[f2503,f804]) ).

fof(f9097,plain,
    ( spl0_828
    | ~ spl0_79
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f2626,f2498,f1077,f9095]) ).

fof(f9095,plain,
    ( spl0_828
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).

fof(f2626,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_79
    | ~ spl0_336 ),
    inference(resolution,[],[f2499,f1079]) ).

fof(f9093,plain,
    ( spl0_827
    | ~ spl0_117
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f2625,f2498,f1267,f9091]) ).

fof(f9091,plain,
    ( spl0_827
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).

fof(f2625,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_117
    | ~ spl0_336 ),
    inference(resolution,[],[f2499,f1269]) ).

fof(f9089,plain,
    ( spl0_826
    | ~ spl0_24
    | ~ spl0_336 ),
    inference(avatar_split_clause,[],[f2624,f2498,f802,f9087]) ).

fof(f9087,plain,
    ( spl0_826
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).

fof(f2624,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X0,X1,tc_nat),tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)) = X0
    | ~ spl0_24
    | ~ spl0_336 ),
    inference(resolution,[],[f2499,f804]) ).

fof(f9085,plain,
    ( spl0_825
    | ~ spl0_108
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f2621,f2494,f1222,f9083]) ).

fof(f9083,plain,
    ( spl0_825
  <=> ! [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_825])]) ).

fof(f2621,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_108
    | ~ spl0_335 ),
    inference(resolution,[],[f2495,f1224]) ).

fof(f9081,plain,
    ( spl0_824
    | ~ spl0_68
    | ~ spl0_335 ),
    inference(avatar_split_clause,[],[f2620,f2494,f1022,f9079]) ).

fof(f9079,plain,
    ( spl0_824
  <=> ! [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_824])]) ).

fof(f2620,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_68
    | ~ spl0_335 ),
    inference(resolution,[],[f2495,f1024]) ).

fof(f9077,plain,
    ( spl0_823
    | ~ spl0_100
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f2618,f2490,f1182,f9075]) ).

fof(f9075,plain,
    ( spl0_823
  <=> ! [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_823])]) ).

fof(f2618,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_100
    | ~ spl0_334 ),
    inference(resolution,[],[f2491,f1184]) ).

fof(f9073,plain,
    ( ~ spl0_99
    | ~ spl0_142
    | spl0_804 ),
    inference(avatar_split_clause,[],[f8993,f8946,f1372,f1177]) ).

fof(f1177,plain,
    ( spl0_99
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).

fof(f8993,plain,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
    | ~ spl0_142
    | spl0_804 ),
    inference(resolution,[],[f8948,f1373]) ).

fof(f8948,plain,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl0_804 ),
    inference(avatar_component_clause,[],[f8946]) ).

fof(f9072,plain,
    ( spl0_822
    | ~ spl0_59
    | ~ spl0_334 ),
    inference(avatar_split_clause,[],[f2617,f2490,f977,f9070]) ).

fof(f9070,plain,
    ( spl0_822
  <=> ! [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_822])]) ).

fof(f2617,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_59
    | ~ spl0_334 ),
    inference(resolution,[],[f2491,f979]) ).

fof(f9052,plain,
    ( spl0_821
    | ~ spl0_79
    | ~ spl0_361
    | ~ spl0_820 ),
    inference(avatar_split_clause,[],[f9048,f9045,f2698,f1077,f9050]) ).

fof(f9050,plain,
    ( spl0_821
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).

fof(f9045,plain,
    ( spl0_820
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).

fof(f9048,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_79
    | ~ spl0_361
    | ~ spl0_820 ),
    inference(forward_demodulation,[],[f9046,f2838]) ).

fof(f9046,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_820 ),
    inference(avatar_component_clause,[],[f9045]) ).

fof(f9047,plain,
    ( spl0_820
    | ~ spl0_79
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f2611,f2478,f1077,f9045]) ).

fof(f2611,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_79
    | ~ spl0_331 ),
    inference(resolution,[],[f2479,f1079]) ).

fof(f9027,plain,
    ( spl0_819
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_818 ),
    inference(avatar_split_clause,[],[f9023,f9020,f2698,f1267,f9025]) ).

fof(f9025,plain,
    ( spl0_819
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).

fof(f9020,plain,
    ( spl0_818
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).

fof(f9023,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_818 ),
    inference(forward_demodulation,[],[f9021,f2837]) ).

fof(f9021,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_818 ),
    inference(avatar_component_clause,[],[f9020]) ).

fof(f9022,plain,
    ( spl0_818
    | ~ spl0_117
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f2610,f2478,f1267,f9020]) ).

fof(f2610,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_117
    | ~ spl0_331 ),
    inference(resolution,[],[f2479,f1269]) ).

fof(f9002,plain,
    ( spl0_817
    | ~ spl0_24
    | ~ spl0_361
    | ~ spl0_816 ),
    inference(avatar_split_clause,[],[f8998,f8995,f2698,f802,f9000]) ).

fof(f9000,plain,
    ( spl0_817
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).

fof(f8995,plain,
    ( spl0_816
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).

fof(f8998,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_Omonom(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_361
    | ~ spl0_816 ),
    inference(forward_demodulation,[],[f8996,f2836]) ).

fof(f8996,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),tc_nat)
    | ~ spl0_816 ),
    inference(avatar_component_clause,[],[f8995]) ).

fof(f8997,plain,
    ( spl0_816
    | ~ spl0_24
    | ~ spl0_331 ),
    inference(avatar_split_clause,[],[f2609,f2478,f802,f8995]) ).

fof(f2609,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),tc_nat)
    | ~ spl0_24
    | ~ spl0_331 ),
    inference(resolution,[],[f2479,f804]) ).

fof(f8992,plain,
    ( spl0_815
    | ~ spl0_38
    | ~ spl0_330 ),
    inference(avatar_split_clause,[],[f2607,f2474,f872,f8990]) ).

fof(f8990,plain,
    ( spl0_815
  <=> ! [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_815])]) ).

fof(f2474,plain,
    ( spl0_330
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).

fof(f2607,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_38
    | ~ spl0_330 ),
    inference(resolution,[],[f2475,f874]) ).

fof(f2475,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) )
    | ~ spl0_330 ),
    inference(avatar_component_clause,[],[f2474]) ).

fof(f8988,plain,
    ( spl0_814
    | ~ spl0_100
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f2601,f2462,f1182,f8986]) ).

fof(f8984,plain,
    ( spl0_813
    | ~ spl0_59
    | ~ spl0_327 ),
    inference(avatar_split_clause,[],[f2600,f2462,f977,f8982]) ).

fof(f8980,plain,
    ( spl0_812
    | ~ spl0_108
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f2598,f2458,f1222,f8978]) ).

fof(f2598,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_108
    | ~ spl0_326 ),
    inference(resolution,[],[f2459,f1224]) ).

fof(f8976,plain,
    ( spl0_811
    | ~ spl0_68
    | ~ spl0_326 ),
    inference(avatar_split_clause,[],[f2597,f2458,f1022,f8974]) ).

fof(f2597,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_68
    | ~ spl0_326 ),
    inference(resolution,[],[f2459,f1024]) ).

fof(f8972,plain,
    ( spl0_810
    | ~ spl0_115
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f2589,f2446,f1257,f8970]) ).

fof(f8968,plain,
    ( spl0_809
    | ~ spl0_77
    | ~ spl0_323 ),
    inference(avatar_split_clause,[],[f2588,f2446,f1067,f8966]) ).

fof(f8964,plain,
    ( spl0_808
    | ~ spl0_38
    | ~ spl0_321 ),
    inference(avatar_split_clause,[],[f2587,f2438,f872,f8962]) ).

fof(f8962,plain,
    ( spl0_808
  <=> ! [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_808])]) ).

fof(f2438,plain,
    ( spl0_321
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).

fof(f2587,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_38
    | ~ spl0_321 ),
    inference(resolution,[],[f2439,f874]) ).

fof(f2439,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) )
    | ~ spl0_321 ),
    inference(avatar_component_clause,[],[f2438]) ).

fof(f8960,plain,
    ( spl0_807
    | ~ spl0_115
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f2581,f2434,f1257,f8958]) ).

fof(f8958,plain,
    ( spl0_807
  <=> ! [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_807])]) ).

fof(f2581,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_115
    | ~ spl0_320 ),
    inference(resolution,[],[f2435,f1259]) ).

fof(f8956,plain,
    ( spl0_806
    | ~ spl0_77
    | ~ spl0_320 ),
    inference(avatar_split_clause,[],[f2580,f2434,f1067,f8954]) ).

fof(f8954,plain,
    ( spl0_806
  <=> ! [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_806])]) ).

fof(f2580,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_77
    | ~ spl0_320 ),
    inference(resolution,[],[f2435,f1069]) ).

fof(f8952,plain,
    ( ~ spl0_804
    | spl0_805
    | ~ spl0_283
    | ~ spl0_724 ),
    inference(avatar_split_clause,[],[f7367,f6856,f2204,f8950,f8946]) ).

fof(f7367,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_283
    | ~ spl0_724 ),
    inference(resolution,[],[f6857,f2205]) ).

fof(f8944,plain,
    ( spl0_803
    | ~ spl0_29
    | ~ spl0_319 ),
    inference(avatar_split_clause,[],[f2578,f2430,f827,f8942]) ).

fof(f8940,plain,
    ( spl0_802
    | ~ spl0_110
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f2577,f2426,f1232,f8938]) ).

fof(f8938,plain,
    ( spl0_802
  <=> ! [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_802])]) ).

fof(f2426,plain,
    ( spl0_318
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).

fof(f2577,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_110
    | ~ spl0_318 ),
    inference(resolution,[],[f2427,f1234]) ).

fof(f2427,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X5,X5,X0) )
    | ~ spl0_318 ),
    inference(avatar_component_clause,[],[f2426]) ).

fof(f8936,plain,
    ( spl0_801
    | ~ spl0_71
    | ~ spl0_318 ),
    inference(avatar_split_clause,[],[f2576,f2426,f1037,f8934]) ).

fof(f8934,plain,
    ( spl0_801
  <=> ! [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_801])]) ).

fof(f2576,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_71
    | ~ spl0_318 ),
    inference(resolution,[],[f2427,f1039]) ).

fof(f8932,plain,
    ( spl0_800
    | ~ spl0_108
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f2540,f2406,f1222,f8930]) ).

fof(f8930,plain,
    ( spl0_800
  <=> ! [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_800])]) ).

fof(f2540,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_108
    | ~ spl0_313 ),
    inference(resolution,[],[f2407,f1224]) ).

fof(f8928,plain,
    ( spl0_799
    | ~ spl0_68
    | ~ spl0_313 ),
    inference(avatar_split_clause,[],[f2539,f2406,f1022,f8926]) ).

fof(f8926,plain,
    ( spl0_799
  <=> ! [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_799])]) ).

fof(f2539,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_68
    | ~ spl0_313 ),
    inference(resolution,[],[f2407,f1024]) ).

fof(f8924,plain,
    ( spl0_798
    | ~ spl0_92
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f2538,f2402,f1142,f8922]) ).

fof(f8922,plain,
    ( spl0_798
  <=> ! [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_798])]) ).

fof(f2402,plain,
    ( spl0_312
  <=> ! [X0,X1] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).

fof(f2538,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_92
    | ~ spl0_312 ),
    inference(resolution,[],[f2403,f1144]) ).

fof(f2403,plain,
    ( ! [X0,X1] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X1,X0),X0) )
    | ~ spl0_312 ),
    inference(avatar_component_clause,[],[f2402]) ).

fof(f8920,plain,
    ( spl0_797
    | ~ spl0_48
    | ~ spl0_312 ),
    inference(avatar_split_clause,[],[f2537,f2402,f922,f8918]) ).

fof(f8918,plain,
    ( spl0_797
  <=> ! [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_797])]) ).

fof(f2537,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_48
    | ~ spl0_312 ),
    inference(resolution,[],[f2403,f924]) ).

fof(f8916,plain,
    ( spl0_796
    | ~ spl0_133
    | ~ spl0_215 ),
    inference(avatar_split_clause,[],[f1783,f1693,f1336,f8914]) ).

fof(f1693,plain,
    ( spl0_215
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).

fof(f1783,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_133
    | ~ spl0_215 ),
    inference(resolution,[],[f1694,f1337]) ).

fof(f1694,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
    | ~ spl0_215 ),
    inference(avatar_component_clause,[],[f1693]) ).

fof(f8912,plain,
    ( spl0_795
    | ~ spl0_133
    | ~ spl0_213 ),
    inference(avatar_split_clause,[],[f1775,f1685,f1336,f8910]) ).

fof(f1685,plain,
    ( spl0_213
  <=> ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).

fof(f1775,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_133
    | ~ spl0_213 ),
    inference(resolution,[],[f1686,f1337]) ).

fof(f1686,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 )
    | ~ spl0_213 ),
    inference(avatar_component_clause,[],[f1685]) ).

fof(f8908,plain,
    ( spl0_794
    | ~ spl0_143
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1754,f1641,f1376,f8906]) ).

fof(f8906,plain,
    ( spl0_794
  <=> ! [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_794])]) ).

fof(f1641,plain,
    ( spl0_202
  <=> ! [X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).

fof(f1754,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_143
    | ~ spl0_202 ),
    inference(resolution,[],[f1642,f1377]) ).

fof(f1642,plain,
    ( ! [X0,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) )
    | ~ spl0_202 ),
    inference(avatar_component_clause,[],[f1641]) ).

fof(f8814,plain,
    ( spl0_793
    | ~ spl0_149
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1738,f1608,f1400,f8812]) ).

fof(f8812,plain,
    ( spl0_793
  <=> ! [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_793])]) ).

fof(f1608,plain,
    ( spl0_194
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).

fof(f1738,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_149
    | ~ spl0_194 ),
    inference(resolution,[],[f1609,f1401]) ).

fof(f1609,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 )
    | ~ spl0_194 ),
    inference(avatar_component_clause,[],[f1608]) ).

fof(f8810,plain,
    ( spl0_792
    | ~ spl0_133
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1726,f1587,f1336,f8808]) ).

fof(f1587,plain,
    ( spl0_189
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X12,X0) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).

fof(f1726,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_133
    | ~ spl0_189 ),
    inference(resolution,[],[f1588,f1337]) ).

fof(f1588,plain,
    ( ! [X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X12,X0) = X12 )
    | ~ spl0_189 ),
    inference(avatar_component_clause,[],[f1587]) ).

fof(f8806,plain,
    ( spl0_791
    | ~ spl0_146
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1708,f1555,f1388,f8804]) ).

fof(f1388,plain,
    ( spl0_146
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
        | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).

fof(f1555,plain,
    ( spl0_181
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).

fof(f1708,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_146
    | ~ spl0_181 ),
    inference(resolution,[],[f1556,f1389]) ).

fof(f1389,plain,
    ( ! [X48] :
        ( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X48))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(X48) )
    | ~ spl0_146 ),
    inference(avatar_component_clause,[],[f1388]) ).

fof(f1556,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 )
    | ~ spl0_181 ),
    inference(avatar_component_clause,[],[f1555]) ).

fof(f8802,plain,
    ( spl0_790
    | ~ spl0_146
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1704,f1551,f1388,f8800]) ).

fof(f1551,plain,
    ( spl0_180
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).

fof(f1704,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_146
    | ~ spl0_180 ),
    inference(resolution,[],[f1552,f1389]) ).

fof(f1552,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
    | ~ spl0_180 ),
    inference(avatar_component_clause,[],[f1551]) ).

fof(f8798,plain,
    ( spl0_789
    | ~ spl0_156
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1700,f1542,f1428,f8796]) ).

fof(f8796,plain,
    ( spl0_789
  <=> ! [X0,X1] :
        ( c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
        | ~ class_HOL_Ozero(X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).

fof(f1542,plain,
    ( spl0_178
  <=> ! [X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X1,X0),X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).

fof(f1700,plain,
    ( ! [X0,X1] :
        ( c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_Polynomial_Opoly(X1)),tc_Polynomial_Opoly(X1)) = X0
        | ~ class_HOL_Ozero(X1) )
    | ~ spl0_156
    | ~ spl0_178 ),
    inference(resolution,[],[f1543,f1429]) ).

fof(f1543,plain,
    ( ! [X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X1,X0),X0) = X1 )
    | ~ spl0_178 ),
    inference(avatar_component_clause,[],[f1542]) ).

fof(f8588,plain,
    ( spl0_788
    | ~ spl0_260
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f6010,f5597,f2007,f8586]) ).

fof(f8586,plain,
    ( spl0_788
  <=> ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).

fof(f6010,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_260
    | ~ spl0_671 ),
    inference(resolution,[],[f5598,f2008]) ).

fof(f8407,plain,
    ( spl0_787
    | ~ spl0_242
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f6009,f5597,f1935,f8405]) ).

fof(f6009,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(X1,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_242
    | ~ spl0_671 ),
    inference(resolution,[],[f5598,f1936]) ).

fof(f8330,plain,
    ( spl0_786
    | ~ spl0_45
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f2393,f2296,f907,f8328]) ).

fof(f8328,plain,
    ( spl0_786
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).

fof(f2393,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X0)
    | ~ spl0_45
    | ~ spl0_306 ),
    inference(resolution,[],[f2297,f909]) ).

fof(f8326,plain,
    ( spl0_785
    | ~ spl0_8
    | ~ spl0_306 ),
    inference(avatar_split_clause,[],[f2391,f2296,f722,f8324]) ).

fof(f8324,plain,
    ( spl0_785
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).

fof(f2391,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),X0)
    | ~ spl0_8
    | ~ spl0_306 ),
    inference(resolution,[],[f2297,f724]) ).

fof(f8312,plain,
    ( spl0_784
    | ~ spl0_79
    | ~ spl0_304 ),
    inference(avatar_split_clause,[],[f2389,f2288,f1077,f8310]) ).

fof(f8310,plain,
    ( spl0_784
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).

fof(f2389,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal),X0)
    | ~ spl0_79
    | ~ spl0_304 ),
    inference(resolution,[],[f2289,f1079]) ).

fof(f8308,plain,
    ( spl0_783
    | ~ spl0_117
    | ~ spl0_304 ),
    inference(avatar_split_clause,[],[f2388,f2288,f1267,f8306]) ).

fof(f8306,plain,
    ( spl0_783
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).

fof(f2388,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X0)
    | ~ spl0_117
    | ~ spl0_304 ),
    inference(resolution,[],[f2289,f1269]) ).

fof(f8304,plain,
    ( spl0_782
    | ~ spl0_24
    | ~ spl0_304 ),
    inference(avatar_split_clause,[],[f2387,f2288,f802,f8302]) ).

fof(f8302,plain,
    ( spl0_782
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).

fof(f2387,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat),X0)
    | ~ spl0_24
    | ~ spl0_304 ),
    inference(resolution,[],[f2289,f804]) ).

fof(f8300,plain,
    ( spl0_781
    | ~ spl0_45
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f2385,f2284,f907,f8298]) ).

fof(f8298,plain,
    ( spl0_781
  <=> ! [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_781])]) ).

fof(f2385,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_45
    | ~ spl0_303 ),
    inference(resolution,[],[f2285,f909]) ).

fof(f8296,plain,
    ( spl0_780
    | ~ spl0_89
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f2384,f2284,f1127,f8294]) ).

fof(f8294,plain,
    ( spl0_780
  <=> ! [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_780])]) ).

fof(f2384,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_89
    | ~ spl0_303 ),
    inference(resolution,[],[f2285,f1129]) ).

fof(f8292,plain,
    ( spl0_779
    | ~ spl0_8
    | ~ spl0_303 ),
    inference(avatar_split_clause,[],[f2383,f2284,f722,f8290]) ).

fof(f8290,plain,
    ( spl0_779
  <=> ! [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_779])]) ).

fof(f2383,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_8
    | ~ spl0_303 ),
    inference(resolution,[],[f2285,f724]) ).

fof(f8288,plain,
    ( spl0_778
    | ~ spl0_45
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f2381,f2280,f907,f8286]) ).

fof(f8286,plain,
    ( spl0_778
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).

fof(f2381,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),X0,tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_302 ),
    inference(resolution,[],[f2281,f909]) ).

fof(f8284,plain,
    ( spl0_777
    | ~ spl0_89
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f2380,f2280,f1127,f8282]) ).

fof(f8282,plain,
    ( spl0_777
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).

fof(f2380,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_302 ),
    inference(resolution,[],[f2281,f1129]) ).

fof(f8280,plain,
    ( spl0_776
    | ~ spl0_8
    | ~ spl0_302 ),
    inference(avatar_split_clause,[],[f2379,f2280,f722,f8278]) ).

fof(f8278,plain,
    ( spl0_776
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).

fof(f2379,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),X0,tc_nat)
    | ~ spl0_8
    | ~ spl0_302 ),
    inference(resolution,[],[f2281,f724]) ).

fof(f8276,plain,
    ( spl0_775
    | ~ spl0_55
    | ~ spl0_300 ),
    inference(avatar_split_clause,[],[f2376,f2272,f957,f8273]) ).

fof(f8273,plain,
    ( spl0_775
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).

fof(f957,plain,
    ( spl0_55
  <=> class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).

fof(f2376,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_55
    | ~ spl0_300 ),
    inference(resolution,[],[f2273,f959]) ).

fof(f959,plain,
    ( class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal)
    | ~ spl0_55 ),
    inference(avatar_component_clause,[],[f957]) ).

fof(f8271,plain,
    ( spl0_774
    | ~ spl0_743
    | ~ spl0_755 ),
    inference(avatar_split_clause,[],[f8222,f8168,f6937,f8269]) ).

fof(f8222,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_743
    | ~ spl0_755 ),
    inference(superposition,[],[f8169,f6938]) ).

fof(f8267,plain,
    ( spl0_773
    | ~ spl0_45
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f2375,f2264,f907,f8265]) ).

fof(f8265,plain,
    ( spl0_773
  <=> ! [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_773])]) ).

fof(f2375,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_45
    | ~ spl0_298 ),
    inference(resolution,[],[f2265,f909]) ).

fof(f8263,plain,
    ( spl0_772
    | ~ spl0_89
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f2374,f2264,f1127,f8261]) ).

fof(f8261,plain,
    ( spl0_772
  <=> ! [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_772])]) ).

fof(f2374,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_89
    | ~ spl0_298 ),
    inference(resolution,[],[f2265,f1129]) ).

fof(f8259,plain,
    ( spl0_771
    | ~ spl0_8
    | ~ spl0_298 ),
    inference(avatar_split_clause,[],[f2373,f2264,f722,f8257]) ).

fof(f8257,plain,
    ( spl0_771
  <=> ! [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_771])]) ).

fof(f2373,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_8
    | ~ spl0_298 ),
    inference(resolution,[],[f2265,f724]) ).

fof(f8255,plain,
    ( spl0_770
    | ~ spl0_100
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2370,f2260,f1182,f8252]) ).

fof(f8252,plain,
    ( spl0_770
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).

fof(f2370,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_100
    | ~ spl0_297 ),
    inference(resolution,[],[f2261,f1184]) ).

fof(f8250,plain,
    ( spl0_769
    | ~ spl0_59
    | ~ spl0_297 ),
    inference(avatar_split_clause,[],[f2369,f2260,f977,f8247]) ).

fof(f8247,plain,
    ( spl0_769
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).

fof(f2369,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_59
    | ~ spl0_297 ),
    inference(resolution,[],[f2261,f979]) ).

fof(f8245,plain,
    ( spl0_768
    | ~ spl0_45
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f2361,f2252,f907,f8243]) ).

fof(f8243,plain,
    ( spl0_768
  <=> ! [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_768])]) ).

fof(f2361,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_45
    | ~ spl0_295 ),
    inference(resolution,[],[f2253,f909]) ).

fof(f8241,plain,
    ( spl0_767
    | ~ spl0_89
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f2360,f2252,f1127,f8239]) ).

fof(f8239,plain,
    ( spl0_767
  <=> ! [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_767])]) ).

fof(f8237,plain,
    ( spl0_766
    | ~ spl0_8
    | ~ spl0_295 ),
    inference(avatar_split_clause,[],[f2359,f2252,f722,f8235]) ).

fof(f8235,plain,
    ( spl0_766
  <=> ! [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_766])]) ).

fof(f2359,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_8
    | ~ spl0_295 ),
    inference(resolution,[],[f2253,f724]) ).

fof(f8230,plain,
    ( spl0_765
    | ~ spl0_110
    | ~ spl0_87
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2357,f2240,f1117,f1232,f8228]) ).

fof(f8228,plain,
    ( spl0_765
  <=> ! [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_765])]) ).

fof(f2240,plain,
    ( spl0_292
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).

fof(f2357,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(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_87
    | ~ spl0_292 ),
    inference(resolution,[],[f2241,f1119]) ).

fof(f2241,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_292 ),
    inference(avatar_component_clause,[],[f2240]) ).

fof(f8206,plain,
    ( spl0_764
    | ~ spl0_71
    | ~ spl0_43
    | ~ spl0_292 ),
    inference(avatar_split_clause,[],[f2356,f2240,f897,f1037,f8204]) ).

fof(f8204,plain,
    ( spl0_764
  <=> ! [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_764])]) ).

fof(f2356,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(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_43
    | ~ spl0_292 ),
    inference(resolution,[],[f2241,f899]) ).

fof(f8202,plain,
    ( spl0_763
    | ~ spl0_79
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2348,f2220,f1077,f8200]) ).

fof(f8200,plain,
    ( spl0_763
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).

fof(f2348,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),X1) = X0
    | ~ spl0_79
    | ~ spl0_287 ),
    inference(resolution,[],[f2221,f1079]) ).

fof(f8198,plain,
    ( spl0_762
    | ~ spl0_117
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2347,f2220,f1267,f8196]) ).

fof(f8196,plain,
    ( spl0_762
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).

fof(f2347,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = X0
    | ~ spl0_117
    | ~ spl0_287 ),
    inference(resolution,[],[f2221,f1269]) ).

fof(f8194,plain,
    ( spl0_761
    | ~ spl0_24
    | ~ spl0_287 ),
    inference(avatar_split_clause,[],[f2346,f2220,f802,f8192]) ).

fof(f8192,plain,
    ( spl0_761
  <=> ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).

fof(f2346,plain,
    ( ! [X0,X1] : hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X0,X1,tc_nat),tc_nat),X1) = X0
    | ~ spl0_24
    | ~ spl0_287 ),
    inference(resolution,[],[f2221,f804]) ).

fof(f8190,plain,
    ( spl0_760
    | ~ spl0_157
    | ~ spl0_285 ),
    inference(avatar_split_clause,[],[f2330,f2212,f1432,f8188]) ).

fof(f8188,plain,
    ( spl0_760
  <=> ! [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_760])]) ).

fof(f2330,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_157
    | ~ spl0_285 ),
    inference(resolution,[],[f2213,f1433]) ).

fof(f8186,plain,
    ( spl0_759
    | ~ spl0_157
    | ~ spl0_283 ),
    inference(avatar_split_clause,[],[f2323,f2204,f1432,f8184]) ).

fof(f8184,plain,
    ( spl0_759
  <=> ! [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_759])]) ).

fof(f2323,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_157
    | ~ spl0_283 ),
    inference(resolution,[],[f2205,f1433]) ).

fof(f8182,plain,
    ( spl0_758
    | ~ spl0_38
    | ~ spl0_280 ),
    inference(avatar_split_clause,[],[f2321,f2192,f872,f8180]) ).

fof(f8180,plain,
    ( spl0_758
  <=> ! [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_758])]) ).

fof(f2192,plain,
    ( spl0_280
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X5,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X5,X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).

fof(f2321,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_38
    | ~ spl0_280 ),
    inference(resolution,[],[f2193,f874]) ).

fof(f2193,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X5,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X5,X0),X0) = X5 )
    | ~ spl0_280 ),
    inference(avatar_component_clause,[],[f2192]) ).

fof(f8178,plain,
    ( spl0_757
    | ~ spl0_45
    | ~ spl0_279 ),
    inference(avatar_split_clause,[],[f2320,f2188,f907,f8176]) ).

fof(f8176,plain,
    ( spl0_757
  <=> ! [X0,X1] : c_Polynomial_Odegree(X0,tc_RealDef_Oreal) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).

fof(f2320,plain,
    ( ! [X0,X1] : c_Polynomial_Odegree(X0,tc_RealDef_Oreal) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ spl0_45
    | ~ spl0_279 ),
    inference(resolution,[],[f2189,f909]) ).

fof(f8174,plain,
    ( spl0_756
    | ~ spl0_89
    | ~ spl0_279 ),
    inference(avatar_split_clause,[],[f2319,f2188,f1127,f8172]) ).

fof(f8172,plain,
    ( spl0_756
  <=> ! [X0,X1] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).

fof(f2319,plain,
    ( ! [X0,X1] : c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
    | ~ spl0_89
    | ~ spl0_279 ),
    inference(resolution,[],[f2189,f1129]) ).

fof(f8170,plain,
    ( ~ spl0_88
    | spl0_755
    | ~ spl0_395
    | ~ spl0_724 ),
    inference(avatar_split_clause,[],[f7379,f6856,f2913,f8168,f1122]) ).

fof(f7379,plain,
    ( ! [X0,X1] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_Osmult(X1,X0,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) )
    | ~ spl0_395
    | ~ spl0_724 ),
    inference(resolution,[],[f6857,f2914]) ).

fof(f8166,plain,
    ( spl0_754
    | ~ spl0_8
    | ~ spl0_279 ),
    inference(avatar_split_clause,[],[f2318,f2188,f722,f8164]) ).

fof(f8164,plain,
    ( spl0_754
  <=> ! [X0,X1] : c_Polynomial_Odegree(X0,tc_nat) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).

fof(f2318,plain,
    ( ! [X0,X1] : c_Polynomial_Odegree(X0,tc_nat) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X0,X1,tc_nat),tc_nat)
    | ~ spl0_8
    | ~ spl0_279 ),
    inference(resolution,[],[f2189,f724]) ).

fof(f8162,plain,
    ( spl0_753
    | ~ spl0_100
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2304,f2172,f1182,f8160]) ).

fof(f8160,plain,
    ( spl0_753
  <=> ! [X0] : c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Odegree(X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).

fof(f2304,plain,
    ( ! [X0] : c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Odegree(X0,tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_275 ),
    inference(resolution,[],[f2173,f1184]) ).

fof(f8158,plain,
    ( spl0_752
    | ~ spl0_59
    | ~ spl0_275 ),
    inference(avatar_split_clause,[],[f2303,f2172,f977,f8156]) ).

fof(f8156,plain,
    ( spl0_752
  <=> ! [X0] : c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Polynomial_Odegree(X0,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).

fof(f2303,plain,
    ( ! [X0] : c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X0,tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) = c_Polynomial_Odegree(X0,tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_275 ),
    inference(resolution,[],[f2173,f979]) ).

fof(f8154,plain,
    ( spl0_751
    | ~ spl0_162
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1539,f1523,f1454,f8152]) ).

fof(f8152,plain,
    ( spl0_751
  <=> ! [X2,X0,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Olattice(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).

fof(f1523,plain,
    ( spl0_177
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).

fof(f1539,plain,
    ( ! [X2,X0,X1] :
        ( c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Olattice(X2) )
    | ~ spl0_162
    | ~ spl0_177 ),
    inference(resolution,[],[f1524,f1455]) ).

fof(f1524,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 )
    | ~ spl0_177 ),
    inference(avatar_component_clause,[],[f1523]) ).

fof(f8150,plain,
    ( spl0_750
    | ~ spl0_161
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1528,f1511,f1450,f8148]) ).

fof(f8148,plain,
    ( spl0_750
  <=> ! [X2,X0,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Olattice(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).

fof(f1511,plain,
    ( spl0_174
  <=> ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).

fof(f1528,plain,
    ( ! [X2,X0,X1] :
        ( c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_fun(X1,X2)) = X0
        | ~ class_Lattices_Olattice(X2) )
    | ~ spl0_161
    | ~ spl0_174 ),
    inference(resolution,[],[f1512,f1451]) ).

fof(f1512,plain,
    ( ! [X0,X1] :
        ( ~ class_Lattices_Oupper__semilattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 )
    | ~ spl0_174 ),
    inference(avatar_component_clause,[],[f1511]) ).

fof(f8146,plain,
    ( spl0_749
    | ~ spl0_124
    | ~ spl0_663 ),
    inference(avatar_split_clause,[],[f5477,f5455,f1300,f8144]) ).

fof(f8144,plain,
    ( spl0_749
  <=> ! [X2,X4,X0,X3,X1] :
        ( c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),c_Polynomial_OpCons(X2,X3,X0),X4,X0) = hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X3),c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X3,X4,X0))
        | hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X1
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).

fof(f5455,plain,
    ( spl0_663
  <=> ! [X5,X10,X0,X12,X3,X8] :
        ( ~ class_HOL_Ozero(X10)
        | hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3
        | c_Polynomial_Opoly__rec(X3,X8,c_Polynomial_OpCons(X5,X12,X10),X0,X10) = hAPP(hAPP(hAPP(X8,X5),X12),c_Polynomial_Opoly__rec(X3,X8,X12,X0,X10)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).

fof(f5477,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),c_Polynomial_OpCons(X2,X3,X0),X4,X0) = hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X3),c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X3,X4,X0))
        | hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X1
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_124
    | ~ spl0_663 ),
    inference(forward_demodulation,[],[f5466,f1301]) ).

fof(f5466,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X1
        | ~ class_HOL_Ozero(X0)
        | c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),c_Polynomial_OpCons(X2,X3,X0),X4,X0) = hAPP(hAPP(hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X2),X3),c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X3,X4,X0)) )
    | ~ spl0_124
    | ~ spl0_663 ),
    inference(superposition,[],[f5456,f1301]) ).

fof(f5456,plain,
    ( ! [X3,X10,X0,X8,X5,X12] :
        ( hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3
        | ~ class_HOL_Ozero(X10)
        | c_Polynomial_Opoly__rec(X3,X8,c_Polynomial_OpCons(X5,X12,X10),X0,X10) = hAPP(hAPP(hAPP(X8,X5),X12),c_Polynomial_Opoly__rec(X3,X8,X12,X0,X10)) )
    | ~ spl0_663 ),
    inference(avatar_component_clause,[],[f5455]) ).

fof(f7836,plain,
    ( ~ spl0_723
    | spl0_748
    | ~ spl0_187
    | ~ spl0_688 ),
    inference(avatar_split_clause,[],[f6664,f6068,f1579,f7834,f6852]) ).

fof(f6068,plain,
    ( spl0_688
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).

fof(f6664,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_187
    | ~ spl0_688 ),
    inference(superposition,[],[f1580,f6069]) ).

fof(f6069,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_688 ),
    inference(avatar_component_clause,[],[f6068]) ).

fof(f6955,plain,
    ( spl0_747
    | ~ spl0_79
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2170,f2064,f1077,f6953]) ).

fof(f6953,plain,
    ( spl0_747
  <=> ! [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_747])]) ).

fof(f2170,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_79
    | ~ spl0_274 ),
    inference(resolution,[],[f2065,f1079]) ).

fof(f6951,plain,
    ( spl0_746
    | ~ spl0_117
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2169,f2064,f1267,f6949]) ).

fof(f6949,plain,
    ( spl0_746
  <=> ! [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_746])]) ).

fof(f2169,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_117
    | ~ spl0_274 ),
    inference(resolution,[],[f2065,f1269]) ).

fof(f6947,plain,
    ( spl0_745
    | ~ spl0_24
    | ~ spl0_274 ),
    inference(avatar_split_clause,[],[f2168,f2064,f802,f6945]) ).

fof(f6945,plain,
    ( spl0_745
  <=> ! [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_745])]) ).

fof(f2168,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_24
    | ~ spl0_274 ),
    inference(resolution,[],[f2065,f804]) ).

fof(f6943,plain,
    ( spl0_744
    | ~ spl0_45
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2163,f2056,f907,f6941]) ).

fof(f6941,plain,
    ( spl0_744
  <=> ! [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_744])]) ).

fof(f2163,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_45
    | ~ spl0_272 ),
    inference(resolution,[],[f2057,f909]) ).

fof(f6939,plain,
    ( spl0_743
    | ~ spl0_89
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2162,f2056,f1127,f6937]) ).

fof(f2162,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_89
    | ~ spl0_272 ),
    inference(resolution,[],[f2057,f1129]) ).

fof(f6935,plain,
    ( ~ spl0_88
    | ~ spl0_153
    | spl0_723 ),
    inference(avatar_split_clause,[],[f6894,f6852,f1416,f1122]) ).

fof(f6894,plain,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_153
    | spl0_723 ),
    inference(resolution,[],[f6854,f1417]) ).

fof(f6854,plain,
    ( ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl0_723 ),
    inference(avatar_component_clause,[],[f6852]) ).

fof(f6934,plain,
    ( spl0_742
    | ~ spl0_8
    | ~ spl0_272 ),
    inference(avatar_split_clause,[],[f2161,f2056,f722,f6932]) ).

fof(f6932,plain,
    ( spl0_742
  <=> ! [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_742])]) ).

fof(f2161,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_8
    | ~ spl0_272 ),
    inference(resolution,[],[f2057,f724]) ).

fof(f6930,plain,
    ( spl0_741
    | ~ spl0_53
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2159,f2052,f947,f6928]) ).

fof(f6928,plain,
    ( spl0_741
  <=> ! [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_741])]) ).

fof(f2159,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_53
    | ~ spl0_271 ),
    inference(resolution,[],[f2053,f949]) ).

fof(f6926,plain,
    ( spl0_740
    | ~ spl0_97
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2158,f2052,f1167,f6924]) ).

fof(f6924,plain,
    ( spl0_740
  <=> ! [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_740])]) ).

fof(f6922,plain,
    ( spl0_739
    | ~ spl0_13
    | ~ spl0_271 ),
    inference(avatar_split_clause,[],[f2157,f2052,f747,f6920]) ).

fof(f6920,plain,
    ( spl0_739
  <=> ! [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_739])]) ).

fof(f2157,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_13
    | ~ spl0_271 ),
    inference(resolution,[],[f2053,f749]) ).

fof(f6918,plain,
    ( spl0_738
    | ~ spl0_53
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2155,f2048,f947,f6916]) ).

fof(f6916,plain,
    ( spl0_738
  <=> ! [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_738])]) ).

fof(f2155,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_53
    | ~ spl0_270 ),
    inference(resolution,[],[f2049,f949]) ).

fof(f6914,plain,
    ( spl0_737
    | ~ spl0_97
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2154,f2048,f1167,f6912]) ).

fof(f6912,plain,
    ( spl0_737
  <=> ! [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_737])]) ).

fof(f2154,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_97
    | ~ spl0_270 ),
    inference(resolution,[],[f2049,f1169]) ).

fof(f6910,plain,
    ( spl0_736
    | ~ spl0_13
    | ~ spl0_270 ),
    inference(avatar_split_clause,[],[f2153,f2048,f747,f6908]) ).

fof(f6908,plain,
    ( spl0_736
  <=> ! [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_736])]) ).

fof(f2153,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_13
    | ~ spl0_270 ),
    inference(resolution,[],[f2049,f749]) ).

fof(f6906,plain,
    ( spl0_735
    | ~ spl0_100
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2150,f2044,f1182,f6904]) ).

fof(f6904,plain,
    ( spl0_735
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(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_735])]) ).

fof(f2150,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_100
    | ~ spl0_269 ),
    inference(resolution,[],[f2045,f1184]) ).

fof(f6902,plain,
    ( spl0_734
    | ~ spl0_59
    | ~ spl0_269 ),
    inference(avatar_split_clause,[],[f2149,f2044,f977,f6900]) ).

fof(f6900,plain,
    ( spl0_734
  <=> ! [X0] : c_HOL_Ominus__class_Ominus(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_734])]) ).

fof(f2149,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_Polynomial_Opoly(tc_RealDef_Oreal)) = X0
    | ~ spl0_59
    | ~ spl0_269 ),
    inference(resolution,[],[f2045,f979]) ).

fof(f6898,plain,
    ( spl0_733
    | ~ spl0_110
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2145,f2023,f1232,f6896]) ).

fof(f2023,plain,
    ( spl0_264
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).

fof(f2145,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_Complex_Ocomplex) = c_Polynomial_Opoly__gcd(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_110
    | ~ spl0_264 ),
    inference(resolution,[],[f2024,f1234]) ).

fof(f2024,plain,
    ( ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X2,X1,X0) )
    | ~ spl0_264 ),
    inference(avatar_component_clause,[],[f2023]) ).

fof(f6893,plain,
    ( spl0_732
    | ~ spl0_71
    | ~ spl0_264 ),
    inference(avatar_split_clause,[],[f2144,f2023,f1037,f6891]) ).

fof(f6891,plain,
    ( spl0_732
  <=> ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).

fof(f2144,plain,
    ( ! [X0,X1] : c_Polynomial_Opoly__gcd(X0,X1,tc_RealDef_Oreal) = c_Polynomial_Opoly__gcd(X1,X0,tc_RealDef_Oreal)
    | ~ spl0_71
    | ~ spl0_264 ),
    inference(resolution,[],[f2024,f1039]) ).

fof(f6889,plain,
    ( spl0_731
    | ~ spl0_30
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2143,f2019,f832,f6887]) ).

fof(f6887,plain,
    ( spl0_731
  <=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).

fof(f2143,plain,
    ( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool),tc_bool) = X0
    | ~ spl0_30
    | ~ spl0_263 ),
    inference(resolution,[],[f2020,f834]) ).

fof(f6885,plain,
    ( spl0_730
    | ~ spl0_75
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2141,f2019,f1057,f6883]) ).

fof(f6883,plain,
    ( spl0_730
  <=> ! [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_730])]) ).

fof(f2141,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_75
    | ~ spl0_263 ),
    inference(resolution,[],[f2020,f1059]) ).

fof(f6881,plain,
    ( spl0_729
    | ~ spl0_23
    | ~ spl0_263 ),
    inference(avatar_split_clause,[],[f2140,f2019,f797,f6879]) ).

fof(f6879,plain,
    ( spl0_729
  <=> ! [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_729])]) ).

fof(f2140,plain,
    ( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat),tc_nat) = X0
    | ~ spl0_23
    | ~ spl0_263 ),
    inference(resolution,[],[f2020,f799]) ).

fof(f6877,plain,
    ( spl0_728
    | ~ spl0_44
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f2135,f2007,f902,f6875]) ).

fof(f2135,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal)
    | ~ spl0_44
    | ~ spl0_260 ),
    inference(resolution,[],[f2008,f904]) ).

fof(f6873,plain,
    ( spl0_727
    | ~ spl0_88
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f2134,f2007,f1122,f6871]) ).

fof(f2134,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex) = c_HOL_Oplus__class_Oplus(X1,X0,tc_Complex_Ocomplex)
    | ~ spl0_88
    | ~ spl0_260 ),
    inference(resolution,[],[f2008,f1124]) ).

fof(f6869,plain,
    ( spl0_726
    | ~ spl0_7
    | ~ spl0_260 ),
    inference(avatar_split_clause,[],[f2133,f2007,f717,f6867]) ).

fof(f6867,plain,
    ( spl0_726
  <=> ! [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_726])]) ).

fof(f2133,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)
    | ~ spl0_7
    | ~ spl0_260 ),
    inference(resolution,[],[f2008,f719]) ).

fof(f6864,plain,
    ( spl0_725
    | ~ spl0_96
    | ~ spl0_116
    | ~ spl0_259 ),
    inference(avatar_split_clause,[],[f2131,f2003,f1262,f1162,f6861]) ).

fof(f6861,plain,
    ( spl0_725
  <=> 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_725])]) ).

fof(f2003,plain,
    ( spl0_259
  <=> ! [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_259])]) ).

fof(f2131,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_116
    | ~ spl0_259 ),
    inference(resolution,[],[f2004,f1264]) ).

fof(f2004,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_259 ),
    inference(avatar_component_clause,[],[f2003]) ).

fof(f6858,plain,
    ( ~ spl0_723
    | spl0_724
    | ~ spl0_187
    | ~ spl0_689 ),
    inference(avatar_split_clause,[],[f6760,f6520,f1579,f6856,f6852]) ).

fof(f6520,plain,
    ( spl0_689
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).

fof(f6760,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_187
    | ~ spl0_689 ),
    inference(superposition,[],[f1580,f6521]) ).

fof(f6521,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_689 ),
    inference(avatar_component_clause,[],[f6520]) ).

fof(f6850,plain,
    ( spl0_722
    | ~ spl0_52
    | ~ spl0_78
    | ~ spl0_259 ),
    inference(avatar_split_clause,[],[f2130,f2003,f1072,f942,f6847]) ).

fof(f6847,plain,
    ( spl0_722
  <=> 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_722])]) ).

fof(f2130,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_78
    | ~ spl0_259 ),
    inference(resolution,[],[f2004,f1074]) ).

fof(f6845,plain,
    ( spl0_721
    | ~ spl0_108
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f2115,f1983,f1222,f6843]) ).

fof(f6843,plain,
    ( spl0_721
  <=> ! [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_721])]) ).

fof(f2115,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
    | ~ spl0_108
    | ~ spl0_254 ),
    inference(resolution,[],[f1984,f1224]) ).

fof(f6841,plain,
    ( spl0_720
    | ~ spl0_68
    | ~ spl0_254 ),
    inference(avatar_split_clause,[],[f2114,f1983,f1022,f6839]) ).

fof(f6839,plain,
    ( spl0_720
  <=> ! [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_720])]) ).

fof(f2114,plain,
    ( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0
    | ~ spl0_68
    | ~ spl0_254 ),
    inference(resolution,[],[f1984,f1024]) ).

fof(f6837,plain,
    ( spl0_719
    | ~ spl0_26
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2109,f1975,f812,f6835]) ).

fof(f6835,plain,
    ( spl0_719
  <=> ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).

fof(f2109,plain,
    ( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_bool)
    | ~ spl0_26
    | ~ spl0_252 ),
    inference(resolution,[],[f1976,f814]) ).

fof(f6833,plain,
    ( spl0_718
    | ~ spl0_57
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2107,f1975,f967,f6831]) ).

fof(f6831,plain,
    ( spl0_718
  <=> ! [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_718])]) ).

fof(f2107,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_57
    | ~ spl0_252 ),
    inference(resolution,[],[f1976,f969]) ).

fof(f6829,plain,
    ( spl0_717
    | ~ spl0_15
    | ~ spl0_252 ),
    inference(avatar_split_clause,[],[f2106,f1975,f757,f6827]) ).

fof(f6827,plain,
    ( spl0_717
  <=> ! [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_717])]) ).

fof(f2106,plain,
    ( ! [X0,X1] : c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat) = c_Lattices_Oupper__semilattice__class_Osup(X1,X0,tc_nat)
    | ~ spl0_15
    | ~ spl0_252 ),
    inference(resolution,[],[f1976,f759]) ).

fof(f6825,plain,
    ( spl0_716
    | ~ spl0_108
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2101,f1959,f1222,f6823]) ).

fof(f6823,plain,
    ( spl0_716
  <=> ! [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_716])]) ).

fof(f2101,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_108
    | ~ spl0_248 ),
    inference(resolution,[],[f1960,f1224]) ).

fof(f6821,plain,
    ( spl0_715
    | ~ spl0_68
    | ~ spl0_248 ),
    inference(avatar_split_clause,[],[f2100,f1959,f1022,f6819]) ).

fof(f6819,plain,
    ( spl0_715
  <=> ! [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_715])]) ).

fof(f2100,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_68
    | ~ spl0_248 ),
    inference(resolution,[],[f1960,f1024]) ).

fof(f6817,plain,
    ( spl0_714
    | ~ spl0_100
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2098,f1955,f1182,f6815]) ).

fof(f6815,plain,
    ( spl0_714
  <=> ! [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_714])]) ).

fof(f2098,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_100
    | ~ spl0_247 ),
    inference(resolution,[],[f1956,f1184]) ).

fof(f6813,plain,
    ( spl0_713
    | ~ spl0_59
    | ~ spl0_247 ),
    inference(avatar_split_clause,[],[f2097,f1955,f977,f6811]) ).

fof(f6811,plain,
    ( spl0_713
  <=> ! [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_713])]) ).

fof(f2097,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_59
    | ~ spl0_247 ),
    inference(resolution,[],[f1956,f979]) ).

fof(f6749,plain,
    ( spl0_712
    | ~ spl0_27
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2092,f1947,f817,f6747]) ).

fof(f2092,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_bool) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_bool)
    | ~ spl0_27
    | ~ spl0_245 ),
    inference(resolution,[],[f1948,f819]) ).

fof(f6745,plain,
    ( spl0_711
    | ~ spl0_58
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2090,f1947,f972,f6743]) ).

fof(f6743,plain,
    ( spl0_711
  <=> ! [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_711])]) ).

fof(f2090,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_58
    | ~ spl0_245 ),
    inference(resolution,[],[f1948,f974]) ).

fof(f6741,plain,
    ( spl0_710
    | ~ spl0_16
    | ~ spl0_245 ),
    inference(avatar_split_clause,[],[f2089,f1947,f762,f6739]) ).

fof(f6739,plain,
    ( spl0_710
  <=> ! [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_710])]) ).

fof(f2089,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,X1,tc_nat) = c_Lattices_Olower__semilattice__class_Oinf(X1,X0,tc_nat)
    | ~ spl0_16
    | ~ spl0_245 ),
    inference(resolution,[],[f1948,f764]) ).

fof(f6737,plain,
    ( spl0_709
    | ~ spl0_108
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2087,f1943,f1222,f6735]) ).

fof(f6735,plain,
    ( spl0_709
  <=> ! [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_709])]) ).

fof(f1943,plain,
    ( spl0_244
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).

fof(f2087,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_108
    | ~ spl0_244 ),
    inference(resolution,[],[f1944,f1224]) ).

fof(f1944,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
    | ~ spl0_244 ),
    inference(avatar_component_clause,[],[f1943]) ).

fof(f6733,plain,
    ( spl0_708
    | ~ spl0_68
    | ~ spl0_244 ),
    inference(avatar_split_clause,[],[f2086,f1943,f1022,f6731]) ).

fof(f6731,plain,
    ( spl0_708
  <=> ! [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_708])]) ).

fof(f2086,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_68
    | ~ spl0_244 ),
    inference(resolution,[],[f1944,f1024]) ).

fof(f6729,plain,
    ( spl0_707
    | ~ spl0_55
    | ~ spl0_243 ),
    inference(avatar_split_clause,[],[f2084,f1939,f957,f6727]) ).

fof(f6727,plain,
    ( spl0_707
  <=> ! [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_707])]) ).

fof(f2084,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_55
    | ~ spl0_243 ),
    inference(resolution,[],[f1940,f959]) ).

fof(f6725,plain,
    ( spl0_706
    | ~ spl0_44
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2083,f1935,f902,f6723]) ).

fof(f6723,plain,
    ( spl0_706
  <=> ! [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_706])]) ).

fof(f6721,plain,
    ( spl0_705
    | ~ spl0_88
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2082,f1935,f1122,f6719]) ).

fof(f6717,plain,
    ( spl0_704
    | ~ spl0_7
    | ~ spl0_242 ),
    inference(avatar_split_clause,[],[f2081,f1935,f717,f6715]) ).

fof(f6715,plain,
    ( spl0_704
  <=> ! [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_704])]) ).

fof(f2081,plain,
    ( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat)
    | ~ spl0_7
    | ~ spl0_242 ),
    inference(resolution,[],[f1936,f719]) ).

fof(f6713,plain,
    ( spl0_703
    | ~ spl0_108
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f2078,f1931,f1222,f6711]) ).

fof(f6711,plain,
    ( spl0_703
  <=> ! [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_703])]) ).

fof(f2078,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_Complex_Ocomplex),X1,tc_Complex_Ocomplex) = X0
    | ~ spl0_108
    | ~ spl0_241 ),
    inference(resolution,[],[f1932,f1224]) ).

fof(f6653,plain,
    ( spl0_702
    | ~ spl0_68
    | ~ spl0_241 ),
    inference(avatar_split_clause,[],[f2077,f1931,f1022,f6651]) ).

fof(f6651,plain,
    ( spl0_702
  <=> ! [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_702])]) ).

fof(f2077,plain,
    ( ! [X0,X1] : c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),X1,tc_RealDef_Oreal) = X0
    | ~ spl0_68
    | ~ spl0_241 ),
    inference(resolution,[],[f1932,f1024]) ).

fof(f6649,plain,
    ( spl0_701
    | ~ spl0_30
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f2076,f1927,f832,f6647]) ).

fof(f6647,plain,
    ( spl0_701
  <=> ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).

fof(f2076,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_bool),tc_bool) = X0
    | ~ spl0_30
    | ~ spl0_240 ),
    inference(resolution,[],[f1928,f834]) ).

fof(f6645,plain,
    ( spl0_700
    | ~ spl0_75
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f2074,f1927,f1057,f6643]) ).

fof(f6643,plain,
    ( spl0_700
  <=> ! [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_700])]) ).

fof(f2074,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_75
    | ~ spl0_240 ),
    inference(resolution,[],[f1928,f1059]) ).

fof(f6641,plain,
    ( spl0_699
    | ~ spl0_23
    | ~ spl0_240 ),
    inference(avatar_split_clause,[],[f2073,f1927,f797,f6639]) ).

fof(f6639,plain,
    ( spl0_699
  <=> ! [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_699])]) ).

fof(f2073,plain,
    ( ! [X0,X1] : c_Lattices_Olower__semilattice__class_Oinf(X0,c_Lattices_Oupper__semilattice__class_Osup(X0,X1,tc_nat),tc_nat) = X0
    | ~ spl0_23
    | ~ spl0_240 ),
    inference(resolution,[],[f1928,f799]) ).

fof(f6637,plain,
    ( spl0_697
    | ~ spl0_698
    | ~ spl0_31
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2072,f1919,f837,f6634,f6630]) ).

fof(f6630,plain,
    ( spl0_697
  <=> c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_bool)) = c_fequal(tc_Polynomial_Opoly(tc_bool)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).

fof(f6634,plain,
    ( spl0_698
  <=> class_HOL_Ozero(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).

fof(f837,plain,
    ( spl0_31
  <=> class_HOL_Oeq(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f2072,plain,
    ( ~ class_HOL_Ozero(tc_bool)
    | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_bool)) = c_fequal(tc_Polynomial_Opoly(tc_bool))
    | ~ spl0_31
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f839]) ).

fof(f839,plain,
    ( class_HOL_Oeq(tc_bool)
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f837]) ).

fof(f6609,plain,
    ( spl0_696
    | ~ spl0_79
    | ~ spl0_80
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2070,f1919,f1082,f1077,f6606]) ).

fof(f6606,plain,
    ( spl0_696
  <=> c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_fequal(tc_Polynomial_Opoly(tc_RealDef_Oreal)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).

fof(f1082,plain,
    ( spl0_80
  <=> class_HOL_Oeq(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).

fof(f2070,plain,
    ( ~ class_HOL_Ozero(tc_RealDef_Oreal)
    | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_RealDef_Oreal)) = c_fequal(tc_Polynomial_Opoly(tc_RealDef_Oreal))
    | ~ spl0_80
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f1084]) ).

fof(f1084,plain,
    ( class_HOL_Oeq(tc_RealDef_Oreal)
    | ~ spl0_80 ),
    inference(avatar_component_clause,[],[f1082]) ).

fof(f6585,plain,
    ( spl0_695
    | ~ spl0_189
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f6004,f5597,f1587,f6583]) ).

fof(f6583,plain,
    ( spl0_695
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).

fof(f6004,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_189
    | ~ spl0_671 ),
    inference(resolution,[],[f5598,f1588]) ).

fof(f6581,plain,
    ( spl0_694
    | ~ spl0_117
    | ~ spl0_118
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2069,f1919,f1272,f1267,f6578]) ).

fof(f6578,plain,
    ( spl0_694
  <=> c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_fequal(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).

fof(f1272,plain,
    ( spl0_118
  <=> class_HOL_Oeq(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).

fof(f2069,plain,
    ( ~ class_HOL_Ozero(tc_Complex_Ocomplex)
    | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_fequal(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_118
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f1274]) ).

fof(f1274,plain,
    ( class_HOL_Oeq(tc_Complex_Ocomplex)
    | ~ spl0_118 ),
    inference(avatar_component_clause,[],[f1272]) ).

fof(f6557,plain,
    ( spl0_693
    | ~ spl0_24
    | ~ spl0_25
    | ~ spl0_238 ),
    inference(avatar_split_clause,[],[f2068,f1919,f807,f802,f6554]) ).

fof(f6554,plain,
    ( spl0_693
  <=> c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_nat)) = c_fequal(tc_Polynomial_Opoly(tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).

fof(f807,plain,
    ( spl0_25
  <=> class_HOL_Oeq(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f2068,plain,
    ( ~ class_HOL_Ozero(tc_nat)
    | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(tc_nat)) = c_fequal(tc_Polynomial_Opoly(tc_nat))
    | ~ spl0_25
    | ~ spl0_238 ),
    inference(resolution,[],[f1920,f809]) ).

fof(f809,plain,
    ( class_HOL_Oeq(tc_nat)
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f807]) ).

fof(f6552,plain,
    ( spl0_692
    | ~ spl0_125
    | ~ spl0_216 ),
    inference(avatar_split_clause,[],[f1791,f1697,f1304,f6550]) ).

fof(f6550,plain,
    ( spl0_692
  <=> ! [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_692])]) ).

fof(f1304,plain,
    ( spl0_125
  <=> ! [X3] : c_Complex_Ocnj(c_Complex_Ocnj(X3)) = X3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).

fof(f1697,plain,
    ( spl0_216
  <=> ! [X3] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3
        | c_Complex_Ocnj(X3) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).

fof(f1791,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != X0
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocnj(X0) )
    | ~ spl0_125
    | ~ spl0_216 ),
    inference(superposition,[],[f1698,f1305]) ).

fof(f1305,plain,
    ( ! [X3] : c_Complex_Ocnj(c_Complex_Ocnj(X3)) = X3
    | ~ spl0_125 ),
    inference(avatar_component_clause,[],[f1304]) ).

fof(f1698,plain,
    ( ! [X3] :
        ( c_Complex_Ocnj(X3) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3 )
    | ~ spl0_216 ),
    inference(avatar_component_clause,[],[f1697]) ).

fof(f6548,plain,
    ( spl0_691
    | ~ spl0_159
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1531,f1519,f1440,f6546]) ).

fof(f6546,plain,
    ( spl0_691
  <=> ! [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_691])]) ).

fof(f1440,plain,
    ( spl0_159
  <=> 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_159])]) ).

fof(f1519,plain,
    ( spl0_176
  <=> ! [X2,X1] :
        ( X1 = X2
        | c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).

fof(f1531,plain,
    ( ! [X0] :
        ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Ocnj(X0)
        | c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = X0 )
    | ~ spl0_159
    | ~ spl0_176 ),
    inference(superposition,[],[f1520,f1442]) ).

fof(f1442,plain,
    ( c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
    | ~ spl0_159 ),
    inference(avatar_component_clause,[],[f1440]) ).

fof(f1520,plain,
    ( ! [X2,X1] :
        ( c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2)
        | X1 = X2 )
    | ~ spl0_176 ),
    inference(avatar_component_clause,[],[f1519]) ).

fof(f6544,plain,
    ( spl0_690
    | ~ spl0_121
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1502,f1476,f1287,f6542]) ).

fof(f6542,plain,
    ( spl0_690
  <=> ! [X0,X1] : c_HOL_Oeq__class_Oeq(tc_prod(X0,X1)) = c_fequal(tc_prod(X0,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).

fof(f1476,plain,
    ( spl0_167
  <=> ! [X0] :
        ( ~ class_HOL_Oeq(X0)
        | c_HOL_Oeq__class_Oeq(X0) = c_fequal(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).

fof(f1502,plain,
    ( ! [X0,X1] : c_HOL_Oeq__class_Oeq(tc_prod(X0,X1)) = c_fequal(tc_prod(X0,X1))
    | ~ spl0_121
    | ~ spl0_167 ),
    inference(resolution,[],[f1477,f1288]) ).

fof(f1477,plain,
    ( ! [X0] :
        ( ~ class_HOL_Oeq(X0)
        | c_HOL_Oeq__class_Oeq(X0) = c_fequal(X0) )
    | ~ spl0_167 ),
    inference(avatar_component_clause,[],[f1476]) ).

fof(f6522,plain,
    ( spl0_689
    | ~ spl0_184
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f6003,f5597,f1567,f6520]) ).

fof(f1567,plain,
    ( spl0_184
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).

fof(f6003,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_184
    | ~ spl0_671 ),
    inference(resolution,[],[f5598,f1568]) ).

fof(f1568,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
    | ~ spl0_184 ),
    inference(avatar_component_clause,[],[f1567]) ).

fof(f6070,plain,
    ( spl0_688
    | ~ spl0_183
    | ~ spl0_671 ),
    inference(avatar_split_clause,[],[f6002,f5597,f1563,f6068]) ).

fof(f1563,plain,
    ( spl0_183
  <=> ! [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_183])]) ).

fof(f6002,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),X0,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X0
    | ~ spl0_183
    | ~ spl0_671 ),
    inference(resolution,[],[f5598,f1564]) ).

fof(f1564,plain,
    ( ! [X0,X1] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 )
    | ~ spl0_183 ),
    inference(avatar_component_clause,[],[f1563]) ).

fof(f6066,plain,
    ( spl0_687
    | ~ spl0_110
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f1914,f1851,f1232,f6064]) ).

fof(f6064,plain,
    ( spl0_687
  <=> ! [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_687])]) ).

fof(f1851,plain,
    ( spl0_232
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).

fof(f1914,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_110
    | ~ spl0_232 ),
    inference(resolution,[],[f1852,f1234]) ).

fof(f1852,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
    | ~ spl0_232 ),
    inference(avatar_component_clause,[],[f1851]) ).

fof(f6062,plain,
    ( spl0_686
    | ~ spl0_71
    | ~ spl0_232 ),
    inference(avatar_split_clause,[],[f1913,f1851,f1037,f6060]) ).

fof(f6060,plain,
    ( spl0_686
  <=> ! [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_686])]) ).

fof(f1913,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_71
    | ~ spl0_232 ),
    inference(resolution,[],[f1852,f1039]) ).

fof(f6058,plain,
    ( spl0_685
    | ~ spl0_92
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f1910,f1843,f1142,f6056]) ).

fof(f6056,plain,
    ( spl0_685
  <=> ! [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_685])]) ).

fof(f1843,plain,
    ( spl0_230
  <=> ! [X5,X0] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).

fof(f1910,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_92
    | ~ spl0_230 ),
    inference(resolution,[],[f1844,f1144]) ).

fof(f1844,plain,
    ( ! [X0,X5] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_230 ),
    inference(avatar_component_clause,[],[f1843]) ).

fof(f6054,plain,
    ( spl0_684
    | ~ spl0_48
    | ~ spl0_230 ),
    inference(avatar_split_clause,[],[f1909,f1843,f922,f6052]) ).

fof(f6052,plain,
    ( spl0_684
  <=> ! [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_684])]) ).

fof(f1909,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_48
    | ~ spl0_230 ),
    inference(resolution,[],[f1844,f924]) ).

fof(f6050,plain,
    ( spl0_683
    | ~ spl0_17
    | ~ spl0_222 ),
    inference(avatar_split_clause,[],[f1890,f1811,f767,f6048]) ).

fof(f6048,plain,
    ( spl0_683
  <=> ! [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_683])]) ).

fof(f767,plain,
    ( spl0_17
  <=> class_Ring__and__Field_Omult__zero(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f1811,plain,
    ( spl0_222
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).

fof(f1890,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_17
    | ~ spl0_222 ),
    inference(resolution,[],[f1812,f769]) ).

fof(f769,plain,
    ( class_Ring__and__Field_Omult__zero(tc_nat)
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f767]) ).

fof(f1812,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) )
    | ~ spl0_222 ),
    inference(avatar_component_clause,[],[f1811]) ).

fof(f6046,plain,
    ( spl0_682
    | ~ spl0_17
    | ~ spl0_221 ),
    inference(avatar_split_clause,[],[f1886,f1807,f767,f6044]) ).

fof(f6044,plain,
    ( spl0_682
  <=> ! [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_682])]) ).

fof(f1807,plain,
    ( spl0_221
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).

fof(f1886,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_17
    | ~ spl0_221 ),
    inference(resolution,[],[f1808,f769]) ).

fof(f1808,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Omult__zero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) )
    | ~ spl0_221 ),
    inference(avatar_component_clause,[],[f1807]) ).

fof(f6042,plain,
    ( spl0_681
    | ~ spl0_81
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f1883,f1803,f1087,f6040]) ).

fof(f6040,plain,
    ( spl0_681
  <=> ! [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_681])]) ).

fof(f1087,plain,
    ( spl0_81
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).

fof(f1883,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_81
    | ~ spl0_220 ),
    inference(resolution,[],[f1804,f1089]) ).

fof(f1089,plain,
    ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex)
    | ~ spl0_81 ),
    inference(avatar_component_clause,[],[f1087]) ).

fof(f6038,plain,
    ( spl0_680
    | ~ spl0_34
    | ~ spl0_220 ),
    inference(avatar_split_clause,[],[f1882,f1803,f852,f6036]) ).

fof(f6036,plain,
    ( spl0_680
  <=> ! [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_680])]) ).

fof(f852,plain,
    ( spl0_34
  <=> class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f1882,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_34
    | ~ spl0_220 ),
    inference(resolution,[],[f1804,f854]) ).

fof(f854,plain,
    ( class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal)
    | ~ spl0_34 ),
    inference(avatar_component_clause,[],[f852]) ).

fof(f6034,plain,
    ( spl0_679
    | ~ spl0_81
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f1880,f1799,f1087,f6032]) ).

fof(f1880,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_81
    | ~ spl0_219 ),
    inference(resolution,[],[f1800,f1089]) ).

fof(f6030,plain,
    ( spl0_678
    | ~ spl0_34
    | ~ spl0_219 ),
    inference(avatar_split_clause,[],[f1879,f1799,f852,f6028]) ).

fof(f6028,plain,
    ( spl0_678
  <=> ! [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_678])]) ).

fof(f1879,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_34
    | ~ spl0_219 ),
    inference(resolution,[],[f1800,f854]) ).

fof(f6001,plain,
    ( spl0_677
    | ~ spl0_79
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f1878,f1795,f1077,f5998]) ).

fof(f5998,plain,
    ( spl0_677
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).

fof(f1878,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_RealDef_Oreal)),tc_RealDef_Oreal)
    | ~ spl0_79
    | ~ spl0_218 ),
    inference(resolution,[],[f1796,f1079]) ).

fof(f5996,plain,
    ( spl0_676
    | ~ spl0_117
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f1877,f1795,f1267,f5993]) ).

fof(f5993,plain,
    ( spl0_676
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).

fof(f1877,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex)
    | ~ spl0_117
    | ~ spl0_218 ),
    inference(resolution,[],[f1796,f1269]) ).

fof(f5991,plain,
    ( spl0_675
    | ~ spl0_24
    | ~ spl0_218 ),
    inference(avatar_split_clause,[],[f1876,f1795,f802,f5988]) ).

fof(f5988,plain,
    ( spl0_675
  <=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).

fof(f1876,plain,
    ( c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_nat)),tc_nat)
    | ~ spl0_24
    | ~ spl0_218 ),
    inference(resolution,[],[f1796,f804]) ).

fof(f5986,plain,
    ( spl0_674
    | ~ spl0_125
    | ~ spl0_176 ),
    inference(avatar_split_clause,[],[f1530,f1519,f1304,f5984]) ).

fof(f5984,plain,
    ( spl0_674
  <=> ! [X0,X1] :
        ( c_Complex_Ocnj(X1) != X0
        | c_Complex_Ocnj(X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).

fof(f1530,plain,
    ( ! [X0,X1] :
        ( c_Complex_Ocnj(X1) != X0
        | c_Complex_Ocnj(X0) = X1 )
    | ~ spl0_125
    | ~ spl0_176 ),
    inference(superposition,[],[f1520,f1305]) ).

fof(f5942,plain,
    ( spl0_673
    | ~ spl0_124
    | ~ spl0_648 ),
    inference(avatar_split_clause,[],[f5187,f5163,f1300,f5940]) ).

fof(f5940,plain,
    ( spl0_673
  <=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( hAPP(X2,hAPP(X3,X4)) != hAPP(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
        | hAPP(c_Fun_Ocomp(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X5,X6,X7),X0) = hAPP(c_Fun_Ocomp(X2,X3,X8,X6,X9),X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).

fof(f5163,plain,
    ( spl0_648
  <=> ! [X40,X38,X39,X0,X11,X1,X8,X9,X37,X10,X33] :
        ( hAPP(X8,hAPP(X9,X1)) != hAPP(X37,hAPP(X38,X33))
        | hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1) = hAPP(c_Fun_Ocomp(X37,X38,X39,X0,X40),X33) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).

fof(f5187,plain,
    ( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( hAPP(X2,hAPP(X3,X4)) != hAPP(X1,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
        | hAPP(c_Fun_Ocomp(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X5,X6,X7),X0) = hAPP(c_Fun_Ocomp(X2,X3,X8,X6,X9),X4) )
    | ~ spl0_124
    | ~ spl0_648 ),
    inference(superposition,[],[f5164,f1301]) ).

fof(f5164,plain,
    ( ! [X40,X38,X10,X0,X11,X39,X1,X8,X37,X9,X33] :
        ( hAPP(X8,hAPP(X9,X1)) != hAPP(X37,hAPP(X38,X33))
        | hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1) = hAPP(c_Fun_Ocomp(X37,X38,X39,X0,X40),X33) )
    | ~ spl0_648 ),
    inference(avatar_component_clause,[],[f5163]) ).

fof(f5816,plain,
    ( ~ spl0_88
    | ~ spl0_133
    | spl0_671 ),
    inference(avatar_split_clause,[],[f5723,f5597,f1336,f1122]) ).

fof(f5723,plain,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
    | ~ spl0_133
    | spl0_671 ),
    inference(resolution,[],[f5599,f1337]) ).

fof(f5599,plain,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | spl0_671 ),
    inference(avatar_component_clause,[],[f5597]) ).

fof(f5603,plain,
    ( ~ spl0_671
    | spl0_672
    | ~ spl0_354
    | ~ spl0_651 ),
    inference(avatar_split_clause,[],[f5331,f5175,f2670,f5601,f5597]) ).

fof(f5601,plain,
    ( spl0_672
  <=> ! [X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_OpCons(X1,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(X0,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).

fof(f5175,plain,
    ( spl0_651
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).

fof(f5331,plain,
    ( ! [X0,X1] :
        ( ~ c_Ring__and__Field_Odvd__class_Odvd(X0,c_Polynomial_OpCons(X1,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | c_Ring__and__Field_Odvd__class_Odvd(X0,v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_354
    | ~ spl0_651 ),
    inference(resolution,[],[f5176,f2671]) ).

fof(f5176,plain,
    ( ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
    | ~ spl0_651 ),
    inference(avatar_component_clause,[],[f5175]) ).

fof(f5541,plain,
    ( spl0_670
    | ~ spl0_124
    | ~ spl0_648 ),
    inference(avatar_split_clause,[],[f5201,f5163,f1300,f5539]) ).

fof(f5539,plain,
    ( spl0_670
  <=> ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(X2,hAPP(X3,X4))
        | hAPP(c_Fun_Ocomp(X2,X3,X8,X6,X9),X4) = hAPP(c_Fun_Ocomp(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X0,X5,X6,X7),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).

fof(f5201,plain,
    ( ! [X2,X3,X0,X1,X8,X6,X9,X7,X4,X5] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(X2,hAPP(X3,X4))
        | hAPP(c_Fun_Ocomp(X2,X3,X8,X6,X9),X4) = hAPP(c_Fun_Ocomp(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X0,X5,X6,X7),X1) )
    | ~ spl0_124
    | ~ spl0_648 ),
    inference(superposition,[],[f5164,f1301]) ).

fof(f5537,plain,
    ( spl0_669
    | ~ spl0_124
    | ~ spl0_617 ),
    inference(avatar_split_clause,[],[f4851,f4790,f1300,f5535]) ).

fof(f5535,plain,
    ( spl0_669
  <=> ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X1
        | c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X0) = X1
        | ~ class_HOL_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).

fof(f4790,plain,
    ( spl0_617
  <=> ! [X10,X0,X3,X8] :
        ( ~ class_HOL_Ozero(X10)
        | c_Polynomial_Opoly__rec(X3,X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X0,X10) = X3
        | hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).

fof(f4851,plain,
    ( ! [X2,X0,X1] :
        ( hAPP(hAPP(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X1) != X1
        | c_Polynomial_Opoly__rec(X1,c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X0) = X1
        | ~ class_HOL_Ozero(X0) )
    | ~ spl0_124
    | ~ spl0_617 ),
    inference(superposition,[],[f4791,f1301]) ).

fof(f4791,plain,
    ( ! [X3,X10,X0,X8] :
        ( hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3
        | c_Polynomial_Opoly__rec(X3,X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X0,X10) = X3
        | ~ class_HOL_Ozero(X10) )
    | ~ spl0_617 ),
    inference(avatar_component_clause,[],[f4790]) ).

fof(f5519,plain,
    spl0_668,
    inference(avatar_split_clause,[],[f242,f5517]) ).

fof(f5517,plain,
    ( spl0_668
  <=> ! [X1,X0,X5,X25,X2,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(X5,X1,X0),X2,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X25,X0),X0),c_Polynomial_Odegree(X2,X0)),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)),X0),X7,X0),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X5,X25,X0),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X25,X0),X0),c_Polynomial_Odegree(X2,X0)),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)),X0),X2,X0),tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).

fof(f242,axiom,
    ! [X2,X0,X1,X7,X5,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
      | c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(X5,X1,X0),X2,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X25,X0),X0),c_Polynomial_Odegree(X2,X0)),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)),X0),X7,X0),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X5,X25,X0),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X25,X0),X0),c_Polynomial_Odegree(X2,X0)),hAPP(c_Polynomial_Ocoeff(X2,X0),c_Polynomial_Odegree(X2,X0)),X0),X2,X0),tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__pCons_0) ).

fof(f5509,plain,
    spl0_667,
    inference(avatar_split_clause,[],[f224,f5507]) ).

fof(f5507,plain,
    ( spl0_667
  <=> ! [X5,X0,X6,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X0),c_HOL_Ominus__class_Ominus(X2,X6,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X0),X6,X0),X0),c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X2,X6,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).

fof(f224,axiom,
    ! [X2,X0,X1,X6,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X0),c_HOL_Ominus__class_Ominus(X2,X6,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X1,X5,X0),X6,X0),X0),c_HOL_Otimes__class_Otimes(X5,c_HOL_Ominus__class_Ominus(X2,X6,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

fof(f5502,plain,
    spl0_666,
    inference(avatar_split_clause,[],[f335,f5500]) ).

fof(f5500,plain,
    ( spl0_666
  <=> ! [X5,X6,X13,X0,X27,X28] :
        ( ~ class_RealVector_Oreal__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X13,X27,X0),X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X6,X27,X0),X28,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X13,X0),X28,X0),X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).

fof(f335,axiom,
    ! [X28,X0,X6,X27,X5,X13] :
      ( ~ class_RealVector_Oreal__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X13,X27,X0),X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X6,X27,X0),X28,X0),X0),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X13,X0),X28,X0),X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).

fof(f5494,plain,
    spl0_665,
    inference(avatar_split_clause,[],[f371,f5492]) ).

fof(f5492,plain,
    ( spl0_665
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).

fof(f371,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

fof(f5490,plain,
    spl0_664,
    inference(avatar_split_clause,[],[f169,f5488]) ).

fof(f5488,plain,
    ( spl0_664
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).

fof(f169,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X4,X3,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X4,X2,X0),X0),c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

fof(f5457,plain,
    spl0_663,
    inference(avatar_split_clause,[],[f449,f5455]) ).

fof(f449,axiom,
    ! [X3,X10,X0,X8,X5,X12] :
      ( ~ class_HOL_Ozero(X10)
      | hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3
      | c_Polynomial_Opoly__rec(X3,X8,c_Polynomial_OpCons(X5,X12,X10),X0,X10) = hAPP(hAPP(hAPP(X8,X5),X12),c_Polynomial_Opoly__rec(X3,X8,X12,X0,X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__rec__pCons_0) ).

fof(f5453,plain,
    spl0_662,
    inference(avatar_split_clause,[],[f239,f5451]) ).

fof(f5451,plain,
    ( spl0_662
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),c_Polynomial_Osynthetic__div(X12,X13,X0),tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) = X12 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).

fof(f239,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),c_Polynomial_Osynthetic__div(X12,X13,X0),tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_H_0) ).

fof(f5438,plain,
    ( ~ spl0_112
    | spl0_661
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_584
    | ~ spl0_638 ),
    inference(avatar_split_clause,[],[f5091,f4990,f4503,f2698,f1267,f5436,f1242]) ).

fof(f5436,plain,
    ( spl0_661
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).

fof(f5091,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_584
    | ~ spl0_638 ),
    inference(forward_demodulation,[],[f5085,f2837]) ).

fof(f5085,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,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),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_584
    | ~ spl0_638 ),
    inference(trivial_inequality_removal,[],[f5079]) ).

fof(f5079,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,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),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_584
    | ~ spl0_638 ),
    inference(superposition,[],[f4991,f4504]) ).

fof(f5425,plain,
    spl0_660,
    inference(avatar_split_clause,[],[f385,f5423]) ).

fof(f5423,plain,
    ( spl0_660
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).

fof(f385,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_2) ).

fof(f5421,plain,
    spl0_659,
    inference(avatar_split_clause,[],[f22,f5419]) ).

fof(f5419,plain,
    ( spl0_659
  <=> ! [X6,X0,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),c_HOL_Ozero__class_Ozero(X0)),X6))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X7))
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).

fof(f22,axiom,
    ! [X0,X6,X7] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),c_HOL_Ozero__class_Ozero(X0)),X6))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X7))
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_2) ).

fof(f5406,plain,
    spl0_658,
    inference(avatar_split_clause,[],[f62,f5404]) ).

fof(f5404,plain,
    ( spl0_658
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),X6))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7))
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).

fof(f62,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),X6))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7))
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_2) ).

fof(f5390,plain,
    spl0_657,
    inference(avatar_split_clause,[],[f252,f5388]) ).

fof(f5388,plain,
    ( spl0_657
  <=> ! [X2,X1,X45,X0,X44,X3,X25,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
        | ~ c_Polynomial_Opdivmod__rel(X7,X3,X44,X45,X0)
        | c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X0)),X44,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X45,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).

fof(f252,axiom,
    ! [X2,X3,X0,X1,X44,X7,X45,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
      | ~ c_Polynomial_Opdivmod__rel(X7,X3,X44,X45,X0)
      | c_Polynomial_Opdivmod__rel(X1,c_HOL_Otimes__class_Otimes(X2,X3,tc_Polynomial_Opoly(X0)),X44,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X45,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__mult_0) ).

fof(f5337,plain,
    spl0_656,
    inference(avatar_split_clause,[],[f368,f5335]) ).

fof(f5335,plain,
    ( spl0_656
  <=> ! [X5,X0,X13,X6,X27] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X5 = X6
        | X13 = X27
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X27,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X27,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).

fof(f368,axiom,
    ! [X0,X6,X27,X5,X13] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X5 = X6
      | X13 = X27
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X27,X0),X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X27,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

fof(f5330,plain,
    spl0_655,
    inference(avatar_split_clause,[],[f403,f5328]) ).

fof(f5328,plain,
    ( spl0_655
  <=> ! [X0,X12,X7] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | X7 = X12
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X12,tc_Polynomial_Opoly(X0))
        | hAPP(c_Polynomial_Ocoeff(X12,X0),c_Polynomial_Odegree(X12,X0)) != hAPP(c_Polynomial_Ocoeff(X7,X0),c_Polynomial_Odegree(X7,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).

fof(f403,axiom,
    ! [X0,X7,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | X7 = X12
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X7,X12,tc_Polynomial_Opoly(X0))
      | hAPP(c_Polynomial_Ocoeff(X12,X0),c_Polynomial_Odegree(X12,X0)) != hAPP(c_Polynomial_Ocoeff(X7,X0),c_Polynomial_Odegree(X7,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__dvd__antisym_0) ).

fof(f5301,plain,
    spl0_654,
    inference(avatar_split_clause,[],[f344,f5299]) ).

fof(f344,axiom,
    ! [X0,X6,X26,X27,X5,X13] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X26,X0),X13,X0) = X27
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),X27,X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

fof(f5185,plain,
    spl0_653,
    inference(avatar_split_clause,[],[f415,f5183]) ).

fof(f5183,plain,
    ( spl0_653
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Otimes__class_Otimes(X1,X3,X0) != c_HOL_Otimes__class_Otimes(X4,X2,X0)
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(X4,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).

fof(f415,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Otimes__class_Otimes(X1,X3,X0) != c_HOL_Otimes__class_Otimes(X4,X2,X0)
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) = c_HOL_Oinverse__class_Odivide(X4,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

fof(f5181,plain,
    spl0_652,
    inference(avatar_split_clause,[],[f414,f5179]) ).

fof(f5179,plain,
    ( spl0_652
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) = X3
        | c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oinverse__class_Odivide(X4,X3,X0)
        | c_HOL_Otimes__class_Otimes(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X4,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).

fof(f414,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) = X3
      | c_HOL_Oinverse__class_Odivide(X1,X2,X0) != c_HOL_Oinverse__class_Odivide(X4,X3,X0)
      | c_HOL_Otimes__class_Otimes(X1,X3,X0) = c_HOL_Otimes__class_Otimes(X4,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

fof(f5177,plain,
    ( ~ spl0_112
    | spl0_651
    | ~ spl0_117
    | ~ spl0_124
    | ~ spl0_361
    | ~ spl0_638 ),
    inference(avatar_split_clause,[],[f5088,f4990,f2698,f1300,f1267,f5175,f1242]) ).

fof(f5088,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,c_Polynomial_Omonom(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex))
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_117
    | ~ spl0_124
    | ~ spl0_361
    | ~ spl0_638 ),
    inference(forward_demodulation,[],[f5087,f2837]) ).

fof(f5087,plain,
    ( ! [X0] :
        ( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,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),v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_124
    | ~ spl0_638 ),
    inference(trivial_inequality_removal,[],[f5076]) ).

fof(f5076,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X0,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),v_p,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) )
    | ~ spl0_124
    | ~ spl0_638 ),
    inference(superposition,[],[f4991,f1301]) ).

fof(f5173,plain,
    spl0_650,
    inference(avatar_split_clause,[],[f138,f5171]) ).

fof(f5171,plain,
    ( spl0_650
  <=> ! [X42,X29,X0,X27,X43,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | ~ class_Ring__and__Field_Odvd(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X42,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(X1,X43,X0),X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Otimes__class_Otimes(X29,X42,X0),X0),X43,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).

fof(f138,axiom,
    ! [X0,X29,X1,X27,X42,X43] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | ~ class_Ring__and__Field_Odvd(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X42,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(X1,X43,X0),X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Otimes__class_Otimes(X29,X42,X0),X0),X43,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).

fof(f5169,plain,
    spl0_649,
    inference(avatar_split_clause,[],[f137,f5167]) ).

fof(f5167,plain,
    ( spl0_649
  <=> ! [X42,X29,X0,X27,X43,X1] :
        ( ~ class_Ring__and__Field_Ocomm__ring(X0)
        | ~ class_Ring__and__Field_Odvd(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X42,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(X1,X43,X0),X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Otimes__class_Otimes(X29,X42,X0),X0),X43,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).

fof(f137,axiom,
    ! [X0,X29,X1,X27,X42,X43] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | ~ class_Ring__and__Field_Odvd(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,X42,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(X1,X43,X0),X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X27,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X1,c_HOL_Otimes__class_Otimes(X29,X42,X0),X0),X43,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).

fof(f5165,plain,
    spl0_648,
    inference(avatar_split_clause,[],[f133,f5163]) ).

fof(f133,axiom,
    ! [X40,X38,X10,X0,X11,X39,X1,X8,X37,X9,X33] :
      ( hAPP(X8,hAPP(X9,X1)) != hAPP(X37,hAPP(X38,X33))
      | hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1) = hAPP(c_Fun_Ocomp(X37,X38,X39,X0,X40),X33) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).

fof(f5140,plain,
    spl0_647,
    inference(avatar_split_clause,[],[f380,f5138]) ).

fof(f5138,plain,
    ( spl0_647
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Otimes__class_Otimes(X12,c_Polynomial_OpCons(X5,X7,X0),tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).

fof(f380,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Otimes__class_Otimes(X12,c_Polynomial_OpCons(X5,X7,X0),tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__right_0) ).

fof(f5136,plain,
    spl0_646,
    inference(avatar_split_clause,[],[f379,f5134]) ).

fof(f5134,plain,
    ( spl0_646
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X7,X0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).

fof(f379,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X7,X0),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pCons__left_0) ).

fof(f5132,plain,
    spl0_645,
    inference(avatar_split_clause,[],[f375,f5130]) ).

fof(f5130,plain,
    ( spl0_645
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).

fof(f375,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_1) ).

fof(f5128,plain,
    spl0_644,
    inference(avatar_split_clause,[],[f334,f5126]) ).

fof(f5126,plain,
    ( spl0_644
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Opcompose(c_Polynomial_OpCons(X5,X12,X0),X7,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),c_HOL_Otimes__class_Otimes(X7,c_Polynomial_Opcompose(X12,X7,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).

fof(f334,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Opcompose(c_Polynomial_OpCons(X5,X12,X0),X7,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),c_HOL_Otimes__class_Otimes(X7,c_Polynomial_Opcompose(X12,X7,X0),tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pcompose__pCons_0) ).

fof(f5124,plain,
    spl0_643,
    inference(avatar_split_clause,[],[f88,f5122]) ).

fof(f5122,plain,
    ( spl0_643
  <=> ! [X0,X12,X5,X28] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X5,X12,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X28,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),c_Polynomial_OpCons(X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).

fof(f88,axiom,
    ! [X28,X0,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X5,X12,X0),X28,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X28,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),c_Polynomial_OpCons(X5,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__pCons_0) ).

fof(f5120,plain,
    spl0_642,
    inference(avatar_split_clause,[],[f9,f5118]) ).

fof(f5118,plain,
    ( spl0_642
  <=> ! [X6,X0,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X7))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).

fof(f9,axiom,
    ! [X0,X6,X7] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),X7))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_1) ).

fof(f5004,plain,
    spl0_641,
    inference(avatar_split_clause,[],[f343,f5002]) ).

fof(f5002,plain,
    ( spl0_641
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).

fof(f343,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_1) ).

fof(f5000,plain,
    spl0_640,
    inference(avatar_split_clause,[],[f338,f4998]) ).

fof(f4998,plain,
    ( spl0_640
  <=> ! [X5,X13,X0,X6,X26] :
        ( ~ class_Ring__and__Field_Oring(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X26,X0),X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).

fof(f338,axiom,
    ! [X0,X6,X26,X5,X13] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X6,X0),X26,X0),X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

fof(f4996,plain,
    spl0_639,
    inference(avatar_split_clause,[],[f281,f4994]) ).

fof(f4994,plain,
    ( spl0_639
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Ouminus__class_Ouminus(X13,X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).

fof(f281,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Ouminus__class_Ouminus(X13,X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_0) ).

fof(f4992,plain,
    spl0_638,
    inference(avatar_split_clause,[],[f280,f4990]) ).

fof(f280,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Ouminus__class_Ouminus(X13,X0))
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(X13,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__iff__poly__eq__0_1) ).

fof(f4988,plain,
    ( ~ spl0_112
    | spl0_636
    | spl0_637
    | ~ spl0_584
    | ~ spl0_593 ),
    inference(avatar_split_clause,[],[f4603,f4565,f4503,f4985,f4982,f1242]) ).

fof(f4982,plain,
    ( spl0_636
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,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_636])]) ).

fof(f4985,plain,
    ( spl0_637
  <=> c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).

fof(f4565,plain,
    ( spl0_593
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X12,X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).

fof(f4603,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_584
    | ~ spl0_593 ),
    inference(trivial_inequality_removal,[],[f4599]) ).

fof(f4599,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_584
    | ~ spl0_593 ),
    inference(superposition,[],[f4566,f4504]) ).

fof(f4566,plain,
    ( ! [X0,X5,X12] :
        ( c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),X5)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X12,X0)
        | ~ class_Ring__and__Field_Oidom(X0) )
    | ~ spl0_593 ),
    inference(avatar_component_clause,[],[f4565]) ).

fof(f4980,plain,
    spl0_635,
    inference(avatar_split_clause,[],[f279,f4978]) ).

fof(f4978,plain,
    ( spl0_635
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),X13)
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).

fof(f279,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),X13)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_0) ).

fof(f4976,plain,
    spl0_634,
    inference(avatar_split_clause,[],[f278,f4974]) ).

fof(f4974,plain,
    ( spl0_634
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),X13)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).

fof(f278,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),X13)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X13,X0),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),X12,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__0__iff__dvd_1) ).

fof(f4972,plain,
    spl0_633,
    inference(avatar_split_clause,[],[f228,f4970]) ).

fof(f4970,plain,
    ( spl0_633
  <=> ! [X5,X13,X0,X6,X26] :
        ( ~ class_Ring__and__Field_Osemiring(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X26,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).

fof(f228,axiom,
    ! [X0,X6,X26,X5,X13] :
      ( ~ class_Ring__and__Field_Osemiring(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X26,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X6,X26,X0),X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X26,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

fof(f4968,plain,
    spl0_632,
    inference(avatar_split_clause,[],[f190,f4966]) ).

fof(f4966,plain,
    ( spl0_632
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).

fof(f190,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0),X2,X0) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

fof(f4964,plain,
    spl0_631,
    inference(avatar_split_clause,[],[f189,f4962]) ).

fof(f4962,plain,
    ( spl0_631
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).

fof(f189,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X3,X2,X0),X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

fof(f4960,plain,
    spl0_630,
    inference(avatar_split_clause,[],[f124,f4958]) ).

fof(f4958,plain,
    ( spl0_630
  <=> ! [X13,X0,X27,X25,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X13 = X27
        | c_HOL_Ozero__class_Ozero(X0) = X25
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X25,X13,X0),X0) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X25,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).

fof(f124,axiom,
    ! [X0,X1,X27,X25,X13] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X13 = X27
      | c_HOL_Ozero__class_Ozero(X0) = X25
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X25,X13,X0),X0) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X25,X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

fof(f4956,plain,
    spl0_629,
    inference(avatar_split_clause,[],[f58,f4954]) ).

fof(f4954,plain,
    ( spl0_629
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).

fof(f58,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_0) ).

fof(f4904,plain,
    spl0_628,
    inference(avatar_split_clause,[],[f412,f4902]) ).

fof(f4902,plain,
    ( spl0_628
  <=> ! [X2,X0,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
        | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X2,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X2,X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).

fof(f412,axiom,
    ! [X2,X0,X7] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
      | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X2,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X2,X7,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_3) ).

fof(f4900,plain,
    spl0_627,
    inference(avatar_split_clause,[],[f374,f4898]) ).

fof(f4898,plain,
    ( spl0_627
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).

fof(f374,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),c_HOL_Ozero__class_Ozero(X0)))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I3_J_0) ).

fof(f4896,plain,
    spl0_626,
    inference(avatar_split_clause,[],[f362,f4894]) ).

fof(f4894,plain,
    ( spl0_626
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X5,X12,X0),c_Polynomial_OpCons(X6,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).

fof(f362,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(X5,X12,X0),c_Polynomial_OpCons(X6,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pCons_0) ).

fof(f4892,plain,
    ( spl0_625
    | ~ spl0_580
    | ~ spl0_595 ),
    inference(avatar_split_clause,[],[f4840,f4586,f4244,f4890]) ).

fof(f4890,plain,
    ( spl0_625
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).

fof(f4586,plain,
    ( spl0_595
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).

fof(f4840,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_580
    | ~ spl0_595 ),
    inference(trivial_inequality_removal,[],[f4836]) ).

fof(f4836,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) )
    | ~ spl0_580
    | ~ spl0_595 ),
    inference(superposition,[],[f4245,f4587]) ).

fof(f4587,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_595 ),
    inference(avatar_component_clause,[],[f4586]) ).

fof(f4888,plain,
    spl0_624,
    inference(avatar_split_clause,[],[f342,f4886]) ).

fof(f4886,plain,
    ( spl0_624
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),X6))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).

fof(f342,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X5),X6))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_Polynomial_OpCons(X5,X12,X0)),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I4_J_0) ).

fof(f4884,plain,
    spl0_623,
    inference(avatar_split_clause,[],[f267,f4882]) ).

fof(f4882,plain,
    ( spl0_623
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_Polynomial_Osynthetic__div(X12,X13,X0),X0) = c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,c_Polynomial_Osynthetic__div(X12,X13,X0),X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).

fof(f267,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_Polynomial_Osynthetic__div(X12,X13,X0),X0) = c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,c_Polynomial_Osynthetic__div(X12,X13,X0),X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__correct_0) ).

fof(f4880,plain,
    spl0_622,
    inference(avatar_split_clause,[],[f176,f4878]) ).

fof(f4878,plain,
    ( spl0_622
  <=> ! [X5,X0,X12,X6,X7] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X5,X12,X0),c_Polynomial_OpCons(X6,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X5,X6,X0),c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).

fof(f176,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(X5,X12,X0),c_Polynomial_OpCons(X6,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(X5,X6,X0),c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__pCons_0) ).

fof(f4876,plain,
    spl0_621,
    inference(avatar_split_clause,[],[f153,f4874]) ).

fof(f4874,plain,
    ( spl0_621
  <=> ! [X0,X12,X25,X7] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X25,tc_Polynomial_Opoly(X0)),c_HOL_Otimes__class_Otimes(X7,X25,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).

fof(f153,axiom,
    ! [X0,X7,X12,X25] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X25,tc_Polynomial_Opoly(X0)),c_HOL_Otimes__class_Otimes(X7,X25,tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__add__left_0) ).

fof(f4872,plain,
    spl0_620,
    inference(avatar_split_clause,[],[f83,f4870]) ).

fof(f4870,plain,
    ( spl0_620
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).

fof(f83,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

fof(f4868,plain,
    spl0_619,
    inference(avatar_split_clause,[],[f8,f4866]) ).

fof(f4866,plain,
    ( spl0_619
  <=> ! [X6,X0,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),c_HOL_Ozero__class_Ozero(X0)),X6))
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).

fof(f8,axiom,
    ! [X0,X6,X7] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),c_HOL_Ozero__class_Ozero(X0)),X6))
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))),c_Polynomial_OpCons(X6,X7,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__code_I2_J_0) ).

fof(f4864,plain,
    spl0_618,
    inference(avatar_split_clause,[],[f1,f4862]) ).

fof(f4862,plain,
    ( spl0_618
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),c_HOL_Oinverse__class_Odivide(X3,X4,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),c_HOL_Otimes__class_Otimes(X2,X4,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

fof(f4792,plain,
    spl0_617,
    inference(avatar_split_clause,[],[f502,f4790]) ).

fof(f502,axiom,
    ! [X3,X10,X0,X8] :
      ( ~ class_HOL_Ozero(X10)
      | c_Polynomial_Opoly__rec(X3,X8,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10)),X0,X10) = X3
      | hAPP(hAPP(hAPP(X8,c_HOL_Ozero__class_Ozero(X10)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X10))),X3) != X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__rec__0_0) ).

fof(f4788,plain,
    spl0_616,
    inference(avatar_split_clause,[],[f349,f4786]) ).

fof(f349,axiom,
    ! [X0,X1,X7,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__add_0) ).

fof(f4784,plain,
    spl0_615,
    inference(avatar_split_clause,[],[f346,f4782]) ).

fof(f346,axiom,
    ! [X0,X1,X7,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Otimes__class_Otimes(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__mult_0) ).

fof(f4780,plain,
    spl0_614,
    inference(avatar_split_clause,[],[f328,f4778]) ).

fof(f4778,plain,
    ( spl0_614
  <=> ! [X25,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).

fof(f328,axiom,
    ! [X0,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_5) ).

fof(f4776,plain,
    spl0_613,
    inference(avatar_split_clause,[],[f327,f4774]) ).

fof(f4774,plain,
    ( spl0_613
  <=> ! [X2,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).

fof(f327,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_6) ).

fof(f4772,plain,
    spl0_612,
    inference(avatar_split_clause,[],[f262,f4770]) ).

fof(f262,axiom,
    ! [X0,X1,X7,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | hAPP(c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Opoly(X12,X0),X1),hAPP(c_Polynomial_Opoly(X7,X0),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__diff_0) ).

fof(f4768,plain,
    spl0_611,
    inference(avatar_split_clause,[],[f209,f4766]) ).

fof(f209,axiom,
    ! [X0,X7,X15,X12] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | hAPP(c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Oplus__class_Oplus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__add_0) ).

fof(f4764,plain,
    spl0_610,
    inference(avatar_split_clause,[],[f134,f4762]) ).

fof(f134,axiom,
    ! [X41,X10,X0,X11,X39,X6,X27,X5,X13] :
      ( hAPP(X5,hAPP(X6,X41)) = hAPP(X13,hAPP(X27,X41))
      | c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(X13,X27,X39,X10,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).

fof(f4760,plain,
    spl0_609,
    inference(avatar_split_clause,[],[f30,f4758]) ).

fof(f30,axiom,
    ! [X0,X7,X15,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ominus__class_Ominus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),hAPP(c_Polynomial_Ocoeff(X7,X0),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__diff_0) ).

fof(f4664,plain,
    spl0_608,
    inference(avatar_split_clause,[],[f420,f4662]) ).

fof(f420,axiom,
    ! [X28,X39,X0,X11,X10,X8,X9] : c_Fun_Ofcomp(c_Fun_Ofcomp(X8,X9,X0,X39,X11),X28,X0,X11,X10) = c_Fun_Ofcomp(X8,c_Fun_Ofcomp(X9,X28,X39,X11,X10),X0,X39,X10),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).

fof(f4660,plain,
    spl0_607,
    inference(avatar_split_clause,[],[f393,f4658]) ).

fof(f393,axiom,
    ! [X28,X39,X0,X11,X10,X8,X9] : c_Fun_Ocomp(X8,c_Fun_Ocomp(X9,X28,X39,X11,X0),X11,X10,X0) = c_Fun_Ocomp(c_Fun_Ocomp(X8,X9,X11,X10,X39),X28,X39,X10,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).

fof(f4656,plain,
    spl0_606,
    inference(avatar_split_clause,[],[f255,f4654]) ).

fof(f255,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

fof(f4652,plain,
    spl0_605,
    inference(avatar_split_clause,[],[f254,f4650]) ).

fof(f254,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

fof(f4648,plain,
    ( ~ spl0_112
    | spl0_603
    | spl0_604
    | ~ spl0_124
    | ~ spl0_593 ),
    inference(avatar_split_clause,[],[f4604,f4565,f1300,f4645,f4642,f1242]) ).

fof(f4642,plain,
    ( spl0_603
  <=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,v_p,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).

fof(f4604,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,v_p,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_124
    | ~ spl0_593 ),
    inference(trivial_inequality_removal,[],[f4596]) ).

fof(f4596,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = v_p
        | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X0,v_p,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) )
    | ~ spl0_124
    | ~ spl0_593 ),
    inference(superposition,[],[f4566,f1301]) ).

fof(f4640,plain,
    spl0_602,
    inference(avatar_split_clause,[],[f241,f4638]) ).

fof(f241,axiom,
    ! [X41,X10,X0,X11,X6,X5,X13] :
      ( hAPP(X5,hAPP(X6,X41)) = hAPP(X13,X41)
      | c_Fun_Ocomp(X5,X6,X11,X10,X0) != c_Fun_Ocomp(c_Fun_Oid(X10),X13,X10,X10,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).

fof(f4636,plain,
    spl0_601,
    inference(avatar_split_clause,[],[f237,f4634]) ).

fof(f237,axiom,
    ! [X0,X6,X27,X5,X13] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),c_HOL_Ominus__class_Ominus(X13,X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

fof(f4632,plain,
    spl0_600,
    inference(avatar_split_clause,[],[f191,f4630]) ).

fof(f191,axiom,
    ! [X0,X6,X27,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

fof(f4628,plain,
    spl0_599,
    inference(avatar_split_clause,[],[f185,f4626]) ).

fof(f185,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
      | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_1) ).

fof(f4624,plain,
    spl0_598,
    inference(avatar_split_clause,[],[f184,f4622]) ).

fof(f184,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
      | c_HOL_Oone__class_Oone(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(X1,X2,X0),X0),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(X1,X2,X0),X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__monic_2) ).

fof(f4620,plain,
    spl0_597,
    inference(avatar_split_clause,[],[f52,f4618]) ).

fof(f52,axiom,
    ! [X2,X0,X1,X7,X5,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
      | c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(X5,X1,X0),X2,c_Polynomial_Osmult(X5,X7,X0),c_Polynomial_Osmult(X5,X25,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).

fof(f4616,plain,
    spl0_596,
    inference(avatar_split_clause,[],[f41,f4614]) ).

fof(f41,axiom,
    ! [X21,X0,X22,X23,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

fof(f4588,plain,
    ( spl0_595
    | ~ spl0_580
    | ~ spl0_584 ),
    inference(avatar_split_clause,[],[f4546,f4503,f4244,f4586]) ).

fof(f4546,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_580
    | ~ spl0_584 ),
    inference(trivial_inequality_removal,[],[f4544]) ).

fof(f4544,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) )
    | ~ spl0_580
    | ~ spl0_584 ),
    inference(superposition,[],[f4245,f4504]) ).

fof(f4571,plain,
    spl0_594,
    inference(avatar_split_clause,[],[f495,f4569]) ).

fof(f495,axiom,
    ! [X6,X5,X12] :
      ( c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,c_Polynomial_OpCons(X6,X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xbasic__cqe__conv2__1(X5,X6,X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_basic__cqe__conv2_0) ).

fof(f4567,plain,
    spl0_593,
    inference(avatar_split_clause,[],[f492,f4565]) ).

fof(f492,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_nat) != c_Polynomial_Oorder(X5,X12,X0)
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Opoly(X12,X0),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_0) ).

fof(f4563,plain,
    spl0_592,
    inference(avatar_split_clause,[],[f410,f4561]) ).

fof(f410,axiom,
    ! [X0,X1,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X5,X12,X0),X0),X1) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X1,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pCons_0) ).

fof(f4559,plain,
    spl0_591,
    inference(avatar_split_clause,[],[f381,f4557]) ).

fof(f381,axiom,
    ! [X0,X7,X12,X25,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(X12,X0),X13) = X25
      | c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_0) ).

fof(f4555,plain,
    spl0_590,
    inference(avatar_split_clause,[],[f365,f4553]) ).

fof(f365,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | c_Polynomial_Osmult(X5,c_HOL_Ominus__class_Ominus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__right_0) ).

fof(f4551,plain,
    spl0_589,
    inference(avatar_split_clause,[],[f60,f4549]) ).

fof(f60,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(X5,c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__right_0) ).

fof(f4543,plain,
    spl0_588,
    inference(avatar_split_clause,[],[f49,f4541]) ).

fof(f4541,plain,
    ( spl0_588
  <=> ! [X0,X13,X12,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X13,X12,X0),c_Polynomial_OpCons(X5,X12,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).

fof(f49,axiom,
    ! [X0,X5,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X13,X12,X0),c_Polynomial_OpCons(X5,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__lemma_0) ).

fof(f4517,plain,
    spl0_587,
    inference(avatar_split_clause,[],[f408,f4515]) ).

fof(f408,axiom,
    ! [X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(X5,X6,X0),X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__monom_0) ).

fof(f4513,plain,
    spl0_586,
    inference(avatar_split_clause,[],[f402,f4511]) ).

fof(f402,axiom,
    ! [X0,X7,X12,X25,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osynthetic__div(X12,X13,X0) = X7
      | c_HOL_Oplus__class_Oplus(X12,c_Polynomial_Osmult(X13,X7,X0),tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X25,X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique_1) ).

fof(f4509,plain,
    spl0_585,
    inference(avatar_split_clause,[],[f364,f4507]) ).

fof(f364,axiom,
    ! [X0,X6,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(X5,X6,X0),X12,X0) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__diff__left_0) ).

fof(f4505,plain,
    ( spl0_584
    | ~ spl0_124
    | ~ spl0_580 ),
    inference(avatar_split_clause,[],[f4487,f4244,f1300,f4503]) ).

fof(f4487,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0)
    | ~ spl0_124
    | ~ spl0_580 ),
    inference(trivial_inequality_removal,[],[f4480]) ).

fof(f4480,plain,
    ( ! [X0] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X0) )
    | ~ spl0_124
    | ~ spl0_580 ),
    inference(superposition,[],[f4245,f1301]) ).

fof(f4501,plain,
    spl0_583,
    inference(avatar_split_clause,[],[f201,f4499]) ).

fof(f201,axiom,
    ! [X0,X6,X15,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(X5,X15,X0),c_Polynomial_Omonom(X6,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(X5,X6,X0),X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__monom_0) ).

fof(f4497,plain,
    spl0_582,
    inference(avatar_split_clause,[],[f59,f4495]) ).

fof(f59,axiom,
    ! [X0,X6,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(X5,X6,X0),X12,X0) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(X5,X12,X0),c_Polynomial_Osmult(X6,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__add__left_0) ).

fof(f4493,plain,
    spl0_581,
    inference(avatar_split_clause,[],[f55,f4491]) ).

fof(f55,axiom,
    ! [X0,X5,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(X5,X12,X0),X13,X0) = c_Polynomial_OpCons(hAPP(c_Polynomial_Opoly(X12,X0),X13),c_Polynomial_Osynthetic__div(X12,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__pCons_0) ).

fof(f4246,plain,
    spl0_580,
    inference(avatar_split_clause,[],[f506,f4244]) ).

fof(f506,axiom,
    ! [X1,X12] :
      ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),X1)
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pad__rule_0) ).

fof(f4242,plain,
    spl0_579,
    inference(avatar_split_clause,[],[f484,f4240]) ).

fof(f484,axiom,
    ! [X0,X1,X7,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(X12,X7,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),hAPP(c_Polynomial_Opoly(X7,X0),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__pcompose_0) ).

fof(f4211,plain,
    spl0_578,
    inference(avatar_split_clause,[],[f407,f4209]) ).

fof(f4209,plain,
    ( spl0_578
  <=> ! [X5,X0,X13,X6,X27] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X27,X0)
        | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X27,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).

fof(f407,axiom,
    ! [X0,X6,X27,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X13,X27,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

fof(f4207,plain,
    spl0_577,
    inference(avatar_split_clause,[],[f398,f4205]) ).

fof(f4205,plain,
    ( spl0_577
  <=> ! [X0,X29,X2,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X1,tc_Polynomial_Opoly(X0))
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X2,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).

fof(f398,axiom,
    ! [X2,X0,X29,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X1,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,X2,tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__greatest_0) ).

fof(f4203,plain,
    spl0_576,
    inference(avatar_split_clause,[],[f323,f4201]) ).

fof(f4201,plain,
    ( spl0_576
  <=> ! [X2,X0,X3,X1,X46] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X1,X3,X0) = X46
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X46,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).

fof(f323,axiom,
    ! [X2,X3,X0,X46,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,X3,X0) = X46
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) != c_HOL_Oplus__class_Oplus(X2,X46,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

fof(f4199,plain,
    spl0_575,
    inference(avatar_split_clause,[],[f271,f4197]) ).

fof(f4197,plain,
    ( spl0_575
  <=> ! [X24,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X24,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X24,X0),c_HOL_Oinverse__class_Odivide(X2,X24,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).

fof(f271,axiom,
    ! [X2,X0,X1,X24] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X1,X2,X0),X24,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X1,X24,X0),c_HOL_Oinverse__class_Odivide(X2,X24,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

fof(f4195,plain,
    spl0_574,
    inference(avatar_split_clause,[],[f270,f4193]) ).

fof(f270,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

fof(f4191,plain,
    spl0_573,
    inference(avatar_split_clause,[],[f266,f4189]) ).

fof(f266,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

fof(f4187,plain,
    spl0_572,
    inference(avatar_split_clause,[],[f265,f4185]) ).

fof(f265,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).

fof(f4183,plain,
    spl0_571,
    inference(avatar_split_clause,[],[f245,f4181]) ).

fof(f4181,plain,
    ( spl0_571
  <=> ! [X6,X0,X14,X5] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Oplus__class_Oplus(X6,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),c_RealVector_OscaleR__class_OscaleR(X5,X14,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).

fof(f245,axiom,
    ! [X0,X6,X14,X5] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Oplus__class_Oplus(X6,X14,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),c_RealVector_OscaleR__class_OscaleR(X5,X14,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Oadd__right_0) ).

fof(f4179,plain,
    spl0_570,
    inference(avatar_split_clause,[],[f244,f4177]) ).

fof(f244,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Oadd_0) ).

fof(f4175,plain,
    spl0_569,
    inference(avatar_split_clause,[],[f235,f4173]) ).

fof(f235,axiom,
    ! [X0,X36,X6,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X5,X36,X0),X6,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X36,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).

fof(f4165,plain,
    spl0_568,
    inference(avatar_split_clause,[],[f233,f4163]) ).

fof(f233,axiom,
    ! [X2,X0,X1,X35] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Otimes__class_Otimes(X35,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).

fof(f4161,plain,
    spl0_567,
    inference(avatar_split_clause,[],[f214,f4159]) ).

fof(f4159,plain,
    ( spl0_567
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X13,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).

fof(f214,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
      | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X13,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

fof(f4157,plain,
    spl0_566,
    inference(avatar_split_clause,[],[f213,f4155]) ).

fof(f4155,plain,
    ( spl0_566
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X13,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).

fof(f213,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X13,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

fof(f4153,plain,
    spl0_565,
    inference(avatar_split_clause,[],[f212,f4151]) ).

fof(f212,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Olower__semilattice__class_Oinf(X6,X13,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

fof(f4149,plain,
    spl0_564,
    inference(avatar_split_clause,[],[f211,f4147]) ).

fof(f211,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X13,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

fof(f4145,plain,
    spl0_563,
    inference(avatar_split_clause,[],[f155,f4143]) ).

fof(f4143,plain,
    ( spl0_563
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).

fof(f155,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

fof(f4141,plain,
    spl0_562,
    inference(avatar_split_clause,[],[f154,f4139]) ).

fof(f154,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Otimes__class_Otimes(X1,X3,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

fof(f4137,plain,
    spl0_561,
    inference(avatar_split_clause,[],[f151,f4135]) ).

fof(f4135,plain,
    ( spl0_561
  <=> ! [X24,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X24,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X24,X0),c_HOL_Otimes__class_Otimes(X2,X24,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).

fof(f151,axiom,
    ! [X2,X0,X1,X24] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X24,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X24,X0),c_HOL_Otimes__class_Otimes(X2,X24,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

fof(f4133,plain,
    spl0_560,
    inference(avatar_split_clause,[],[f149,f4131]) ).

fof(f149,axiom,
    ! [X2,X0,X1,X35] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Otimes__class_Otimes(X35,c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X35,X1,X0),c_HOL_Otimes__class_Otimes(X35,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).

fof(f4129,plain,
    spl0_559,
    inference(avatar_split_clause,[],[f148,f4127]) ).

fof(f148,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

fof(f4125,plain,
    ( ~ spl0_74
    | spl0_558
    | ~ spl0_187
    | ~ spl0_322 ),
    inference(avatar_split_clause,[],[f4063,f2442,f1579,f4123,f1052]) ).

fof(f1052,plain,
    ( spl0_74
  <=> class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).

fof(f4123,plain,
    ( spl0_558
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).

fof(f2442,plain,
    ( spl0_322
  <=> ! [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_322])]) ).

fof(f4063,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_RealDef_Oreal)
        | ~ class_Ring__and__Field_Odvd(tc_RealDef_Oreal) )
    | ~ spl0_187
    | ~ spl0_322 ),
    inference(superposition,[],[f1580,f2443]) ).

fof(f2443,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_322 ),
    inference(avatar_component_clause,[],[f2442]) ).

fof(f4121,plain,
    spl0_557,
    inference(avatar_split_clause,[],[f128,f4119]) ).

fof(f128,axiom,
    ! [X0,X6,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(X5,c_Polynomial_OpCons(X6,X12,X0),X0) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_Polynomial_Osmult(X5,X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__pCons_0) ).

fof(f4117,plain,
    spl0_556,
    inference(avatar_split_clause,[],[f98,f4115]) ).

fof(f4115,plain,
    ( spl0_556
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X13,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).

fof(f98,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X13,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

fof(f4113,plain,
    spl0_555,
    inference(avatar_split_clause,[],[f97,f4111]) ).

fof(f4111,plain,
    ( spl0_555
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X13,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).

fof(f97,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X13,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

fof(f4109,plain,
    spl0_554,
    inference(avatar_split_clause,[],[f96,f4107]) ).

fof(f96,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_Lattices_Oupper__semilattice__class_Osup(X6,X13,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X6,X0),c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

fof(f4105,plain,
    spl0_553,
    inference(avatar_split_clause,[],[f95,f4103]) ).

fof(f95,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add__join(X0)
      | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X13,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(X5,X13,X0),c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

fof(f4101,plain,
    spl0_552,
    inference(avatar_split_clause,[],[f90,f4099]) ).

fof(f90,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

fof(f4097,plain,
    spl0_551,
    inference(avatar_split_clause,[],[f89,f4095]) ).

fof(f89,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X1,X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0),c_Lattices_Olower__semilattice__class_Oinf(X3,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

fof(f4093,plain,
    spl0_550,
    inference(avatar_split_clause,[],[f51,f4091]) ).

fof(f4091,plain,
    ( spl0_550
  <=> ! [X24,X0,X2,X1] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X24,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X24,X0),c_HOL_Oinverse__class_Odivide(X2,X24,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).

fof(f51,axiom,
    ! [X2,X0,X1,X24] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X1,X2,X0),X24,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X1,X24,X0),c_HOL_Oinverse__class_Odivide(X2,X24,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

fof(f4089,plain,
    spl0_549,
    inference(avatar_split_clause,[],[f50,f4087]) ).

fof(f50,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(X5,X6,X0),X13,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(X5,X13,X0),c_HOL_Oinverse__class_Odivide(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

fof(f4085,plain,
    spl0_548,
    inference(avatar_split_clause,[],[f28,f4083]) ).

fof(f4083,plain,
    ( spl0_548
  <=> ! [X6,X0,X14,X5] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ominus__class_Ominus(X6,X14,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),c_RealVector_OscaleR__class_OscaleR(X5,X14,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).

fof(f28,axiom,
    ! [X0,X6,X14,X5] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ominus__class_Ominus(X6,X14,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),c_RealVector_OscaleR__class_OscaleR(X5,X14,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Odiff__right_0) ).

fof(f4054,plain,
    spl0_547,
    inference(avatar_split_clause,[],[f27,f4052]) ).

fof(f27,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__right_Odiff_0) ).

fof(f4050,plain,
    spl0_546,
    inference(avatar_split_clause,[],[f15,f4048]) ).

fof(f15,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X1,X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0),c_Lattices_Oupper__semilattice__class_Osup(X3,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

fof(f4046,plain,
    spl0_545,
    inference(avatar_split_clause,[],[f14,f4044]) ).

fof(f14,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Odistrib__lattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

fof(f3945,plain,
    ( ~ spl0_113
    | spl0_544
    | ~ spl0_187
    | ~ spl0_311 ),
    inference(avatar_split_clause,[],[f3887,f2398,f1579,f3943,f1247]) ).

fof(f1247,plain,
    ( spl0_113
  <=> class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).

fof(f3943,plain,
    ( spl0_544
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).

fof(f3887,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_Complex_Ocomplex)
        | ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) )
    | ~ spl0_187
    | ~ spl0_311 ),
    inference(superposition,[],[f1580,f2399]) ).

fof(f3923,plain,
    spl0_543,
    inference(avatar_split_clause,[],[f499,f3921]) ).

fof(f3921,plain,
    ( spl0_543
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X5,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).

fof(f499,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osmult(X5,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_0) ).

fof(f3919,plain,
    spl0_542,
    inference(avatar_split_clause,[],[f411,f3917]) ).

fof(f3917,plain,
    ( spl0_542
  <=> ! [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_542])]) ).

fof(f411,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(f3915,plain,
    spl0_541,
    inference(avatar_split_clause,[],[f261,f3913]) ).

fof(f261,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) = c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__left_0) ).

fof(f3911,plain,
    spl0_540,
    inference(avatar_split_clause,[],[f260,f3909]) ).

fof(f260,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Otimes__class_Otimes(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__smult__right_0) ).

fof(f3907,plain,
    spl0_539,
    inference(avatar_split_clause,[],[f259,f3905]) ).

fof(f259,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X3,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X1,X3,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

fof(f3884,plain,
    spl0_538,
    inference(avatar_split_clause,[],[f251,f3882]) ).

fof(f251,axiom,
    ! [X0,X1,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_Polynomial_Osmult(X5,X12,X0),X0),X1) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).

fof(f3880,plain,
    spl0_537,
    inference(avatar_split_clause,[],[f222,f3878]) ).

fof(f222,axiom,
    ! [X2,X0,X1] :
      ( ~ class_SEQ_Obanach(X0)
      | ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__exp__exp_0) ).

fof(f3876,plain,
    spl0_536,
    inference(avatar_split_clause,[],[f196,f3874]) ).

fof(f3874,plain,
    ( spl0_536
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).

fof(f196,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

fof(f3872,plain,
    spl0_535,
    inference(avatar_split_clause,[],[f162,f3870]) ).

fof(f162,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__cancel_0) ).

fof(f3868,plain,
    spl0_534,
    inference(avatar_split_clause,[],[f159,f3866]) ).

fof(f3866,plain,
    ( spl0_534
  <=> ! [X0,X12,X5,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).

fof(f159,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult__iff_1) ).

fof(f3864,plain,
    spl0_533,
    inference(avatar_split_clause,[],[f158,f3862]) ).

fof(f158,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_1) ).

fof(f3860,plain,
    spl0_532,
    inference(avatar_split_clause,[],[f157,f3858]) ).

fof(f157,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_2) ).

fof(f3856,plain,
    spl0_531,
    inference(avatar_split_clause,[],[f139,f3854]) ).

fof(f3854,plain,
    ( spl0_531
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
        | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).

fof(f139,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_4) ).

fof(f3852,plain,
    spl0_530,
    inference(avatar_split_clause,[],[f126,f3850]) ).

fof(f3850,plain,
    ( spl0_530
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).

fof(f126,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

fof(f3848,plain,
    spl0_529,
    inference(avatar_split_clause,[],[f125,f3846]) ).

fof(f3846,plain,
    ( spl0_529
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).

fof(f125,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X1,X0),c_HOL_Otimes__class_Otimes(X2,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

fof(f3838,plain,
    spl0_528,
    inference(avatar_split_clause,[],[f100,f3836]) ).

fof(f100,axiom,
    ! [X0,X15,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(X5,X12,X0),X0),X15) = c_HOL_Otimes__class_Otimes(X5,hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__smult_0) ).

fof(f3834,plain,
    spl0_527,
    inference(avatar_split_clause,[],[f82,f3832]) ).

fof(f82,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

fof(f3830,plain,
    spl0_526,
    inference(avatar_split_clause,[],[f70,f3828]) ).

fof(f70,axiom,
    ! [X2,X0,X1] :
      ( ~ class_SEQ_Obanach(X0)
      | ~ class_RealVector_Oreal__normed__field(X0)
      | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(X1,X2,X0),X0) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(X1,X0),c_Transcendental_Oexp(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__diff_0) ).

fof(f3826,plain,
    spl0_525,
    inference(avatar_split_clause,[],[f68,f3824]) ).

fof(f68,axiom,
    ! [X28,X0,X1,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0),X1) = hAPP(c_Polynomial_Opoly(X12,X0),c_HOL_Oplus__class_Oplus(X28,X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__offset__poly_0) ).

fof(f3822,plain,
    spl0_524,
    inference(avatar_split_clause,[],[f57,f3820]) ).

fof(f57,axiom,
    ! [X2,X0,X1,X7,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X7,X25,X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X7,X2,tc_Polynomial_Opoly(X0)),X25,tc_Polynomial_Opoly(X0)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_0) ).

fof(f3818,plain,
    spl0_523,
    inference(avatar_split_clause,[],[f56,f3816]) ).

fof(f56,axiom,
    ! [X0,X5,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pCons_0) ).

fof(f3814,plain,
    spl0_522,
    inference(avatar_split_clause,[],[f54,f3812]) ).

fof(f3812,plain,
    ( spl0_522
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Oidom(X0)
        | X5 = X6
        | c_HOL_Ouminus__class_Ouminus(X6,X0) = X5
        | c_HOL_Otimes__class_Otimes(X5,X5,X0) != c_HOL_Otimes__class_Otimes(X6,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).

fof(f54,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | X5 = X6
      | c_HOL_Ouminus__class_Ouminus(X6,X0) = X5
      | c_HOL_Otimes__class_Otimes(X5,X5,X0) != c_HOL_Otimes__class_Otimes(X6,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

fof(f3767,plain,
    ( ~ spl0_22
    | spl0_521
    | ~ spl0_187
    | ~ spl0_310 ),
    inference(avatar_split_clause,[],[f3709,f2366,f1579,f3765,f792]) ).

fof(f792,plain,
    ( spl0_22
  <=> class_Ring__and__Field_Odvd(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f3765,plain,
    ( spl0_521
  <=> ! [X0] : c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).

fof(f2366,plain,
    ( spl0_310
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).

fof(f3709,plain,
    ( ! [X0] :
        ( c_Ring__and__Field_Odvd__class_Odvd(X0,X0,tc_nat)
        | ~ class_Ring__and__Field_Odvd(tc_nat) )
    | ~ spl0_187
    | ~ spl0_310 ),
    inference(superposition,[],[f1580,f2367]) ).

fof(f2367,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
    | ~ spl0_310 ),
    inference(avatar_component_clause,[],[f2366]) ).

fof(f3741,plain,
    spl0_520,
    inference(avatar_split_clause,[],[f490,f3739]) ).

fof(f490,axiom,
    ! [X12] :
      ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X12))
      | c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X12),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_1) ).

fof(f3737,plain,
    spl0_519,
    inference(avatar_split_clause,[],[f471,f3735]) ).

fof(f471,axiom,
    ! [X31,X0,X12] :
      ( ~ class_HOL_Ozero(X0)
      | hBOOL(hAPP(X31,X12))
      | ~ hBOOL(hAPP(X31,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0))))
      | hBOOL(hAPP(X31,c_Polynomial_Osko__Polynomial__XpCons__induct__1__2(X31,X0))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__induct_0) ).

fof(f3733,plain,
    spl0_518,
    inference(avatar_split_clause,[],[f448,f3731]) ).

fof(f448,axiom,
    ! [X0,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X13,X0) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(X0),tc_Polynomial_Opoly(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__divmod__0_0) ).

fof(f3729,plain,
    spl0_517,
    inference(avatar_split_clause,[],[f378,f3727]) ).

fof(f378,axiom,
    ! [X0,X5,X30] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) = c_HOL_Oplus__class_Oplus(X30,c_HOL_Otimes__class_Otimes(X5,X30,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

fof(f3706,plain,
    spl0_516,
    inference(avatar_split_clause,[],[f377,f3704]) ).

fof(f377,axiom,
    ! [X0,X5,X30] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X30,X0),X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X5,c_HOL_Oone__class_Oone(X0),X0),X30,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

fof(f3702,plain,
    spl0_515,
    inference(avatar_split_clause,[],[f283,f3700]) ).

fof(f3700,plain,
    ( spl0_515
  <=> ! [X5,X0,X6,X1] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | X5 = X6
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_RealVector_OscaleR__class_OscaleR(X5,X1,X0) != c_RealVector_OscaleR__class_OscaleR(X6,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).

fof(f283,axiom,
    ! [X0,X1,X6,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | X5 = X6
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_RealVector_OscaleR__class_OscaleR(X5,X1,X0) != c_RealVector_OscaleR__class_OscaleR(X6,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).

fof(f3698,plain,
    spl0_514,
    inference(avatar_split_clause,[],[f225,f3696]) ).

fof(f225,axiom,
    ! [X0,X1,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | hAPP(c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X1) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Opoly(X12,X0),X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__minus_0) ).

fof(f3694,plain,
    spl0_513,
    inference(avatar_split_clause,[],[f188,f3692]) ).

fof(f188,axiom,
    ! [X28,X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X28,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__single_0) ).

fof(f3690,plain,
    spl0_512,
    inference(avatar_split_clause,[],[f156,f3688]) ).

fof(f156,axiom,
    ! [X0,X15,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | hAPP(c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0),X15) = c_HOL_Ouminus__class_Ouminus(hAPP(c_Polynomial_Ocoeff(X12,X0),X15),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__minus_0) ).

fof(f3579,plain,
    ( spl0_511
    | ~ spl0_66
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1770,f1677,f1012,f3577]) ).

fof(f3577,plain,
    ( spl0_511
  <=> ! [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_511])]) ).

fof(f1012,plain,
    ( spl0_66
  <=> class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).

fof(f1677,plain,
    ( spl0_211
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).

fof(f1770,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
    | ~ spl0_66
    | ~ spl0_211 ),
    inference(resolution,[],[f1678,f1014]) ).

fof(f1014,plain,
    ( class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal)
    | ~ spl0_66 ),
    inference(avatar_component_clause,[],[f1012]) ).

fof(f1678,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 )
    | ~ spl0_211 ),
    inference(avatar_component_clause,[],[f1677]) ).

fof(f3535,plain,
    ( spl0_510
    | ~ spl0_106
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1769,f1677,f1212,f3533]) ).

fof(f1212,plain,
    ( spl0_106
  <=> class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).

fof(f1769,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_106
    | ~ spl0_211 ),
    inference(resolution,[],[f1678,f1214]) ).

fof(f1214,plain,
    ( class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex)
    | ~ spl0_106 ),
    inference(avatar_component_clause,[],[f1212]) ).

fof(f3496,plain,
    ( spl0_509
    | ~ spl0_21
    | ~ spl0_211 ),
    inference(avatar_split_clause,[],[f1768,f1677,f787,f3494]) ).

fof(f3494,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(f787,plain,
    ( spl0_21
  <=> class_OrderedGroup_Omonoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f1768,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) = X0
    | ~ spl0_21
    | ~ spl0_211 ),
    inference(resolution,[],[f1678,f789]) ).

fof(f789,plain,
    ( class_OrderedGroup_Omonoid__add(tc_nat)
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f787]) ).

fof(f3492,plain,
    ( spl0_508
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_507 ),
    inference(avatar_split_clause,[],[f3488,f3485,f2698,f1267,f3490]) ).

fof(f3485,plain,
    ( spl0_507
  <=> ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).

fof(f3488,plain,
    ( ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1
    | ~ spl0_117
    | ~ spl0_361
    | ~ spl0_507 ),
    inference(forward_demodulation,[],[f3486,f2837]) ).

fof(f3486,plain,
    ( ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1
    | ~ spl0_507 ),
    inference(avatar_component_clause,[],[f3485]) ).

fof(f3487,plain,
    spl0_507,
    inference(avatar_split_clause,[],[f494,f3485]) ).

fof(f494,axiom,
    ! [X1] : hAPP(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),tc_Complex_Ocomplex),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mpoly__base__conv_I3_J_0) ).

fof(f3483,plain,
    spl0_506,
    inference(avatar_split_clause,[],[f452,f3481]) ).

fof(f452,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Oorder(X5,X12,X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(X12,X0),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_2) ).

fof(f3479,plain,
    spl0_505,
    inference(avatar_split_clause,[],[f450,f3477]) ).

fof(f3477,plain,
    ( spl0_505
  <=> ! [X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Ocoeff(X12,X0),c_Polynomial_Odegree(X12,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).

fof(f450,axiom,
    ! [X0,X12] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(X0) != hAPP(c_Polynomial_Ocoeff(X12,X0),c_Polynomial_Odegree(X12,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_leading__coeff__0__iff_0) ).

fof(f3475,plain,
    spl0_504,
    inference(avatar_split_clause,[],[f422,f3473]) ).

fof(f422,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

fof(f3471,plain,
    spl0_503,
    inference(avatar_split_clause,[],[f421,f3469]) ).

fof(f421,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).

fof(f3467,plain,
    spl0_502,
    inference(avatar_split_clause,[],[f417,f3465]) ).

fof(f417,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(X5,X0),c_HOL_Osgn__class_Osgn(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).

fof(f3463,plain,
    spl0_501,
    inference(avatar_split_clause,[],[f416,f3461]) ).

fof(f416,axiom,
    ! [X2,X0,X1] :
      ( ~ class_RealVector_Oreal__normed__div__algebra(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__mult_0) ).

fof(f3459,plain,
    spl0_500,
    inference(avatar_split_clause,[],[f413,f3457]) ).

fof(f3457,plain,
    ( spl0_500
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).

fof(f413,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).

fof(f3455,plain,
    spl0_499,
    inference(avatar_split_clause,[],[f404,f3453]) ).

fof(f404,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).

fof(f3451,plain,
    ( spl0_498
    | ~ spl0_66
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1766,f1673,f1012,f3449]) ).

fof(f3449,plain,
    ( spl0_498
  <=> ! [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_498])]) ).

fof(f1673,plain,
    ( spl0_210
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).

fof(f1766,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_66
    | ~ spl0_210 ),
    inference(resolution,[],[f1674,f1014]) ).

fof(f1674,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Omonoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
    | ~ spl0_210 ),
    inference(avatar_component_clause,[],[f1673]) ).

fof(f3447,plain,
    spl0_497,
    inference(avatar_split_clause,[],[f372,f3445]) ).

fof(f372,axiom,
    ! [X0,X6,X13] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X6,X13,X0),X13,X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

fof(f3443,plain,
    spl0_496,
    inference(avatar_split_clause,[],[f352,f3441]) ).

fof(f3441,plain,
    ( spl0_496
  <=> ! [X6,X0,X5,X1] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_RealVector_OscaleR__class_OscaleR(X6,X1,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).

fof(f352,axiom,
    ! [X0,X1,X6,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_RealVector_OscaleR__class_OscaleR(X6,X1,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).

fof(f3439,plain,
    spl0_495,
    inference(avatar_split_clause,[],[f351,f3437]) ).

fof(f351,axiom,
    ! [X0,X6,X5,X25] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).

fof(f3435,plain,
    spl0_494,
    inference(avatar_split_clause,[],[f337,f3433]) ).

fof(f337,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__right_0) ).

fof(f3431,plain,
    spl0_493,
    inference(avatar_split_clause,[],[f332,f3429]) ).

fof(f332,axiom,
    ! [X2,X0,X1,X25] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(X25,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OscaleR_0) ).

fof(f3427,plain,
    spl0_492,
    inference(avatar_split_clause,[],[f312,f3425]) ).

fof(f3425,plain,
    ( spl0_492
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).

fof(f312,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Otimes__class_Otimes(X5,X6,X0) != c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

fof(f3423,plain,
    spl0_491,
    inference(avatar_split_clause,[],[f310,f3421]) ).

fof(f3421,plain,
    ( spl0_491
  <=> ! [X5,X0,X6] :
        ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Otimes__class_Otimes(X5,X6,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).

fof(f310,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Otimes__class_Otimes(X5,X6,X0) != c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

fof(f3419,plain,
    spl0_490,
    inference(avatar_split_clause,[],[f264,f3417]) ).

fof(f264,axiom,
    ! [X0,X6,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(X5,c_Polynomial_Osmult(X6,X12,X0),X0) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(X5,X6,X0),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__smult_0) ).

fof(f3415,plain,
    spl0_489,
    inference(avatar_split_clause,[],[f250,f3413]) ).

fof(f250,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X1,X0),c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).

fof(f3411,plain,
    spl0_488,
    inference(avatar_split_clause,[],[f249,f3409]) ).

fof(f249,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).

fof(f3407,plain,
    ( spl0_487
    | ~ spl0_106
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1765,f1673,f1212,f3405]) ).

fof(f1765,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_106
    | ~ spl0_210 ),
    inference(resolution,[],[f1674,f1214]) ).

fof(f3403,plain,
    spl0_486,
    inference(avatar_split_clause,[],[f246,f3401]) ).

fof(f246,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).

fof(f3399,plain,
    spl0_485,
    inference(avatar_split_clause,[],[f220,f3397]) ).

fof(f3397,plain,
    ( spl0_485
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_RealVector_Oreal__algebra(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).

fof(f220,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_RealVector_Oreal__algebra(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) = c_HOL_Otimes__class_Otimes(X1,c_RealVector_OscaleR__class_OscaleR(X5,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).

fof(f3395,plain,
    spl0_484,
    inference(avatar_split_clause,[],[f219,f3393]) ).

fof(f3393,plain,
    ( spl0_484
  <=> ! [X0,X5,X2,X1] :
        ( ~ class_RealVector_Oreal__algebra(X0)
        | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).

fof(f219,axiom,
    ! [X2,X0,X1,X5] :
      ( ~ class_RealVector_Oreal__algebra(X0)
      | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X2,X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).

fof(f3391,plain,
    spl0_483,
    inference(avatar_split_clause,[],[f217,f3389]) ).

fof(f217,axiom,
    ! [X0,X6,X5,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_RealVector_OscaleR__class_OscaleR(X25,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).

fof(f3387,plain,
    spl0_482,
    inference(avatar_split_clause,[],[f215,f3385]) ).

fof(f215,axiom,
    ! [X0,X6,X5,X25] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(X25,X5,X0),X6,X0) = c_RealVector_OscaleR__class_OscaleR(X25,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).

fof(f3383,plain,
    spl0_481,
    inference(avatar_split_clause,[],[f183,f3381]) ).

fof(f183,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).

fof(f3379,plain,
    spl0_480,
    inference(avatar_split_clause,[],[f181,f3377]) ).

fof(f181,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).

fof(f3375,plain,
    spl0_479,
    inference(avatar_split_clause,[],[f180,f3373]) ).

fof(f180,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(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_compl__sup_0) ).

fof(f3371,plain,
    spl0_478,
    inference(avatar_split_clause,[],[f178,f3369]) ).

fof(f178,axiom,
    ! [X0,X6,X15,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Osmult(X5,c_Polynomial_Omonom(X6,X15,X0),X0) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(X5,X6,X0),X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__monom_0) ).

fof(f3367,plain,
    spl0_477,
    inference(avatar_split_clause,[],[f163,f3365]) ).

fof(f3365,plain,
    ( spl0_477
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).

fof(f163,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

fof(f3363,plain,
    ( spl0_476
    | ~ spl0_21
    | ~ spl0_210 ),
    inference(avatar_split_clause,[],[f1764,f1673,f787,f3361]) ).

fof(f3361,plain,
    ( spl0_476
  <=> ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).

fof(f1764,plain,
    ( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X0
    | ~ spl0_21
    | ~ spl0_210 ),
    inference(resolution,[],[f1674,f789]) ).

fof(f3359,plain,
    spl0_475,
    inference(avatar_split_clause,[],[f147,f3357]) ).

fof(f147,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X3,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

fof(f3355,plain,
    spl0_474,
    inference(avatar_split_clause,[],[f146,f3353]) ).

fof(f146,axiom,
    ! [X0,X22,X23,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

fof(f3351,plain,
    spl0_473,
    inference(avatar_split_clause,[],[f143,f3349]) ).

fof(f143,axiom,
    ! [X21,X0,X22,X20] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

fof(f3347,plain,
    spl0_472,
    inference(avatar_split_clause,[],[f142,f3345]) ).

fof(f142,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

fof(f3343,plain,
    spl0_471,
    inference(avatar_split_clause,[],[f122,f3341]) ).

fof(f122,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(X5,X6,X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

fof(f3339,plain,
    spl0_470,
    inference(avatar_split_clause,[],[f121,f3337]) ).

fof(f3337,plain,
    ( spl0_470
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).

fof(f121,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

fof(f3335,plain,
    spl0_469,
    inference(avatar_split_clause,[],[f120,f3333]) ).

fof(f3333,plain,
    ( spl0_469
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).

fof(f120,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

fof(f3331,plain,
    spl0_468,
    inference(avatar_split_clause,[],[f119,f3329]) ).

fof(f119,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

fof(f3327,plain,
    spl0_467,
    inference(avatar_split_clause,[],[f118,f3325]) ).

fof(f118,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X2,X3,X0),X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,c_Lattices_Oupper__semilattice__class_Osup(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

fof(f3323,plain,
    spl0_466,
    inference(avatar_split_clause,[],[f109,f3321]) ).

fof(f109,axiom,
    ! [X0,X27,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(X13,c_HOL_Oplus__class_Oplus(X5,X27,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

fof(f3319,plain,
    ( spl0_465
    | ~ spl0_38
    | ~ spl0_205 ),
    inference(avatar_split_clause,[],[f1761,f1653,f872,f3316]) ).

fof(f3316,plain,
    ( spl0_465
  <=> 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_465])]) ).

fof(f1653,plain,
    ( spl0_205
  <=> ! [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_205])]) ).

fof(f1761,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_38
    | ~ spl0_205 ),
    inference(resolution,[],[f1654,f874]) ).

fof(f1654,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_205 ),
    inference(avatar_component_clause,[],[f1653]) ).

fof(f3314,plain,
    spl0_464,
    inference(avatar_split_clause,[],[f108,f3312]) ).

fof(f108,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

fof(f3310,plain,
    spl0_463,
    inference(avatar_split_clause,[],[f107,f3308]) ).

fof(f107,axiom,
    ! [X0,X27,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X13,X27,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X13,X0),X27,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

fof(f3306,plain,
    spl0_462,
    inference(avatar_split_clause,[],[f106,f3304]) ).

fof(f3304,plain,
    ( spl0_462
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).

fof(f106,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Oab__semigroup__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

fof(f3302,plain,
    spl0_461,
    inference(avatar_split_clause,[],[f105,f3300]) ).

fof(f105,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

fof(f3298,plain,
    spl0_460,
    inference(avatar_split_clause,[],[f103,f3296]) ).

fof(f103,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

fof(f3294,plain,
    spl0_459,
    inference(avatar_split_clause,[],[f102,f3292]) ).

fof(f102,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X13,X0),X0) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

fof(f3290,plain,
    spl0_458,
    inference(avatar_split_clause,[],[f86,f3288]) ).

fof(f86,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__assoc_0) ).

fof(f3286,plain,
    spl0_457,
    inference(avatar_split_clause,[],[f85,f3284]) ).

fof(f85,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X1,c_Polynomial_Opoly__gcd(X2,X3,X0),X0) = c_Polynomial_Opoly__gcd(X2,c_Polynomial_Opoly__gcd(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__left__commute_0) ).

fof(f3282,plain,
    spl0_456,
    inference(avatar_split_clause,[],[f61,f3280]) ).

fof(f61,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(X5,X6,X0),c_Lattices_Olower__semilattice__class_Oinf(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

fof(f3278,plain,
    spl0_455,
    inference(avatar_split_clause,[],[f53,f3276]) ).

fof(f53,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ominus__class_Ominus(X2,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).

fof(f3274,plain,
    ( spl0_454
    | ~ spl0_108
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1756,f1645,f1222,f3272]) ).

fof(f1645,plain,
    ( spl0_203
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).

fof(f1756,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_108
    | ~ spl0_203 ),
    inference(resolution,[],[f1646,f1224]) ).

fof(f1646,plain,
    ( ! [X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 )
    | ~ spl0_203 ),
    inference(avatar_component_clause,[],[f1645]) ).

fof(f3270,plain,
    spl0_453,
    inference(avatar_split_clause,[],[f46,f3268]) ).

fof(f3268,plain,
    ( spl0_453
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).

fof(f46,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

fof(f3266,plain,
    spl0_452,
    inference(avatar_split_clause,[],[f45,f3264]) ).

fof(f3264,plain,
    ( spl0_452
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).

fof(f45,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

fof(f3262,plain,
    spl0_451,
    inference(avatar_split_clause,[],[f44,f3260]) ).

fof(f44,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

fof(f3258,plain,
    spl0_450,
    inference(avatar_split_clause,[],[f43,f3256]) ).

fof(f43,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X2,X3,X0),X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,c_Lattices_Olower__semilattice__class_Oinf(X1,X3,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

fof(f3254,plain,
    spl0_449,
    inference(avatar_split_clause,[],[f32,f3252]) ).

fof(f3252,plain,
    ( spl0_449
  <=> ! [X2,X18,X0,X16,X17,X19,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X18 = X19
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X19,X16,X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X18,X17,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).

fof(f32,axiom,
    ! [X2,X0,X18,X1,X19,X16,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X18 = X19
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X19,X16,X0)
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X18,X17,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).

fof(f3250,plain,
    spl0_448,
    inference(avatar_split_clause,[],[f31,f3248]) ).

fof(f3248,plain,
    ( spl0_448
  <=> ! [X2,X17,X0,X18,X16,X19,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X16 = X17
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X19,X16,X0)
        | ~ c_Polynomial_Opdivmod__rel(X1,X2,X18,X17,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).

fof(f31,axiom,
    ! [X2,X0,X1,X18,X19,X16,X17] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X16 = X17
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X19,X16,X0)
      | ~ c_Polynomial_Opdivmod__rel(X1,X2,X18,X17,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).

fof(f3231,plain,
    ( spl0_447
    | ~ spl0_68
    | ~ spl0_203 ),
    inference(avatar_split_clause,[],[f1755,f1645,f1022,f3229]) ).

fof(f3229,plain,
    ( spl0_447
  <=> ! [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_447])]) ).

fof(f1755,plain,
    ( ! [X0] : c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_68
    | ~ spl0_203 ),
    inference(resolution,[],[f1646,f1024]) ).

fof(f3212,plain,
    ( spl0_446
    | ~ spl0_100
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1753,f1641,f1182,f3210]) ).

fof(f3210,plain,
    ( spl0_446
  <=> ! [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_446])]) ).

fof(f1753,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Ominus__class_Ominus(X0,X0,tc_Complex_Ocomplex)
    | ~ spl0_100
    | ~ spl0_202 ),
    inference(resolution,[],[f1642,f1184]) ).

fof(f3200,plain,
    ( spl0_444
    | ~ spl0_445 ),
    inference(avatar_split_clause,[],[f510,f3197,f3194]) ).

fof(f3194,plain,
    ( spl0_444
  <=> ! [X1] : c_HOL_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),t_a),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).

fof(f3197,plain,
    ( spl0_445
  <=> class_Ring__and__Field_Ocomm__semiring__0(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).

fof(f510,axiom,
    ! [X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(t_a)
      | c_HOL_Ozero__class_Ozero(t_a) = hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(t_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),t_a),t_a),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_basic__cqe__conv1_I3_J_0) ).

fof(f3192,plain,
    spl0_443,
    inference(avatar_split_clause,[],[f445,f3190]) ).

fof(f445,axiom,
    ! [X0,X7,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_0) ).

fof(f3188,plain,
    spl0_442,
    inference(avatar_split_clause,[],[f384,f3186]) ).

fof(f3186,plain,
    ( spl0_442
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Odegree(X12,X0) != c_HOL_Ozero__class_Ozero(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(X12,X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).

fof(f384,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Odegree(X12,X0) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osynthetic__div(X12,X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_1) ).

fof(f3184,plain,
    spl0_441,
    inference(avatar_split_clause,[],[f383,f3182]) ).

fof(f3182,plain,
    ( spl0_441
  <=> ! [X13,X0,X12] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_Polynomial_Odegree(X12,X0) = c_HOL_Ozero__class_Ozero(tc_nat)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osynthetic__div(X12,X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).

fof(f383,axiom,
    ! [X0,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Odegree(X12,X0) = c_HOL_Ozero__class_Ozero(tc_nat)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Osynthetic__div(X12,X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__eq__0__iff_0) ).

fof(f3180,plain,
    spl0_440,
    inference(avatar_split_clause,[],[f359,f3178]) ).

fof(f359,axiom,
    ! [X0,X30] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X30,X30,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(X0),c_HOL_Oone__class_Oone(X0),X0),X30,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

fof(f3176,plain,
    ( spl0_439
    | ~ spl0_59
    | ~ spl0_202 ),
    inference(avatar_split_clause,[],[f1752,f1641,f977,f3174]) ).

fof(f3174,plain,
    ( spl0_439
  <=> ! [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_439])]) ).

fof(f1752,plain,
    ( ! [X0] : c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X0,tc_RealDef_Oreal)
    | ~ spl0_59
    | ~ spl0_202 ),
    inference(resolution,[],[f1642,f979]) ).

fof(f3172,plain,
    spl0_438,
    inference(avatar_split_clause,[],[f341,f3170]) ).

fof(f341,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X13,X0),c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

fof(f3168,plain,
    spl0_437,
    inference(avatar_split_clause,[],[f340,f3166]) ).

fof(f340,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X13,X5,X0),c_HOL_Otimes__class_Otimes(X13,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).

fof(f3164,plain,
    spl0_436,
    inference(avatar_split_clause,[],[f336,f3162]) ).

fof(f336,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X0)
      | c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(X5,X0),X12,X0) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(X5,X12,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__minus__left_0) ).

fof(f3160,plain,
    spl0_435,
    inference(avatar_split_clause,[],[f326,f3158]) ).

fof(f3158,plain,
    ( spl0_435
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Polynomial_Opos__poly(X12,X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X5,X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).

fof(f326,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Polynomial_Opos__poly(X12,X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(X5,X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_0) ).

fof(f3156,plain,
    spl0_434,
    inference(avatar_split_clause,[],[f253,f3154]) ).

fof(f3154,plain,
    ( spl0_434
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X3,X0) = X1
        | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) != X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).

fof(f253,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X3,X0) = X1
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) != X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

fof(f3152,plain,
    spl0_433,
    inference(avatar_split_clause,[],[f210,f3150]) ).

fof(f210,axiom,
    ! [X0,X15,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(X5,X15,X0),tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(X5,X0),X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__monom_0) ).

fof(f3148,plain,
    spl0_432,
    inference(avatar_split_clause,[],[f208,f3146]) ).

fof(f3146,plain,
    ( spl0_432
  <=> ! [X0,X12] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_Polynomial_Opos__poly(X12,X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_Polynomial_Opos__poly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).

fof(f208,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_Polynomial_Opos__poly(X12,X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_Polynomial_Opos__poly(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__total_0) ).

fof(f3144,plain,
    spl0_431,
    inference(avatar_split_clause,[],[f204,f3142]) ).

fof(f3142,plain,
    ( spl0_431
  <=> ! [X0,X3,X2,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X2 = X3
        | c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).

fof(f204,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X2 = X3
      | c_HOL_Oplus__class_Oplus(X1,X2,X0) != c_HOL_Oplus__class_Oplus(X1,X3,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

fof(f3140,plain,
    spl0_430,
    inference(avatar_split_clause,[],[f165,f3138]) ).

fof(f3138,plain,
    ( spl0_430
  <=> ! [X13,X0,X12,X5] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_Polynomial_OpCons(X5,X12,X0) != c_Polynomial_Osmult(X13,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).

fof(f165,axiom,
    ! [X0,X5,X12,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_Polynomial_OpCons(X5,X12,X0) != c_Polynomial_Osmult(X13,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__unique__lemma_0) ).

fof(f3136,plain,
    spl0_429,
    inference(avatar_split_clause,[],[f140,f3134]) ).

fof(f3134,plain,
    ( spl0_429
  <=> ! [X6,X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | X5 = X6
        | c_HOL_Ozero__class_Ozero(X0) = X6
        | c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).

fof(f140,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X5 = X6
      | c_HOL_Ozero__class_Ozero(X0) = X6
      | c_HOL_Oone__class_Oone(X0) != c_HOL_Oinverse__class_Odivide(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

fof(f3132,plain,
    ( spl0_428
    | ~ spl0_38
    | ~ spl0_200 ),
    inference(avatar_split_clause,[],[f1751,f1632,f872,f3129]) ).

fof(f3129,plain,
    ( spl0_428
  <=> 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_428])]) ).

fof(f1632,plain,
    ( spl0_200
  <=> ! [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_200])]) ).

fof(f1751,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_38
    | ~ spl0_200 ),
    inference(resolution,[],[f1633,f874]) ).

fof(f1633,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_200 ),
    inference(avatar_component_clause,[],[f1632]) ).

fof(f3127,plain,
    spl0_427,
    inference(avatar_split_clause,[],[f136,f3125]) ).

fof(f136,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Polynomial_Osmult(X5,X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_1) ).

fof(f3123,plain,
    spl0_426,
    inference(avatar_split_clause,[],[f101,f3121]) ).

fof(f101,axiom,
    ! [X0,X15,X5,X30] :
      ( ~ class_HOL_Ozero(X0)
      | X15 = X30
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X30,X0),X0),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_1) ).

fof(f3119,plain,
    spl0_425,
    inference(avatar_split_clause,[],[f64,f3117]) ).

fof(f64,axiom,
    ! [X0,X12] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,X0),X0,X0)
      | c_Polynomial_Odegree(X12,X0) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_constant__degree_0) ).

fof(f3115,plain,
    spl0_424,
    inference(avatar_split_clause,[],[f63,f3113]) ).

fof(f3113,plain,
    ( spl0_424
  <=> ! [X0,X12] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_Polynomial_Odegree(X12,X0) != c_HOL_Ozero__class_Ozero(tc_nat)
        | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,X0),X0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).

fof(f63,axiom,
    ! [X0,X12] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_Polynomial_Odegree(X12,X0) != c_HOL_Ozero__class_Ozero(tc_nat)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,X0),X0,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_constant__degree_1) ).

fof(f3099,plain,
    ( spl0_423
    | ~ spl0_92
    | ~ spl0_199 ),
    inference(avatar_split_clause,[],[f1750,f1628,f1142,f3096]) ).

fof(f3096,plain,
    ( spl0_423
  <=> 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_423])]) ).

fof(f1628,plain,
    ( spl0_199
  <=> ! [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_199])]) ).

fof(f1750,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_92
    | ~ spl0_199 ),
    inference(resolution,[],[f1629,f1144]) ).

fof(f1629,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_199 ),
    inference(avatar_component_clause,[],[f1628]) ).

fof(f3066,plain,
    ( spl0_422
    | ~ spl0_55
    | ~ spl0_197 ),
    inference(avatar_split_clause,[],[f1745,f1620,f957,f3063]) ).

fof(f3063,plain,
    ( spl0_422
  <=> 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_422])]) ).

fof(f1620,plain,
    ( spl0_197
  <=> ! [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_197])]) ).

fof(f1745,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_55
    | ~ spl0_197 ),
    inference(resolution,[],[f1621,f959]) ).

fof(f1621,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_197 ),
    inference(avatar_component_clause,[],[f1620]) ).

fof(f3029,plain,
    ( spl0_421
    | ~ spl0_108
    | ~ spl0_196 ),
    inference(avatar_split_clause,[],[f1743,f1616,f1222,f3026]) ).

fof(f3026,plain,
    ( spl0_421
  <=> 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_421])]) ).

fof(f1616,plain,
    ( spl0_196
  <=> ! [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_196])]) ).

fof(f1743,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_108
    | ~ spl0_196 ),
    inference(resolution,[],[f1617,f1224]) ).

fof(f1617,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_196 ),
    inference(avatar_component_clause,[],[f1616]) ).

fof(f3016,plain,
    spl0_420,
    inference(avatar_split_clause,[],[f489,f3014]) ).

fof(f489,axiom,
    ! [X12] :
      ( c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex)
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__1(X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra_0) ).

fof(f3012,plain,
    spl0_419,
    inference(avatar_split_clause,[],[f475,f3010]) ).

fof(f475,axiom,
    ! [X0,X1,X7,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
      | ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__def_1) ).

fof(f3008,plain,
    spl0_418,
    inference(avatar_split_clause,[],[f474,f3006]) ).

fof(f3006,plain,
    ( spl0_418
  <=> ! [X2,X0,X25,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
        | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X7,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).

fof(f474,axiom,
    ! [X2,X0,X7,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X7
      | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X7,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_0) ).

fof(f3004,plain,
    spl0_417,
    inference(avatar_split_clause,[],[f473,f3002]) ).

fof(f3002,plain,
    ( spl0_417
  <=> ! [X2,X0,X25,X7] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X25
        | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X7,X25,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).

fof(f473,axiom,
    ! [X2,X0,X7,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X25
      | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,X7,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0__iff_1) ).

fof(f3000,plain,
    spl0_416,
    inference(avatar_split_clause,[],[f470,f2998]) ).

fof(f2998,plain,
    ( spl0_416
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).

fof(f470,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X1
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_0) ).

fof(f2996,plain,
    spl0_415,
    inference(avatar_split_clause,[],[f469,f2994]) ).

fof(f2994,plain,
    ( spl0_415
  <=> ! [X2,X0,X1] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).

fof(f469,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X2
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Opoly__gcd(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__zero__iff_1) ).

fof(f2992,plain,
    ( spl0_414
    | ~ spl0_39
    | ~ spl0_195 ),
    inference(avatar_split_clause,[],[f1740,f1612,f877,f2989]) ).

fof(f2989,plain,
    ( spl0_414
  <=> 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_414])]) ).

fof(f877,plain,
    ( spl0_39
  <=> class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f1740,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_39
    | ~ spl0_195 ),
    inference(resolution,[],[f1613,f879]) ).

fof(f879,plain,
    ( class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal)
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f877]) ).

fof(f2987,plain,
    spl0_413,
    inference(avatar_split_clause,[],[f466,f2985]) ).

fof(f2985,plain,
    ( spl0_413
  <=> ! [X0,X12,X28] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).

fof(f466,axiom,
    ! [X28,X0,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__eq__0__iff_0) ).

fof(f2983,plain,
    spl0_412,
    inference(avatar_split_clause,[],[f464,f2981]) ).

fof(f2981,plain,
    ( spl0_412
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X5,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).

fof(f464,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = X12
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X5,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_1) ).

fof(f2979,plain,
    spl0_411,
    inference(avatar_split_clause,[],[f394,f2977]) ).

fof(f394,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

fof(f2975,plain,
    spl0_410,
    inference(avatar_split_clause,[],[f388,f2973]) ).

fof(f2973,plain,
    ( spl0_410
  <=> ! [X0,X12,X7] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | X7 = X12
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).

fof(f388,axiom,
    ! [X0,X7,X12] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | X7 = X12
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X12),X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_0) ).

fof(f2971,plain,
    spl0_409,
    inference(avatar_split_clause,[],[f363,f2969]) ).

fof(f2969,plain,
    ( spl0_409
  <=> ! [X13,X0] :
        ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
        | ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X13,X0),X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).

fof(f363,axiom,
    ! [X0,X13] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X13,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

fof(f2967,plain,
    spl0_408,
    inference(avatar_split_clause,[],[f348,f2965]) ).

fof(f348,axiom,
    ! [X2,X0,X29,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,X2,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_1) ).

fof(f2963,plain,
    spl0_407,
    inference(avatar_split_clause,[],[f347,f2961]) ).

fof(f347,axiom,
    ! [X2,X0,X29,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X29,X1,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X29,c_Polynomial_Opoly__gcd(X1,X2,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__poly__gcd__iff_0) ).

fof(f2959,plain,
    spl0_406,
    inference(avatar_split_clause,[],[f333,f2957]) ).

fof(f2957,plain,
    ( spl0_406
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).

fof(f333,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Olower__semilattice__class_Oinf(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__0__imp__0_0) ).

fof(f2955,plain,
    spl0_405,
    inference(avatar_split_clause,[],[f324,f2953]) ).

fof(f2953,plain,
    ( spl0_405
  <=> ! [X0,X12,X7] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Polynomial_Opos__poly(X12,X0)
        | ~ c_Polynomial_Opos__poly(X7,X0)
        | c_Polynomial_Opos__poly(c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).

fof(f324,axiom,
    ! [X0,X7,X12] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(X12,X0)
      | ~ c_Polynomial_Opos__poly(X7,X0)
      | c_Polynomial_Opos__poly(c_HOL_Otimes__class_Otimes(X12,X7,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__mult_0) ).

fof(f2951,plain,
    spl0_404,
    inference(avatar_split_clause,[],[f223,f2949]) ).

fof(f2949,plain,
    ( spl0_404
  <=> ! [X2,X0,X1] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).

fof(f223,axiom,
    ! [X2,X0,X1] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).

fof(f2947,plain,
    ( spl0_403
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1737,f1608,f1222,f2945]) ).

fof(f1737,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_108
    | ~ spl0_194 ),
    inference(resolution,[],[f1609,f1224]) ).

fof(f2943,plain,
    spl0_402,
    inference(avatar_split_clause,[],[f175,f2941]) ).

fof(f175,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

fof(f2939,plain,
    spl0_401,
    inference(avatar_split_clause,[],[f174,f2937]) ).

fof(f174,axiom,
    ! [X0,X6] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Otimes__class_Otimes(X6,X6,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X6,X0),c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

fof(f2935,plain,
    spl0_400,
    inference(avatar_split_clause,[],[f172,f2933]) ).

fof(f2933,plain,
    ( spl0_400
  <=> ! [X6,X0,X5] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).

fof(f172,axiom,
    ! [X0,X6,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).

fof(f2931,plain,
    spl0_399,
    inference(avatar_split_clause,[],[f170,f2929]) ).

fof(f2929,plain,
    ( spl0_399
  <=> ! [X6,X0,X5] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).

fof(f170,axiom,
    ! [X0,X6,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

fof(f2927,plain,
    spl0_398,
    inference(avatar_split_clause,[],[f164,f2925]) ).

fof(f164,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(X5,X6,X0),X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

fof(f2923,plain,
    spl0_397,
    inference(avatar_split_clause,[],[f127,f2921]) ).

fof(f2921,plain,
    ( spl0_397
  <=> ! [X0,X12,X7] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Polynomial_Opos__poly(X12,X0)
        | ~ c_Polynomial_Opos__poly(X7,X0)
        | c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).

fof(f127,axiom,
    ! [X0,X7,X12] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(X12,X0)
      | ~ c_Polynomial_Opos__poly(X7,X0)
      | c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(X12,X7,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__add_0) ).

fof(f2919,plain,
    spl0_396,
    inference(avatar_split_clause,[],[f81,f2917]) ).

fof(f81,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | c_Ring__and__Field_Odvd__class_Odvd(X12,c_Polynomial_Osmult(X5,X7,X0),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__smult_0) ).

fof(f2915,plain,
    spl0_395,
    inference(avatar_split_clause,[],[f80,f2913]) ).

fof(f80,axiom,
    ! [X0,X7,X5,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X12,X7,tc_Polynomial_Opoly(X0))
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(X5,X12,X0),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__cancel_0) ).

fof(f2911,plain,
    spl0_394,
    inference(avatar_split_clause,[],[f66,f2909]) ).

fof(f2909,plain,
    ( spl0_394
  <=> ! [X6,X0,X5] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).

fof(f66,axiom,
    ! [X0,X6,X5] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).

fof(f2907,plain,
    spl0_393,
    inference(avatar_split_clause,[],[f65,f2905]) ).

fof(f65,axiom,
    ! [X0,X1,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(X5,X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).

fof(f2903,plain,
    ( spl0_392
    | ~ spl0_68
    | ~ spl0_194 ),
    inference(avatar_split_clause,[],[f1736,f1608,f1022,f2901]) ).

fof(f1736,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_68
    | ~ spl0_194 ),
    inference(resolution,[],[f1609,f1024]) ).

fof(f2899,plain,
    spl0_391,
    inference(avatar_split_clause,[],[f42,f2897]) ).

fof(f2897,plain,
    ( spl0_391
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).

fof(f42,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_Lattices_Oupper__semilattice__class_Osup(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__0__imp__0_0) ).

fof(f2895,plain,
    spl0_390,
    inference(avatar_split_clause,[],[f35,f2893]) ).

fof(f35,axiom,
    ! [X0,X5,X13] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X13
      | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(X5,X13,X0),X13,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

fof(f2891,plain,
    spl0_389,
    inference(avatar_split_clause,[],[f4,f2889]) ).

fof(f4,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

fof(f2887,plain,
    spl0_388,
    inference(avatar_split_clause,[],[f3,f2885]) ).

fof(f3,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oring(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

fof(f2878,plain,
    ( spl0_387
    | ~ spl0_29
    | ~ spl0_193 ),
    inference(avatar_split_clause,[],[f1734,f1604,f827,f2876]) ).

fof(f2876,plain,
    ( spl0_387
  <=> ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).

fof(f1734,plain,
    ( ! [X0] : c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X0,tc_bool),tc_bool) = X0
    | ~ spl0_29
    | ~ spl0_193 ),
    inference(resolution,[],[f1605,f829]) ).

fof(f2853,plain,
    ( spl0_386
    | ~ spl0_85
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1733,f1600,f1107,f2850]) ).

fof(f2850,plain,
    ( spl0_386
  <=> 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_386])]) ).

fof(f1107,plain,
    ( spl0_85
  <=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).

fof(f1600,plain,
    ( spl0_192
  <=> ! [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_192])]) ).

fof(f1733,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_85
    | ~ spl0_192 ),
    inference(resolution,[],[f1601,f1109]) ).

fof(f1109,plain,
    ( class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex)
    | ~ spl0_85 ),
    inference(avatar_component_clause,[],[f1107]) ).

fof(f1601,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_192 ),
    inference(avatar_component_clause,[],[f1600]) ).

fof(f2829,plain,
    ( spl0_385
    | ~ spl0_41
    | ~ spl0_192 ),
    inference(avatar_split_clause,[],[f1732,f1600,f887,f2826]) ).

fof(f2826,plain,
    ( spl0_385
  <=> 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_385])]) ).

fof(f887,plain,
    ( spl0_41
  <=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f1732,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_41
    | ~ spl0_192 ),
    inference(resolution,[],[f1601,f889]) ).

fof(f889,plain,
    ( class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal)
    | ~ spl0_41 ),
    inference(avatar_component_clause,[],[f887]) ).

fof(f2792,plain,
    spl0_384,
    inference(avatar_split_clause,[],[f515,f2790]) ).

fof(f2790,plain,
    ( spl0_384
  <=> ! [X0,X12,X7] :
        ( ~ class_Int_Oring__char__0(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X7 = X12
        | c_Polynomial_Opoly(X12,X0) != c_Polynomial_Opoly(X7,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).

fof(f515,axiom,
    ! [X0,X7,X12] :
      ( ~ class_Int_Oring__char__0(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X7 = X12
      | c_Polynomial_Opoly(X12,X0) != c_Polynomial_Opoly(X7,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__eq__iff_0) ).

fof(f2788,plain,
    spl0_383,
    inference(avatar_split_clause,[],[f501,f2786]) ).

fof(f2786,plain,
    ( spl0_383
  <=> ! [X5,X0,X15] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Omonom(X5,X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).

fof(f501,axiom,
    ! [X0,X15,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_Omonom(X5,X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0__iff_0) ).

fof(f2784,plain,
    spl0_382,
    inference(avatar_split_clause,[],[f498,f2782]) ).

fof(f2782,plain,
    ( spl0_382
  <=> ! [X5,X0,X12] :
        ( ~ class_HOL_Ozero(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X5,X12,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).

fof(f498,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) != c_Polynomial_OpCons(X5,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__0__iff_0) ).

fof(f2780,plain,
    ( spl0_381
    | ~ spl0_110
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1731,f1596,f1232,f2778]) ).

fof(f2778,plain,
    ( spl0_381
  <=> ! [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_381])]) ).

fof(f1596,plain,
    ( spl0_191
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).

fof(f1731,plain,
    ( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_110
    | ~ spl0_191 ),
    inference(resolution,[],[f1597,f1234]) ).

fof(f1597,plain,
    ( ! [X0,X5] :
        ( ~ class_Ring__and__Field_Ofield(X0)
        | c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 )
    | ~ spl0_191 ),
    inference(avatar_component_clause,[],[f1596]) ).

fof(f2776,plain,
    spl0_380,
    inference(avatar_split_clause,[],[f488,f2774]) ).

fof(f2774,plain,
    ( spl0_380
  <=> ! [X12] :
        ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X12)
        | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X12)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).

fof(f488,axiom,
    ! [X12] :
      ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__1(X12)
      | c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(X12,tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xfundamental__theorem__of__algebra__alt__2(X12)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fundamental__theorem__of__algebra__alt_0) ).

fof(f2772,plain,
    spl0_379,
    inference(avatar_split_clause,[],[f477,f2770]) ).

fof(f477,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__0__0_0) ).

fof(f2768,plain,
    spl0_378,
    inference(avatar_split_clause,[],[f467,f2766]) ).

fof(f467,axiom,
    ! [X2,X0] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X2,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__0_0) ).

fof(f2764,plain,
    spl0_377,
    inference(avatar_split_clause,[],[f427,f2762]) ).

fof(f2762,plain,
    ( spl0_377
  <=> ! [X2,X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | X1 = X2
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).

fof(f427,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | X1 = X2
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X1,X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

fof(f2760,plain,
    spl0_376,
    inference(avatar_split_clause,[],[f419,f2758]) ).

fof(f2758,plain,
    ( spl0_376
  <=> ! [X5,X0,X6,X15] :
        ( ~ class_HOL_Ozero(X0)
        | X5 = X6
        | c_Polynomial_Omonom(X6,X15,X0) != c_Polynomial_Omonom(X5,X15,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).

fof(f419,axiom,
    ! [X0,X6,X15,X5] :
      ( ~ class_HOL_Ozero(X0)
      | X5 = X6
      | c_Polynomial_Omonom(X6,X15,X0) != c_Polynomial_Omonom(X5,X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__iff_0) ).

fof(f2756,plain,
    spl0_375,
    inference(avatar_split_clause,[],[f401,f2754]) ).

fof(f2754,plain,
    ( spl0_375
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olower__semilattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).

fof(f401,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

fof(f2752,plain,
    spl0_374,
    inference(avatar_split_clause,[],[f400,f2750]) ).

fof(f400,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

fof(f2748,plain,
    spl0_373,
    inference(avatar_split_clause,[],[f370,f2746]) ).

fof(f370,axiom,
    ! [X0,X15,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_Polynomial_Odegree(c_Polynomial_Omonom(X5,X15,X0),X0) = X15 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__monom__eq_0) ).

fof(f2744,plain,
    spl0_372,
    inference(avatar_split_clause,[],[f367,f2742]) ).

fof(f2742,plain,
    ( spl0_372
  <=> ! [X5,X0,X6] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X6,X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).

fof(f367,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X6,X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

fof(f2740,plain,
    spl0_371,
    inference(avatar_split_clause,[],[f366,f2738]) ).

fof(f2738,plain,
    ( spl0_371
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ouminus__class_Ouminus(X5,X0) = X6
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).

fof(f366,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X5,X0) = X6
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).

fof(f2736,plain,
    ( spl0_370
    | ~ spl0_71
    | ~ spl0_191 ),
    inference(avatar_split_clause,[],[f1730,f1596,f1037,f2734]) ).

fof(f2734,plain,
    ( spl0_370
  <=> ! [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_370])]) ).

fof(f1730,plain,
    ( ! [X0] : c_HOL_Oinverse__class_Odivide(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_71
    | ~ spl0_191 ),
    inference(resolution,[],[f1597,f1039]) ).

fof(f2732,plain,
    spl0_369,
    inference(avatar_split_clause,[],[f361,f2730]) ).

fof(f361,axiom,
    ! [X10,X0,X11,X1,X8,X9] : hAPP(X8,hAPP(X9,X1)) = hAPP(c_Fun_Ocomp(X8,X9,X10,X0,X11),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).

fof(f2728,plain,
    spl0_368,
    inference(avatar_split_clause,[],[f319,f2726]) ).

fof(f2726,plain,
    ( spl0_368
  <=> ! [X5,X0,X1] :
        ( ~ class_Int_Onumber__ring(X0)
        | ~ class_Ring__and__Field_Oidom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Oplus__class_Oplus(X1,X5,X0) != X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).

fof(f319,axiom,
    ! [X0,X1,X5] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Oplus__class_Oplus(X1,X5,X0) != X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

fof(f2724,plain,
    spl0_367,
    inference(avatar_split_clause,[],[f257,f2722]) ).

fof(f2722,plain,
    ( spl0_367
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).

fof(f257,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

fof(f2720,plain,
    spl0_366,
    inference(avatar_split_clause,[],[f256,f2718]) ).

fof(f256,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

fof(f2716,plain,
    spl0_365,
    inference(avatar_split_clause,[],[f207,f2714]) ).

fof(f2714,plain,
    ( spl0_365
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X6 = X13
        | c_HOL_Oplus__class_Oplus(X6,X5,X0) != c_HOL_Oplus__class_Oplus(X13,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).

fof(f207,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X6 = X13
      | c_HOL_Oplus__class_Oplus(X6,X5,X0) != c_HOL_Oplus__class_Oplus(X13,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

fof(f2712,plain,
    spl0_364,
    inference(avatar_split_clause,[],[f206,f2710]) ).

fof(f2710,plain,
    ( spl0_364
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
        | X6 = X13
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).

fof(f206,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
      | X6 = X13
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

fof(f2708,plain,
    spl0_363,
    inference(avatar_split_clause,[],[f205,f2706]) ).

fof(f2706,plain,
    ( spl0_363
  <=> ! [X6,X13,X0,X5] :
        ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
        | X6 = X13
        | c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X13,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).

fof(f205,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
      | X6 = X13
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) != c_HOL_Oplus__class_Oplus(X5,X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

fof(f2704,plain,
    spl0_362,
    inference(avatar_split_clause,[],[f187,f2702]) ).

fof(f187,axiom,
    ! [X0,X7] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I1_J_0) ).

fof(f2700,plain,
    spl0_361,
    inference(avatar_split_clause,[],[f132,f2698]) ).

fof(f132,axiom,
    ! [X0,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_Polynomial_Omonom(X5,c_HOL_Ozero__class_Ozero(tc_nat),X0) = c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__0_0) ).

fof(f2696,plain,
    spl0_360,
    inference(avatar_split_clause,[],[f131,f2694]) ).

fof(f2694,plain,
    ( spl0_360
  <=> ! [X5,X6,X10,X0,X14,X36] :
        ( X5 = X36
        | c_Pair(X5,X6,X0,X10) != c_Pair(X36,X14,X0,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).

fof(f131,axiom,
    ! [X10,X0,X36,X6,X14,X5] :
      ( X5 = X36
      | c_Pair(X5,X6,X0,X10) != c_Pair(X36,X14,X0,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).

fof(f2692,plain,
    ( spl0_359
    | ~ spl0_44
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1729,f1587,f902,f2690]) ).

fof(f2690,plain,
    ( spl0_359
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).

fof(f1729,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
    | ~ spl0_44
    | ~ spl0_189 ),
    inference(resolution,[],[f1588,f904]) ).

fof(f2688,plain,
    spl0_358,
    inference(avatar_split_clause,[],[f130,f2686]) ).

fof(f2686,plain,
    ( spl0_358
  <=> ! [X5,X10,X0,X14,X6,X36] :
        ( X6 = X14
        | c_Pair(X5,X6,X0,X10) != c_Pair(X36,X14,X0,X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).

fof(f130,axiom,
    ! [X10,X0,X36,X6,X14,X5] :
      ( X6 = X14
      | c_Pair(X5,X6,X0,X10) != c_Pair(X36,X14,X0,X10) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).

fof(f2684,plain,
    spl0_357,
    inference(avatar_split_clause,[],[f115,f2682]) ).

fof(f2682,plain,
    ( spl0_357
  <=> ! [X34,X0,X33,X1] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X33 = X34
        | c_HOL_Ominus__class_Ominus(X1,X1,X0) != c_HOL_Ominus__class_Ominus(X33,X34,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).

fof(f115,axiom,
    ! [X0,X1,X34,X33] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X33 = X34
      | c_HOL_Ominus__class_Ominus(X1,X1,X0) != c_HOL_Ominus__class_Ominus(X33,X34,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

fof(f2680,plain,
    spl0_356,
    inference(avatar_split_clause,[],[f92,f2678]) ).

fof(f92,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(X1,tc_Polynomial_Opoly(X0)),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__left_0) ).

fof(f2676,plain,
    spl0_355,
    inference(avatar_split_clause,[],[f91,f2674]) ).

fof(f91,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X1,c_HOL_Ouminus__class_Ouminus(X2,tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__minus__right_0) ).

fof(f2672,plain,
    spl0_354,
    inference(avatar_split_clause,[],[f25,f2670]) ).

fof(f25,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

fof(f2668,plain,
    spl0_353,
    inference(avatar_split_clause,[],[f24,f2666]) ).

fof(f24,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

fof(f2664,plain,
    spl0_352,
    inference(avatar_split_clause,[],[f23,f2662]) ).

fof(f23,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0),c_HOL_Otimes__class_Otimes(X6,c_HOL_Ozero__class_Ozero(X0),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

fof(f2660,plain,
    spl0_351,
    inference(avatar_split_clause,[],[f21,f2658]) ).

fof(f21,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | X5 = X6
      | c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).

fof(f2656,plain,
    spl0_350,
    inference(avatar_split_clause,[],[f20,f2654]) ).

fof(f20,axiom,
    ! [X0,X6,X7,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | X7 = X12
      | c_Polynomial_OpCons(X6,X7,X0) != c_Polynomial_OpCons(X5,X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).

fof(f2652,plain,
    spl0_349,
    inference(avatar_split_clause,[],[f11,f2650]) ).

fof(f11,axiom,
    ! [X10,X0,X11,X1,X8,X9] : hAPP(c_Fun_Ofcomp(X8,X9,X10,X11,X0),X1) = hAPP(X9,hAPP(X8,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).

fof(f2648,plain,
    ( spl0_348
    | ~ spl0_88
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1728,f1587,f1122,f2646]) ).

fof(f2646,plain,
    ( spl0_348
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).

fof(f1728,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_88
    | ~ spl0_189 ),
    inference(resolution,[],[f1588,f1124]) ).

fof(f2615,plain,
    ( spl0_347
    | ~ spl0_7
    | ~ spl0_189 ),
    inference(avatar_split_clause,[],[f1727,f1587,f717,f2613]) ).

fof(f2613,plain,
    ( spl0_347
  <=> ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).

fof(f1727,plain,
    ( ! [X0] : c_Polynomial_Osmult(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
    | ~ spl0_7
    | ~ spl0_189 ),
    inference(resolution,[],[f1588,f719]) ).

fof(f2586,plain,
    ( spl0_346
    | ~ spl0_62
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1711,f1555,f992,f2584]) ).

fof(f2584,plain,
    ( spl0_346
  <=> ! [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_346])]) ).

fof(f992,plain,
    ( spl0_62
  <=> class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).

fof(f1711,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0
    | ~ spl0_62
    | ~ spl0_181 ),
    inference(resolution,[],[f1556,f994]) ).

fof(f994,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal)
    | ~ spl0_62 ),
    inference(avatar_component_clause,[],[f992]) ).

fof(f2536,plain,
    spl0_345,
    inference(avatar_split_clause,[],[f500,f2534]) ).

fof(f500,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(f2532,plain,
    ( spl0_344
    | ~ spl0_103
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1710,f1555,f1197,f2530]) ).

fof(f2530,plain,
    ( spl0_344
  <=> ! [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_344])]) ).

fof(f1197,plain,
    ( spl0_103
  <=> class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).

fof(f1710,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0
    | ~ spl0_103
    | ~ spl0_181 ),
    inference(resolution,[],[f1556,f1199]) ).

fof(f1199,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
    | ~ spl0_103 ),
    inference(avatar_component_clause,[],[f1197]) ).

fof(f2528,plain,
    spl0_343,
    inference(avatar_split_clause,[],[f476,f2526]) ).

fof(f476,axiom,
    ! [X0,X1,X7,X25] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | X1 = X25
      | ~ c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,X25,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0__iff_1) ).

fof(f2524,plain,
    spl0_342,
    inference(avatar_split_clause,[],[f463,f2522]) ).

fof(f463,axiom,
    ! [X0,X7] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X7,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__left_0) ).

fof(f2520,plain,
    spl0_341,
    inference(avatar_split_clause,[],[f462,f2518]) ).

fof(f462,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Otimes__class_Otimes(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__poly__0__right_0) ).

fof(f2516,plain,
    ( spl0_339
    | ~ spl0_340 ),
    inference(avatar_split_clause,[],[f453,f2513,f2510]) ).

fof(f2510,plain,
    ( spl0_339
  <=> ! [X12] :
        ( c_HOL_Ozero__class_Ozero(t_a) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X12)
        | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,t_a),t_a,t_a) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).

fof(f2513,plain,
    ( spl0_340
  <=> class_Ring__and__Field_Oidom(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).

fof(f453,axiom,
    ! [X12] :
      ( ~ class_Ring__and__Field_Oidom(t_a)
      | c_HOL_Ozero__class_Ozero(t_a) != v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(X12)
      | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(X12,t_a),t_a,t_a) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__decompose_0) ).

fof(f2508,plain,
    spl0_338,
    inference(avatar_split_clause,[],[f451,f2506]) ).

fof(f451,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__dvd__iff_3) ).

fof(f2504,plain,
    spl0_337,
    inference(avatar_split_clause,[],[f447,f2502]) ).

fof(f447,axiom,
    ! [X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_OAbs__poly(c_COMBK(c_HOL_Ozero__class_Ozero(X0),X0,tc_nat),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__poly__def_0) ).

fof(f2500,plain,
    spl0_336,
    inference(avatar_split_clause,[],[f390,f2498]) ).

fof(f390,axiom,
    ! [X0,X5,X12] :
      ( ~ class_HOL_Ozero(X0)
      | hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(X5,X12,X0),X0),c_HOL_Ozero__class_Ozero(tc_nat)) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__pCons__0_0) ).

fof(f2496,plain,
    spl0_335,
    inference(avatar_split_clause,[],[f387,f2494]) ).

fof(f387,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),c_HOL_Oplus__class_Oplus(X5,X6,X0),X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

fof(f2492,plain,
    spl0_334,
    inference(avatar_split_clause,[],[f386,f2490]) ).

fof(f386,axiom,
    ! [X2,X3,X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X3,X0),c_HOL_Oplus__class_Oplus(X2,X3,X0),X0) = X2 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

fof(f2488,plain,
    ( spl0_333
    | ~ spl0_18
    | ~ spl0_181 ),
    inference(avatar_split_clause,[],[f1709,f1555,f772,f2486]) ).

fof(f2486,plain,
    ( spl0_333
  <=> ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).

fof(f772,plain,
    ( spl0_18
  <=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f1709,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),X0,tc_nat) = X0
    | ~ spl0_18
    | ~ spl0_181 ),
    inference(resolution,[],[f1556,f774]) ).

fof(f774,plain,
    ( class_OrderedGroup_Omonoid__mult(tc_nat)
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f772]) ).

fof(f2484,plain,
    spl0_332,
    inference(avatar_split_clause,[],[f358,f2482]) ).

fof(f358,axiom,
    ! [X10,X11,X8,X13] : hAPP(c_Fun_Ocomp(c_COMBK(X13,X10,X11),X8,X11,X10,t_a),v_x) = X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).

fof(f2480,plain,
    spl0_331,
    inference(avatar_split_clause,[],[f339,f2478]) ).

fof(f339,axiom,
    ! [X0,X5] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_Polynomial_OpCons(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__pCons__0_0) ).

fof(f2476,plain,
    spl0_330,
    inference(avatar_split_clause,[],[f325,f2474]) ).

fof(f325,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nprt__neg_0) ).

fof(f2472,plain,
    spl0_329,
    inference(avatar_split_clause,[],[f313,f2470]) ).

fof(f2470,plain,
    ( spl0_329
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).

fof(f313,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oplus__class_Oplus(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

fof(f2468,plain,
    spl0_328,
    inference(avatar_split_clause,[],[f284,f2466]) ).

fof(f2466,plain,
    ( spl0_328
  <=> ! [X6,X0,X5] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).

fof(f284,axiom,
    ! [X0,X6,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) = c_RealVector_OscaleR__class_OscaleR(X6,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).

fof(f2464,plain,
    spl0_327,
    inference(avatar_split_clause,[],[f277,f2462]) ).

fof(f277,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X6,X5,X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

fof(f2460,plain,
    spl0_326,
    inference(avatar_split_clause,[],[f263,f2458]) ).

fof(f263,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Ominus__class_Ominus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

fof(f2456,plain,
    spl0_325,
    inference(avatar_split_clause,[],[f195,f2454]) ).

fof(f2454,plain,
    ( spl0_325
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).

fof(f195,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).

fof(f2452,plain,
    spl0_324,
    inference(avatar_split_clause,[],[f194,f2450]) ).

fof(f194,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

fof(f2448,plain,
    spl0_323,
    inference(avatar_split_clause,[],[f193,f2446]) ).

fof(f193,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

fof(f2444,plain,
    ( spl0_322
    | ~ spl0_62
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1707,f1551,f992,f2442]) ).

fof(f1707,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_62
    | ~ spl0_180 ),
    inference(resolution,[],[f1552,f994]) ).

fof(f2440,plain,
    spl0_321,
    inference(avatar_split_clause,[],[f179,f2438]) ).

fof(f179,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pprt__neg_0) ).

fof(f2436,plain,
    spl0_320,
    inference(avatar_split_clause,[],[f141,f2434]) ).

fof(f141,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | c_HOL_Ouminus__class_Ouminus(X1,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(X0),X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

fof(f2432,plain,
    spl0_319,
    inference(avatar_split_clause,[],[f117,f2430]) ).

fof(f117,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_HOL_Ominus__class_Ominus(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).

fof(f2428,plain,
    spl0_318,
    inference(avatar_split_clause,[],[f113,f2426]) ).

fof(f113,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Oone__class_Oone(X0) = c_HOL_Oinverse__class_Odivide(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).

fof(f2424,plain,
    spl0_317,
    inference(avatar_split_clause,[],[f19,f2422]) ).

fof(f19,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,X13,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

fof(f2420,plain,
    spl0_316,
    inference(avatar_split_clause,[],[f18,f2418]) ).

fof(f18,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(X5,X6,X0),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

fof(f2416,plain,
    spl0_315,
    inference(avatar_split_clause,[],[f17,f2414]) ).

fof(f17,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X6,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

fof(f2412,plain,
    spl0_314,
    inference(avatar_split_clause,[],[f16,f2410]) ).

fof(f16,axiom,
    ! [X0,X6,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X5,X13,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X13,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

fof(f2408,plain,
    spl0_313,
    inference(avatar_split_clause,[],[f12,f2406]) ).

fof(f12,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X6,X0),X0) = X6 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

fof(f2404,plain,
    spl0_312,
    inference(avatar_split_clause,[],[f2,f2402]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(X1,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__minus_0) ).

fof(f2400,plain,
    ( spl0_311
    | ~ spl0_103
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1706,f1551,f1197,f2398]) ).

fof(f1706,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_103
    | ~ spl0_180 ),
    inference(resolution,[],[f1552,f1199]) ).

fof(f2368,plain,
    ( spl0_310
    | ~ spl0_18
    | ~ spl0_180 ),
    inference(avatar_split_clause,[],[f1705,f1551,f772,f2366]) ).

fof(f1705,plain,
    ( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat) = X0
    | ~ spl0_18
    | ~ spl0_180 ),
    inference(resolution,[],[f1552,f774]) ).

fof(f2344,plain,
    ( spl0_309
    | ~ spl0_79
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1703,f1542,f1077,f2342]) ).

fof(f2342,plain,
    ( spl0_309
  <=> ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).

fof(f1703,plain,
    ( ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = X0
    | ~ spl0_79
    | ~ spl0_178 ),
    inference(resolution,[],[f1543,f1079]) ).

fof(f2310,plain,
    ( spl0_308
    | ~ spl0_117
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1702,f1542,f1267,f2308]) ).

fof(f2308,plain,
    ( spl0_308
  <=> ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).

fof(f1702,plain,
    ( ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = X0
    | ~ spl0_117
    | ~ spl0_178 ),
    inference(resolution,[],[f1543,f1269]) ).

fof(f2302,plain,
    spl0_307,
    inference(avatar_split_clause,[],[f521,f2300]) ).

fof(f521,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__root_1) ).

fof(f2298,plain,
    spl0_306,
    inference(avatar_split_clause,[],[f520,f2296]) ).

fof(f520,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__0_0) ).

fof(f2294,plain,
    spl0_305,
    inference(avatar_split_clause,[],[f509,f2292]) ).

fof(f509,axiom,
    ! [X1,X13] : hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(X13,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),tc_Complex_Ocomplex),X1) = X13,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mpoly__base__conv_I2_J_0) ).

fof(f2290,plain,
    spl0_304,
    inference(avatar_split_clause,[],[f504,f2288]) ).

fof(f504,axiom,
    ! [X0,X15] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0),X15) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__0_0) ).

fof(f2286,plain,
    spl0_303,
    inference(avatar_split_clause,[],[f481,f2284]) ).

fof(f481,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(f2282,plain,
    spl0_302,
    inference(avatar_split_clause,[],[f480,f2280]) ).

fof(f480,axiom,
    ! [X28,X0] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X28,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_offset__poly__0_0) ).

fof(f2278,plain,
    spl0_301,
    inference(avatar_split_clause,[],[f465,f2276]) ).

fof(f465,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opdivmod__rel(X1,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pdivmod__rel__by__0_0) ).

fof(f2274,plain,
    spl0_300,
    inference(avatar_split_clause,[],[f461,f2272]) ).

fof(f461,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Oordered__idom(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)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__poly__def_0) ).

fof(f2270,plain,
    ( spl0_299
    | ~ spl0_24
    | ~ spl0_178 ),
    inference(avatar_split_clause,[],[f1701,f1542,f802,f2268]) ).

fof(f2268,plain,
    ( spl0_299
  <=> ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_nat),tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).

fof(f1701,plain,
    ( ! [X0] : c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X0,tc_nat),tc_nat) = X0
    | ~ spl0_24
    | ~ spl0_178 ),
    inference(resolution,[],[f1543,f804]) ).

fof(f2266,plain,
    spl0_298,
    inference(avatar_split_clause,[],[f460,f2264]) ).

fof(f460,axiom,
    ! [X0,X13] :
      ( ~ 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)),X13,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_synthetic__div__0_0) ).

fof(f2262,plain,
    spl0_297,
    inference(avatar_split_clause,[],[f459,f2260]) ).

fof(f459,axiom,
    ! [X0] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__poly__code_I1_J_0) ).

fof(f2258,plain,
    spl0_296,
    inference(avatar_split_clause,[],[f458,f2256]) ).

fof(f458,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_2) ).

fof(f2254,plain,
    spl0_295,
    inference(avatar_split_clause,[],[f457,f2252]) ).

fof(f457,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(X5,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__right_0) ).

fof(f2250,plain,
    spl0_294,
    inference(avatar_split_clause,[],[f433,f2248]) ).

fof(f2248,plain,
    ( spl0_294
  <=> ! [X0,X1] :
        ( ~ class_RealVector_Oreal__normed__vector(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X1
        | c_HOL_Osgn__class_Osgn(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).

fof(f433,axiom,
    ! [X0,X1] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X1
      | c_HOL_Osgn__class_Osgn(X1,X0) != c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).

fof(f2246,plain,
    spl0_293,
    inference(avatar_split_clause,[],[f432,f2244]) ).

fof(f2244,plain,
    ( spl0_293
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).

fof(f432,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Osgn__class_Osgn(X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).

fof(f2242,plain,
    spl0_292,
    inference(avatar_split_clause,[],[f430,f2240]) ).

fof(f430,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Odivision__by__zero(X0)
      | ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).

fof(f2238,plain,
    spl0_291,
    inference(avatar_split_clause,[],[f426,f2236]) ).

fof(f2236,plain,
    ( spl0_291
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X5 = X6
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).

fof(f426,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X5 = X6
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

fof(f2234,plain,
    spl0_290,
    inference(avatar_split_clause,[],[f425,f2232]) ).

fof(f2232,plain,
    ( spl0_290
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Oab__group__add(X0)
        | X5 = X6
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).

fof(f425,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | X5 = X6
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Ominus__class_Ominus(X5,X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

fof(f2230,plain,
    spl0_289,
    inference(avatar_split_clause,[],[f389,f2228]) ).

fof(f2228,plain,
    ( spl0_289
  <=> ! [X2,X0,X1] :
        ( ~ class_HOL_Oeq(X0)
        | X1 = X2
        | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X1),X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).

fof(f389,axiom,
    ! [X2,X0,X1] :
      ( ~ class_HOL_Oeq(X0)
      | X1 = X2
      | ~ hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X1),X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equals_0) ).

fof(f2226,plain,
    spl0_288,
    inference(avatar_split_clause,[],[f322,f2224]) ).

fof(f2224,plain,
    ( spl0_288
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).

fof(f322,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ozero__class_Ozero(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

fof(f2222,plain,
    spl0_287,
    inference(avatar_split_clause,[],[f221,f2220]) ).

fof(f221,axiom,
    ! [X0,X1,X5] :
      ( ~ class_HOL_Ozero(X0)
      | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(X5,X1,X0),X0),X1) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__monom_0) ).

fof(f2218,plain,
    spl0_286,
    inference(avatar_split_clause,[],[f200,f2216]) ).

fof(f200,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_1) ).

fof(f2214,plain,
    spl0_285,
    inference(avatar_split_clause,[],[f199,f2212]) ).

fof(f199,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(X1,X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__dvd__iff_0) ).

fof(f2210,plain,
    spl0_284,
    inference(avatar_split_clause,[],[f198,f2208]) ).

fof(f198,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_1) ).

fof(f2206,plain,
    spl0_283,
    inference(avatar_split_clause,[],[f197,f2204]) ).

fof(f197,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X1,X2,X0)
      | ~ c_Ring__and__Field_Odvd__class_Odvd(X1,c_HOL_Ouminus__class_Ouminus(X2,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__minus__iff_0) ).

fof(f2202,plain,
    spl0_282,
    inference(avatar_split_clause,[],[f166,f2200]) ).

fof(f2200,plain,
    ( spl0_282
  <=> ! [X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X1),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).

fof(f166,axiom,
    ! [X0,X1] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)),X1),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def_1) ).

fof(f2198,plain,
    spl0_281,
    inference(avatar_split_clause,[],[f135,f2196]) ).

fof(f2196,plain,
    ( spl0_281
  <=> ! [X2,X0,X1] :
        ( ~ class_HOL_Ozero(X0)
        | X1 = X2
        | c_Polynomial_Ocoeff(X1,X0) != c_Polynomial_Ocoeff(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).

fof(f135,axiom,
    ! [X2,X0,X1] :
      ( ~ class_HOL_Ozero(X0)
      | X1 = X2
      | c_Polynomial_Ocoeff(X1,X0) != c_Polynomial_Ocoeff(X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__inject_0) ).

fof(f2194,plain,
    spl0_280,
    inference(avatar_split_clause,[],[f123,f2192]) ).

fof(f123,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Olordered__ab__group__add(X0)
      | c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(X5,X0),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(X5,X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_prts_0) ).

fof(f2190,plain,
    spl0_279,
    inference(avatar_split_clause,[],[f69,f2188]) ).

fof(f69,axiom,
    ! [X28,X0,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X0)
      | c_Polynomial_Odegree(X12,X0) = c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(X12,X28,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__offset__poly_0) ).

fof(f2186,plain,
    spl0_278,
    inference(avatar_split_clause,[],[f48,f2184]) ).

fof(f48,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0),X0) = c_HOL_Ozero__class_Ozero(tc_nat) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__smult__eq_0) ).

fof(f2182,plain,
    spl0_277,
    inference(avatar_split_clause,[],[f34,f2180]) ).

fof(f2180,plain,
    ( spl0_277
  <=> ! [X6,X0,X5] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | X5 = X6
        | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).

fof(f34,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | X5 = X6
      | c_HOL_Ouminus__class_Ouminus(X5,X0) != c_HOL_Ouminus__class_Ouminus(X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

fof(f2178,plain,
    spl0_276,
    inference(avatar_split_clause,[],[f33,f2176]) ).

fof(f2176,plain,
    ( spl0_276
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Oboolean__algebra(X0)
        | X1 = X2
        | c_HOL_Ouminus__class_Ouminus(X1,X0) != c_HOL_Ouminus__class_Ouminus(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).

fof(f33,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(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_compl__eq__compl__iff_0) ).

fof(f2174,plain,
    spl0_275,
    inference(avatar_split_clause,[],[f13,f2172]) ).

fof(f13,axiom,
    ! [X0,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(X12,tc_Polynomial_Opoly(X0)),X0) = c_Polynomial_Odegree(X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__minus_0) ).

fof(f2066,plain,
    spl0_274,
    inference(avatar_split_clause,[],[f503,f2064]) ).

fof(f503,axiom,
    ! [X0,X15] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(X0),X15,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monom__eq__0_0) ).

fof(f2062,plain,
    spl0_273,
    inference(avatar_split_clause,[],[f497,f2060]) ).

fof(f497,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)) = c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(X0),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__eq__0__iff_1) ).

fof(f2058,plain,
    spl0_272,
    inference(avatar_split_clause,[],[f496,f2056]) ).

fof(f496,axiom,
    ! [X0,X12] :
      ( ~ 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),X12,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__0__left_0) ).

fof(f2054,plain,
    spl0_271,
    inference(avatar_split_clause,[],[f483,f2052]) ).

fof(f483,axiom,
    ! [X0,X12] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__poly__code_I2_J_0) ).

fof(f2050,plain,
    spl0_270,
    inference(avatar_split_clause,[],[f482,f2048]) ).

fof(f482,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(f2046,plain,
    spl0_269,
    inference(avatar_split_clause,[],[f479,f2044]) ).

fof(f479,axiom,
    ! [X0,X12] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ominus__class_Ominus(X12,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),tc_Polynomial_Opoly(X0)) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__poly__code_I2_J_0) ).

fof(f2042,plain,
    ( spl0_267
    | ~ spl0_268 ),
    inference(avatar_split_clause,[],[f443,f2039,f2035]) ).

fof(f2035,plain,
    ( spl0_267
  <=> 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_267])]) ).

fof(f2039,plain,
    ( spl0_268
  <=> class_OrderedGroup_Olordered__ab__group__add(t_a) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).

fof(f443,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(f2033,plain,
    spl0_266,
    inference(avatar_split_clause,[],[f438,f2031]) ).

fof(f438,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

fof(f2029,plain,
    spl0_265,
    inference(avatar_split_clause,[],[f399,f2027]) ).

fof(f2027,plain,
    ( spl0_265
  <=> ! [X2,X1,X8] :
        ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X8,t_a,t_b)
        | hAPP(X8,X1) = hAPP(X8,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).

fof(f399,axiom,
    ! [X2,X1,X8] :
      ( ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(X8,t_a,t_b)
      | hAPP(X8,X1) = hAPP(X8,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_constant__def_0) ).

fof(f2025,plain,
    spl0_264,
    inference(avatar_split_clause,[],[f392,f2023]) ).

fof(f392,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Polynomial_Opoly__gcd(X1,X2,X0) = c_Polynomial_Opoly__gcd(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__commute_0) ).

fof(f2021,plain,
    spl0_263,
    inference(avatar_split_clause,[],[f382,f2019]) ).

fof(f382,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

fof(f2017,plain,
    spl0_262,
    inference(avatar_split_clause,[],[f357,f2015]) ).

fof(f357,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

fof(f2013,plain,
    ( spl0_261
    | ~ spl0_27
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1540,f1523,f817,f2011]) ).

fof(f2011,plain,
    ( spl0_261
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).

fof(f1540,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_bool) = X0
    | ~ spl0_27
    | ~ spl0_177 ),
    inference(resolution,[],[f1524,f819]) ).

fof(f2009,plain,
    spl0_260,
    inference(avatar_split_clause,[],[f355,f2007]) ).

fof(f355,axiom,
    ! [X0,X5,X13] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,X13,X0) = c_HOL_Oplus__class_Oplus(X13,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

fof(f2005,plain,
    spl0_259,
    inference(avatar_split_clause,[],[f331,f2003]) ).

fof(f331,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(f2001,plain,
    spl0_258,
    inference(avatar_split_clause,[],[f321,f1999]) ).

fof(f1999,plain,
    ( spl0_258
  <=> ! [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_258])]) ).

fof(f321,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(f1997,plain,
    spl0_257,
    inference(avatar_split_clause,[],[f318,f1995]) ).

fof(f318,axiom,
    ! [X0,X1] :
      ( ~ class_Int_Onumber__ring(X0)
      | ~ class_Ring__and__Field_Oidom(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

fof(f1993,plain,
    spl0_256,
    inference(avatar_split_clause,[],[f306,f1991]) ).

fof(f1991,plain,
    ( spl0_256
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = X5
        | c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).

fof(f306,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oordered__ab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | c_HOL_Ouminus__class_Ouminus(X5,X0) != X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

fof(f1989,plain,
    spl0_255,
    inference(avatar_split_clause,[],[f304,f1987]) ).

fof(f304,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = X5
      | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

fof(f1985,plain,
    spl0_254,
    inference(avatar_split_clause,[],[f269,f1983]) ).

fof(f269,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X5,X6,X0),X6,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

fof(f1981,plain,
    spl0_253,
    inference(avatar_split_clause,[],[f248,f1979]) ).

fof(f1979,plain,
    ( spl0_253
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).

fof(f248,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

fof(f1977,plain,
    spl0_252,
    inference(avatar_split_clause,[],[f247,f1975]) ).

fof(f247,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0) = c_Lattices_Oupper__semilattice__class_Osup(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

fof(f1973,plain,
    spl0_251,
    inference(avatar_split_clause,[],[f240,f1971]) ).

fof(f1971,plain,
    ( spl0_251
  <=> ! [X5,X0,X12] :
        ( ~ class_Ring__and__Field_Oordered__idom(X0)
        | ~ c_Polynomial_Opos__poly(X12,X0)
        | c_Polynomial_Opos__poly(c_Polynomial_OpCons(X5,X12,X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).

fof(f240,axiom,
    ! [X0,X5,X12] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | ~ c_Polynomial_Opos__poly(X12,X0)
      | c_Polynomial_Opos__poly(c_Polynomial_OpCons(X5,X12,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).

fof(f1969,plain,
    ( spl0_250
    | ~ spl0_58
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1538,f1523,f972,f1967]) ).

fof(f1967,plain,
    ( spl0_250
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).

fof(f1538,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_RealDef_Oreal) = X0
    | ~ spl0_58
    | ~ spl0_177 ),
    inference(resolution,[],[f1524,f974]) ).

fof(f1965,plain,
    spl0_249,
    inference(avatar_split_clause,[],[f232,f1963]) ).

fof(f1963,plain,
    ( spl0_249
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).

fof(f232,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).

fof(f1961,plain,
    spl0_248,
    inference(avatar_split_clause,[],[f231,f1959]) ).

fof(f231,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(X5,c_HOL_Ouminus__class_Ouminus(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).

fof(f1957,plain,
    spl0_247,
    inference(avatar_split_clause,[],[f230,f1955]) ).

fof(f230,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(X5,X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

fof(f1953,plain,
    spl0_246,
    inference(avatar_split_clause,[],[f227,f1951]) ).

fof(f1951,plain,
    ( spl0_246
  <=> ! [X2,X0,X1] :
        ( ~ class_Lattices_Olattice(X0)
        | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).

fof(f227,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

fof(f1949,plain,
    spl0_245,
    inference(avatar_split_clause,[],[f226,f1947]) ).

fof(f226,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,X2,X0) = c_Lattices_Olower__semilattice__class_Oinf(X2,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

fof(f1945,plain,
    spl0_244,
    inference(avatar_split_clause,[],[f186,f1943]) ).

fof(f186,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(X5,X0) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

fof(f1941,plain,
    spl0_243,
    inference(avatar_split_clause,[],[f177,f1939]) ).

fof(f177,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oordered__idom(X0)
      | c_HOL_Osgn__class_Osgn(X5,X0) = c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).

fof(f1937,plain,
    spl0_242,
    inference(avatar_split_clause,[],[f94,f1935]) ).

fof(f94,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

fof(f1933,plain,
    spl0_241,
    inference(avatar_split_clause,[],[f87,f1931]) ).

fof(f87,axiom,
    ! [X0,X6,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(X5,X6,X0),X6,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

fof(f1929,plain,
    spl0_240,
    inference(avatar_split_clause,[],[f29,f1927]) ).

fof(f29,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Lattices_Olattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,c_Lattices_Oupper__semilattice__class_Osup(X1,X2,X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

fof(f1925,plain,
    ( spl0_239
    | ~ spl0_16
    | ~ spl0_177 ),
    inference(avatar_split_clause,[],[f1537,f1523,f762,f1923]) ).

fof(f1923,plain,
    ( spl0_239
  <=> ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).

fof(f1537,plain,
    ( ! [X0] : c_Lattices_Olower__semilattice__class_Oinf(X0,X0,tc_nat) = X0
    | ~ spl0_16
    | ~ spl0_177 ),
    inference(resolution,[],[f1524,f764]) ).

fof(f1921,plain,
    spl0_238,
    inference(avatar_split_clause,[],[f5,f1919]) ).

fof(f5,axiom,
    ! [X0] :
      ( ~ class_HOL_Ozero(X0)
      | ~ class_HOL_Oeq(X0)
      | c_HOL_Oeq__class_Oeq(tc_Polynomial_Opoly(X0)) = c_fequal(tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__poly__def__raw_0) ).

fof(f1908,plain,
    ( spl0_237
    | ~ spl0_26
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1529,f1511,f812,f1906]) ).

fof(f1906,plain,
    ( spl0_237
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).

fof(f1529,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_bool) = X0
    | ~ spl0_26
    | ~ spl0_174 ),
    inference(resolution,[],[f1512,f814]) ).

fof(f1874,plain,
    spl0_236,
    inference(avatar_split_clause,[],[f682,f1872]) ).

fof(f682,axiom,
    ! [X50,X51,X0] :
      ( X50 = X51
      | ~ hBOOL(hAPP(hAPP(c_fequal(X0),X50),X51)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).

fof(f1870,plain,
    ( spl0_123
    | ~ spl0_124 ),
    inference(avatar_contradiction_clause,[],[f1869]) ).

fof(f1869,plain,
    ( $false
    | spl0_123
    | ~ spl0_124 ),
    inference(trivial_inequality_removal,[],[f1868]) ).

fof(f1868,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | spl0_123
    | ~ spl0_124 ),
    inference(superposition,[],[f1297,f1301]) ).

fof(f1297,plain,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x)
    | spl0_123 ),
    inference(avatar_component_clause,[],[f1295]) ).

fof(f1295,plain,
    ( spl0_123
  <=> c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).

fof(f1867,plain,
    ( spl0_124
    | ~ spl0_122
    | ~ spl0_235 ),
    inference(avatar_split_clause,[],[f1866,f1863,f1291,f1300]) ).

fof(f1866,plain,
    ( ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X1)
    | ~ spl0_122
    | ~ spl0_235 ),
    inference(forward_demodulation,[],[f1864,f1292]) ).

fof(f1292,plain,
    ( c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex)
    | ~ spl0_122 ),
    inference(avatar_component_clause,[],[f1291]) ).

fof(f1865,plain,
    spl0_235,
    inference(avatar_split_clause,[],[f522,f1863]) ).

fof(f522,axiom,
    ! [X1] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_resolve__eq__raw_I1_J_0) ).

fof(f1861,plain,
    spl0_234,
    inference(avatar_split_clause,[],[f434,f1859]) ).

fof(f1859,plain,
    ( spl0_234
  <=> ! [X0,X1] :
        ( ~ class_SEQ_Obanach(X0)
        | ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).

fof(f434,axiom,
    ! [X0,X1] :
      ( ~ class_SEQ_Obanach(X0)
      | ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_Transcendental_Oexp(X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_exp__not__eq__zero_0) ).

fof(f1857,plain,
    spl0_233,
    inference(avatar_split_clause,[],[f431,f1855]) ).

fof(f1855,plain,
    ( spl0_233
  <=> ! [X2,X0] :
        ( ~ class_RealVector_Oreal__normed__field(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).

fof(f431,axiom,
    ! [X2,X0] :
      ( ~ class_RealVector_Oreal__normed__field(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X2,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

fof(f1853,plain,
    spl0_232,
    inference(avatar_split_clause,[],[f428,f1851]) ).

fof(f428,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

fof(f1849,plain,
    spl0_231,
    inference(avatar_split_clause,[],[f424,f1847]) ).

fof(f1847,plain,
    ( spl0_231
  <=> ! [X5,X0] :
        ( ~ class_RealVector_Oreal__vector(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).

fof(f424,axiom,
    ! [X0,X5] :
      ( ~ class_RealVector_Oreal__vector(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).

fof(f1845,plain,
    spl0_230,
    inference(avatar_split_clause,[],[f423,f1843]) ).

fof(f423,axiom,
    ! [X0,X5] :
      ( ~ class_RealVector_Oreal__normed__vector(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_RealVector_OscaleR__class_OscaleR(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).

fof(f1841,plain,
    spl0_229,
    inference(avatar_split_clause,[],[f396,f1839]) ).

fof(f396,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X1,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd1_0) ).

fof(f1837,plain,
    spl0_228,
    inference(avatar_split_clause,[],[f395,f1835]) ).

fof(f395,axiom,
    ! [X2,X0,X1] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(X1,X2,X0),X2,tc_Polynomial_Opoly(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__gcd__dvd2_0) ).

fof(f1833,plain,
    ( spl0_227
    | ~ spl0_57
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1527,f1511,f967,f1831]) ).

fof(f1831,plain,
    ( spl0_227
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).

fof(f1527,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_RealDef_Oreal) = X0
    | ~ spl0_57
    | ~ spl0_174 ),
    inference(resolution,[],[f1512,f969]) ).

fof(f1829,plain,
    spl0_226,
    inference(avatar_split_clause,[],[f300,f1827]) ).

fof(f300,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

fof(f1825,plain,
    spl0_225,
    inference(avatar_split_clause,[],[f298,f1823]) ).

fof(f1823,plain,
    ( spl0_225
  <=> ! [X6,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).

fof(f298,axiom,
    ! [X0,X6] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

fof(f1821,plain,
    spl0_224,
    inference(avatar_split_clause,[],[f297,f1819]) ).

fof(f1819,plain,
    ( spl0_224
  <=> ! [X5,X0] :
        ( ~ class_RealVector_Oreal__normed__algebra(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).

fof(f297,axiom,
    ! [X0,X5] :
      ( ~ class_RealVector_Oreal__normed__algebra(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

fof(f1817,plain,
    spl0_223,
    inference(avatar_split_clause,[],[f295,f1815]) ).

fof(f295,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

fof(f1813,plain,
    spl0_222,
    inference(avatar_split_clause,[],[f294,f1811]) ).

fof(f294,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

fof(f1809,plain,
    spl0_221,
    inference(avatar_split_clause,[],[f293,f1807]) ).

fof(f293,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Omult__zero(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

fof(f1805,plain,
    spl0_220,
    inference(avatar_split_clause,[],[f292,f1803]) ).

fof(f292,axiom,
    ! [X0,X6] :
      ( ~ 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),X6,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

fof(f1801,plain,
    spl0_219,
    inference(avatar_split_clause,[],[f291,f1799]) ).

fof(f291,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

fof(f1797,plain,
    spl0_218,
    inference(avatar_split_clause,[],[f243,f1795]) ).

fof(f243,axiom,
    ! [X0] :
      ( ~ class_HOL_Ozero(X0)
      | c_HOL_Ozero__class_Ozero(tc_nat) = c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(X0)),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_degree__0_0) ).

fof(f1790,plain,
    ( spl0_217
    | ~ spl0_15
    | ~ spl0_174 ),
    inference(avatar_split_clause,[],[f1526,f1511,f757,f1788]) ).

fof(f1788,plain,
    ( spl0_217
  <=> ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).

fof(f1526,plain,
    ( ! [X0] : c_Lattices_Oupper__semilattice__class_Osup(X0,X0,tc_nat) = X0
    | ~ spl0_15
    | ~ spl0_174 ),
    inference(resolution,[],[f1512,f759]) ).

fof(f1699,plain,
    spl0_216,
    inference(avatar_split_clause,[],[f486,f1697]) ).

fof(f486,axiom,
    ! [X3] :
      ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = X3
      | c_Complex_Ocnj(X3) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__zero__iff_0) ).

fof(f1695,plain,
    spl0_215,
    inference(avatar_split_clause,[],[f441,f1693]) ).

fof(f441,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

fof(f1691,plain,
    spl0_214,
    inference(avatar_split_clause,[],[f440,f1689]) ).

fof(f1689,plain,
    ( spl0_214
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).

fof(f440,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

fof(f1687,plain,
    spl0_213,
    inference(avatar_split_clause,[],[f439,f1685]) ).

fof(f439,axiom,
    ! [X0,X1] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

fof(f1683,plain,
    spl0_212,
    inference(avatar_split_clause,[],[f437,f1681]) ).

fof(f1681,plain,
    ( spl0_212
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
        | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).

fof(f437,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

fof(f1679,plain,
    spl0_211,
    inference(avatar_split_clause,[],[f436,f1677]) ).

fof(f436,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

fof(f1675,plain,
    spl0_210,
    inference(avatar_split_clause,[],[f435,f1673]) ).

fof(f435,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__add(X0)
      | c_HOL_Oplus__class_Oplus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

fof(f1671,plain,
    spl0_209,
    inference(avatar_split_clause,[],[f406,f1669]) ).

fof(f1669,plain,
    ( spl0_209
  <=> ! [X0,X8,X10] : c_Fun_Ofcomp(X8,c_Fun_Oid(X10),X0,X10,X10) = X8 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).

fof(f406,axiom,
    ! [X10,X0,X8] : c_Fun_Ofcomp(X8,c_Fun_Oid(X10),X0,X10,X10) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).

fof(f1667,plain,
    spl0_208,
    inference(avatar_split_clause,[],[f405,f1665]) ).

fof(f1665,plain,
    ( spl0_208
  <=> ! [X9,X0,X10] : c_Fun_Ofcomp(c_Fun_Oid(X0),X9,X0,X0,X10) = X9 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).

fof(f405,axiom,
    ! [X10,X0,X9] : c_Fun_Ofcomp(c_Fun_Oid(X0),X9,X0,X0,X10) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).

fof(f1663,plain,
    spl0_207,
    inference(avatar_split_clause,[],[f330,f1661]) ).

fof(f330,axiom,
    ! [X10,X0,X9] : c_Fun_Ocomp(c_Fun_Oid(X10),X9,X10,X10,X0) = X9,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).

fof(f1659,plain,
    spl0_206,
    inference(avatar_split_clause,[],[f329,f1657]) ).

fof(f329,axiom,
    ! [X10,X0,X8] : c_Fun_Ocomp(X8,c_Fun_Oid(X0),X0,X10,X0) = X8,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).

fof(f1655,plain,
    spl0_205,
    inference(avatar_split_clause,[],[f320,f1653]) ).

fof(f320,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(f1651,plain,
    spl0_204,
    inference(avatar_split_clause,[],[f317,f1649]) ).

fof(f1649,plain,
    ( spl0_204
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ogroup__add(X0)
        | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).

fof(f317,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

fof(f1647,plain,
    spl0_203,
    inference(avatar_split_clause,[],[f316,f1645]) ).

fof(f316,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ominus__class_Ominus(X5,c_HOL_Ozero__class_Ozero(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

fof(f1643,plain,
    spl0_202,
    inference(avatar_split_clause,[],[f314,f1641]) ).

fof(f314,axiom,
    ! [X0,X1] :
      ( ~ class_OrderedGroup_Oab__group__add(X0)
      | c_HOL_Ozero__class_Ozero(X0) = c_HOL_Ominus__class_Ominus(X1,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

fof(f1639,plain,
    ( spl0_201
    | ~ spl0_31
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1503,f1476,f837,f1636]) ).

fof(f1636,plain,
    ( spl0_201
  <=> c_HOL_Oeq__class_Oeq(tc_bool) = c_fequal(tc_bool) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).

fof(f1503,plain,
    ( c_HOL_Oeq__class_Oeq(tc_bool) = c_fequal(tc_bool)
    | ~ spl0_31
    | ~ spl0_167 ),
    inference(resolution,[],[f1477,f839]) ).

fof(f1634,plain,
    spl0_200,
    inference(avatar_split_clause,[],[f307,f1632]) ).

fof(f307,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(f1630,plain,
    spl0_199,
    inference(avatar_split_clause,[],[f290,f1628]) ).

fof(f290,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(f1626,plain,
    spl0_198,
    inference(avatar_split_clause,[],[f289,f1624]) ).

fof(f1624,plain,
    ( spl0_198
  <=> ! [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_198])]) ).

fof(f289,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(f1622,plain,
    spl0_197,
    inference(avatar_split_clause,[],[f288,f1620]) ).

fof(f288,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(f1618,plain,
    spl0_196,
    inference(avatar_split_clause,[],[f287,f1616]) ).

fof(f287,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(f1614,plain,
    spl0_195,
    inference(avatar_split_clause,[],[f285,f1612]) ).

fof(f285,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(f1610,plain,
    spl0_194,
    inference(avatar_split_clause,[],[f276,f1608]) ).

fof(f276,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ogroup__add(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X5,X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

fof(f1606,plain,
    spl0_193,
    inference(avatar_split_clause,[],[f275,f1604]) ).

fof(f275,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Oboolean__algebra(X0)
      | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(X1,X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

fof(f1602,plain,
    spl0_192,
    inference(avatar_split_clause,[],[f238,f1600]) ).

fof(f238,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(f1598,plain,
    spl0_191,
    inference(avatar_split_clause,[],[f203,f1596]) ).

fof(f203,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ofield(X0)
      | c_HOL_Oinverse__class_Odivide(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).

fof(f1594,plain,
    ( spl0_190
    | ~ spl0_80
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1501,f1476,f1082,f1591]) ).

fof(f1591,plain,
    ( spl0_190
  <=> c_HOL_Oeq__class_Oeq(tc_RealDef_Oreal) = c_fequal(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).

fof(f1501,plain,
    ( c_HOL_Oeq__class_Oeq(tc_RealDef_Oreal) = c_fequal(tc_RealDef_Oreal)
    | ~ spl0_80
    | ~ spl0_167 ),
    inference(resolution,[],[f1477,f1084]) ).

fof(f1589,plain,
    spl0_189,
    inference(avatar_split_clause,[],[f182,f1587]) ).

fof(f182,axiom,
    ! [X0,X12] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(X0),X12,X0) = X12 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_smult__1__left_0) ).

fof(f1585,plain,
    spl0_188,
    inference(avatar_split_clause,[],[f167,f1583]) ).

fof(f1583,plain,
    ( spl0_188
  <=> ! [X0,X1] :
        ( ~ class_HOL_Oeq(X0)
        | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X1),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).

fof(f167,axiom,
    ! [X0,X1] :
      ( ~ class_HOL_Oeq(X0)
      | hBOOL(hAPP(hAPP(c_HOL_Oeq__class_Oeq(X0),X1),X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__class_Oeq__refl_0) ).

fof(f1581,plain,
    spl0_187,
    inference(avatar_split_clause,[],[f79,f1579]) ).

fof(f79,axiom,
    ! [X0,X29,X6] :
      ( ~ class_Ring__and__Field_Odvd(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X6,c_HOL_Otimes__class_Otimes(X6,X29,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).

fof(f1577,plain,
    spl0_186,
    inference(avatar_split_clause,[],[f78,f1575]) ).

fof(f78,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X5,X6,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

fof(f1573,plain,
    spl0_185,
    inference(avatar_split_clause,[],[f77,f1571]) ).

fof(f77,axiom,
    ! [X0,X6,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Otimes__class_Otimes(X6,X5,X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

fof(f1569,plain,
    spl0_184,
    inference(avatar_split_clause,[],[f75,f1567]) ).

fof(f75,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

fof(f1565,plain,
    spl0_183,
    inference(avatar_split_clause,[],[f74,f1563]) ).

fof(f74,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_Omul__1_0) ).

fof(f1561,plain,
    spl0_182,
    inference(avatar_split_clause,[],[f73,f1559]) ).

fof(f1559,plain,
    ( spl0_182
  <=> ! [X5,X0] :
        ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
        | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).

fof(f73,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

fof(f1557,plain,
    spl0_181,
    inference(avatar_split_clause,[],[f72,f1555]) ).

fof(f72,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X5,X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

fof(f1553,plain,
    spl0_180,
    inference(avatar_split_clause,[],[f71,f1551]) ).

fof(f71,axiom,
    ! [X0,X5] :
      ( ~ class_OrderedGroup_Omonoid__mult(X0)
      | c_HOL_Otimes__class_Otimes(X5,c_HOL_Oone__class_Oone(X0),X0) = X5 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

fof(f1549,plain,
    ( spl0_179
    | ~ spl0_118
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1500,f1476,f1272,f1546]) ).

fof(f1546,plain,
    ( spl0_179
  <=> c_HOL_Oeq__class_Oeq(tc_Complex_Ocomplex) = c_fequal(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).

fof(f1500,plain,
    ( c_HOL_Oeq__class_Oeq(tc_Complex_Ocomplex) = c_fequal(tc_Complex_Ocomplex)
    | ~ spl0_118
    | ~ spl0_167 ),
    inference(resolution,[],[f1477,f1274]) ).

fof(f1544,plain,
    spl0_178,
    inference(avatar_split_clause,[],[f47,f1542]) ).

fof(f47,axiom,
    ! [X0,X1] :
      ( ~ class_HOL_Ozero(X0)
      | c_Polynomial_OAbs__poly(c_Polynomial_Ocoeff(X1,X0),X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_coeff__inverse_0) ).

fof(f1525,plain,
    spl0_177,
    inference(avatar_split_clause,[],[f409,f1523]) ).

fof(f409,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Olower__semilattice(X0)
      | c_Lattices_Olower__semilattice__class_Oinf(X1,X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

fof(f1521,plain,
    spl0_176,
    inference(avatar_split_clause,[],[f391,f1519]) ).

fof(f391,axiom,
    ! [X2,X1] :
      ( X1 = X2
      | c_Complex_Ocnj(X1) != c_Complex_Ocnj(X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cancel__iff_0) ).

fof(f1517,plain,
    spl0_175,
    inference(avatar_split_clause,[],[f111,f1515]) ).

fof(f1515,plain,
    ( spl0_175
  <=> ! [X31,X0,X10,X32] : hAPP(c_COMBK(X31,X0,X10),X32) = X31 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).

fof(f111,axiom,
    ! [X31,X10,X0,X32] : hAPP(c_COMBK(X31,X0,X10),X32) = X31,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).

fof(f1513,plain,
    spl0_174,
    inference(avatar_split_clause,[],[f99,f1511]) ).

fof(f99,axiom,
    ! [X0,X1] :
      ( ~ class_Lattices_Oupper__semilattice(X0)
      | c_Lattices_Oupper__semilattice__class_Osup(X1,X1,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

fof(f1509,plain,
    ( spl0_173
    | ~ spl0_25
    | ~ spl0_167 ),
    inference(avatar_split_clause,[],[f1499,f1476,f807,f1506]) ).

fof(f1506,plain,
    ( spl0_173
  <=> c_HOL_Oeq__class_Oeq(tc_nat) = c_fequal(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).

fof(f1499,plain,
    ( c_HOL_Oeq__class_Oeq(tc_nat) = c_fequal(tc_nat)
    | ~ spl0_25
    | ~ spl0_167 ),
    inference(resolution,[],[f1477,f809]) ).

fof(f1498,plain,
    spl0_172,
    inference(avatar_split_clause,[],[f681,f1496]) ).

fof(f1496,plain,
    ( spl0_172
  <=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).

fof(f681,axiom,
    ! [X0,X1] : hBOOL(hAPP(hAPP(c_fequal(X0),X1),X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).

fof(f1494,plain,
    spl0_171,
    inference(avatar_split_clause,[],[f680,f1492]) ).

fof(f680,axiom,
    ! [X48] :
      ( ~ class_HOL_Ozero(X48)
      | ~ class_HOL_Oeq(X48)
      | class_HOL_Oeq(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Oeq) ).

fof(f1490,plain,
    spl0_170,
    inference(avatar_split_clause,[],[f478,f1488]) ).

fof(f1488,plain,
    ( spl0_170
  <=> ! [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_170])]) ).

fof(f478,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(f1486,plain,
    spl0_169,
    inference(avatar_split_clause,[],[f303,f1484]) ).

fof(f1484,plain,
    ( spl0_169
  <=> ! [X0] :
        ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
        | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).

fof(f303,axiom,
    ! [X0] :
      ( ~ class_Ring__and__Field_Ozero__neq__one(X0)
      | c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

fof(f1482,plain,
    spl0_168,
    inference(avatar_split_clause,[],[f302,f1480]) ).

fof(f1480,plain,
    ( spl0_168
  <=> ! [X5,X0] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
        | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).

fof(f302,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,c_HOL_Ozero__class_Ozero(X0),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

fof(f1478,plain,
    spl0_167,
    inference(avatar_split_clause,[],[f202,f1476]) ).

fof(f202,axiom,
    ! [X0] :
      ( ~ class_HOL_Oeq(X0)
      | c_HOL_Oeq__class_Oeq(X0) = c_fequal(X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equals__eq_0) ).

fof(f1474,plain,
    spl0_166,
    inference(avatar_split_clause,[],[f10,f1472]) ).

fof(f10,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(X0),X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).

fof(f1468,plain,
    spl0_165,
    inference(avatar_split_clause,[],[f534,f1466]) ).

fof(f534,axiom,
    ! [X48,X49] :
      ( ~ class_Lattices_Olattice(X48)
      | class_Lattices_Olattice(tc_fun(X49,X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

fof(f1464,plain,
    spl0_164,
    inference(avatar_split_clause,[],[f533,f1462]) ).

fof(f533,axiom,
    ! [X48,X49] :
      ( ~ class_Lattices_Oboolean__algebra(X48)
      | class_Lattices_Oboolean__algebra(tc_fun(X49,X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).

fof(f1460,plain,
    spl0_163,
    inference(avatar_split_clause,[],[f532,f1458]) ).

fof(f1458,plain,
    ( spl0_163
  <=> ! [X48,X49] :
        ( ~ class_Lattices_Odistrib__lattice(X48)
        | class_Lattices_Odistrib__lattice(tc_fun(X49,X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).

fof(f532,axiom,
    ! [X48,X49] :
      ( ~ class_Lattices_Odistrib__lattice(X48)
      | class_Lattices_Odistrib__lattice(tc_fun(X49,X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

fof(f1456,plain,
    spl0_162,
    inference(avatar_split_clause,[],[f531,f1454]) ).

fof(f531,axiom,
    ! [X48,X49] :
      ( ~ class_Lattices_Olattice(X48)
      | class_Lattices_Olower__semilattice(tc_fun(X49,X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

fof(f1452,plain,
    spl0_161,
    inference(avatar_split_clause,[],[f530,f1450]) ).

fof(f530,axiom,
    ! [X48,X49] :
      ( ~ class_Lattices_Olattice(X48)
      | class_Lattices_Oupper__semilattice(tc_fun(X49,X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

fof(f1448,plain,
    spl0_160,
    inference(avatar_split_clause,[],[f487,f1445]) ).

fof(f1445,plain,
    ( spl0_160
  <=> 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_160])]) ).

fof(f487,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(f1443,plain,
    spl0_159,
    inference(avatar_split_clause,[],[f376,f1440]) ).

fof(f376,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(f1438,plain,
    spl0_158,
    inference(avatar_split_clause,[],[f268,f1436]) ).

fof(f268,axiom,
    ! [X0,X1] : hAPP(c_Fun_Oid(X0),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).

fof(f1434,plain,
    spl0_157,
    inference(avatar_split_clause,[],[f26,f1432]) ).

fof(f26,axiom,
    ! [X0,X5] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
      | c_Ring__and__Field_Odvd__class_Odvd(X5,X5,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

fof(f1430,plain,
    spl0_156,
    inference(avatar_split_clause,[],[f679,f1428]) ).

fof(f679,axiom,
    ! [X48] :
      ( ~ class_HOL_Ozero(X48)
      | class_HOL_Ozero(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__HOL_Ozero) ).

fof(f1426,plain,
    spl0_155,
    inference(avatar_split_clause,[],[f678,f1424]) ).

fof(f678,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X48)
      | class_Int_Onumber__ring(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

fof(f1422,plain,
    spl0_154,
    inference(avatar_split_clause,[],[f677,f1420]) ).

fof(f1420,plain,
    ( spl0_154
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oordered__idom(X48)
        | class_Int_Oring__char__0(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).

fof(f677,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oordered__idom(X48)
      | class_Int_Oring__char__0(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).

fof(f1418,plain,
    spl0_153,
    inference(avatar_split_clause,[],[f676,f1416]) ).

fof(f676,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Odvd) ).

fof(f1414,plain,
    spl0_152,
    inference(avatar_split_clause,[],[f675,f1412]) ).

fof(f675,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oidom(X48)
      | class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).

fof(f1410,plain,
    spl0_151,
    inference(avatar_split_clause,[],[f674,f1408]) ).

fof(f674,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X48)
      | class_Ring__and__Field_Oring(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).

fof(f1406,plain,
    spl0_150,
    inference(avatar_split_clause,[],[f673,f1404]) ).

fof(f1404,plain,
    ( spl0_150
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oordered__idom(X48)
        | class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).

fof(f673,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oordered__idom(X48)
      | class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).

fof(f1402,plain,
    spl0_149,
    inference(avatar_split_clause,[],[f672,f1400]) ).

fof(f672,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Oab__group__add(X48)
      | class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).

fof(f1398,plain,
    spl0_148,
    inference(avatar_split_clause,[],[f671,f1396]) ).

fof(f1396,plain,
    ( spl0_148
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
        | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).

fof(f671,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
      | class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).

fof(f1394,plain,
    spl0_147,
    inference(avatar_split_clause,[],[f670,f1392]) ).

fof(f1392,plain,
    ( spl0_147
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
        | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).

fof(f670,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
      | class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).

fof(f1390,plain,
    spl0_146,
    inference(avatar_split_clause,[],[f669,f1388]) ).

fof(f669,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).

fof(f1386,plain,
    spl0_145,
    inference(avatar_split_clause,[],[f668,f1384]) ).

fof(f668,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__ring(X48)
      | class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).

fof(f1382,plain,
    spl0_144,
    inference(avatar_split_clause,[],[f667,f1380]) ).

fof(f1380,plain,
    ( spl0_144
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
        | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).

fof(f667,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
      | class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).

fof(f1378,plain,
    spl0_143,
    inference(avatar_split_clause,[],[f666,f1376]) ).

fof(f666,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Oab__group__add(X48)
      | class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add) ).

fof(f1374,plain,
    spl0_142,
    inference(avatar_split_clause,[],[f665,f1372]) ).

fof(f665,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__ring__1(X48)
      | class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).

fof(f1370,plain,
    spl0_141,
    inference(avatar_split_clause,[],[f664,f1368]) ).

fof(f664,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oordered__idom(X48)
      | class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).

fof(f1366,plain,
    spl0_140,
    inference(avatar_split_clause,[],[f663,f1364]) ).

fof(f1364,plain,
    ( spl0_140
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
        | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).

fof(f663,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).

fof(f1362,plain,
    spl0_139,
    inference(avatar_split_clause,[],[f662,f1360]) ).

fof(f662,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
      | class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).

fof(f1358,plain,
    spl0_138,
    inference(avatar_split_clause,[],[f661,f1356]) ).

fof(f1356,plain,
    ( spl0_138
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
        | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).

fof(f661,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
      | class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).

fof(f1354,plain,
    spl0_137,
    inference(avatar_split_clause,[],[f660,f1352]) ).

fof(f1352,plain,
    ( spl0_137
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
        | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).

fof(f660,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocomm__monoid__add(X48)
      | class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).

fof(f1350,plain,
    spl0_136,
    inference(avatar_split_clause,[],[f659,f1348]) ).

fof(f1348,plain,
    ( spl0_136
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
        | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).

fof(f659,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1346,plain,
    spl0_135,
    inference(avatar_split_clause,[],[f658,f1344]) ).

fof(f658,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
      | class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).

fof(f1342,plain,
    spl0_134,
    inference(avatar_split_clause,[],[f657,f1340]) ).

fof(f657,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__0(X48)
      | class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

fof(f1338,plain,
    spl0_133,
    inference(avatar_split_clause,[],[f656,f1336]) ).

fof(f656,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Ocomm__semiring__1(X48)
      | class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

fof(f1334,plain,
    spl0_132,
    inference(avatar_split_clause,[],[f655,f1332]) ).

fof(f1332,plain,
    ( spl0_132
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oidom(X48)
        | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).

fof(f655,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oidom(X48)
      | class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).

fof(f1330,plain,
    spl0_131,
    inference(avatar_split_clause,[],[f654,f1328]) ).

fof(f1328,plain,
    ( spl0_131
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
        | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).

fof(f654,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
      | class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1326,plain,
    spl0_130,
    inference(avatar_split_clause,[],[f653,f1324]) ).

fof(f653,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oordered__idom(X48)
      | class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).

fof(f1322,plain,
    spl0_129,
    inference(avatar_split_clause,[],[f652,f1320]) ).

fof(f1320,plain,
    ( spl0_129
  <=> ! [X48] :
        ( ~ class_Ring__and__Field_Oordered__idom(X48)
        | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).

fof(f652,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oordered__idom(X48)
      | class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).

fof(f1318,plain,
    spl0_128,
    inference(avatar_split_clause,[],[f651,f1316]) ).

fof(f1316,plain,
    ( spl0_128
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
        | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).

fof(f651,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
      | class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f1314,plain,
    spl0_127,
    inference(avatar_split_clause,[],[f650,f1312]) ).

fof(f650,axiom,
    ! [X48] :
      ( ~ class_Ring__and__Field_Oidom(X48)
      | class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).

fof(f1310,plain,
    spl0_126,
    inference(avatar_split_clause,[],[f525,f1308]) ).

fof(f1308,plain,
    ( spl0_126
  <=> ! [X48] :
        ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
        | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X48)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).

fof(f525,axiom,
    ! [X48] :
      ( ~ class_OrderedGroup_Ocancel__comm__monoid__add(X48)
      | class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X48)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f1306,plain,
    spl0_125,
    inference(avatar_split_clause,[],[f350,f1304]) ).

fof(f350,axiom,
    ! [X3] : c_Complex_Ocnj(c_Complex_Ocnj(X3)) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__cnj__cnj_0) ).

fof(f1302,plain,
    ( spl0_122
    | spl0_124 ),
    inference(avatar_split_clause,[],[f524,f1300,f1291]) ).

fof(f524,axiom,
    ! [X35] :
      ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),X35)
      | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f1298,plain,
    ( ~ spl0_122
    | ~ spl0_123 ),
    inference(avatar_split_clause,[],[f523,f1295,f1291]) ).

fof(f523,axiom,
    ( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != hAPP(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),v_x)
    | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f1289,plain,
    spl0_121,
    inference(avatar_split_clause,[],[f529,f1287]) ).

fof(f529,axiom,
    ! [X48,X49] : class_HOL_Oeq(tc_prod(X49,X48)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__HOL_Oeq) ).

fof(f1285,plain,
    ~ spl0_120,
    inference(avatar_split_clause,[],[f485,f1282]) ).

fof(f1282,plain,
    ( spl0_120
  <=> c_Complex_Oii = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).

fof(f485,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(f1280,plain,
    ~ spl0_119,
    inference(avatar_split_clause,[],[f354,f1277]) ).

fof(f1277,plain,
    ( spl0_119
  <=> c_Complex_Oii = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).

fof(f354,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(f1275,plain,
    spl0_118,
    inference(avatar_split_clause,[],[f649,f1272]) ).

fof(f649,axiom,
    class_HOL_Oeq(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Oeq) ).

fof(f1270,plain,
    spl0_117,
    inference(avatar_split_clause,[],[f648,f1267]) ).

fof(f648,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

fof(f1265,plain,
    spl0_116,
    inference(avatar_split_clause,[],[f647,f1262]) ).

fof(f647,axiom,
    class_SEQ_Obanach(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__SEQ_Obanach) ).

fof(f1260,plain,
    spl0_115,
    inference(avatar_split_clause,[],[f646,f1257]) ).

fof(f646,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

fof(f1255,plain,
    spl0_114,
    inference(avatar_split_clause,[],[f645,f1252]) ).

fof(f645,axiom,
    class_Int_Oring__char__0(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

fof(f1250,plain,
    spl0_113,
    inference(avatar_split_clause,[],[f644,f1247]) ).

fof(f644,axiom,
    class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odvd) ).

fof(f1245,plain,
    spl0_112,
    inference(avatar_split_clause,[],[f643,f1242]) ).

fof(f643,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

fof(f1240,plain,
    spl0_111,
    inference(avatar_split_clause,[],[f642,f1237]) ).

fof(f642,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

fof(f1235,plain,
    spl0_110,
    inference(avatar_split_clause,[],[f641,f1232]) ).

fof(f641,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

fof(f1230,plain,
    spl0_109,
    inference(avatar_split_clause,[],[f640,f1227]) ).

fof(f1227,plain,
    ( spl0_109
  <=> class_RealVector_Oreal__field(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).

fof(f640,axiom,
    class_RealVector_Oreal__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).

fof(f1225,plain,
    spl0_108,
    inference(avatar_split_clause,[],[f639,f1222]) ).

fof(f639,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

fof(f1220,plain,
    spl0_107,
    inference(avatar_split_clause,[],[f638,f1217]) ).

fof(f638,axiom,
    class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).

fof(f1215,plain,
    spl0_106,
    inference(avatar_split_clause,[],[f637,f1212]) ).

fof(f637,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

fof(f1210,plain,
    spl0_105,
    inference(avatar_split_clause,[],[f636,f1207]) ).

fof(f1207,plain,
    ( spl0_105
  <=> class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).

fof(f636,axiom,
    class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).

fof(f1205,plain,
    spl0_104,
    inference(avatar_split_clause,[],[f635,f1202]) ).

fof(f1202,plain,
    ( spl0_104
  <=> class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).

fof(f635,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

fof(f1200,plain,
    spl0_103,
    inference(avatar_split_clause,[],[f634,f1197]) ).

fof(f634,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

fof(f1195,plain,
    spl0_102,
    inference(avatar_split_clause,[],[f633,f1192]) ).

fof(f633,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(f1190,plain,
    spl0_101,
    inference(avatar_split_clause,[],[f632,f1187]) ).

fof(f1187,plain,
    ( spl0_101
  <=> class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).

fof(f632,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(f1185,plain,
    spl0_100,
    inference(avatar_split_clause,[],[f631,f1182]) ).

fof(f631,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

fof(f1180,plain,
    spl0_99,
    inference(avatar_split_clause,[],[f630,f1177]) ).

fof(f630,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(f1175,plain,
    spl0_98,
    inference(avatar_split_clause,[],[f629,f1172]) ).

fof(f1172,plain,
    ( spl0_98
  <=> class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).

fof(f629,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(f1170,plain,
    spl0_97,
    inference(avatar_split_clause,[],[f628,f1167]) ).

fof(f628,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

fof(f1165,plain,
    spl0_96,
    inference(avatar_split_clause,[],[f627,f1162]) ).

fof(f627,axiom,
    class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

fof(f1160,plain,
    spl0_95,
    inference(avatar_split_clause,[],[f626,f1157]) ).

fof(f1157,plain,
    ( spl0_95
  <=> class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).

fof(f626,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(f1155,plain,
    spl0_94,
    inference(avatar_split_clause,[],[f625,f1152]) ).

fof(f1152,plain,
    ( spl0_94
  <=> class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).

fof(f625,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

fof(f1150,plain,
    spl0_93,
    inference(avatar_split_clause,[],[f624,f1147]) ).

fof(f1147,plain,
    ( spl0_93
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).

fof(f624,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

fof(f1145,plain,
    spl0_92,
    inference(avatar_split_clause,[],[f623,f1142]) ).

fof(f623,axiom,
    class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

fof(f1140,plain,
    spl0_91,
    inference(avatar_split_clause,[],[f622,f1137]) ).

fof(f622,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

fof(f1135,plain,
    spl0_90,
    inference(avatar_split_clause,[],[f621,f1132]) ).

fof(f621,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

fof(f1130,plain,
    spl0_89,
    inference(avatar_split_clause,[],[f620,f1127]) ).

fof(f620,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(f1125,plain,
    spl0_88,
    inference(avatar_split_clause,[],[f619,f1122]) ).

fof(f619,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(f1120,plain,
    spl0_87,
    inference(avatar_split_clause,[],[f618,f1117]) ).

fof(f618,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(f1115,plain,
    spl0_86,
    inference(avatar_split_clause,[],[f617,f1112]) ).

fof(f1112,plain,
    ( spl0_86
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).

fof(f617,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(f1110,plain,
    spl0_85,
    inference(avatar_split_clause,[],[f616,f1107]) ).

fof(f616,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(f1105,plain,
    spl0_84,
    inference(avatar_split_clause,[],[f615,f1102]) ).

fof(f1102,plain,
    ( spl0_84
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).

fof(f615,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

fof(f1100,plain,
    spl0_83,
    inference(avatar_split_clause,[],[f614,f1097]) ).

fof(f614,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(f1095,plain,
    spl0_82,
    inference(avatar_split_clause,[],[f613,f1092]) ).

fof(f1092,plain,
    ( spl0_82
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).

fof(f613,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(f1090,plain,
    spl0_81,
    inference(avatar_split_clause,[],[f612,f1087]) ).

fof(f612,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(f1085,plain,
    spl0_80,
    inference(avatar_split_clause,[],[f611,f1082]) ).

fof(f611,axiom,
    class_HOL_Oeq(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Oeq) ).

fof(f1080,plain,
    spl0_79,
    inference(avatar_split_clause,[],[f610,f1077]) ).

fof(f610,axiom,
    class_HOL_Ozero(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).

fof(f1075,plain,
    spl0_78,
    inference(avatar_split_clause,[],[f609,f1072]) ).

fof(f609,axiom,
    class_SEQ_Obanach(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__SEQ_Obanach) ).

fof(f1070,plain,
    spl0_77,
    inference(avatar_split_clause,[],[f608,f1067]) ).

fof(f608,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

fof(f1065,plain,
    spl0_76,
    inference(avatar_split_clause,[],[f607,f1062]) ).

fof(f1062,plain,
    ( spl0_76
  <=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).

fof(f607,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).

fof(f1060,plain,
    spl0_75,
    inference(avatar_split_clause,[],[f606,f1057]) ).

fof(f606,axiom,
    class_Lattices_Olattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olattice) ).

fof(f1055,plain,
    spl0_74,
    inference(avatar_split_clause,[],[f605,f1052]) ).

fof(f605,axiom,
    class_Ring__and__Field_Odvd(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odvd) ).

fof(f1050,plain,
    spl0_73,
    inference(avatar_split_clause,[],[f604,f1047]) ).

fof(f604,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

fof(f1045,plain,
    spl0_72,
    inference(avatar_split_clause,[],[f603,f1042]) ).

fof(f603,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

fof(f1040,plain,
    spl0_71,
    inference(avatar_split_clause,[],[f602,f1037]) ).

fof(f602,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

fof(f1035,plain,
    spl0_70,
    inference(avatar_split_clause,[],[f601,f1032]) ).

fof(f1032,plain,
    ( spl0_70
  <=> class_RealVector_Oreal__field(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).

fof(f601,axiom,
    class_RealVector_Oreal__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).

fof(f1030,plain,
    spl0_69,
    inference(avatar_split_clause,[],[f600,f1027]) ).

fof(f1027,plain,
    ( spl0_69
  <=> class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).

fof(f600,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(f1025,plain,
    spl0_68,
    inference(avatar_split_clause,[],[f599,f1022]) ).

fof(f599,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

fof(f1020,plain,
    spl0_67,
    inference(avatar_split_clause,[],[f598,f1017]) ).

fof(f598,axiom,
    class_RealVector_Oreal__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).

fof(f1015,plain,
    spl0_66,
    inference(avatar_split_clause,[],[f597,f1012]) ).

fof(f597,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

fof(f1010,plain,
    spl0_65,
    inference(avatar_split_clause,[],[f596,f1007]) ).

fof(f1007,plain,
    ( spl0_65
  <=> class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).

fof(f596,axiom,
    class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).

fof(f1005,plain,
    spl0_64,
    inference(avatar_split_clause,[],[f595,f1002]) ).

fof(f1002,plain,
    ( spl0_64
  <=> class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).

fof(f595,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

fof(f1000,plain,
    spl0_63,
    inference(avatar_split_clause,[],[f594,f997]) ).

fof(f594,axiom,
    class_Lattices_Odistrib__lattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Odistrib__lattice) ).

fof(f995,plain,
    spl0_62,
    inference(avatar_split_clause,[],[f593,f992]) ).

fof(f593,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

fof(f990,plain,
    spl0_61,
    inference(avatar_split_clause,[],[f592,f987]) ).

fof(f592,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(f985,plain,
    spl0_60,
    inference(avatar_split_clause,[],[f591,f982]) ).

fof(f982,plain,
    ( spl0_60
  <=> class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).

fof(f591,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(f980,plain,
    spl0_59,
    inference(avatar_split_clause,[],[f590,f977]) ).

fof(f590,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

fof(f975,plain,
    spl0_58,
    inference(avatar_split_clause,[],[f589,f972]) ).

fof(f589,axiom,
    class_Lattices_Olower__semilattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Olower__semilattice) ).

fof(f970,plain,
    spl0_57,
    inference(avatar_split_clause,[],[f588,f967]) ).

fof(f588,axiom,
    class_Lattices_Oupper__semilattice(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Lattices_Oupper__semilattice) ).

fof(f965,plain,
    spl0_56,
    inference(avatar_split_clause,[],[f587,f962]) ).

fof(f962,plain,
    ( spl0_56
  <=> class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).

fof(f587,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(f960,plain,
    spl0_55,
    inference(avatar_split_clause,[],[f586,f957]) ).

fof(f586,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(f955,plain,
    spl0_54,
    inference(avatar_split_clause,[],[f585,f952]) ).

fof(f952,plain,
    ( spl0_54
  <=> class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).

fof(f585,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(f950,plain,
    spl0_53,
    inference(avatar_split_clause,[],[f584,f947]) ).

fof(f584,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

fof(f945,plain,
    spl0_52,
    inference(avatar_split_clause,[],[f583,f942]) ).

fof(f583,axiom,
    class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

fof(f940,plain,
    spl0_51,
    inference(avatar_split_clause,[],[f582,f937]) ).

fof(f937,plain,
    ( spl0_51
  <=> class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).

fof(f582,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(f935,plain,
    spl0_50,
    inference(avatar_split_clause,[],[f581,f932]) ).

fof(f932,plain,
    ( spl0_50
  <=> class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).

fof(f581,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

fof(f930,plain,
    spl0_49,
    inference(avatar_split_clause,[],[f580,f927]) ).

fof(f927,plain,
    ( spl0_49
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).

fof(f580,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

fof(f925,plain,
    spl0_48,
    inference(avatar_split_clause,[],[f579,f922]) ).

fof(f579,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

fof(f920,plain,
    spl0_47,
    inference(avatar_split_clause,[],[f578,f917]) ).

fof(f578,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

fof(f915,plain,
    spl0_46,
    inference(avatar_split_clause,[],[f577,f912]) ).

fof(f577,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

fof(f910,plain,
    spl0_45,
    inference(avatar_split_clause,[],[f576,f907]) ).

fof(f576,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(f905,plain,
    spl0_44,
    inference(avatar_split_clause,[],[f575,f902]) ).

fof(f575,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(f900,plain,
    spl0_43,
    inference(avatar_split_clause,[],[f574,f897]) ).

fof(f574,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(f895,plain,
    spl0_42,
    inference(avatar_split_clause,[],[f573,f892]) ).

fof(f892,plain,
    ( spl0_42
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).

fof(f573,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(f890,plain,
    spl0_41,
    inference(avatar_split_clause,[],[f572,f887]) ).

fof(f572,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(f885,plain,
    spl0_40,
    inference(avatar_split_clause,[],[f571,f882]) ).

fof(f882,plain,
    ( spl0_40
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f571,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

fof(f880,plain,
    spl0_39,
    inference(avatar_split_clause,[],[f570,f877]) ).

fof(f570,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(f875,plain,
    spl0_38,
    inference(avatar_split_clause,[],[f569,f872]) ).

fof(f569,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(f870,plain,
    spl0_37,
    inference(avatar_split_clause,[],[f568,f867]) ).

fof(f568,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(f865,plain,
    spl0_36,
    inference(avatar_split_clause,[],[f567,f862]) ).

fof(f862,plain,
    ( spl0_36
  <=> class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f567,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(f860,plain,
    spl0_35,
    inference(avatar_split_clause,[],[f566,f857]) ).

fof(f857,plain,
    ( spl0_35
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f566,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(f855,plain,
    spl0_34,
    inference(avatar_split_clause,[],[f565,f852]) ).

fof(f565,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(f850,plain,
    spl0_33,
    inference(avatar_split_clause,[],[f564,f847]) ).

fof(f564,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(f845,plain,
    spl0_32,
    inference(avatar_split_clause,[],[f563,f842]) ).

fof(f842,plain,
    ( spl0_32
  <=> class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f563,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(f840,plain,
    spl0_31,
    inference(avatar_split_clause,[],[f562,f837]) ).

fof(f562,axiom,
    class_HOL_Oeq(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oeq) ).

fof(f835,plain,
    spl0_30,
    inference(avatar_split_clause,[],[f561,f832]) ).

fof(f561,axiom,
    class_Lattices_Olattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

fof(f830,plain,
    spl0_29,
    inference(avatar_split_clause,[],[f560,f827]) ).

fof(f560,axiom,
    class_Lattices_Oboolean__algebra(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).

fof(f825,plain,
    spl0_28,
    inference(avatar_split_clause,[],[f559,f822]) ).

fof(f559,axiom,
    class_Lattices_Odistrib__lattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

fof(f820,plain,
    spl0_27,
    inference(avatar_split_clause,[],[f558,f817]) ).

fof(f558,axiom,
    class_Lattices_Olower__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

fof(f815,plain,
    spl0_26,
    inference(avatar_split_clause,[],[f557,f812]) ).

fof(f557,axiom,
    class_Lattices_Oupper__semilattice(tc_bool),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

fof(f810,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f556,f807]) ).

fof(f556,axiom,
    class_HOL_Oeq(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oeq) ).

fof(f805,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f555,f802]) ).

fof(f555,axiom,
    class_HOL_Ozero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ozero) ).

fof(f800,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f554,f797]) ).

fof(f554,axiom,
    class_Lattices_Olattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

fof(f795,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f553,f792]) ).

fof(f553,axiom,
    class_Ring__and__Field_Odvd(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

fof(f790,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f552,f787]) ).

fof(f552,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

fof(f785,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f551,f782]) ).

fof(f782,plain,
    ( spl0_20
  <=> class_Ring__and__Field_Osemiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f551,axiom,
    class_Ring__and__Field_Osemiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

fof(f780,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f550,f777]) ).

fof(f550,axiom,
    class_Lattices_Odistrib__lattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

fof(f775,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f549,f772]) ).

fof(f549,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

fof(f770,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f548,f767]) ).

fof(f548,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

fof(f765,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f547,f762]) ).

fof(f547,axiom,
    class_Lattices_Olower__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

fof(f760,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f546,f757]) ).

fof(f546,axiom,
    class_Lattices_Oupper__semilattice(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

fof(f755,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f545,f752]) ).

fof(f752,plain,
    ( spl0_14
  <=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f545,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(f750,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f544,f747]) ).

fof(f544,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

fof(f745,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f543,f742]) ).

fof(f742,plain,
    ( spl0_12
  <=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f543,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

fof(f740,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f542,f737]) ).

fof(f737,plain,
    ( spl0_11
  <=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f542,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

fof(f735,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f541,f732]) ).

fof(f732,plain,
    ( spl0_10
  <=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f541,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

fof(f730,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f540,f727]) ).

fof(f540,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

fof(f725,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f539,f722]) ).

fof(f539,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(f720,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f538,f717]) ).

fof(f538,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(f715,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f537,f712]) ).

fof(f712,plain,
    ( spl0_6
  <=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f537,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(f710,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f536,f707]) ).

fof(f707,plain,
    ( spl0_5
  <=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f536,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

fof(f705,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f535,f702]) ).

fof(f702,plain,
    ( spl0_4
  <=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f535,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

fof(f700,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f528,f697]) ).

fof(f697,plain,
    ( spl0_3
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f528,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add) ).

fof(f695,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f527,f692]) ).

fof(f692,plain,
    ( spl0_2
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f527,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(f690,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f526,f687]) ).

fof(f687,plain,
    ( spl0_1
  <=> class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f526,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) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : ALG437-1 : TPTP v8.2.0. Released v4.1.0.
% 0.15/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sat May 18 22:41:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (8214)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.40  % (8221)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)
% 0.22/0.41  % (8217)WARNING: value z3 for option sas not known
% 0.22/0.41  % (8215)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.41  % (8216)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  % (8218)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.41  % (8219)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  % (8220)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  % (8217)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)
% 0.22/0.48  TRYING [1]
% 0.22/0.50  TRYING [2]
% 2.14/0.70  TRYING [1]
% 2.14/0.73  TRYING [3]
% 2.58/0.74  TRYING [2]
% 8.18/1.54  TRYING [1]
% 8.31/1.55  TRYING [2]
% 9.29/1.72  TRYING [3]
% 9.29/1.76  TRYING [3]
% 15.22/2.56  TRYING [4]
% 21.20/3.41  % (8219)First to succeed.
% 21.61/3.46  % (8219)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8214"
% 21.61/3.47  % (8219)Refutation found. Thanks to Tanya!
% 21.61/3.47  % SZS status Unsatisfiable for theBenchmark
% 21.61/3.47  % SZS output start Proof for theBenchmark
% See solution above
% 21.83/3.50  % (8219)------------------------------
% 21.83/3.50  % (8219)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 21.83/3.50  % (8219)Termination reason: Refutation
% 21.83/3.50  
% 21.83/3.50  % (8219)Memory used [KB]: 35716
% 21.83/3.50  % (8219)Time elapsed: 3.050 s
% 21.83/3.50  % (8219)Instructions burned: 8331 (million)
% 21.83/3.50  % (8214)Success in time 3.085 s
%------------------------------------------------------------------------------